United States     Office Of Water  ,   September 1995
       Environmental Protection  (4503F)       FINAL REVIEW DRAFT
       Agency       Washington, DC

              September, 1995
          Nonpoint Source Control Branch
            U.S.E.P.A. Headquarters
             401 M Street, S.W.
            Washington, DC 20460

     This nonpoint source (NPS)  monitoring and evaluation guide is
written for use by both those who fund and approve monitoring and
evaluation  (M&E)  plans  and those who perform  the  monitoring and
evaluation.   For  example,  federal, state,  and  regional agencies
that  support  M&E  activities may  use  the  guide  to  assess  the
technical merit of  proposed M&E plans.  Those  agencies,  private
groups, and university personnel  that  perform M&E may use this
guide  to  formu;latfe their  M&E plans.    This guide  is  in  no  way
intended to supersede proven nonpoint source  M&E  plans  currently in
use, but it is intended as  both  a check against existing M&E plans
and an outline ifoaj developing new NPS M&E plans.

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.. .. .. .. .. .. .. ..
.. .. .. ..
OVERVIEW OF NPS PROBLEM. . . . . . . . . . .
A. . Definition of a Nonpoint Source
B. Nature and Scope of the Nonpoint Source Problem.
A. Monitoring Goals. . . . . . . . .. ....
B. Monitoring Objectives . . . .
C. Monitoring Level. . . . . . . . .
D. Monitoring Scale . . . . .
.. .. .. ..
.. .. .. ..
. iii
. vii
. 1-1
. 1-1
. . 1-1
A. Introduction . . . . . . . . . . . . .
B. Categorical Listing of Monitoring Guidances Reviewed
C. Guidance Reviews. . . . . . . .
. 111-1
. . 111-1
. 111-2
. . 111-5
A. Variability.. . . . . .
B. Streams............
C. Lakes..............
D. Estuaries.. . . . . .
E. Coastal Waters. . . . . . . .
F. Ground Water. . . . . . . . . . .
Data Needs. . . . . . . . . . .
Data Types. . . . . . . . . . .
Data Sources. . . . . . . . . . . .
A. Samples and Sampling. . . . . . . . .
. B. Monitoring Approaches. . . . . . . . . .
C. Ground Water Monitoring. . . . . .
D. Example Monitoring Programs. . . . .
A. Introduction..........
B. Habitat Assessment. . . . . . .
C. Overview of Biological Assessment Approaches
D. Reference Sites and Conditions
E. Rapid Bioassessment Protocols. .
F. The Multimetric Approach for Biological Assessment
G. Sampling Considerations. . . . .
H. Biomonitoring Program Design
I. Monitoring Trends in Biological Conditions
.. .. .. ..
.. .. .. ..
. IV-17
. IV-21
. . V-1
. V-1
. V-3
. VI-30
. VI-31
. VII-1
. VII-1
. VII-4
. VII-6

Overview of Some State Programs.
A. Introduction
B. Exploratory Analysis
C. Summary (Descriptive) Statistics
D. Trend Testing.
E. Extreme Analysis
F. Multivariate Analyses.
G. Special Treatment of Environmental Data.
A. Introduction
B. Data Quality Objectives.
C. Elements of a Quality Assurance
D. Field Operations Program
E. Laboratory Operations.
F. Data and Reports
Appendix A.
Appendix B.
Appendix C.
Appendix D.
Appendix E.
Appendix F.
Appendix G.
Appendix H.
Appendix I.
Appendix J.
Appendix K.
Appendix L.
Appendix M.
Appendix N.
Appendix o.
Appendix P.
Appendix Q.
Appendix R.
Appendix S.
Appendix T.
Appendix U.
Appendix V.
Chain of Custody Procedures.
Normal Distribution.
Chi-square Distribution.
F Distribution
Skewness Test.
Kurtosis Test.
Coefficients for W Test for Normality.
W Test Percentage Points
Noncentral t-Distribution .
Population Correlation Coefficient
Transformation of Linearization.
Multiple Regression Example - Hand Calculated
Multiple Regression Example - Computerized
Example Use of R-Square .
Confidence Limits for the Median of Any
Continuous Distribution.
Quantities of the Spearman Test Statistic.
Probabilities for the Mann-Kendall Nonparametric
Test for Trend
Quantiles of the Spearman Test Statistic
Quantiles of the Wilconxon Signed Rank Test
Nonparametric 95 and 90 percentile confidence
intervals on a proportions
Sample sizes for one-sided nonparametric
tolerance limits
Project Plan
. VIII-49
. VIII-63
. IX-I0
. IX-25
. IX-30
. IX-34
. A-I
. B-1
. C-l
. D-l
. E-l
. F-l
. G-l
. H-l
. I-I
. J-l
. K-l
. L-l
. N-l
. 0-1
. P-l
. Q-1
. R-l
. S-l
. T-l
. U-l
. V-I
. REF-l

National Summary of Nonpoint Source Problems
Relationship of monitoring objectives and
Guidance Review Chart
Comparison of means by site for CAC (ug/l) at
Highland Silver Lake, May 1981 - March 1984.
Applications of six probability sampling
designs to estimate means and totals.
Long-term monitored parameters for each level
in the St. Albans Bay watershed.
Related long-term monitored parameters in the
St. Albans Bay watershed.
Monitored parameters for the short-term
intensive studies.
Water quality sampling schedule for the St.
Albans watershed.
Years of sampling for each monitored level in
the St. Albans watershed.
Methods of water quality analysis.
Specific problems to be addressed for each
monitoring component.
Monitoring plan for regional network.
Monitoring plan for small watershed site.
Monitoring plan for field site 1. 
Monitoring plan for field site 2. 
General strenths and limitations of
biological monitoring and assessment
VI - 3 :;

Five tiers of the rapid bioassessment
Fish IBI metrics used in various regions of
North America.
Examples of metric suites used for analysis
of macroinvertebrate assemblages
Scoring criteria for the core metrics as
determined by the 25th percentile of the
metric values from the Middle Rockies-Central
Scoring criteria for the metrics as
determined by the 25th percentile of the
metric values for the aggregated
subecoregions for Florida streams.
Comparison of probabalistic and targeted
monitoring designs.
Waterbody stratification hierarchy.
Summary of the primary technical issues
related to biological monitoring for nonpoint
source evaluations.
Selected biomonitoring program components.
Methods for characterizing data.
Methods for routing data analysis.
Raw data by time period
Normalized data.
Total nitrogen runoff concentrations for a
single s~orm event in Florida.
Total nitrogen runoff concentrations for a
single storm evnet in Florida and example
calculations for the EMC.
Selected summary statistics for mean
abundance per grab from 1991 through 1992 for
the Louisiana Province of EMAP from large
rivers and small rivers.

Example analysis of the Shapiro-Wilk W test
using mean abundance per grab data for the
Louisiana Province of EMAP for small rivers.
Example application of Spearman's rho test
for evaluating independence.
Sample sizes required for estimating the true
Errors in hypothesis testing.
Highland Silver Lake TSS data for Site 1.
Nonparametric evaluation of post-
implementation data using the Wilcoxon Signed
ranks test.
Summary of parametric tests used to evaluate
difference between means.
Nonparametric evaluation of post-
implementation data using the Mann-Whitney
Sign test for comparing daily BOD5
concentrations at two locations.
Spearman's test for total nitrogen and total
phosphorus correlation.
Stream trout population.
One-way ANOVA.
Waller-Duncan k-ratio and Bonferroni t-test
Two-way ANOVA table.
Two-way ANOVA.
Waller-Duncan k-ratio and Bonferroni t-test
Waller-Duncan k-ratio and Bonferroni t-test
Two-way ANOVA with interaction.
Two-way ANOVA with interaction.
VI I I -- 7 9
VI I I -- 82
VIII -- 88
VI I I -- 93
VI I I -- 98
VI I I -- 98

Annual total rainfall for 21 years.
Sign calculation for Cox and Stuart test.
Data difference calculation for Mann-Kendall
Runoff sampler calibration data.
Linear regression output.
Theoretical log-probability frequency
Linearized rainfall frequency variate for
equation 8.142.
Linearized rainfall duration variate for
equation 8.142.
Common QA and QC activities.
Elements required in an EPA Quality Assurance
Project Plan.
Checklist of items that should be considered
in the field operations section of a QA/QC
Checklist of items that should be considered
in the laboratory operations section of a
QA/QC program.

IV -12
Monitoring in perspective
. II-2
Flow and pollutant concentrations for
a single storm event in the Honey
Creek watershed, Ohio.
. IV-2
Time course of phosphorus loading from
the West Branch Delaware River and output
from Cannonsville Reservoir.
. IV-3
Mean total suspended solids concentrations
(mg/L) in Highland Silver Lake, Illinois,
May 1981-March 1984 .
. VI-4
Mixing of salt water and fresh water in
an estuary
. IV-5
Contour map of nitrate concentrations
recorded from Galena aquifer inventory
water samples (Iowa)
. IV-6
Seasonal adjustment to discharges of
sediment, in clay and silt sizes, White
River near Kadoka, SD .
. IV-8
Seasonal relationship between sediment
concentration, sediment load, discharge,
and precipitation for Fern Ridge Dam,
. IV-9
Schematic diagram of stream vertical
showing relative position of sediment
load terms
Vertical sediment concentration and flow
velocity distribution in a typical stream
cross section.
Phytoplankton chlorophyll a concentration
in Chautauqua Lake's northern basin and
southern basin, 1977
IV -13
Typical thermal stratification of a lake
into the epilimnetic, metalimnetic, and
hypolimnetic water strata.
Temperature and dissolved oxygen profiles
for Barren River Lake in 1979 .

IV -13
IV -15
IV -1 7
Factors contributing to lateral
differences in lake quality.
Chesapeake Bay salinity levels over time
and space.
IV - 19
Physical features affecting lateral
salinity gradients in an estuary
Permeable sand layer underlain by a
clay layer
Two-aquifer system with opposite flow
Effect of permeability change on shape
of pollution plume
Map of the Rock Creek Rural Clean Water
Program study area, Twin Falls County,
St. Albans Bay watershed, Franklin County,
Vermont sampling locations
State locus of Bellevue NURP .
Bellevue stream systems
Bellevue sampling sites
Location of Conestoga River headwaters
area and four monitoring components.
Location of monitoring facilities for
regional network
Location of monitoring facilities for
small watershed sites.
Location of monitoring facilities for
field site 1
Field site 2, Lancaster Co., PA
Approaches to establishing reference
. VII-16
Selection and application of the different
tiers of RBP depend on monitoring objectives VII-18

Organizational structure of attributes
that can serve as metrics
. VII-20
Regions in which various fish IBI metrics
have been used.
. VII-21
Some trends that might be observed during
the course of a biological monitoring
. VII-39
Trend in biological condition (based on the
multimetric ICI) of the Cuyohaga River at
Independence, Ohio.
. VII-44
Dissolved oxygen concentrations from 1980
through 1989 for the Delaware River at Reedy
Island, Delaware using a time series plot. VIII-12
Dissolved oxygen concentrations from 1980
through 1989 for the Delaware River at Reedy
Island, Delaware using a histogram. VIII-13
Stem and leaf plot of dissolved oxygen
concentrations f~om 1980 through 1989 for
the Delaware River at Reedy Island, DelawareVIII-13
Box and whisker plot of dissolved oxygen
concentrations from 1980 through 1989 for
the Delaware River at Reedy Island, DelawareVllI-1S
Box and whisker plot of mean abundance per
grab from 1991 through 1992 for the Louisiana
Province of the Environmental Monitoring and
Assessment Program. . VIII-17
Bivariate scatter plot of total suspended
solids and flow at 36th Street storm sewer
in Denver, Colorado
Time series plot of dissolved orthophosphate
from 1989 through 1994 for portions of the
Delaware River.
Precipitation, runoff, total nitrogen, and
total phosphorus from a single storm event
in Florida.
Examples of several frequency distributions
and their respective cumulative frequency

Autocorrelation (correlogram) for dissolved
oxygen data from 1980 through 1989 for the
Delaware River at Reedy Island, Delaware.
A normal distribution
. . . . . .
The effect of changing ~ in the normal
distribution while keeping a constant
The effect of changing a in the normal
distribution while keeping ~ constant
Change of scale
. . . . . .
. . . . .
Standard normal distribution and example
of t-distribution ....,....
Chi-square distribution
. . . .
F distribution.
. . . . . . . .
Some examples of symmetric distributions.
Examples of skewed distributions.
Symmetric distributions of varying
kurtosis. . . . . . . . . . . .
Normal distribution
. . . .
. . . .
VIII-22. Relationship between a and ~.
VIII-23. Pre-implementation data set. .
VIII-24. post-implementation data set.
VIII-25. Log-transformed pre-implementation data

set . . . . . . . .
VIII-26. Log-transformed post-implementation data

set. . . . . . . . . . .
. . . .
VIII-27. One-sided t-test.
VIII-28. Parameter Y vs. X for three time periods.
VIII-29. General representation of regression between
paired observations of parameters, Y and
X, each unit of time has its unique slope. VIII-110
VIII-30. Types of time series. . . . . . . . .
. VIII-113

Split versus flowrate
VIII-32. Plot of residuals versus predicted
VIII-33. Plot of residuals versus predicted
VIII-34. Plot of residuals versus time.
VIII-35. TIme sequence plot of residuals.
VIII-36. Regression line with confidence
VIII-37. Regression line with confidence
VIII-38. Plot of mean and individual value
confidence limits.
VIII-39. One-hour rainfall to be expected at a
return period of 2 years.
VIII-40. 24-hour rainfall to be expected at a
return period of 2 years.
VIII-41. One-hour rainfall to be expected at a
return period of 100 years.
VIII-42. 24-hour rainfall to be expected at a
return period of 100 years.
Sample organization chart for a quality
assurance project plan.
Sample qualtiy assurance objectives
Sample custody chart.
. VIII-124
. VIII-127
. VIII-128
. VIII-129
. VIII-130
. VIII-138
. VIII-138
. VIII-139
. VIII-146
. VIII-147
. VIII-148
. VIII-149


Definition of a Nonpoint Source
Nonpoint sources of water pollution are both diffuse in nature
and difficult to define. Technically, the term "nonpoint source"
is defined to mean any source of water pollution that does not meet
the legal definition of "point source" in section 502(14) of the
Clean Water Act. That definition states:
The term "point source" means any discernible, confined
and discrete conveyance, including but not limited to any
pipe, ditch, channel, tunnel, conduit, well, discrete
fissure, container, rolling stock, concentrated animal
feeding operation, or vessel or other floating craft,
from which pollutants are or may be discharged. This
term does not include agricultural storm water discharges
and return flows from irrigated agriculture.
The distinction between nonpoint sources and diffuse point
sources is sometimes unclear. Although diffuse runoff is generally
treated as nonpoint source pollution, runoff that enters and is
discharged from conveyances such as those described above is
treated as a point source discharge and hence is subject to the
permit requirements of the Clean Water Act. In contrast, nonpoint
sources are not subject to federal permit requirements.
Nonpoint source pollution is the pollution of our nation's
waters caused by rainfall or snowmelt moving over and through the
ground. As the runoff moves, it picks up and carries away natural
pollutants and pollutants resulting from human activity, finally
depositing them into lakes, rivers, wetlands, coastal waters, and
ground waters. In addition, hydrologic modification is a form of
nonpoint source pollution that often adversely affects the
biological and physical integrity of surface waters.
Nature and Scope of the Nonpoint Source Problem
Nonpoint sources can generate both conventional (e.g.,
bacteria, oxygen-demanding substances) and toxic pollutants, just
as point sources do. Although nonpoint sources can contribute many
of the same kinds of pollutants, these pollutants are generated in
different volumes, combinations, and concentrations. Pollutants
from nonpoint sources are mobilized primarily during storm or
snowmelt events. Consequently, NPS pollution episodes are generally
less frequent and shorter in duration than continuous point source
discharges. However, it should be noted that NPS impacts on a
downstream or down gradient water resource can be continuous due
to, for example, (1) upstream/upgradient mixing, (2) multiple
sources, (3) flow dynamics, and (4) chemical, physical, or
biological processes.

Over the last decade, significant achievements have been made
nationally in the protection and enhancement of water quality.
Much of this progress, however, has been accomplished by
controlling point sources of pollution. While some state and local
NPS management programs have been developed and implemented,
pollutant loads from nonpoint sources present continuing problems
for achieving water quality goals and maintaining designated uses
in 'many parts of the United States. Data from the National Water
Quality Inventory 1992 Report to Congress (USEPA, 1992) indicate
that nonpoint sources negatively affect rivers and streams in 46 of
55 states and territories; lakes, reservoirs, and ponds in 41 of 55
states and territories (including the District of Columbia);
estuaries and coastal waters in 16 of 29 coastal states and
territories; and the Great Lakes in 5 of 8 Great Lakes states. The
categories of nonpoint source pollution affecting these waterbodies
included agriculture, resource extraction, silviculture, hydrologic
and habitat modification, construction, atmospheric deposition,
flow modification, land disposal, and onsite disposal systems.
According to the report, agriculture is the primary nonpoint
pollution source affecting rivers and streams. Thirty-one states
and territories list it as a major source of water quality
impairment. Seventy-two percent of the impaired river and stream
miles were reported to be affected by agricultural sources of
pollution. Other nonpoint sources that affect rivers and streams
include resource extraction, silviculture, and hydrologic and
habitat modification, which are listed as major sources of water
quality impairment by 21, 13, and 22 states, respectively.
Agriculture was also considered the most significant nonpoint
source affecting lakes, reservoirs, and ponds. Fifty-six percent
of impaired lake, reservoir, and pond surface acres are negatively
impacted by agriculture, followed by hydrologic and habitat
modification (23%), onsite disposal systems (OSDS, 16%), flow
modification (13%), and resource extraction (6%). Thirty states
listed agriculture as a major source of impairment to the water
quality of lakes, reservoirs, and ponds; 15 states listed
hydrologic and habitat modification; 13 listed resource extraction,
6 listed OSDS; and 5 listed flow modification.
The water quality of estuaries and coastal waters is also more
impaired by agriculture than by' any other nonpoint source.
Agriculture negatively impacts 43 percent of the impaired estuarine
and coastal water area and is listed as a major source of
impairment by seven coastal states (not including the Great Lakes
states) . Resource extraction is listed as a maj or source of
impairment to estuarine and coastal waters by three coastal states,
construction is listed as major by one coastal state, atmospheric
deposition is listed as major by one territory, and hydrologic and
habitat modification is listed as major by one coastal state.
Five of the eight Great Lakes states list nonpoint source
pollution as affecting the quality of their Great Lakes shoreline

miles. Each of the nonpoint sources atmospheric deposition, land
disposal, and construction is listed by one Great Lakes state as a
major source of impairment to Great Lakes shoreline water quality.
Atmospheric deposition is reported to be a major source of
impairment to 50 percent of the impaired Great Lakes shoreline
miles, followed by land disposal,' which affects 31 percent, and
construction, which affects 2 percent.
Table 1-1 summarizes the information on the impairment of the
Nation's water quality by nonpoint sources of pollution.
Effects of Nonpoint Source Pollutants
Sediment, nutrients, pathogens, habitat alteration, salts,
toxic substances, petroleum products, pesticides ~nd herbicides,
and hydrologic modifications are the pollutants contributed to
surface and ground waters by various nonpoint sources. Each of
these pollutants can have negative effects on aquatic systems and
in some cases on human health. The nutrients nitrogen and
phosphorus are contained in commercial fertilizers and manure.
Addition of excessive amounts of nutrients to marine and freshwater
systems, where nitrogen and phosphorus, respectively, are generally
limiting to plant growth, can lead to eutrophication. Animal
wastes from agriculture and pets also contain oxygen-demanding
substances that deplete dissolved oxygen when carried into aquatic
systems. Suspended sediments in runoff from nonirrigated cropland,
overgrazing on rangeland and pastureland, livestock grazing along
stream banks, urban runoff, and construction reduce sunlight to
aquatic plants, smother fish spawning areas, and clog filter
feeders and fish gills. Turbidity also reduces the aesthetic
attractiveness of recreational surface waters. Salts from
irrigation water concentrate at the soil surface through the
evapotranspiration process. Salts used on roads accumulate along
the edges of roads or are carried via storm sewer systems to
surface waters. Salts cause soil structure to break down, decrease
water infiltration, and in high concentrations can be toxic to
plants or decrease productivity. Some pesticides are persistent in
aquatic systems and biomagnify in animal tissue (primarily fish) as
they are passed up through the food chain. This has detrimental
physiological effects and negative human health impacts.
Herbicides that are toxic to aquatic plants remove a food source
for many aquatic animals, as well as the protective cover that
aquatic vegetation offers to many organisms. Finally, habitat
impacts from soil trampling, stream bank erosion after excessive
grazing, conversion of natural habitats to agricultural systems,
urbanization, and silvicultural practices diminish riparian
vegetation, increase erosion, and alter plant species composition
in riparian areas (Khaleel et al., 1980).

Table 1-1. Sources of nonpoint source pollution and their contribution to the impairment of the Nation's water
quality .
AGRICULTURE Major' 31 30 7 
 Percent" 159,353 miles 3,091,585 3,539 square 
  (72%) acres (56%) miles (43%) 
RESOURCE Major' 21 13 3 
 Percent" 23,697 miles 343,915 acres 998 square 
  (11 %) (6%) miles (12%) 
HYDROLOGIC & Major' 22 15 1 
MODIFICA TION Percent" 15,119 miles 1,275,583 457 square 
  (7%) acres (23%) miles (6%) 
 Percent" 16,236 miles   
ONSITE Major'  6  
SYSTEMS Percent"  874,265 acres  
!   (16%)  
FLOW Major'  5  
 Percent"  716,189 acres  
 Percent"   664 square 41 shoreline
    miles (8%) miles (2%)
ATMOSPHERIC Major'   1 1
 Percent"   466 square 946 shoreline
    miles (6%) miles (50%)
 Percent"    576 shoreline
     miles (31%)
TOTAL  221,877 8,071,260 8,303 impaired 5,1 71 impaired
IMPAIRED  impaired miles impaired acres square miles shoreline miles
(Source: USEPA 1992)
'Usted as major factor contributing to water quality impairment
"Percent of total impaired length or area impaired by the particular source

Agricultural Nonpoint Source Pollution
Nonpoint source pollution from agriculture comes from several
individual sources, including nonirrigated cropland (both row and
field) , irrigated cropland, rangeland and pastureland, and
livestock facilities. The primary pollutants associated with
agriculture are sediment, nutrients, animal wastes, salts, and
pesticides, which are contributed to surface and ground waters in
varying degrees by individual agricultural sources (Bailey and
Waddell, 1979; Dressing et al., 1982; Kreglow et al., 1982; Maas et
al., 1982; Maas et al., 1984). Agriculture also has direct impacts
on the habitats of aquatic species.
Urban Nonpoint Source Pollution
Urbanization adversely affects surface waters through the
addition of many of the pollutants discussed above and through
dramatic changes to stream hydrology in urbanized areas. From the
perspective of nonpoint source pollution impacts, urbanization is
best characterized as a process by which pervious, naturally
vegetated land is converted to impervious surfaces through which
storm water cannot percolate to reach the soil beneath and upon
which numerous pollutants are deposited and then carried by storm
water quickly and directly to surface waters. These changes result
in dramatic hydrologic, water quality, and aquatic habitat impacts
(Field et al., 1977).
Storm water that runs off roofs, lawns, streets, industrial
sites, and other pervious and impervious areas washes a number of
pollutants into urban lakes and streams (Hawkins et al., 1974).
Runoff that percolates through the soil to ground water supplies
carries these pollutants with it. The hydrologic changes resulting
from urbanization include increased peak discharges of storm water
runoff, increased runoff volume, increased runoff velocity,
decreased time before runoff reaches surface waters, and reduced
stream flow during low-flow periods.
A large percentage of the pollutant load in urban runoff is
composed of sediment and debris from decaying pavements and
buildings that can clog sewers and waterways, reduce hydraulic
capacity, increase the chance of flooding, and degrade aquatic
habitats. Other urban pollutants include heavy metals and
inorganic chemicals (including copper, lead, zinc, and cyanides)
from brake linings on automobiles, industrial activities, and
building materials (USEPA, 1983b); oils, greases, antifreeze, and
other automotive fluids that drip or are disposed of onto
pavements; nutrients in fertilizers that are applied to residential
lawns, parks, golf courses, and along transportation rights-of-way;
fecal bacteria that are contained in pet wastes and leaking septic
tanks (which also contain excess nutrients); and road salts, which
are a problem primarily in northern urban areas.

Urbanization often entails modifications to stream courses in
the urban area to accommodate roadways, buildings, waterfronts,
residential developments, and the like. Stream course
modifications are also undertaken to protect urban areas from flood
damage, but the modifications cause their own set of NPS impacts.
Levees along streams serve to protect areas from flooding, but also
decrease the natural supply of sediment reaching floodplain areas.
Rather than being dispersed over a floodplain, the sediment
contained in flowing water during high-flow periods is carried to
stream and river deltas, where it accumulates due to the natural
loss of flow velocity at deltas. This sediment can impede
navigation and smother biological communities in these areas. The
sediment that is redirected downstream is lost to the floodplain.
A periodic resupply of nutrient-rich sediment is important to
wetland and floodplain ecosystem function, and its loss has
negative ecological consequences. In coastal marshes, this loss of
a natural resupply of sediment and fresh water leads to subsidence
of marshlands and infiltration of saline waters. The biological
communities in these areas are unable to survive the resultant
increase in salinity, and there is a shift toward marine
ecosystems. Coastal marshes are biologically diverse and
productive, and their loss can result in severe economic loss.
Mining Nonpoint Source Pollution
Although mining activities are not as widespread as
agriculture, the water quality effects resulting from mining are
usually much more harmful. Sedimentation rates from mining can be
extraordinarily high (Mitsch et al., 1983). Entire streams might
become biologically dead as a result of acidic mine drainage (water
with low pH released from mining areas). Other pollutants in
mining runoff with potentially serious effects include heavy metals
and radioactive materials. Active mine sites can pose a number of
potential water quality problems. Most of these, however, are
considered to be point source problems and are regulated under
state and. federal National Pollutant Discharge Elimination System
(NPDES) permits (USEPA, 1978a). The primary NPS pollution problems
associated with mining are sediment-laden runoff from haul roads
and runoff polluted with acid, sediment, salts, and metals from the
spoil and tailings piles. Both of these problems arise from both
active and inactive mines, and both ground and surface waters are
. adversely affected. In the western United States, water quality
effects from metal and uranium mining are more serious than those
from other types of mining. Acid drainage from coal mines is a
greater problem in the eastern and midwestern states, where the
most damage occurs in the heavily mined areas of the mid-Atlantic
and Appalachian regions. Stream quality in these regions is
severely degraded by drainage from abandoned coal mines.
5 .
Silvicultural Nonpoint Source Pollution
The smaller areal extent of forest management activities, less
intensive site preparation, infrequent harvest, and lower frequency

of pesticide and nutrient applications in a given year all result
in silviculture generating a smaller volume of total NPS pollutants
than agriculture nationwide (Bailey and Waddell, 1979) .
Silvicultural activities can nonetheless cause significant
localized NPS pollution problems (USEPA, 1978a). The impact of
this localized NPS pollution is often disproportionately large
compared to NPS impacts in other areas because forested watersheds
often contain the Nation's highest quality waters, which are the
source of many municipal water supplies and are prized for cold-
water fisheries, high-economic-value recreation, and aesthetics.
Silvicultural activities that generate NPS pollution include
road building, pesticide and herbicide application, harvesting and
logging operations, site preparation to promote revegetation, and
timber stand improvement (USDA, 1981). Sediment, which results
primarily from road construction and harvesting, is the major
pollutant by volume from silvicultural activities (USEPA, 1980a).
Soil type, slope, climate, and the best management practices used
on a site have a large effect on the delivery of sediment to
forested water courses. The Illinois Environmental Protection
Agency found that road building and road use are the major causes
of erosion and soil loss from silvicultural activities (IEPA,
1979) .
Fertilizers and pesticides are used increasingly in
silviculture, but unlike annual agricultural applications they are
typically applied only once or twice during a 20- to 35-year period
on any given harvestable forested tract of land. The contribution
of chemicals to lakes and streams is less frequently a problem for
silviculture than for agriculture, though localized problems can
result if practices such as aerial spraying are employed near a
water course. Debris from silvicultural operations that is left in
or is carried to streams contributes excessive organic matter to
waterbodies, thereby decreasing dissolved oxygen levels and causing
changes in flow patterns. Water temperature increases occur when
streamside vegetation is removed during harvests, and this can
severely impact cold-water aquatic ecosystems that are adapted to
narrow temperature ranges.
6 .
Construction Nonpoint Source Pollution
On a national basis, the water quality degradation caused by
NPS pollution from construction activities is not nearly as great
as the amount caused by other major nonpoint sources (Bailey and
Waddell, 1979). This is due, in part, to improved construction
erosion control by local jurisdictions. In addition, construction
sites are often dispersed and, as a result, usually create only
localized problems. States reported construction as a source of
degradation to only estuaries, coastal waters, and wetlands, and
estimated that it degrades only 8 percent of impacted estuarine
square miles and 7 percent of impacted coastal shoreline miles
(USEPA, 1992). Eight states reported road construction as a source
of degradation to wetlands.

Where construction activities are intensive, localized impacts
on water quality can be severe because excessive loads are
discharged in short time spans. Erosion rates from construction
sites typically are 10 to 20 times those of agricultural lands
(U.S. House of Representatives, 1980). Sediment is the main
construction site pollutant, though sediment from construction
sites accounts for only about 4 to 5 percent of nationwide sediment
loads in receiving waters (USEPA, 1980b). Other pollutants
generated by construction activities are nutrients (primarily
phosphorus and nitrogen) from fertilizers, which bind to sediment
particles or dissolve in solution (USEPA, 1978a); chemicals in
pesticides that are used to control weeds and insects at
construction sites; petroleum products and construction chemicals,
such as cleaning solvents, paints, asphalt, acids, and salts; and
solid wastes, ranging from coffee cups to trees and other debris
left at construction sites (USEPA, 1984e). Some of these materials
are toxic to aquatic organisms (including shellfish and fish) and
make them unfit for human consumption. These pollutants also make
water unfit for use as drinking water and for contact recreation.


~onitoring Goals
Overall goals established in the EPA Deputy Administrator's
1983 monitoring policy memo (USEPA, 1985c) are to:
Meet the full range of current and future Agency needs
for environmental data.
Ensure monitoring is technically and scientifically
Ensure environmental monitoring data are managed to
facilitate both access and appropriate use in Agency
decision making.
Ensure effective and coordinated Agency-wide
processes for planning and execution of monitoring
Ensure that roles and responsibilities are clear in
regard to monitoring management and implementation by EPA
and state officials.
An attempt to put monitoring into perspective is presented in
Figure 11-1, taken from the National Water Monitoring Panel (USEPA,
1975). It is obvious that if each functional purpose is to be
productive, the proper information must be provided by the
monitoring program. It also should be clear that persons
. responsible for monitoring must maintain a frequent and substantive
contact with those programs requiring information. Finally, there
is need for coordination among all aspects of a monitoring program.

The following, taken from a monitoring and evaluation workshop
manual (Simons et al., 1981), discusses the conceptual design of a
monitoring system:
In order for any monitoring network to be designed and
implemented, the overall objective as well as the monitoring
objective should be analyzed to assess what type of data [are] .
required to fulfill these objectives. An overall objective is
of broad scope; for example, a water supply system or a sewage
treatment system. A much smaller objective which is
formulated under the overall objective is the monitoring
objective. Examples are: stream flow measurement; water
quality measurements; precipitation measurements; etc. It
must be kept in mind that the overall objective determines the
nature of the monitoring objective. For example, if the
overall objective was enforcement of water quality laws, the
monitoring objective would be to monitor the water quality
variables in the jurisdiction area; but how is the monitoring
to be done? In this case, sampling every night may miss
industrial pollution loads, and monitoring upstream of
industrialized areas would do the same. Here the overall
objective conceptually defines the sampling frequency and
spatial location of the monitoring network. The exact number,
location and sampling frequency for monitoring stations must
bow to social, political, legal, and financial considerations.

Figure II-1.
Monitoring in perspective. (SOURCE: USEPA, 1975).

Monitoring Objectives
Identifying and concisely stating the monitoring objectives
are critical steps in the development of a monitoring program.
Numerous authors attest to the importance of clearly specifying
monitoring program objectives prior to designing the program or
collecting any data. Plafkin et ale (1989, p. 3-1) state
"...selection of the appropriate bioassessment approach depends on
the objectives of the study." A monitoring guidance published by
the U.S. Department of Agriculture {USDA-SCS, 1989, p. iv (draft
states "Setting objectives for monitoring clarifies the purposes of
the study and keeps it on track." Monitoring program objectives
must be detailed enough to define precisely what data and
inform~tion will have to be gathered and how that data and
information will help address the NPS problem at hand.
Monitoring program design includes selection of sampling
locations, sampling strategy, sampling variables, data analysis
techniques, length of monitoring program, and level of effort and
resources. Vague or inaccurate statements of objectives lead to
program designs that only partially fulfill management needs or
provide redundant data that would not help address the NPS problem.
If the monitoring objective is to determine presence or absence of
an NPS impact, a simple sampling survey might be conducted in a few
select locations. If the objective is to calibrate or verify a
model, more extensive sampling over a well-defined area might be
necessary. Depending on the type of predicti ve mOdeling, a
strategic sampling program might be performed within a short time
frame to allow calibration and verification of the model. In this
way monitoring program design and scale are dependent on the stated
monitoring objectives.
Monitoring programs can be implemented for one or many
reasons. The more common objectives of monitoring programs are
discussed briefly below.
Monitoring Objective Category:
Problem Identification
1.1. Objective
Meeting this objective involves an investigation of key parameters
to determine the general condition of a habitat or water quality.
Biological monitoring is particularly useful when this is the
1.2. objective B: Determine
investigation is necessary
It might be necessary to determine whether waterbody impairment is
severe enough to warrant management attention. Preliminary
monitoring might reveal that a problem is more complicated or more
serious than originally thought and that more intensive monitoring
studies are called for.
Monitoring Objective Category:
Regulatory Compliance

2.1. Objective C:
Assess compliance with water quality
Measurements of individual pollutants in waterbodies are taken to
determine whether violations of water quality standards are
occurring. Monitoring for this purpose is usually conducted on a
smail (plot) scale. caution is necessary to be certain that
measured water quality is causally linked to the source being
assessed for compliance.
3.1. Objective D: Measure the effectiveness
individual conservation practices
Individual BMPs are monitored to determine the extent of pollution
control attributable to them. Monitoring can typically be
conducted at a plot or field scale, and measurements should be
taken as close as possible to where the BMP is implemented.
studies of some individual practices can often be conducted in a
relatively short time  5 yr), but this depends on the BMP being
3.2. Objective E:
Measure BMP program effectiveness
This monitoring usually must be conducted on a watershed scale
because the combined effect of a few or several BMPs is being
investigated. It must be conducted over a long term  5 yr)
because BMP implementation can take years to affect water quality.
This type of monitoring is difficult because of a lack of control
conditions, the presence of reserves of pollutants in soil and
sediments, the effect of there being many land uses within a study
area, and the necessity to account for the effects of many
landowners with differing means of implementing the same BMPs.
Monitoring Objective
4.1. Objective F:
Define a water quality problem
Monitoring might be required to determine the cause of an
environmental problem, such as degraded fish habitat or an algal
bloom. When conducting monitoring for this purpose, it is
important to monitor the appropriate water quality characteristics
and account for climatic factors to establish a cause-and-effect
4.2. Objective G:
the problem
Determine the geographical extent of
Even if a problem is known to exist, the areal extent of the
problem might not be known. Does it affect only a stream reach, or
are problems in the downstream lake attributable to the same sourc:e

that affects the stream reach?
determine this.
Monitoring might be necessary to
4.3. objective H: Determine the temporal variability of
the problem and its time of occurrence

Some pollution sources are emitted only during certain parts of the
year or in association with certain events, such as storms.
similarly, a constant source of pollution might be a problem only
during a particular time of the year, such as during fish spawning.
Determining the temporal aspect of a pollution problem will help
focus management on times when it will have the most impact.
4.4. Objective I:
Identify the sources .of the problem
Determining that a problem exists is often far easier than
determining its source because there are often many potential
sources. Monitoring will help identify the sources of a problem,
and further monitoring (under other objectives) can determine their
individual significance.
4.5. Objective J: Quantify the relative contribution of
nonpoint sources
Point and nonpoint sources often affect the same waterbody, and
monitoring might be required to determine the contribution of each
to water quality impairment. Quantitative determination of the
contribution of each source of a particular pollutant is important.
This can often be accomplished with several coordinated plot
studies and within a short time frame.
4.6. Objective K: Determine the relative impact of
nonpoint sources
This objective requires more intensive monitoring because it is
focused on the relative impact or importance of each source of a
pollutant to the impairment of a waterbody. Factors such as the
timing of pollutant contributions relative to the hydrological
cycle of the waterbody and the ecology of' the biological
communities must be factored into the analysis. The distance of
pollutant sources to receiving waters, the fate and transport of
pollutants from different sources, the magnitude of pollutant
contribution from each source, and the distance to the impaired
resource of concern (as distinguished from distance to a point of
entry into a receiving waterbody, which might be some distance from
the actual impairment) are all important factors to consider when
determining the relative impacts of different sources.
Monitoring Objective Category:
Management Alternatives
5.1. Objective L:
Determine fate and transport
Determination of where a pollutant goes after its introduction into
the environment, how it changes chemically, where it ends up, and

by what means it travels will indicate what sources need to be
controlled. This does not usually require a long monitoring
period; it can be done over a short time (1-2 yr or more) and in a
small area with frequent sampling.
5.2. Objective M:
Locate critical areas
A determination of which areas within a watershed are most critical
in causing waterbody impairment, and therefore should be the focus
of pollution control efforts, is important to the development of a
management strategy. For instance, a high erosion rate on land far
from a receiving waterbody might have a lower pOllution-causing
potential than an area with a lower erosion rate near to a
receiving waterbody. Monitoring for this purpose is usually
conducted over a short time period, so it is critical that climatic
factors be accounted for. Monitoring to locate critical areas
should be basinwide to target subwatersheds for BMP implementation.
5.3. Objective N:
Analyze trends
The objective here is to answer the question, "How is water quality
changing over time?" Baseline monitoring is part of trend analysis
because establishing a baseline is crucial to analyzing trends.
However, baseline monitoring is generally thought of as determining
a condition prior to pollutant entry or prior to a change in
waterbody condition, whether beneficial or detrimental.
controlling for influencing factors such as climate is necessary if
baseline monitoring is to be used as a reference point for trend
analysis and management decisions.
5.4. Objective 0:
Determine the level of control needed
Monitoring for this objective involves not only an assessment of
the degree of impairment and the degree of pollutant reduction
needed to achieve a specified level of environmental quality, bu1:
also an analysis of the pollutant reduction capabilities of
individual BMPs. The latter can be seen as a separate step, i.e.,
th~ first step being to determine the amount of pollution reduction
required, and the next a determination of what BMPs can be used to
achieve the reduction. Because BMPs are the pollutant control
mechanisms that must be used to reduce pollutant inputs, however,
the two exercises are really two aspects of a single management
goa 1.
5.5. Objective P:
Make wasteload allocations
This objective is to determine the land uses or intensity of
existing land uses that can be practiced while maintaining the
ecological integrity of receiving waterbodies. This monitoring
objective is often associated with point sources, but it is a
valuable tool for NPS pollutant control as well. Receiving
waterbodies must be monitored to achieve this objective, and a good
knowledge of the actual pollutant contributions of individual
sources is required. For NPS pollution waste load allocation,
extensive monitoring is often required.

Monitoring Objective Category:
Model Development
6.1. Objective Q:
Calibrate models
Monitoring is necessary to determine values for uncertain or
unmeasurable parameters in a model before it can be used to predict
the effect of management techniques or activities.
6.2. Objective R:
verify models
Model verification involves the simulation of cases covering the
full range of model uses and comparison to observed data to
establish confidence in the model. If premodeling monitoring data
are not available, observed data will have to be collected through
a monitoring program for comparison to model runs. Calibration
might be an aspect of model verification. Once a model has been
verified, it can be used to assist managers with management
6.3. Objective S:
Test models
Monitoring is needed to fit or calibrate a model to local
conditions and to verify a model's applicability to a particular
situation. One problem encountered in model calibration and
verification is that many models are meant to simulate long-term
average conditions, but monitoring data are often restricted to a
short time frame.
Monitoring Objective Category:
7.1. Objective T:
Conduct research
Research monitoring is done to address specific research questions.
Research monitoring is generally conducted on a plot scale, is
well-controlled, and is limited to a very specific question.
Monitoring and data analysis techniques for research and for other
types of monitoring are often very similar, and the difference
between them is often one of objective rather than approach. A
critical examination of articles of relevant and well-conducted
research projects in which monitoring is a key element can provide
excellent guidance for the design of a monitoring program.
Monitoring Level
Monitoring level refers to the level of effort required for
data collection, the amount and type of data that must be
collected, and the equipment and personnel needed to conduct a
monitoring program. A low monitoring level might entail no more
than a site visit to qualitatively describe riparian vegetation
condition. A high monitoring level might involve extensive benthic
macro invertebrate sampling and taxonomic analysis coupled with
physical and chemical water quality sampling conducted over a
period of years.
Monitoring level, like monitoring program design, is also
largely determined by a monitoring program's objectives, though

there is some leeway in choice of monitoring level for aChieving
most monitoring objectives. A high monitoring level is required to
achieve some monitoring objectives, while other objectives can be
achieved with a lower monitoring level. However, when a low
monitoring level can be used, the use of a higher monitoring level
is not precluded. In addition to monitoring objectives, the
monitoring level is chosen based on availability of staff, time,
money, and equipment; physical location of the resource being
monitored; season; and complexity of the problem being monitored.
Three levels of monitoring are described here. Monitoring
programs have been divided elsewhere into fewer (two) or more
(four) monitoring levels, but a division into three levels allows
for adequate distinction between the levels without drawing
unnecessarily fine distinctions that would be applicable only to
limited circumstances. .
Level I:
Preliminary Assessment
Level I monitoring relies largely on empirical observations and
best professional judgment (BPJ). The use of data is limited to
those readily available, such as historical data and information
available from sources such as those listed in Chapter 5. An
assessment of this historical data is part of a preliminary
assessment. Limited field work is involved, such as a site survey
to verify land use or vegetation type. Level I monitoring can be
used for a variety of purposes, including:
determine whether a water quality problem exists
determine whether water quality goals are being met
assess current conditions
document water quality problems
document water quality standards violations
determine general water quality.
Level II:
Problem Characterization
Level II monitoring uses qualitative and quantitative data in
addition to level I monitoring information. Example uses of level
II monitoring include:
locate critical areas
identify sources and evaluate their relative
characterize critical conditions
characterize pollutant fate and transport.
Data collection is necessary for level II monitoring but is limited
to parameters that can be measured with limited equipment, time,
and staff. Biological monitoring parameters for level II
monitoring might include coliform bacteria count, phytoplankton and
zooplankton density, areal extent and species of macrophytes,
benthic macro invertebrate families and distribution, and fish
species. Habitat quality monitoring parameters might include
stream substrate type, flow, channel morphology, riparian cover
density, and shoreline habitat condition. Physical and chemical
monitoring variables for level II monitoring include water

temperature, sedimentation rate, water transparency,
phosphorus concentration, and nitrogen concentration.
Level III:
Long-term Monitoring (>5 years)
Level III monitoring relies primarily on quantitative data to
provide detailed analyses of water quality problems and to build
time series data for assessing trends, determining management
program effectiveness, and regulatory compliance. Some uses of
level III monitoring include:
perform trend analysis
determine causality
demonstrate BMP program effectiveness
conduct research
define biological criteria for water quality
define a desired future condition
determine compliance with state water quality
determine whether it is necessary to modify a
make wasteload allocations.
BMP system
Biological parameters for level III monitoring include those from
levels I and II plus pathogens, viruses, intestinal parasites,
periphyton, and a more det~iled analysis of macrophytes, such as a
calculation of biomass from in-water plot collections. Level III
monitoring habitat parameters might include flow at high and low
flow events, water velocity, water depth, coarse particulate
organic matter (CPOM), and interstitial water. A substratum
habitat description, including 'parent material and presence of
trash, organic matter, odors, oils, and sewage might be necessary,
as well as a determination of anaerobic conditions.
Monitoring Scale
The scale of a monitoring program has two components: a time
or temporal scale and an areal or geographic scale. The temporal
scale is the amount of time required to accomplish the program
objectives. It can vary from an afternoon to many (>5) years. The
geographic scale can also vary from quite small, such as plots
along a single stream reach, to very large, such as an entire
watershed. The temporal and geographic scales, like a program's
design and monitoring level, are primarily determined by the
program's objectives. Hence, unspecific or unclear monitoring
objectives present a barrier to selecting the appropriate temporal
and geographic scales. However, as with monitoring level, there is
often some leeway in selecting both temporal and geographic scales
to achieve specif ic obj ecti ves. Other factors that should be
considered to determine appropriate temporal and geographic scales
include: (1) available resources (staff and money); (2) time frame
within which managers require specific information; (3) type of
water resource being monitored; and (4) complexity of the NPS
As mentioned above,
objectives of the program.
both scales are dependent on the
If the main objective is to determine

the present biological condition of a stream, then sampling at a
few stations in a stream reach over 1 or 2 days might suffice. If
the objective is to determine the effectiveness of a nutrient
management program for reducing nutrient inputs to a downstream
lake, then monitoring a subwatershed for 5 years or longer might be
necessary. Depending on the objectives of the monitoring program,
it might be necessary to monitor only the waterbody with the water
quality problem, or it might be necessary to include areas that
have contributed to the problem in the past, areas containing
suspected sources of the problem, or a combination of these areas.
There is no formula for determining appropriate geographic and
temporal scales for any particular monitoring program. Rather,
once the objectives of the monitoring program have been determined,
a combined analysis of them and any background information on the
water quality problem being addressed should make it clear what
overall monitoring scale is necessary to reach the objectives.
A monitoring program to be conducted on a watershed scale must,
include a decision about a watershed's size. The effective size of
a watershed is influenced by drainage patterns, stream order,
stream permanence, climate, number of landowners in the area,
homogeneity of land uses , watershed geology, and geomorphology.
Each of these factors is important because each has an influence on
stream characteristics, while no direct relationship exists between
watershed area and stream characteristics. Watersheds larger than
50,000 acres might contain enough heterogeneity to preclude the use
of a single monitoring program.
The temporal and geographic scales of a monitoring program
will usually be similar to the level of the monitoring program (I,
II or III). That is, level I programs are more likely to be of
short duration and limited geographic extent, while level III
programs are more likely to be of longer duration and larger areal
extent. Studies to assess the present condition of a waterbody can
often be completed in a season, or less than a year, and by
sampling in select places. Problem characterization studies or
trend analyses take longer and are more involved in terms of the
parameters to be monitored, the area that must be monitored, and
the amount of data that must be collected. Model validation
monitoring includes both a first phase of model calibration and a
second phase of model verification, and overall can take anywhere
from a few months to several years.
Table II-l presents approximate monitoring scales for the
monitoring objectives listed above.

Table II-l.
Relationship of monitoring objectives and scales.
 Q G
 S M
D 0 H
A: Determine whether an impairment exists
8: Determine whether further investigation is necessary
C: Assess water quality standards compliance
D: Measure individual 8MP effectiveness
E: Measure 8MP program effectiveness
F: Define a water quality problem
G: Determine the geographical extent of a problem
H: Determine the temporal variability and time of occurrence of a problem
I: Identify sources of a problem
J: Quantify the relative contribution of nonpoint sources
K: Determine the relative impact of nonpoint sources
. L: Determine fate and transport
M: Locate critical areas
N: Analyze trends
0: Determine the level of control needed
P: Make watershed allocations
Q: Calibrate models
R: Verify models
s: Test models
T: Conduct research


Numerous guidance documents have been developed, or are in
development, to assist resource managers in developing and
implementing monitoring programs for both point and nonpoint
sources of pollution. This chapter presents a review of numerous
monitoring guidances for both point and nonpoint pollution.
Guidances specific to point source control program monitoring are
reviewed because very often receiving waterbodies contain
contaminants from both point and nonpoint sources of pollution and
resource managers must take both point and nonpoint sources into
account when devising a monitoring program. Since point source
monitoring programs are not specifically the topic of this guidance
document, one or more of the guidances reviewed here for designing
and implementing point source monitoring programs should be
consulted if point source monitoring is required as part of a
monitoring program.
Despite their different focuses, point and nonpoint source
pollution monitoring programs often have similar or identical
designs, objectives, parameters to be measured, and statistical
analyses. Therefore, the guidance provided in this document is
generally applicable to point source monitoring programs, and
guidance for point source monitoring is generally applicable to
nonpoint sourcemoni toring programs. A possible exception is
monitoring programs for a specific mandated program, such as the
301(h) or 403(c) program. These programs often have specific legal
monitoring requirements, and the appropriate monitoring guidance
should be consulted when designing and implementing a monitoring
program for one of the programs.
The guidances reviewed in this chapter discuss virtually every
aspect of NPS pollution monitoring, including monitoring program
design and objectives, sample types and sampling methods, chemical
and physical water quality parameters, biological monitoring, data
analysis and management, and quality assurance and quality control.
However, all of these points are not discussed in each guidance
reviewed. Therefore, to help the reader find the guidance(s) most
appropriate to specific needs, each review highlights those aspects
of monitoring which are stressed in the particular guidance.
Grouping the guidances according to some seemingly logical
system is both easy and diff icul t: easy because they can be
grouped in any of a hundred ways with no one grouping being
superior and difficult for the same reason-they follow no natural
organization. Therefore, for lack of a better system, they are
grouped under the following headings:
General Monitoring Guidances and References
Guidances for Stream and River Monitoring
Guidances for Lake and Reservoir Monitoring
Guidances for Watershed Monitoring
Guidances for Ground Water Monitoring

Guidances for Biological Monitoring
Program-Specific Monitoring Guidances
There is some reasoning behind this grouping. The reviews
have been organized primarily according to the type of waterbody or
waterbody system to which the guidance is most applicable, i.e.,
streams and rivers, lakes and reservoirs, or watersheds. Guidances
that are not specific to one type of waterbody are grouped under
the remaining headings. For example, a guidance for biological
monitoring in streams and rivers is listed under "Guidances for
Stream and River Monitoring," whereas a biological monitoring
guidance that is not specific to waterbody type is listed under
"Guidances for Biological Monitoring." Numerous guidances are not
specif ic to either a waterbody type or a particular type of
. monitoring, and these are listed under "General Monitoring
Guidances and References." Guidances specific to programs mandated
under the Clean Water Act, su~h as the NPDES program or the
National Estuary Program, are listed separately.
A complete listing of the guidances reviewed in this chapter
is presented first, followed by the individual guidance reviews.
A table at the end of the chapter indicates at a glance the aspects
of monitoring addressed in each guidance. The numbers at the top
of the table correspond to the numbers preceding the guidance
titles in this listing and in the reviews.
2 .
Categorical Listing of Monitoring Guidances Reviewed
General Monitoring Guidances and References
Water Quality Monitoring.
3. .
The Nonpoint Source Manager's Guide to Water Quality and Land
Treatment Monitoring. Coffey, Spooner, and Smolen 1993.

Designing Effective Nonpoint Source Water Quality Monitoring
Programs. Maas 1989.
Water Quality Monitoring for the Clean Water Partnership. A
Guidance Document. Minnesota Pollution Control Agency 1989.
Evaluating the Effectiveness
Practices in Meeting Water
Dissmeyer 1994.
of Forestry Best Management
Quality Goals or Standards.
Volunteer Water Monitoring:
USEPA 1990.
A Guide for State Managers.
Volunteer Estuary Monitoring:
USEPA 1993.
A Methods Manual.
The Volunteer Monitor. The National Newsletter of Volunteer
Water Quality Monitoring.
Water-Quality Monitoring in the united States.
Intergovernmental Task Force on Monitoring Water Quality 1994.

Water-Quali ty Moni toring in the United states. Technical
Appendixes. Intergovernmental Task Force on Monitoring Water
Quality 1994.
Guidance for state Water Monitoring and Wasteload Allocation
Programs. , USEPA 1985.
Guidelines for Evaluation of Agricul tural Nonpoint Source
Water Quality Projects. USEPA 1981.
Guidances for stream and River Monitoring
Monitoring Guidelines to Evaluate Effects of Forestry
Activities on streams in the Pacific Northwest and Alaska.
MacDonald, Smart and Wissmar 1991.
Moni toring Protocols to Evaluate Water Quality Effects of
Grazing Management of Western Rangeland streams. USEPA Draft.
Rapid Bioassessment Protocols for Use in streams and Rivers:
Benthic Macroinvertebrates and Fish. USEPA 1989.
An Improved Biotic
Hilsenhoff 1987.
Using the Index of
Environmental Quality
Lyons 1992.
Biotic Integrity (IBI) to Measure
in Warmwater streams of Wisconsin.
Handbook: Stream Sampling
Applications. USEPA 1986.
Evaluation Monitoring of stream Habitat During
Watershed Projects. Simonson and Lyons 1992.
Evaluation Monitoring of Stream Fish Communities During
Priority Watershed Projects. Simonson and Lyons 1992.
Techniques for Detecting Effects of Urban and Rural Land-Use
Practices on stream-Water Chemistry in Selected Watersheds in
Texas, Minnesota, and Illinois. Walker 1993.
3 .
Guidances for Lake and Reservoir Monitoring
Monitoring Lake and Reservoir Restoration.
USEPA 1990.
Volunteer Lake Monitoring:
A Methods Manual.
USEPA 1991.
Technical support Manual: Waterbody Surveys and Assessments
for conducting Use Attainability Analyses. Volumes I-III.
USEPA 1983-1984.
Guidances for Watershed Monitoring

Monitoring Primer for Range Watersheds.
Bedill and Buckhouse
seminar Publication: The National Rural Clean Water Program
Symposium. 10 years of controlling agricul tural nonpoint
source pollution: The RCWP experience. USEPA 1992.
Guidances for Ground Water Monitoring
A Review of Methods for Assessing Nonpoint Source Contaminated
Ground-Water Discharge to Surface Water. USEPA 1991.
Guidances for Biological Monitoring
Bioaccumulation Monitoring Guidance: Selection of Target
Species and Review of Available Bioaccumulation Data. Volume
I. USEPA 1987.
Fish Field and Laboratory Methods
Biological Integrity of Surface Waters.
for Evaluating
USEPA 1993.
Biological Field and Laboratory Methods for Measuring thE~
Quality of Surface Waters and Effluents. USEPA 1973.
Methods for Sampling Fish Communities as
National Water-quality Assessment Program.
and Gurtz 1993.
a Part of the
Meador, Cuffney
Program-specific Monitoring Guidances
Watershed Monitoring and Reporting for section 319 National
Monitoring Program Projects. USEPA 1991.
Monitoring Guidance for the National Estuary Program.
QC-QA Plan Rural Nonpoint.
USGS 1992.
NPDES storm Water Sampling Guidance Document.
USEPA 1992.
Water Quality Standards Handbook.
USEPA 1983.
Environmental Monitoring and Assessment Program:
Indicators. USEPA 1990.
RCRA Ground-Water Monitoring Technical Enforcement Guidance
Document. USEPA 1986.
Summary of U.S. EPA-Approved Methods, Standard Methods, and
other Guidance for 301(h) Monitoring variables. USEPA 1985.
Ecological Assessments of Hazardous Waste sites:
Laboratory Reference Document. USEPA 1989.
A Field and

statistical Analysis of Ground-Water Monitoring Data at RCRA
Facilities - Interim Final Guidance. USEPA 1989.
42. - CWA section 403:
Procedural and Monitoring Guidance.
Guidance Reviews
General Monitoring Guidances and References
Water Quality Monitoring.
USDA-SCS, Draft.
REFERENCE: USDA-SCS. 1993. Water Quality Monitoring. Draft. June.
CONTENTS: Defining water quality problem; Objectives; Scale of study; Variable selection; Sample
type; Sampling location; Sampling frequency and duration; Monitoring study designs; Station type;
Sample collection and analysis; Land use and management monitoring; Data management.
MAIN FOCUS: Primarily useful for designing a monitoring program. Thoroughly discusses all
aspects of monitoring program design (site selection, parameter selection, sampling program design)
with numerous examples and illustrations to help the reader determine what is most appropriate
for particular applications.
This document describes methods for monitoring water quality
responses to land use, land management activities, and conservation
practices in streams, lakes, and ground water. It is intended to
be a comprehensive guidance for water quality managers who have
little experience in monitoring study design and implementation.
The many purposes that monitoring studies can serve are discussed
to help water quality managers define the scope of their monitoring
programs.. Examples of programs meant to serve the different
purposes are included.
Specific guidance is provided on designing a monitoring study,
setting up a monitoring station, and analyzing water quality data.
Worksheets are provided to facilitate rapid and complete monitoring
study design. The document is divided into two parts. Part 1
contains 12 chapters, each of which covers a specific step of
monitoring study design: (1) define water quality problem, (2)
define monitoring objectives, (3) determine study scale, (4) select
water quality variables, (5) select sample type, (6) determine
sampling locations, (7) determine sampling frequency and duration,
(8) describe statistical design, (9) design station type, (10)
describe sample collection and analysis methods, (11) describe land
use monitoring, and (12) describe data management. Part 2
discusses statistical analysis of monitoring results.
The Nonpoint Source Manager's Guide to Water Quality and Land
Treatment Monitoring. Coffey, Spooner, and Smolen 1993.

REFERENCE: Coffey, S.W.,J. Spooner, and M.D. Smolen. 1993. The Nonpoint Source Manager's
Guide to Land Treatment and Water Quality Monitoring. NCSU Water Quality Group, Department
of Biological and Agricultural Engineering, North Carolina State University, Raleigh, North
CONTENTS: Overview of monitoring program; Management objectives and problem development;
Monitoring program objectives; Monitoring program design; Data collection; Data analysis; Program
MAIN FOCUS: Specifically addresses monitoring to track land treatments. Distinguishes between
two levels of monitoring: Level I-basic, low-cost monitoring; and Level II-more intensive and
comprehensive, at higher cost. Water quality and land treatment monitoring parameters are
discussed separately for each level of monitoring.
This guide discusses the objectives and design of monitoring'
pro,gram used to evaluate present conditions, identify water quality
problems, detect trends and impacts, and document water quality
improvements associated with the implementation of land treatments.
variations in monitoring program objectives and designs to make
them appropriate for streams, lakes, wetlands, and reservoirs are
indicated. Two levels 'of detail, applicable to different
monitoring objectives, are discussed separately for each of three
types of monitoring programs: land use and land treatment
monitoring, water quality monitoring, and loading rate monitoring.
For each level of detail and each type of monitoring, appropriate
biological, habi tat, physical,. and chemical variables are
A chapter on the design of monitoring programs emphasizes the
importance of monitoring both land treatments and water quality to
provide feedback on the impact of land management activities on
water quality. Guidance on the use of existing data in monitoring
program design is provided, and estimated costs for some procedures
are included to help water quality managers estimate monitoring
program budgets. Only brief discussions of data collection and
analysis and program evaluation are presented. While this guidance
primarily addresses agricultural land treatments, it is equally
applicable to designing and implementing programs to monitor the
effects of other types of land treatments, or general status and
trend monitoring programs.
3 .
Designing Effective Nonpoint Source Water Quality Monitoring
Programs. Maas 1989.
The purpose of this document is to provide guidance to those
involved in NPS pollution control in designing and carrying out
successful and cost-efficient water quality monitoring programs.
It is intended as a technical document to provide NPS monitoring
professionals with the necessary resource materials to make
informed decisions regarding the design of water quality monitoring

REFERENCE: Maas, R.P. 1989. Designing Effective Nonpoint Source Water Quality Monitoring
Programs. Prepared for the Tennessee Valley Authority. November.
CONTENTS: I. General guidance for developing nonpoint source monitoring programs:
Background; Purposes and objectives of water quality monitoring in NPS projects; Source
inventories; Water sampling in NPS control projects; NPS water quality monitoring designs;
Biological monitoring; Using preliminary data to get the most from your water quality monitoring
program; Determining the minimum detectable change in water quality required to be observable
from an NPS water quality monitoring program; Matching purposes and design of nonpoint source
water quality monitoring programs; II. Case study: Oostanaula Creek, Tennessee.
MAIN FOCUS: Focuses primarily on monitoring program design for documenting the benefit of
NPS control programs; Provides details (i.e.,monitoring program design, statistical analyses) about
time-trend and paired watershed designs; Includes a case study of implementing a cost-effective NPS
monitoring program.
programs. It should also provide NPS program managers with
sufficient background to evaluate technical decisions on NPS
monitoring strategies for their consistency with an overall purpose
and their probability of documenting water quality improvement.
This document focuses primarily on experience gained through state
and federal agricultural and urban NPS projects, such as the Model
Implementation Program, initiated in 1978, and the Rural Clean
Water Program, initiated in 1980. (from author's preface)
A particularly useful application of NPS monitoring information is
to document the beneficial effect of an NPS control program on
water quality. This, however, can be a particularly difficult
monitoring objective to fulfill. This document examines monitoring
design characteristics that maximize the ability to achieve this
4 .
Water Quality Monitoring for the Clean Water Partnership. A
Guidance Document. Minnesota Pollution Control Agency 1989.
REFERENCE: Clean Water Partnership. 1989. Water Quality Monitoring for the Clean Water
Partnership. A Guidance Document. Minnesota Pollution Control Agency, Division of Water
Quality. March.
CONTENTS: Purpose; Steps in developing a monitoring plan; Water quality parameters; Sampling
site selection; Sampling strategies; Hydrology; Quality Assurance/Quality Control.
MAIN FOCUS: Brief discussion of each monitoring parameter covering reason for its
measurement, considerations for measuring the parameter, and sampling and analysis techniques.
This guidance covers all of the technical steps in developing and
implementing monitoring programs for the evaluation of the effect

of projects on water quality. Brief descriptions of each of the
parameters to be monitored constitute most of the document. The
monitoring program described is one that meets the requirements for
Clean Water Partnership projects.
Evaluating the Effectiveness
Practices in Meeting Water
Dissmeyer 1994.
of Forestry Best
Quality Goals or
REFERENCE: USDA-FS. 1994. Evaluating the Effectiveness of Forestry Best Management Practices
in Meeting Water Quality Goals or Standards. By G.E. Dissmeyer, USDA Forest Service, Southern
Region, Atlanta, Georgia. Miscellaneous Publication 1520. June.
CONTENTS: Planning monitoring projects; Quality assurance/quality control; Statistical
considerations; Selecting the appropriate BMP effectiveness monitoring level; Monitoring methods;
Deciding on BMP effectiveness: Some case histories.
MAIN FOCUS: Discussion of four levels of monitoring for different monitoring program objectives.
Focuses on monitoring program design for determination ofBMP effectiveness, management activity
water quality impact, choice of BMPs for best water quality protection, and BMP effectiveness
longevity. Discussions of numerous monitoring protocols, with references to detailed descriptions
for further information.
This manual is intended to assist managers and staff in developing
water quality monitoring plans to evaluate the effectiveness of
forestry BMPs in meeting water quality goals or standards for
streams, including chemical, physical, biological, and habitat
integrity. The focus is on monitoring project design and
parameters and methods selection. The methods discussed in the
document are appropriate for fourth order streams and smaller.
Monitoring project design is discussed with the intention of
separating. the NPS impact of management activities from other NPS
impacts. The document also addresses assessments of how long BMPs
remain effective and which BMPs best protect water quality.
Effectiveness monitoring is separated into four levels, depending
on program needs. Monitoring methods for chemical, physical,
biological and habitat integrity are recommended to achieve each of
the four monitoring levels. Generally, the reader is referred to
the original literature or to other documents for procedural
details of the monitoring methods, and this guide serves as a
manual for monitoring program design.
Volunteer Water Monitoring:
USEPA 1990.
A Guide for state Managers.
This guide is directed toward those contemplating setting up a
volunteer monitoring program. Nearly every aspect of creating a
successful monitoring program is discussed, including attracting
volunteers, keeping volunteers interested and motivated, finding

REFERENCE: USEPA. 1990. Volunteer Water Monitoring: A Guidefor State Managers. U.S.
Environmental Protection Agency, Office of Water, Washington, DC. EPA 440/4-90-010.
CONTENTS: Volunteers in water monitoring; Planning a volunteer monitoring program;
Implementing a volunteer monitoring program; Providing credible information; Costs and funding.
Appendix: Descriptions of five successful programs.
MAIN FOCUS: A guide to the administrative details of a volunteer monitoring program, including
training volunteers, funding, program design, and media relationships. Presentations of volunteer
monitoring programs in the appendix provide good examples of program implementation to meet
differing needs and to deal with different local and state requirements. State contacts are provided.
funding sources, quality assurance and quality control, and
ensuring that the collected data are put to use. The techniques
and methods of monitoring are discussed in other manuals (e.g.,
Volunteer Lake Monitoring: A Methods Manual).
Descriptions of five state volunteer monitoring programs are
provided: Illinois, Kentucky, New York, Ohio, and the Chesapeake
Bay. Each discussion provides details of program objectives, how
volunteers were recruited and trained, sampling protocols, data
management, program administration, volunteer recognition, and
expenses and funding. state contact names, addresses and phone
numbers are provided for each program.
Volunteer Estuary Monitoring:
A Methods Manual.
USEPA 1993.
REFERENCE: USEPA. 1993. Volunteer estuary monitoring: A methods manual.
Environmental Protection. Agency, Office of Water. EPA 842-B-93-004. December.
CONTENTS: Our troubled estuaries; Setting the stage; Monitoring dissolved oxygen; Monitoring
nutrients and phytoplankton; Monitoring submerged aquatic vegetation; Monitoring bacteria;
Monitoring other estuarine conditions; Training volunteers; Presenting monitoring results;
MAIN FOCUS: Clearly written, intended to serve a lay audience. Step-by-step descriptions of
common estuary monitoring methods.
This manual is meant to be a companion to three other EPA
documents: Volunteer Water Monitoring: A Guide for state
Managers, Volunteer Lake Monitoring: A Methods Manual, and
Volunteer stream Monitoring: A Methods Manual (in progress as of
12/93) . The manual reviews those water quality parameters
considered most important to monitor to determine an estuary's
water quality: dissolved oxygen, bacteria, nutrients,
phytoplankton, and submerged aquatic vegetation. Each chapter
discusses why it is important to monitor the particular parameter,

the role of the parameter in estuarine ecology, and sampling
equipment for taking measurements of the parameter. Methods for
sampling the parameter are set out in easy-to-follow steps. Two
introductory chapters discuss the state of the nations's estuaries,
basic estuarine ecology, basic monitoring equipment, and gross
conditions to note while monitoring, such as temperature and
shoreline condition. other chapters discuss volunteer training,
the importance of credible data, and data presentation techniques.
supply houses are listed in one appendix, and quality assurance is
addressed in another.
The Volunteer Monitor. The National Newsletter of Volunteer
Water Quality Monitoring.
REFERENCE: The Volunteer Monitor. Published by the Coastal Resources Center, The University
of Rhode Island, Rhode Island Sea Grant Program, Narragansett, Rhode Island, 02882.
CONTENTS: Vary from issue to issue. Example issue (vol. 3, no. 1, Fall 1991): Special topic:
biological monitoring; Monitoring groups need a national association; EPA Lakes Methods manual;
Wetlands field guide; Lake monitoring network; Technical tips; Doing your own lab analysis for
fecal coliform; Monitoring aquatic plants; Monitoring diseased eelgrass; Local bank sponsors River
Rescue; Third National Volunteer Monitoring Conference set.
MAIN FOCUS: Typically provides information on monitoring programs throughout the country,
new publications, materials and technical methods, contacts for equipment supplies, school
programs, and information On monitoring particular plants or animals.
The Volunteer Monitor is a newsletter published by Rhode Island Sea
Grant devoted entirely to topics related to volunteer monitoring.
Issues contain articles on a diversity of topics, including
. chemical, physical, and biological monitoring, reviews of documents
related to monitoring, EPA activities, monitoring conferences,
monitoring associations, equipment and methods, data collection and
analysis, public education, and technology transfer. Information
on purchasing monitoring supplies and articles of special interest,
such as on methods to monitor particular species or habitats, are
regularly published.
Water-Quality Monitoring in the united states.
Intergovernmental Task Force on Monitoring Water Quality 1994.
The Intergovernmental Task Force on Monitoring Water Quality was
established to address a need for greater coordination among
agencies collecting water-quality information to make that
information more meaningful to all users. This is the second
annual report of the ITFM. It describes the progress of the ITFM
and its task groups in developing concepts, guidelines, and
procedures for use in a nationwide monitoring strategy. The
recommendations of the ITFM will be refined in 1994, its third and
lqst year, and published in its final report. The information in

REFERENCE: ITFM. 1994. Water-quality monitoring in the United States. Intergovernmental Task
Force on Monitoring Water Quality, Interagency Advisory Committee on Water Data, Water
Information Coordination Program. Washington, DC. January.
CONTENTS: Executive summary; Second year's progress-answering the questions; Third year
plan; Conclusions and recommendations.
MAIN FOCUS: In-depth discussions of monitoring program problems that program managers need
to consider.
this document specifically addresses the needs and direction of the
nationwide monitoring effort, but members of the ITFM have given
careful thought to problems that plague many monitoring programs
and the monitoring program concepts and issues discussed in this
report should be considered seriously by anyone undertaking or
modifying a monitoring program.
Water-Quali ty Monitoring in the united states. Technical
Appendixes. Intergovernmental Task Force on Monitoring Water
Quality 1994.
REFERENCE: ITFM. .1994. Water-quality monitoring in the United States. Technical appendixes.
Intergovernmental Task Force on Monitoring Water Quality, Interagency Advisory Committee on
Water Data, Water Information Coordination Program. Washington, DC. January.
CONTENTS: Glossary; Framework for water-quality monitoring; Charter for the National Water-
quality Monitoring Council; Indicators for meeting management objectives-summary matrix;
Indicators for meeting management objectives-rationale matrix; Indicator selection criteria;
Ecoregions, reference conditions, and index calibration; Multimetric approach for describing
ecological conditions; Charter for Methods and Data Comparability Council; Data comparability and
performance-based methods policy paper-comparability of data-collection methods; Target
audiences, monitoring objectives, and format considerations for reporting water-quality information;
Annotated bibliography of selected outstanding water-quality reports; Ground-water-quality
monitoring framework; Ground-water indicators.
MAIN FOCUS: Discussions of numerous technical points related to the national monitoring
program, including indicators, ecoregions, and multimetrics. Provides useful charts and graphs
related to these topics.
This companion document to the ITFM 1993 report provides detailed
discussions of the more technical aspects of the national
monitoring program. In addition, general information on monitoring
programs, such as program objectives and design, are discussed in
the context of the national program. Numerous tables related to
the technical topics discussed consolidate much information

contained in many other technical monitoring document in a single
Guidance for state Water Monitoring and Wasteload Allocation
Programs. USEPA 1985.
REFERENCE: u.s. EPA. 1985. Guidance/or State Water Monitoring and Wasteload Allocation
Programs. U.S. Environmental Protection Agency, Office of Water Regulations and Standards,
Washington, DC. EPA 440/4-85-031. October.
CONTENTS: Overview of water quality program monitoring; Monitoring for water quality-based
controls; Monitoring for compliance and enforcement; Water quality assessments; Quality assurance;
Data reporting; Total maximum daily loads and wasteload allocations.
MAIN FOCUS: Provides a general overview of state water quality monitoring responsibilities under
, the Clean Water Act (pre-1987). '
This guidance is oriented toward program management and does not
contain extensive technical information on monitoring programs.
The guidance is intended to be used by states and EPA regional
offices for developing the monitoring and waste load allocation
po~tions of annual state 106 and 205(j) work programs. Monitoring
and wasteload allocation activities are defined in accordance with
EPA regulations. Two principal areas are covered by the guidance.
The first is an outline of the objectives of the water monitoring
pr0gram, and the second is a description of the process for
calculating total maximum daily loads (TMDL) and waste load
allocations for point sources (wasteload allocations, WLA) and
nonpoint sources (load allocations, LA) of pollution.
Separate chapters of the guidance address different aspects of
state programs (conducting water quality assessments, developing
water quality-based controls, and assessing compliance), and for
each of these program aspects the guidance discusses the type of
data needed, who is responsible for doing the work, the methods to
be used, data reporting requirements, parameters, and uses of the
data. References to technical guidance and sample program
checklists are provided in an appendix.
Guidelines for Evaluation of Agricultural Nonpoint Source
Water Quality Projects. USEPA 1981.
Th,is guidance was developed under EPA I S Rural Nonpoint Source
Control Water Quality Evaluation and Technical Assistance project
as a joint effort of EPA and USDA. It is intended to provide basic
gU,idelines for measuring water quality changes and estimating
socioeconomic impacts resulting from NPS pollution control
programs. Monitoring requirements for a basic, level I monitoring
program are discussed, as well as more intensive requirements for

REFERENCE: USEP A. 1981. Guidelines for Evaluation of Agricultural Nonpoint Source Water
Quality Projects. U.S. Environmental Protection Agency. L.R. Shuyler, EPA project officer.
Prepared under the Rural Nonpoint Source Control Water Quality Evaluation and Technical
Assistance project.
CONTENTS: Evaluation procedures for nonpoint source control measures; Evaluation and
sampling needs; Streams; Lakes; Ground water; Socioeconomic evaluation.
MAIN FOCUS: The sections on streams and lakes contain an assessment of evaluation alternatives
and specific monitoring recommendations relevant to the type of receiving water, including guidance
for identification of impacted beneficial uses. The important characteristics that should be
monitored of each receiving water type are discussed.
a detailed monitoring program. The guidance provided in this
document is basic in the sense that the parameters that should be'
measured for minimum level I and level II assessments are mentioned
and discussed briefly, but no guidance for taking measurements,
identifying monitoring stations, designing a monitoring program, or
analyzing results is provided. Emphasis is placed on the
collection of historical data prior to monitoring and monitoring
physical, chemical, and biological characteristics that will
indicate present condition 'and changes in those characteristics due
to BMP implementation.
A separate section on socioeconomic evaluation of NPS pollution
control programs is provided. Questions of impacts to farmer
income, overall project value with respect to alternative community
needs, and choices of alternative environmental projects are
mentioned as important considerations prior to the implementation
of a NPS pollution control project. Two levels of socioeconomic
evaluations are discussed. A level I evaluation considers the
effects of a NPS pollution control proj ect on land use, crop
production, income, pollution control effectiveness, and project
efficiency in a cost/benefit sense. A level II evaluation includes
the elements of a level I evaluation as well as an estimation of
community and off-farm impacts and an evaluation of alternative
options. Tables at the end of the paper summarize the
recommendations presented in the text.
Guidances for stream and River Monitoring
Monitoring Guidelines to Evaluate Effects of Forestry
Activities on streams in the Pacific Northwest and Alaska.
MacDonald, Smart, and Wissmar 1991.
The focus of these guidelines is on monitoring water quality in
streams, and it does not directly address monitoring in lakes,
reservoirs, or other downstream areas. The discussions are also
limited to conditions in the Pacific Northwest and Alaska, which
reduces the scope of conditions and activities considered in the
document. However, the information provided on monitoring
objectives and monitoring parameters is generally applicable.

REFERENCE: MacDonald, L.H.,A.W. Smart, and R.C. Wissmar. 1991. Monitoring Guidelines
to Evaluate Effects of Forestry Activities on Streams in the Pacific Northwest and Alaska. U.S.
Environmental Protection Agency, Region 10, Water Division, Seattle, Washington. EPA/910/9-91-
001. May.
CONTENTS: Part I: Context and structure of monitoring projects; Statistical considerations in
water quality monitoring; Principles of developing a monitoring plan and selecting the monitoring
parameters; parameter recommendations and interactions. Part II: Physical and chemical
constituents; Changes in flow; sediment; Channel characteristics; Riparian monitoring; Aquatic
MAIN FOCUS: Provides a good review of the importance of proper statistical design in a
monitoring program. Tabulates monitoring parameters according to their usefulness for monitoring
different land treatments. Specific to monitoring stream conditions in the Pacific Northwest and
Inf,ormation on monitoring to detect the water quality impacts of
grazing, mining, and recreation is also provided because these
activities occur on or near lands where forestry activities are
conducted and it can be difficult to separate the water quality
impacts of these activities from those of forestry operations.
The document has two parts. Part 1 discusses seven purposes of
monitoring, legal requirements for NPS pollution monitoring,
statistical considerations in water quality monitoring, monitoring
plan development, and the selection of monitoring parameters.,
MODitoring parameters are recommended for different forestry-
related activities (e.g., forest harvest, road construction). Part
2 is a comprehensive discussion of individual monitoring parameters
and is intended to facilitate the selection of the most appropriate
monitoring parameters for specific monitoring objectives. This is
not a technical guidance on sampling procedures or statistical
analyses used for monitoring programs, but rather a comprehensive
discussion of the various elements of a monitoring program to help
water resource or forestry operations managers make informed
decisions concerning monitoring programs. References are provided
to direct the reader to the appropriate technical guidance where
Monitoring Protocols to Evaluate Water Quality Effects o.f
Grazing Management of Western Rangeland streams. USEPA Draft.
This document describes a monitoring system to assess the impacts
of I grazing on water quality in streams of the western united states
and protocols used to assess changes in water quality that result
from stream restoration projects. Protocols that are easy to use
and cost-effective (i.e., have reduced sampling frequency,
minimized need for specialized equipment, and a reduced requirement
for laboratory analyses) were selected. The document focuses on
monitoring attributes of the stream channel, stream bank, and

REFERENCE: USEPA. 1993. Monitoring Protocols to Evaluate Water Quality Effects of Grazing
Management of Western Rangeland Streams. U.S. Environmental Protection Agency, Region 10,
Water Division, Surface Water Branch. EPA 910/R-93-017. October.
CONTENTS: Impacts of grazing on water quality and beneficial uses; Monitoring plan procedure;
Stratification, reconnaissance, and classification of rangeland riverine riparian areas;
Evaluation/recommendation of monitoring methods: Stream temperature and shade; Nutrients;
Bacterial indicators; Stream channel morphology; Streambank stability; Substrate fine sediment; Pool
quality; Streamside vegetation.
MAIN FOCUS: Describes a methodology to classify a stream and riparian vegetation prior to
selecting monitoring sites. Provides tables of monitoring parameter attributes (sampling frequency,
collection time necessary, equipment requirements, lab costs, level of expertise needed). Detailed
information on recommended methods is provided.
streamside vegetation that are important to the support of aquatic
life and that are impacted by grazing. A discussion of the impacts
of grazing on stream ecosystems provides a basis for selecting
monitoring parameters, and a procedure to develop a monitoring plan
is recommended. Methods to stratify and classify stream reaches
based on stream type, dominant soils, and riparian vegetation
communities are described, and provide a basis for selecting
monitoring sites and reference areas. Forms for recording data and
a list of equipment needed for each protocol are provided.
Monitoring methods that are commonly used to assess the effects of
grazing on water quality are described and the attributes of each
are tabulated. The advantages and disadvantages of the methods are
described and tabulated for ease of comparison, and recommendations
for specific protocols are made based on ease of use and cost-
effectiveness. These recommended protocols are then thoroughly
described, including data collection and analysis procedures. The
recommended protocols are stream temperature and shade, nutrients,
bacterial indicators, stream channel morphology, streambank
stability, substrate fine sediment, pool quality, and streamside
vegetation. A list of references pertaining to each protocol is
provided at the end of the discussion of each one. The usefulness
of the recommended protocols is not limited to monitoring the
-impacts of grazing, and the reader should find the discussions of
the protocols valuable if the same protocols are being considered
for monitoring the water quality effects of other land use
activities. Other references should be consulted for specific
guidance on sampling and statistical analysis of data.
Rapid Bioassessment Protocols for Use in streams and Rivers:
Benthic Macroinvertebrates and Fish. USEPA 1989.
This is a
comprehensive technical reference for bioassessment
for streams and rivers. . Three macro invertebrate
and two fish protocols - are presented. The

REFERENCE: U.S. EPA. 1989. Rapid Bioassessment Protocols for Use in Streams and Rivers:
Benthic Macroinvertebrates and Fish. U.S. Environmental Protection Agency, Office of Water,
Washington, DC. EPA/440/4-89/001. May.
CONTENTS: The concept of biomonitoring; Overview of protocols and summary of components;
Quality assurance/quality control; Habitat assessment and physicochemical parameters; Benthic
macro invertebrate biosurvey and data analysis; Fish biosurvey and data analysis; Integration of
habitat, water quality, and hiosurvey data. Appendices: Guidance for use of field and laboratory
data sheets; Rapid bioassessment subsampling methods for benthic protocols; Family and species-
level macro invertebrate tolerance classifications; Tolerance, trophic guilds, and origins of selected
fish species.
MAIN FOCUS: Provides both an introduction to the concept of biomonitoring and detailed
methods sections for conducting rapid bioassessment protocols. Sample data sheets for all protocols
are provided, and data analysis and interpretation is thoroughly discussed.
macro invertebrate protocols were tested in wadable freshwater
streams, though they should be applicable to large freshwater
rivers as well. They were developed by consolidating various
procedures in use by various state water quality agencies, and they
require levels of effort r~nging from fairly simple to rigorous.
The fish protocols were validated in freshwater streams and large
rivers and are therefore equally applicable to both. They were
developed based on previous work by other researchers and on
standard fish population assessment models.
The document contains an introduction to the biomonitoring approach
of detecting aquatic life impairments and estimating their
severity. Procedures for assessing the habitat where the sampling
is done are explained, and the physical and chemical parameters
relevant to biological survey data interpretation are discussed.
Complete instructions for conducting benthic biosurveys and fish
surveys are provided, laboratory methods and data analysis
te~hniques are explained, and quality assurance and quality control
are addressed. Field data forms and guidance for their use are
An Improved Biotic
Hilsenhoff 1987.
Hilsenhoff introduced a biotic index for evaluating the water
quality of streams in 1977, and offers improvements to it in this
paper. The initial index assigned tolerance values of 0-5 t.o
species, but after evaluation of over 1000 samples the index has
been revised to accommodate tolerance values of 0-10 to provide
greater precision. Tolerance values of species are provided in an
appendix. Some orders of arthropods are difficult to identify, and
the problems associated with those orders are discussed. A revised
procedure for collecting, sorting, and evaluating samples using the
biotic index presented in the paper is provided.

REFERENCE: Hilsenhoff, W.L. 1987. An Improved Biotic Index o/Organic Stream Pollution. The
Great Lakes Entomologist 1:31-39.
CONTENTS: Abstract; Reassignment of tolerance values; identification; Collection and evaluation
of samples; Literature cited; Appendix 1: Tolerance values for stream arthropods.
MAIN FOCUS: Provides a discussion of identification problems specific to insect orders. Includes
a detailed discussion of proper stream arthropod collection techniques. An appendix provides
revised tolerance values for stream arthropods.
Using the Index of
Environmental Quality
Lyons 1992.
Biotic Integrity (IBI) to Measure
in Warmwater streams of Wisconsin.
REFERENCE: Lyons, J. 1992. Using the Index 0/ Biotic Integrity (IBI) to Measure Environmental
Quality in Warmwater Streams o/Wisconsin. U.S. Department of Agriculture, Forest Service, North
Central Forest Experiment Station. General Technical Report NC-149.
CONTENTS: General considerations; Applying the IBI in Wisconsin warmwater streams:
Collecting and processing the field data; Analyzing the data; Interpreting IBI scores.
MAIN FOCUS: Complete discussion of data analysis. Provides Maximum Species Richness plots
for data interpretation. Applicable to similar streams in nearby states.
This paper summarizes the results of a 4-year fish collection and
data analysis effort aimed at developing a version of the IBI for
warmwater Wisconsin streams. The paper is designed primarily as a
"how to" manual and therefore contains little discussion of the
principles of the IBI. Discussion focuses on collection of fish
samples for analysis, and analysis and interpretation of the data.
Maximum Species Richness (MSR) plots for data interpretation are
Because of the similarity in stream characteristics and fish fauna
between Wisconsin and parts of adjacent states, the Wisconsin
version of the IBI described in this paper should be useful in
southeastern and northeastern Minnesota, the entire Upper Peninsula
and the northern Lower Peninsula of Michigan, extreme northwestern
Illinois, and extreme northeastern Iowa.
Handbook: stream Sampling
Applications. USEPA 1986.
This report discusses sampling requirements in support of waste
load allocation studies in rivers and streams. Two approaches to
waste load allocation are addressed: the chemical-specific

REFERENCE: USEP A. 1986. Handbook: Stream Samplingfor Waste Load Allocation Applications.
U.S. Environmental Protection Agency, Office of Research and Development, Washington, DC.
EP A/625/6-86/0 13. September.
CONTENTS: Sampling requirements for waste load allocation modeling; Sampling requirements
for conventional pollutants; Sampling requirements for toxic pollutants; Whole effluent approach;
Example application.
MAIN FOCUS: Summarizes data requirements for modeling applications and discusses the
applicability and advantages of numerous models. Flow charts for modeling approaches and
parameter formulas are provided.
approach and the whole effluent approach. Numerical or analytical
toxicant fate models are used to implement the chemical-specific
approach. Modeling requirements and sampling guidelines are
delineated for this method.
For the whole effluent approach, the method is summarized and then
instream dye study requirements are presented. The repor1:
concludes with example applications of the chemical-specific
approach for conventional and toxic pollutants.
This guidance does not discuss equipment requirements, personnel
requirements, sample collection, stream characterization, or
laboratory analytical techniques. The primary purpose of thf~
document is to assist water quality specialists in designing stream
surveys to support modeling applications for waste load
applications. The data collection process required to calibrate,
ve~ify, and apply models used for waste load allocations to
critical design conditions is described.
Evaluation Monitoring of stream Habitat During
Watershed projects. Simonson and Lyons 1992.
REFERENCE: Simonson, T., and J. Lyons. 1992a. Evaluation Monitoring of Stream Habitat During
Priority Watershed Projects. Wisconsin Department of Natural Resources. May.
CONTENTS: Station summary data sheet; Station map data sheet; Station flow data sheet; Transect
data sheet; Appendix: Gear used for habitat sampling.
MAIN FOCUS: Each data element to be recorded is explained separately. Data recording forms
are provided.
This paper describes all of the data elements to be recorded during
evaluation phase monitoring of fish habitat for WDNR Priority
Watershed Projects. The purpose of the monitoring is to document
changes in fish communities and fish habitat that occur in streams

where improved land use practices are implemented to reduce NPSP.
The level of detail given for each data element make this paper a
manual for conducting an evaluation, not just a discussion of data
elements. Two sets of sample data entry sheets are provided, one
blank and one filled out with example data. The gear needed to
conduct an evaluation is described in an appendix, and the names
and addresses of suppliers are provided.
Evaluation Monitoring of stream Fish Communities During
priority watershed Projects. Simonson and Lyons 1992.
REFERENCE: Simonson, T., and I. Lyons. 1992b. Evaluation Monitoring of Stream Fish
Communities During Priority Watershed Projects. Wisconsin Department of Natural Resources.
CONTENTS: Station summary data sheet; Catch summary data sheet; Individual fish data sheet.
MAIN FOCUS: Each data element to be recorded is explained separately. Data recording forms
are provided.
This paper, the companion to simonson and Lyons' paper Evaluation
Monitoring of stream Habitat During Priority Watershed Projects,
describes the data elements to be recorded during evaluation phase
monitoring of fish communities for WDNR Priority Watershed
Projects. This paper is similar in content to that paper, except
that only one set (blank) of data sheets is provided.
Techniques for Detecting Effects of Urban and Rural Land-Use
Practices on stream-Water Chemistry in Selected Watersheds in
Texas, Minnesota, and Illinois. USGS 1993.
REFERENCE: Walker, I.F. 1993. Techniques for Detecting Effects of Urban and Rural Land-Use
Practices on Stream-Water Chemistry in Selected Watersheds in Texas, Minnesota, and Illinois. U.S.
Geological Survey and Wisconsin Department of Natural Resources. USGS Open-file Report 93-
CONTENTS: Techniques for detecting effects ofland-use practices on water chemistry; Application
of techniques to selected watersheds; Summary and conclusions.
MAIN FOCUS: Statistical techniques for the detection of effects of land-use practices on water
chemistry are applied to selected watersheds. Alternative procedures for assessing the effects of
land-use practices are compared.

There is little information available about the effectiveness of
best management practices at the watershed scale. This report:
presents a discussion of several parametric and nonparametric:
statistical techniques for detecting changes in water-chemistry
data. The use of storm load data is discussed as an alternative to
using fixed-frequency instantaneous concentration data.
st~tistical techniques were applied to three urban watersheds in
Texas and Minnesota and three rural watersheds in Illinois. For
the urban watersheds, single- and paired-site data collection
strategies were considered. For the rural watersheds, the selected
techniques were found not to be effective at identifying changes.
Th~ use of regressions improved the ability to detect changes.
(from author abstract)
3 .
Guidances for Lake and Reservoir Monitoring
Monitoring Lake and Reservoir Restoration.
USEPA 1990.
REFERENCE: USEPA. 1990. Monitoring Lake and Reservoir Restoration. U.S. Environmental
Protection Agency, Office of Water, Washington, DC. EPA 440/4-90-007. August.
CONTENTS: Planning the monitoring program; Monitoring methods; Watershed monitoring; In-
lake restoration techniques and monitoring; A long-term monitoring protocol; Case study:
Detection of trends and sampling strategy evaluations.
MAIN FOCUS: Three levels of watershed monitoring are discussed. Complete discussions of lake
, and reservoir restoration objectives and the methods used to achieve the objectives are provided.
This manual is a technical supplement to The Lake and Reservoi,r
Restoration Guidance Manual (USEPA, 1988) and provides guidance for
, both design and implementation of a monitoring program by outlining
specific standards for specific types of lake restoration and
p~otection projects. It is intended to guide monitoring carried
out under the Clean Lakes Program in connection with the Phase II
or implementation portion of a lake restoration project. Phase I
or diagnostic/feasibility monitoring is more exploratory in nature
and more generic in terms of parameters used, and it is not
directly addressed in this guidance. The primary users of this
guidance are expected to be Regional EPA Clean Lakes projec::t
officers, state and local project managers, and project sponsors
and consultants.
Procedures for performing in-lake sampling, measuring stream flo'~,
handling and preserving samples, and analyzing data are described.
Tnree levels of watershed monitoring are described: watershlad
i~ventories, limited stream monitoring, and comprehensive watershed
monitoring. Control techniques for four lake restoration
o~jectives are described. The four objectives are the control of
nuisance algae, an increase in depth, the control of nuisance
plants, and the mitigation of acidic condi tions. Where

appropriate, monitoring parameters for both during and after the
treatments are tabulated and discussed. Formulas for the
calculation of monitoring parameters are provided. Guidance is
also provided for implementing a'long-term monitoring protocol.
Volunteer Lake Monitoring:
A Methods Manual.
USEPA 1991.
REFERENCE: USEPA. 1991. Volunteer Lake Monitoring: A Methods Manual. U.S.
Environmental Protection Agency, Office of Water, Washington, DC. EPA 440/4-91-002.
CONTENTS: Focusing on a lake condition; Monitoring algae; Monitoring aquatic plants;
Monitoring dissolved oxygen; Monitoring other lake conditions; Training citizen volunteers;
Presenting monitoring results. Appendix: Scientific supply houses.
MAIN FOCUS: Specifically addresses lake monitoring. Provides step-by-step instructions for
setting up and implementing a volunteer lake monitoring program. Sample data collection forms
are provided, and a discussion on lake ecology provides background for volunteer monitors. Well-
This manual presents specific information on volunteer lake water
quality monitoring methods. It is intended for organizers of
volunteer lake monitoring programs and for the volunteers. who
actually sample lake conditions. It summarizes the steps necessary
to plan and manage a volunteer monitoring program, including
setting general goals, identifying the uses and users of collected
data, and establishing sound quality assurance procedures. The
document concentrates special attention on three of the most common
lake pollution problems: increased algal growth, increased growth
of rooted aquatic plants, and lowered or fluctuating levels of
dissolved oxygen. It also briefly discusses other lake pollution
problems: sedimentation, turbidity, lake acidification, and
bacteriological conditions. Appropriate parameters to monitor and
specific steps for each selected monitoring method are identified,
and example sampling forms are provided.
Technical Support Manual: Waterbody Surveys and Assessments
for conducting Use Attainability Analyses. Volumes I-III.
USEPA 1983-1984.
These documents contain EPA guidance to assist states in
implementing the revised Water Quality Standards Regulation that
appeared in the Federal Register in November 1983. Consideration
of the suitability of a waterbody for attaining a given use is an
integral part of the water quality standards review and revision
process. This guidance is intended to assist states in determining
the uses currently being achieved, the potential uses of the
waterbodies, and the causes of any impairment of the uses. A
framework for determining the attainable aquatic protection use is
described and parameters to be used to make the determinations

REFERENCE: USEPA. 1983. Technical Support Manual: Waterbody Surveys and Assessmentsfor
Conducting Use Attainability Analyses. Volume I. U.S. Environmental Protection Agency, Office
of Water, Washington, DC. November.
USEP A. 1984. Technical Support Manual: Waterbody Surveys and Assessments for Conducting Use
Attainability Analyses. Volume II: Estuarine systems. U.S. Environmental Protection Agency,
Office of Water, Washington, DC.
USEPA. 1984. Technical Support Manual: Waterbody Surveys and Assessments for Conducting Use
Attainability Analyses. Volume III: Lake systems. U.S. Environmental Protection Agency, Office
of Water, Washington, DC. November.
CONTENTS: Volume I: Physical evaluations; Chemical evaluations; Biological evaluations;
Interpretation. Volume II: Physical and chemical characteristics; Characteristics of plant and
animal communities; Synthesis and interpretation. Volume III: Physical and chemical
characteristics; Biological characteristics; Synthesis and interpretation.
MAIN FOCUS: A general discussion of conducting physical, chemical, and biological analyses of
river and stream, estuarine, and lake systems.
mentioned above are provided. Methods and approaches that can be
used by states for conducting use attainability analyses are
discussed. Volume I discusses rivers and streams, Volume II
discusses estuarine systems, and Volume III discusses lake systems.
Guidances for Watershed Monitoring
Monitoring Primer for Range Watersheds.
Bedill and Buckhouse
REFERENCE: Not available.
CONTENTS: Basis and rationale for monitoring in range watersheds; Water' quality in the context
of range watersheds; Some new concepts to go with the current ones; Environmental factors and
range watersheds; Management of range watersheds which directly affects water quality; Monitoring
methods and measurements.
MAIN FOCUS: Provides a good introduction to monitoring terms and concepts. While directed
toward range monitoring, the terms and concepts are generally applicable to all monitoring.
This short document provides a general introduction to monitoring
in the context of rangeland management. Watersheds are defined,
their characteristics and functions are described, and the
r~tionale behind their being the unit for rangeland management and
monitoring is discussed. The focus of the document is on
monitoring riparian areas and vegetation, not upland areas or

streams. A general discussion of the concepts and steps involved
in designing and implementing a rangeland monitoring program is
provided. Detailed information on designing a monitoring program,
selecting monitoring parameters and protocols, sampling procedures,
and data analysis is not provided.
seminar Publication: The National Rural Clean Water Program
Symposium. 10 Years of Controlling Agricul tural Nonpoint
Source Pollution: The RCWP Experience. USEPA 1992.
REFERENCE: USEP A. 1992. Seminar Publication: The National Rural Clean Water Program
Symposium. 10 Years o/Controlling Agricultural Nonpoint Source Pollution: The RCWP Experience.
September 13-17, 1992. U.S. Environmental Protection Agency, Office of Research and
Development, Office of Water, Washington, DC. EPA/625/R-92/006. August.
CONTENTS: Water quality and land treatment monitoring; Relating water quality to land
treatment; Land treatment and operation and maintenance of BMPs; Project coordination and
farmer participation; Institutional arrangements, program administration, and project spin-offs;
Information and education; Socioeconomics, technology transfer, lessons learned; Research needs
and future vision; Additional information.
MAIN FOCUS: Reports of hands-on experiences encountered during nonpoint source and
watershed project implementation. Since the RCWP had projects in states from most regions of
the United States, this document contains specific information relevant to a variety of circumstances.
This symposium proceedings is intended to provide guidance for
state nonpoint source programs and local watershed projects. It is
the result of 10 years of experience of the National Rural Clean
Water Program, and the papers in this document address both the
successes and difficulties experienced in the 21 projects that
composed the program. The papers included in the proceedings were
peer reviewed. Most of the papers address individual projects of
the RCWP, and they provide valuable insights into the variety of
approaches and solutions for addressing specific circumstances and
obstacles that may be encountered during the implementation of a
nonpoint source or watershed program. In this respect the
information in this document goes beyond the general "how-to"
information provided in most guidance documents.
Guidances for Ground Water Monitoring
A Review of Methods for Assessing Nonpoint Source contaminated
Ground-Water Discharge to Surface Water. USEPA 1991.
This document is a summary of methods that have been applied to
measure or estimate nonpoint-source-contaminated ground-water
discharge to surface water. An overview of methods is presented,
but this guidance is not a manual for employing the methods

REFERENCE: USEPA. 1991. A Review of Methods for Assessing Nonpoint Source Contaminated
Ground-Water Discharge to Surface Water. U.S. Environmental Protection Agency, Office of Water,
Washington, DC. EPA 570/9-91-010. April.
CONTENTS: Methods for measuring or estimating nonpoint source contaminated ground-water
discharge to surface water; The impact of nonpoint source contaminated ground-water discharge
to surface water in water quality-limited water bodies: determining total maximum daily load and
waste load allocations.
MAIN FOCUS: Each method is thoroughly described, including any limitations and assumptions
in its use, the expertise needed to apply it, and data inputs and data outputs. A short evaluation
of the method and relevant references with full citations are then provided.
deScribed. After the review of analytical methods, a separatE~
chapter presents an overview of the total maximum daily load
assessment and waste load allocation processes and discusses thE!
applicability of the methods described. Some of the methods
reviewed are the use of seepage meters, geophysical techniques,
numerical models, and isotope methods.
An 'annotated bibliography is available as a companion volume to
th~s report. The papers that provided the background for this
guidance are referenced throughout and are abstracted in the
ann,otated bibliography. Full citations for each of the background
papers are provided in this report.
Guidances for Biological Monitoring
Bioaccumulation Monitoring Guidance: Selection of Target
species and Review of Available Bioaccumulation Data. USEPA,
REFERENCE: USEPA. 1987. Bioaccumulation Monitoring Guidance: Selection of Target Species
and Review of Available Bioaccumulation Data. Volume I. U.S. Environmental Protection Agency,
Office of Marine and Estuarine Protection, Washington, DC. EPA 430/9-86-005. March.
CONTENTS: Recommended target species; Additional sampling considerations; Historical data for
target species; Summary of recommendations.
MAIN FOCUS: Specifically addresses monitoring fish and macro invertebrates for bioaccumulation
of toxic substances. A separate section discusses the use of historic data, and data summaries of
metals and priority pollutant concentrations for target species are prov~ded for reference.
Thi~ guidance is intended for 301(h} programs, but the information
presented is applicable to bioaccumulation monitoring in general.
Guidance for the selection of target species for bioaccumulation
monitoring is its main focus. A compilation, evaluation, and

summarization of recent (1987) data on concentrations of priority
pollutants in the suggested target species is included. This
information provides a set of data for comparative purposes, to aid
the user in interpreting data. The document explains the ranking
procedure and criteria used to select the target species. Selected
target species are tabulated geographically. Species of fish are
selected for the geographic areas of Massachusetts to Virginia, and
California and Washington, and macro invertebrates are selected for
Massachusetts to Virginia; Alaska to California; Florida, the
Virgin Islands, and Puerto Rico; and Hawaii. Information on the
types of tissue to analyze, the time of sampling, and the use of
historical data is provided as well.
Fish Field and Laboratory Methods
Biological Integrity of Surface Waters.
for Evaluating
USEPA 1993.
REFERENCE: USEPA. 1993. Fish Field and Laboratory Methods for Evaluating the Biological
Integrity of Surface Waters. u.s. Environmental Protection Agency, Office of Research and
Development, Washington, DC. EPA/600/R-92/111. March.
CONTENTS: Quality assurance and quality control; Safety and health; Sample collection for
analysis of the structure and function of fish communities; Specimen processing techniques; Sample
analysis techniques; Special techniques; Fish bioassessment protocols for use in streams and rivers;
Family-level ichthyoplankton index methods; Fish health and condition assessment profile methods;
. Guidelines for fish sampling and tissue preparation for bioaccumulative contaminants; Fisheries
MAIN FOCUS: Provides guidance for all methods of fish colleCtion, from netting to electro fishing,
and rapid bioassessment protocols. A sample analysis section discusses fish identification and how
specimens are measured and weighed properly for data analysis purposes. Separate sections discuss
fish kill investigations and marking and tagging techniques. The fisheries bibliography is
This document describes guidelines and standardized procedures for
the use of fish in evaluating the biological integrity of surface
waters, and it provides biomonitoring programs with fisheries
. methods for measuring the status and trends of environmental
pollution. Separate chapters in the document describe a variety of
fish collection methods, including the use of nets, electricity,
chemicals, and hook and line; specimen handling; specimen analysis;
and methods to calculate the age of fish. The use of fish for
rapid bioassessments of habitat and water quality impacts to fish
populations is also discussed. A section on special techniques
discusses flesh tainting methodology (used to relate flavor
impairment to a particular waste source), fish kill investigations,
and Instream Flow Incremental Methodology (IFIM), which measures
impacts to fish and other aquatic organisms resulting from changes
in instream flow. An extensive bibliography that is organized by
topic is provided. It includes a section on fish identification,

with the references separated by geographic region of the United
states and by marine and freshwater species.
Biological field and laboratory methods for measuring th~3
quality of surface waters and effluents. USEPA 1973.
REFERENCE: USEPA. 1973. Biologicalfield and laboratory methodsfor measuring the quality of
, surface waters and ejJluents. u.s. Environmental Protection Agency, National Environmental
Research Center, Office of Research and Development, Cincinnati, Ohio. Program Element
IBA027. C.!. Weber, ed. EPA-670/4-73-OOl. July. .
I CONTENTS: Biometrics; Plankton; Periphyton; Macrophyton; Macroinvertebrates; Fish; Bioassay;
MAIN FOCUS: A section on biometrics provides a complete discussion of data analysis. Bioassays
for phytoplankton/algae, periphyton, macroinvertebrates, and fish are discussed.
This manual was published to provide pollution biologists with a
methods reference guide for measuring the effects of environmental
contaminants on freshwater and marine organisms. Both field and
laboratory methods are discussed for fish, macroinvertebrates,
plankton, periphyton, and macrophyton. A section on biometrics
prpvides a full discussion of sampling (simple random and
stratified random) and statistical analysis methods (T-test, chi
square, F-test, and analysis of variance, confidence intervals and
linear regression). sections on different types of organisms to be
sampled (e.g., fish, periphyton) discuss sample collection and
preservation, sample preparation and analysis, sampling methods,
and special techniques where appropriate. References are provided
for each section of the manual. Special sections on fathead minnow
an~ brook trout chronic tests are included in a section on bioassay
techniques. An appendix contains data recording sheets and a
discussion of equipment and supplies.
Methods for Sampling Fish Communities as
National Water-quality Assessment Program.
and Gurtz 1993.
a Part
of the
This document provides detailed procedures for evaluations of fish
community structure. The procedures are intended to facilitate
standardization of collection methods and fish community
descriptions to facilitate unbiased evaluations of relations among
physical, chemical, and biological components of water-quality
conditions. The methods described are standard for use in streams
ranging from headwaters to large rivers. Electrofishing and
seining are the methods stressed in the document, but others are
considered. Sampling program design and sample processing ar.e
discussed in detail, and forms for recording data are provided.
(from introduction)

REFERENCE: Meador, M.R., T.F. Cuffney and M.E. Gurtz. 1993. Methods for Sampling Fish
Communities as a Part o/the National Water-quality Assessment Program. U.S. Geological Survey
Open-file Report 93-104.
CONTENTS: National Water-quality Assessment sampling design; Fish community sampling design;
Fish community sampling considerations; Methods for sampling fish communities; Biological quality-
assurance unit; Field data sheets; Summary.
MAIN FOCUS: This manual documents standard procedures for evaluating stream fish
communities. It focuses on electro fishing and seining. Taxonomic identification, measurements, and
external examination of fish specimens are discussed and forms are provided for data entry.
Program-specific Monitoring Guidances
Watershed Monitoring and Reporting for section 319 National
Monitoring Program Projects. USEPA 1991.
REFERENCE: USEPA. 1991. Watershed Monitoring and Reporting for Section 319 National
Monitoring Program Projects. U.S. Environmental Protection Agency, Office of Water, Washington,
DC. August. .
CONTENTS: Selection criteria for National Monitoring Program projects; NonPoint Source
Management System (NPSMS) software; Management file; Monitoring plan file; Annual report file.
MAIN FOCUS: Outlines the types of data that should be collected and documentation that should
be kept for watershed monitoring projects; specifically addresses the requirements of the National
Monitoring Program established pursuant to CW A ~ 319.
Under section 319 of the Clean Water Act as amended in 1987, EPA is
establishing a national program to intensively monitor and evaluate
a subset of watershed projects. A nationally consistent protocol
is to be followed by' the projects, and EPA has developed and
distributed a national framework for the National Monitoring
Program. This guidance provides monitoring and reporting
guidelines for the program.
Nonpoint Source Management System (NPSMS) software has been
deve~oped and distributed to states that have received grants under
section 319 of the Clean Water Act. The software facilitates
information tracking and reporting under the National Monitoring
Program. It is menu-driven, and this document discusses the proper
entry of data into the software system and provides a step-by-step
guide to it. Much of the information presented is therefore not of
relevance to the reader interested in designing a monitoring
program, though there is limited discussion of monitoring
objectives, monitoring program design, and monitoring parameters.

Monitoring Guidance for the National Estuary Program.
- 1991.
REFERENCE: USEPA. 1991. Monitoring Guidance for the National Estuary Program. U.S.
Environmental Protection Agency, Office of Water. EPA 503/8-91-002. August.
CONTENTS: Develop monitoring objectives and performance objectives; Establish testable
hypotheses and select statistical methods; Select analytical methods and alternative sampling designs;
Evaluate monitoring program performance; Implement monitoring study and data analysis;
Communicate program results; Appendices: Case studies; Methods.
MAIN FOCUS: Appendices contain case studies of the Puget Sound and Chesapeake Bay
monitoring programs, and detailed methods sections. Methods sections include water column
physical and chemical parameters, sediment, plankton, aquatic vegetation, benthos, fish,
bioaccumulation, and bacteria and viruses. Each method section discusses monitoring design,
analytical methods, QA/QC, and statistics for the parameter.
The National Estuary Program (NEP) was created by the Water Quality
Act of 1987 to promote long-term planning and management in
nationally significant estuaries threatened by pollution,
development, or overuse. Management conferences, wi th
representatives from EPA, the affected state(s), local governments,
the scientific community, and citizen's groups, are established to
develop Comprehensive Conservation and Management Plans (CCMPs) for
the estuaries. The first task of a management conference is to
identify and characterize the problems in the estuary. Then, based
on the findings a CCMP is developed to guide the implementation of
actions undertaken to overcome the identified problems and protect
the estu~rine environment. A requirement of the enacting
legislation is that the effectiveness of actions taken pursuant to
CCMPs be monitored, and this document provides guidance on the
design, implementation, and evaluation of NEP monitoring programs.
NEP monitoring programs are designed to serve two goal&-to measure
the effectiveness of management actions and programs implemented
under CCMPs, and to provide essential information that can be used
to redirect and refocus the estuarine management efforts. Because
the intended audience for this document is those involved in
estuary management efforts, including environmental mangers,
governmental agencies, and citizens, this guidance discusses both
background issues and technical aspects relevant to estuarine
monitoring programs.
This guidance presents a systems design approach to designing a
monitoring program, with discussions of each of the steps involved
in the approach: developing monitoring program objectives,
designing a monitoring program, establishing hypotheses, selecting
statistical methods and sampling designs, evaluating the monitoring

program I S performance, and managing and analyzing data. An
extensive methods section is organized according to the parameter
being monitored, e.g., water column chemistry, sediment grain size,
aquatic vegetation, fish community structure, viral pathogens, etc.
Numerous references to other texts providing in-depth discussions
of each step in monitoring program design are provided. Two case
studies, the puget Sound Ambient Monitoring Program and the
Chesapeake Bay Monitoring Program, are used to provide examples
from existing estuarine monitoring programs. In addition, the case
studies also address options for funding monitoring programs, how
to incorporate existing monitoring studies into a coordinated
basin-wide monitoring effort, and methods for determining the
effectiveness and feasibility of monitoring efforts.
QC-QA Plan Rural Nonpoint.
USGS 1992.
REFERENCE: Not available.
CONTENTS: QC Procedures; Field Procedures; Record Keeping;. Sample Processing; Quality
Assurance; Blank Sample Processing.
MAIN FOCUS: Provides a detailed description of field sampling and laboratory sample analysis
techniques. Analysis of blank samples for quality assurance is discussed in detail as well.
This short (5-page) document describes the quality control and
quality assurance procedures that apply to all USGS rural nonpoint
data collection activities. Field procedures for sample collection
are described in detail. Sampling frequency, equipment
specifications, and general sampling procedures are discussed to
ensure consistent sample collection techniques at all USGS rural
nonpoint collection points. Laboratory procedures for sample
analysis are discussed in similar detail. The document notes what
records are to be kept. Quality assurance consists of regular
analysis of blank samples and equipment maintenance, both of which
are discussed.
NPDES storm Water Sampling Guidance Document.
USEPA 1992.
This guidance is intended for operators of facilities that
discharge storm water containing industrial pollutants and
operators of large and medium sized municipal separate storm sewer
systems. Its purpose is to assist facility operators and/or owners
in planning for and fulfilling the NPDES storm water discharge
sampling requirements for NPDES permit applications. The
information presented pertains to individual industrial storm water
applications, group storm water applications, and municipal storm
water permit applications. The guidance was issued in support of
EPA regulations and policy initiatives involving the development
and implementation of a national storm water program, and serves as
. 111-29

REFERENCE: USEPA. 1992. NPDES Storm Water Sampling Guidance Document. U.S.
Environmental Protection Agency, Office of Water. Washington, DC. EPA 833-B-92-OO1. July.
CONTENTS: Background for storm water sampling; Fundamentals of sampling; Analytical
considerations; Flexibility in sampling; Health and safety.
MAIN FOCUS: Contains a good discussion of grab and composite samples, sample collection
methods, and sample handling and documentation. Addresses many points specific to the NPDES
program. .
Agency guidance.
The legal requirements of storm water sampling under the Clean
Water Act are explained, and storm water sampling methodologies,
other measurements necessary for permit compliance (e.g., flow,
rainfall), sample documentation, and sample analysis requirements
are discussed. Modifications to standard sampling procedures,
which are allowed under specific circumstances on a case-by-case
basis, are explained. Acceptable techniques for manual and
automatic sample collection are described. Health and safety
considerations are also discussed.
NPDES storm water permit requirements are the focus of this
guidance, and much of the information provided in it is not
directly related to monitoring the water quality and habitat
effects of NPS pollution. However, the technical information that
it contains on choosing sampling locations and sampling procedures
shpuld be useful to those monitoring storm water as part of an NPS
monitoring program.
Water Quality standards Handbook.
USEPA 1983.
REFERENCE: USEPA. 1983. Water Qualiry Standards Handbook. U.S. Environmental Protection
Agency, Office of Water Regulations and Standards. Washington, DC. December.
CONTENTS: Water quality standards review and revision process; General program guidance;
Water body survey and assessment guidance for conducting use attainability analyses; guidelines for
deriving site-specific water quality criteria. Appendices: Bioassay test methods; Determination of
statistically significantly different LC50 values; Case studies.
MAIN FOCUS: Provides a complete discussion of the state water quality standards development
process and the process for conducting water body surveys and use attainability analyses. Excellent
background material on state water quality standards and stream classification systems.
This guidance is meant to assist states in implementing the 1983
water quality standards regulation (48 FR 51400, November 8). It
is not a monitoring guidance per se, but rather a guidance for

determining whether a waterbody survey and/or use attainability
analysis, as required by the Clean Water Act, meets specifications
set forth by EPA. Numerous case studies illustrate acceptable
state approaches.
The handbook provides a general description of the standards
setting process, information on program administrative policies and
procedures, and a description of analyses used to determine
appropriate water uses and criteria. states are to use the data
and analyses set forth in this document, or similar data and
analyses, to conduct use attainability analyses or to establish
water quality criteria. Certain regulatory requirements to which
states must adhere when they develop water quality criteria are
discussed as well. EPA has determined that certain types of
scientific and technical data and analyses are necessary in order
for the public and EPA to conduct informed reviews of proposed
water quality standards. Data and analyses required for this
purpose are noted. Explanations of terms and concepts used in the
regulatory language, e.g., mixing zone and antidegradation, are
While this document does not provide guidance on the development or
implementation of a monitoring program, it is a useful reference
for those interested in the rationale behind and derivation of
water quality standards. Monitoring is an essential step in
setting and modifying site-specific water quality standards.
Therefore, this document is valuable as a companion to documents
that deal more directly with monitoring program design and
Environmental Monitoring and Assessment Program:
Indicators. USEPA 1990.
REFERENCE: USEPA. 1990. Environmental Monitoring and Assessment Program: Ecological
Indicators. U.S. Environmental Protection Agency, Office of Research and Development,
Washington, DC. EPA/600/3-90/060. September.
CONTENTS: EMAP indicator concepts; Indicator strategy for near coastal waters; Indicator
strategy for inland surface waters; Indicator strategy for wetlands; Indicator strategy for forests;
Indicator strategy for arid lands; Indicator strategy for agroecosystems; Indicators relevant to
multiple resource categories; Indicator strategy for atmospheric stressors; Conclusions and future
directions; Appendices (indicator fact sheets).
MAIN FOCUS: EMAP indicators are related to ecological and social (e.g., recreation) variables
and to monitoring objectives. The reasoning behind the choice of each indicator is fully explained.
The Environmental Monitoring and Assessment Program (EMAP) was
initiated by EPA's Office of Research and Development to provide
data for improved assessment of the Nation's ecological resources.
Under the program, several integrated monitoring networks will be

implemented by the mid-1990s to (1) estimate current status and
trends in indicators of ecological condition and (2) monitor
indicators of pollutant exposure and habitat condition and identify
cause-and-effect associations between indicators and adverse
cortditions. This report presents the approach proposed to describe
ecological condition; defines a common strategy within the program
for selecting and prioritizing; and summarizes the indicators
chosen for evaluation as core indicators for near-coastal waters,
inland surface waters, wetlands, forests, arid lands, and
EMAP is a large-scale national monitoring program whose scope is
beyond the reach of most state, local, or regional monitoring
efforts. Therefore, the objectives and design of the program will
not be similar to many smaller monitoring programs. However, the
discussions of monitoring indicators for the six ecosystem types
mentioned above provide valuable information on types of indicators
to choose for different monitoring goals. Indicators that were
considered for EMAP but were not chosen for it are also discussed,
wh~ch provides valuable information as well in that it points out
for what purposes these monitoring parameters are inappropriate.
Fact sheets for each of the indicators chosen for EMAP are included
as appendices. Each fact sheet discusses the particular
indicator's application, measurement, variability, and primary
prpblems, and provides pertinent references.
RCRA Ground-Water Monitoring Technical Enforcement Guidance
Document. USEPA 1986.
REFERENCE: USEPA. 1986. RCRA Ground-Water Monitoring Technical Enforcement Guidance
Document. U.S. Environmental Protection Agency, Office of Solid Waste and Emergency Response,
Washington, DC. OSWER-9950.1. September.
CONTENTS: Characterization of site hydrogeology; Placement of detection monitoring wells;
Monitoring well design and construction; Sampling and analysis; Statistical analysis of detection
monitoring data; Assessment monitoring.
MAIN FOCUS: Provides technical information on site characterization, well placement, and well
design and construction. Sample collection, handling and preservation techniques are thoroughly
This guidance describes in detail what EPA deems to be the
essential components of a ground water monitoring system that meet:s
the goals of the Resource Conservation and Recovery Act (RCRA). It
is intended to be used by enforcement officials, permit writers,
field inspectors, and attorneys at the federal and state levels t:o
assist them in making informed decisions regarding the adequacy of
existing or proposed ground water monitoring systems.
. III-32

The guidance contains technical information on site
characterization, well design and construction, and assessment of
contamination of ground water. Hydrogeologic regimes vary widely
from site to site, and this guidance does not attempt to address
all possible circumstances for the purposes of ground water
monitoring programs. It does provide a framework within which a
decision-making process can be applied using site-specific
Ground water monitoring is a specific type of monitoring and may be
beyond the scope of many monitoring programs. While this guidance
is specific to the RCRA program, the protocols prese'nted are
rigorous and could be used to provide defensible data for any
ground water monitoring program.
Summary of u.S. EPA-Approved Methods, Standard Methods, and
Other Guidance for 301(h) Monitoring Variables. USEPA 1985.
REFERENCE: USEPA. 1985. Summary of u.s. EPA-Approved Methods, Standard Methods, and
Other Guidancefor 301 (h) Monitoring Variables. U.S. Environmental Protection Agency, Office of
Water, Washington, DC. EPA 503/4-90-002. September.
CONTENTS: Introduction; Table 1: U.S. EPA-Approved Methods and Guidance Documents for
Measuring Biological, Sediment, and Water Quality Variables in 301(h) Monitoring Programs;
Water Quality Variables; Sediment Analyses; Biological Variables; References.
MAIN FOCUS: A convenient listing of where to find information on analytical techniques for many
monitoring variables.
This is a short (16-page) document that tabulates the types of
analytical methods available for the water quality, sediment, and
biological variables used in 301 (h) monitoring programs. The
methods are listed as EPA-approved, EPA-suggested, standard, or
additional, and the availability of guidance for each method is
noted. Following the table is a brief note specifying method
numbers (e.g., USEPA method No. 150.1; additional procedure No.
413.2) for each of the variables listed. A list of references at
the end of the document indicates where to find information about
each of the monitoring variables and analytical methods.
Ecological Assessments of Hazardous Waste sites:
Laboratory Reference Document. USEPA 1989.
A Field and
This is a comprehensive field and laboratory reference document for
the design, implementation, and interpretation of ecological risk
assessments, and it specifically addresses assessments of hazardous
waste sites. Complete discussions of ecological endpoints,
assessment methods, statistical considerations, toxicity testing,
field assessments, and data interpretation are provided. The

REFERENCE: USEPA. 1989. Ecological Assessments of Hazardous Waste Sites: A Field and
Laboratory Reference Document. U.S. Environmental Protection Agency, Office of Research and
Development, Washington, DC. EPN600/3-89/013. March. W. Warren-Hicks, B.R. Parkhurst,
and S.S. Baker, Jr., eds.
CONTENTS: Ecological endpoints; Assessment strategies and approaches; Field sampling design;
Quality assurance and data quality objective; Toxicity tests; Biomarkers; Field assessments; Data
MAIN FOCUS: A comprehensive discussion of all aspects of ecological risk assessment. A specific
list of references follows each subsection that discusses a technical aspect of risk assessment.
section on toxicity testing is divided into subsections on aquatic,
tetrestrial, and microbial tests; the section on field assessments
is divided into subsections on aquatic, vegetation, terrestrial
vertebrates, and terrestrial invertebrates.
statistical Analysis of Ground-Water Monitoring Data at RCRA
Facilities - Interim Final Guidance. USEPA 1989.
REFERENCE: USEPA. 1989. Statistical Analysis of Ground-Water Monitoring Data at RCRA
Facilities -Interim Final Guidance. U.S. Environmental Protection Agency, Office of Solid Waste,
Waste Management Division, Washington, DC. EPA/530-SW-89-026. NTIS PB89-151047.
February .
, CONTENTS: Regulatory overview; Choosing a sampling interval; Choosing a statistical method;
Background well to compliance well comparisons; Comparisons with MCLs or ACLs; Control charts
for intra-well comparisons; Miscellaneous topics; Appendices.
MAIN FOCUS: Detailed discussion of all aspects of statistical analyses of ground-water monitoring
data. Flow charts are provided to assist the reader in choosing the proper statistical method and
interpreting data.
The hazardous waste regulations under the Resource Conservation and
Recovery Act (RCRA) require owners and operators of hazardous waste
facilities to use design features and control measures that prevent
the release of hazardous waste into ground water. This document
provides guidance to RCRA facility permit applicants and writers
concerning the statistical analysis of ground-water monitoring data
at RCRA facilities. Sections of the document provide an overview
of regulations concerning the statistical analyses of ground-water
monitoring data; hydrogeologic parameters to consider when choosing
a sampling interval; guidance on choosing an appropriate
statistical method; statistical methods that may be used to
ev~luate ground-water monitoring data; statistical procedures that
are appropriate for special circumstances; and special topics.

Appendices C9ver general statistical considerations, a glossary of
statistical terms, statistical tables, and references.
42. - CWA section 403:
Procedural and Monitoring Guidance.
REFERENCE: USEPA. 1994. CWA Section 403: Procedural and Monitoring Guidance. U.S.
Environmental Protection Agency, Office of Water, Oceans and Coastal Protection Division,
Washington, DC. EPA 842-B-94-OO3. March.
CONTENTS: Section 403 procedure; Options for monitoring under the basis of "no irreparable
harm"; Summary of monitoring methods: physical characteristics, water chemistry, sediment
chemistry, sediment grain size, benthic community structure, fish and shellfish pathology, fish
populations, plankton, habitat identification methods, bioaccumulation, pathogens, effluent
characterization, mesocosms and microcosms.
MAIN FOCUS: Each monitoring parameter is dealt with separately, with a separate discussion of
monitoring design, analytical methods, QA/QC, statistical considerations, and use of data. An
appendix contains an extensive list of monitoring methods references.
This document is designed to provide EPA Regions and NPDES-
authorized states with a framework for the decision-making process
for section 403 (ocean dumping) evaluations and to provide guidance
on the type and level of monitoring that should be required as part
of permit issuance under the "no irreparable harm" provisions of
section 403. options for monitoring under the basis of no
irreparable harm, including criteria for evaluating perceived
potential impact and establishing monitoring requirements to assess
actual impacts, are discussed. Summaries o~ monitoring methods for
evaluating numerous parameters (see contents listing) are provided.
Each method section contains an explanation of the usefulness of
the parameter of concern in a 403 monitoring program and a
discussion of analytical methods, the use of data generated, and
considerations of monitoring design, statistical design, and
quality assurance/quality control.

SUBJECTS DISCUSSED 1 2 3 4 5 6 7 9 10 11 12 13 14 15 17 18 19 20 21 22 
Guidance  for Monitoringz            ... ......... 1\.....   ..../. .',. Ii. .'..,) .  
Streams & Rivers . .  . . .  - 8 -  . . . . . . .  . 
Lakes & Reservoirs . .  .  .  . . .          . 
Estuaries/Marine      . . . .            
Ground Water .   .    . .            
Storm Water                     
Land Use .  .  .    .            
Land Management .    .                
Forest       .    .            
Agriculture   -      .            
Watersheds . . .      .          . . 
Program Elements:                     
Objectives . . - . . . . . . .   . .  . . .  . 
Design   . . . . . .  . .   . . .  . . .  . 
Protocols .    .   . .    . . .  . .  . 
Parameters .   . .   . .    . . . . . .   
Related Subjects:                     
Data Analvsis 8 .   . .       . . .    . . 
Data Management . . .   .   . .    .      . 
QA/QC    .  . . . .  . .    .      . 
Stream  Classification             .        
(Table continued on next page)

SUBJECTS DISCUSSED 1 2 3 4 5 6 7 9 10 11 12 13 14 15 17 18 19 20 21 22 
Samples and Sampling:                   . ..... .  
              ....   ,.:. ".  
Types of Samples -   -   -     -  - - .   , . 
Sampling Equipment -                    
sampling Techniques    -   -       -   - -  . 
sample Handling .      -       .      . 
Sample Documentation       -       . .     . 
Sample Analysis -      -       .      . 
Sampling Locations . .  -   -     . . - - - - . . "
samPling Frequency 8   -   -     - - .      . 
          - - . . 
Health and Safety                     
Monitoring Parameters:                     
Physical Constituents  .  . .  -     . . -   .   . 
Chemical Constituents    .. .  .       .   -   - 
Nutrients    .  -   .     - .       . 
Sediment   . -       .   . . .      . 
Bacteria & Viruses  -  -   .  -   . .        
Phytoplankton - .  .   .          ..   . 
Zooplankton  - .  . ..    .            
Macroinvertebrates - .   -    .   .  .       
Fish    . -   .       .  . .   .  -
AqUatic Vegetation - .   .  .  -   .  .   .   . 
Riparian Vegetation  -       .   . . .       
Habitat Quality  .   -        . .       
Flow    -   .     .   .  .   -   -
Channel Morphology     -    .   . . .   .  .  
Bank stability     -        . .   .    

Water Quality Monitoring. USDA-SCS Draft.
The Nonpoint Source Manager's Guide to Waler Quality and LAnd Treatmenl Monitoring. Coffey, Spooner and Smolen 1993.
Designing effective nonpoint source water quality moniloring programs: Maas 1989.
Water quality monitoring for the Clean Waler Partnership. A guidance document. Minnesota Pollution Control Agency 1989.
Evaluating the effectiveness of forestry best management practices in meeting water quality goals or standards. Dissmeyer 1994.
Volunteer Water Monitoring: A Guide for State Managers. USEPA 1990.
Volunteer eSlllary monitoring: A methods manual. USEPA 1993.
Water-quality monitoring in the United States. Intergovernmental Task Force on Monitoring Water Quality 1994.
Water-quality monitoring in the United States. Technical appendixes. Intergovernmental Task Force on Monitoring Water Quality 1994.
Guidancefor State Water Monitoring and Wasteload Allocation Programs. USEPA 1985.
Guidelines for Evaluation of Agricullllral Nonpoint Source Water Quality Projects. USEPA 1981.
MonilOring Guidelines to Evaluate Effects of Forestry Activities on Slreams in the Pacific Northwest and Alaska. MacDonald, Smart and Wissmar 1991.
MonilOring Protocols 10 Evaluate Water Quality Effects of Grazing Management of WeSlem Rangeland Streams. USEPA Draft.
Rapid Bioassessment Protocols for Use in Slreanzs and Rivers: Benthic Macroinve'1ebrates and Fish. USEPA 1989.
Using lhe Index of Biotic Integrity (lBI) to Measure Environmental Quality in Warn/water Streanzs of Wisconsin. Lyons 1992.
Handbook: Stream Sampling for Waste Load Allocation Applications. USEPA 1986.
Evaluation Monitoring of Slream Habitat During Priority Watershed Projects. Simonson and Lyons 1992.
Evaluation Monitoring of Slream Fish Communities During PI10rity Watershed Projects. Simonson and Lyons 1992.
Techniques for detecting effects of urban and mralland-use practices on stream-water chemistry in selected watersheds in Texas, Minnesola. and Illinois. Walker 1993.
MonilOring LAke and Reservoir Restoration. USEPA 1990.

SUBJECTS DISCUSSED 23 24 25 26 27 28 29 30 31 32 33 35 36 37 38 39 40 41 42 
Guidance for Monitoring:               ,.  " .....:",  
Streams & Rivers  -  .   . . . .   - -   .   
Lakes & Reservoirs . .  .   . .  .   . .      
Estuaries/Marine  .    . "   . .   -  '   . 
Ground Water    . .          .  . ,  
Storm Water            -        
Land Use     .                
Land Management    .                
Forest                -      
Ranqe     .           .      
AQriculture    .          .      
Watersheds    . .          .      
               . .        
Program Elements:                    
Objectives  .  .    . .  . ,   . ,  .  . 
Design     . .   . . ,  .    .  ' . . 
Protocols       . . . .        . . . 
Parameters    .   . . .      . '  "   
Related Subiects:                    
Data Analysis      - . .     .  .  . . . 
Data Management .   .   .  ,         .  
QA/QC   .      .  .  .    .  .  , 
Stream Classification                    

SUBJECTS DISCUSSED 23 24 25 26 27 28 29 30 31 32 33 35 36 37 38 39 40 41 42  
Samples and Sampling:                  . .:. :::".:p..:....:  
Types of Samples .    . .. .. . .   .     .. . .  
Samplinq Equipment                     
Sampling Techniques .    ..  .. , ..      ..  ,  .  
Sample Handling       . .. .   .   .  .    
          .  .           -. 
Sample Documentation       ..   .   '      
Sample Analysis       . .. .   .     .    
Sampling Locations .     .   .     . ..   . .  
Sampling Frequency '     '   "     ' "   . .  
Health and Safety       .     .   ,      
              . .          
Monitoring Parameters:                     
Physical Constituents . ..     .    .     .   .  
Chemical Constituents "      .    ..     . .  .  
Nutrients             .     .     
Sediment   ' .         .     .   .  
Bacteria   ..               .    - 
& Viruses          .       .  
Phytoplankton "       "        "     
Zooplankton         .   .     .   .  
Macroinvertebrates  ..    .  .   .     .   .  
Fish     .    . . . .  .     .   .  
Aquatic  Vegetation ..          .          
Riparian Vegetation  ..                   
Habitat  Quality  .     .            .  
Flow     .         .        .  
Channel  Morphology  ..                   
Bank stability                     

Volunteer Lake Monitoring: A Methods Manual. USEPA 1991.
Technical suppon manual: Waterbody surveys and assessments for conducting use allainability analyses. Volumes I-III. USEP A 1983-1984.
Monitoring Primer for Range Watersheds. Bedill and Buckhouse Draft.
Seminar Publication: The National Rural Clean Water Program Symposium. 10 years of controlling agricultUral nonpoint source pollution: The RCWP experience. USEPA 1992.
A Review of Methods for Assessing Nonpoint Source Contaminated Ground- Water Discharge to Suiface Water. USEP A 1991.
Bioaccumulation Monitoring Guidance: Selection of Target Species and Review of Available Bioaccumulation Data. Volume I. USEPA 1987.
Fish Field and Laboratory Methodsfor Evaluating the Biological1ntegrity of Suiface Waters. USEPA 1993.
Biological field and laboratory methods for measuring the quality of suiface waters and ejJIuents. USEPA 1973.
Methodsfor sampling fish communities as a pan of the National Water-quality Assessment Program. Meador, CutTney and Gurtz 1993.
Watershed Moniloring and Reportingfor Seclion 319 National Monilaring Program Projects. USEPA 1991.
Monilo/ing Guidancefor the Nalional Eslllary Program. USEPA 1991.
NPDES Stonn Waler Sampling Guidance Document. USEPA 1992.
Water Quality Standards Handbook. USEPA 1983. .
Environmental Monila/ing and Assessment Program: Ecological1ndicalars. USEPA 1990.
RCRA Ground-Water Monila/ing Technical Enforcement Guidance Document. USEPA 1986.
Summaty of u.s. EPA-approved melhods, standard melhods, and olher guidance for 301 (h) monilaling variables. USEP A 1985.
Ecological assessments of hazardous waste siles: A field and laboralary reference document. USEP A 1989.
Statistical analysis of ground-waler monilOling data at RCRA facilities - 1nterim final guidance. USEP A 1989.
CWA section 403: Procedural and Monila/ing guidance. USEPA 1994.


The water resource to be monitored must be understood before
a monitoring plan that provides sufficient information for meeting
the monitoring objectives can be developed. Options for tracking
water quality vary with the type of water resource. For example,
'a monitoring program for ephemeral streams can be different from
that for perennial streams or large rivers. Lakes, wetlands,
riparian zones, estuaries, and near-shore coastal waters all
present different monitoring considerations. Although upstream-
downstream designs work on rivers and streams, they are generally
less effective on natural lakes where linear flow is not prevalent.
Similarly, estuaries present difficulties in monitoring loads
because of the shifting flows and changing salinity caused by the
tides. A successful monitoring program must take into
consideration the uniqu~ features of the water resources involved
and must be structured to either adapt to those features or avoid
Monitoring programs must address both temporal and spatial
variability because these variabilities are key factors that
determine the impact that NPS pollution has on a water resource.
Temporal variability can be of short or long duration. As shown in
Figure IV-l, water quality can vary tremendously over the course of
a single storm event. Many water resources also undergo seasonal
changes or changes that occur over the course of several years,
decades, or even centuries (Figure IV-2). A water resource can
vary in the short or long term, or both. There is often
insufficient information to describe much of the very long-term
variability (years or decades) associated with a given water
resource. The temporal variability referred to in this document is
that which generally occurs on the minutes-to-a year time scale.
Spatial variability is the other major component of NPS water
quality variability. Within a given stream, lake, estuary, or
aquifer there is usually some spatial differential in water
quality. For example, in Figure IV-3 the total .suspended solids
concentrations vary across the reservoir. Inlets to the reservoir
(points of concentration) are closer to higher concentrations of
suspended materials, and thus they show higher total suspended
solids levels than areas near the dam outlet where substantial
settling of larger particles, dilution, and dispersion have already
occurred. As another example, salinity levels in an estuary vary
with depth (spatial variability must be considered in three
dimensions) at the salt wedge as the more saline ocean water flows
under the fresh water from the stream (Figure IV-4). Water quality
can also vary considerably in an aquifer underlying agricultural
lands. The example in Figure IV-5 shows how nitrate levels can
differ substantially from location to location.

        s         s 
Q       A s  i       G 
%       (I)       B 
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    JUNE. 1981        JUNE 1981    
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 7. 8. 9. Ie. ". 12. 13. 1 ~.  7. 8. 8. Ie. 11. 12. 13. 1 -.. 
    ..JUNE 1981        JUNE 1881    
Figure IV-i. Flow and pollutant concentrations for a single storm
event in the Honey Creek watershed, Ohio. (SOURCE: Baker et al.,



- - - 01_"'11. 01"",
. . ... DriMi", water Wi",*IWO'
- 'nout frOIR wet'"""
Figure IV-2. Time course of phosphorus loading from the West
Branch Delaware River and output from CannonsvillEi Reservoir.
SOURCE: Brown et al., 1986)

Figure IV-3. Mean total suspended solids concentrations (mg/L) in
Highland Silver Lake, Illinois, May 1981-March 1984. (SOURCE:
Davenport and Kelly, 1984)

Ocean --+
.:",:,:',:,<."".... .

IV-4. Mixing
USEPA, 1983a)

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. ,
. '-
, --~
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. . . .
to . . .
, '
, .
Nitrate CoA.-.Ulw (Nov,-Dec..-)
~ CGnIow 1rIIW"fGI- 20 MQ/I
~ ~ ". S8II88III CanIaIr .......
Figure IV-5. Contour map of nitrate concentrations recorded from
Galena aquifer inventory water samples (Iowa). (SOURCE: Hallberg
et al., 1983)

Freshwater streams can be classified on the basis of flow
at tributes as intermittent or perennial streams. Intermittent
streams do not flow at all times and serve as conveyance systems
for runoff. Perennial streams always flow and usually have
significant inputs from ground water or interflow.
For intermittent streams, seasonal variability is a very
significant factor in determining pollutant loads and water
quality. During some periods sampling might be impossible due to
the absence of flow. Seasonal flow variability in perennial
streams can be caused by seasonal patterns in precipitation or
snowmelt, reservoir discharges, or irrigation practices.
For many streams the greatest concentrations of suspended
sediment and other pollutants occur during spring runoff or
snowmelt periods. Figure IV-6 shows the monthly variations in the
sediment.-discharge relationship for the White River, South Dakota.
Figure IV-7 shows the seasonal relationship between sediment
concentrations and discharge for the Fern Ridge Dam, Oregon.
Concentrations of both particulate and soluble chemical parameters
have been shown to vary throughout the course of a rainfall event
in many studies across the Nation. This short-term variability
should be considered in developing monitoring programs for flowing
(lotic) waterbodies.
Spatial variability is largely lateral for both intermittent
and perennial streams. Vertical variability does exist, however,
and can be very important in both stream types (e.g., during runoff
events, in tidal waters, and in deep, slow-moving streams). Intake
depth is often a key factor in stream sampling. For example, slow-
moving, larger streams can show considerable water quality
variability with depth, particularly for parameters such as
suspended solids, dissolved oxygen, and algal productivity. Figure
IV-8 illus~rates the relative location of suspended load and bed
load iri a stream vertically. Suspended sediment samples must be
taken with an understanding of the vertical distribution of both
sediment concentration and flow velocity (Brakensiek et al., 1979),
as illustrated in Figure IV- 9. When sampling bed sediment or
monitoring biological parameters, it is important to recognize the
potential for significant lateral and vertical variation in the
toxicity and contaminant levels of bed sediments (USEPA, 1987).
Lakes can be categorized in several ways, but a useful
grouping for monitoring guidance is related to the extent of
vertical and lateral mixing of the waterbody. Therefore, lakes are
considered to be either mixed or stratified for the purpose of this
guidance. Mixed lakes are those lakes in which water quality (as
determined by measurement of the parameters and attributes of
interest) is homogenous throughout, and stratified lakes are

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! I
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Figure IV-7. Seasonal relationship between sediment concentration,
sediment load, discharge, and precipitation for Fern Ridge Dam,
Oregon. (SOURCE: Thomas, 1970)

  IY   IY  IY  
 ~~. .1      
r ~        
i ....        
Q ~        
E t W8111  Su IQencIIII  "'-'III  Totll
. . LOIO -  -  - 
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Figure IV-B. Schematic diagram of stream vertical showing relative
position of sediment load terms. (SOURCE: Brakensiek et al., 1979)

Water S4.rfece

I Average
I /' Spatial
I-'" Cone.
Chlnnel I Bed
Figure IV-9. Vertical sediment concericration and flow
distribution in a typical stream cross section.
Brakensiek et al., 1979)

considered to be those lakes which have lateral or vertical water
quality differentials in the lake parameters and attributes
of interest. Totally mixed lakes, if they exist, are certainly few
in number, but it might be useful to perform monitoring in selected
homogenous portions of stratified lakes to simplify data
interpretation. Similarly, for lakes that exhibit significant
seasonal mixing, it might be beneficial to monitor during a time
period in which they are mixed. For some monitoring objectives,
however, it might be best to monitor during periods of peak
Temporal variability concerns are similar for mixed and
stratified lakes. Seasonal changes are often obvious, but should
not be assumed to be similar for all lakes or even the same for
different parts of any individual lake (Figure IV-10). Due to the
importance of factors such as precipitation characteristics,
climate, lake basin morphology, and hydraulic retention
characteristics, seasonal variability should be at least
qualitatively assessed before any lake monitoring program 18
Short-term variability is also an inherent characteristic of
most still (lentic) waterbodies. Parameters such as pH, dissolved
oxygen, and temperature can vary considerably over the course of a
day. Monitoring programs targeted toward biological parameters
should be structured to account for this short-term variability.
It is often the. case that small lakes and reservoirs respond
rapidly to runoff events. This factor can be very important in
cases where lake water quality will be correlated to land treatment
activities or stream water quality.
In stratified lakes spatial variability can be lateral or
vertical. The classic stratified lake is one in which there is an
epilimnion and a hypolimnion (Figure IV-11).. Water quality can
vary considerably between the two strata, so sampling depth is an
important consideration when monitoring vertically stratified
lakes. Temperature and dissolved oxygen profiles of a flood-
control reservoir in Kentucky illustrate vertically stratified and
mixed conditions for these two parameters (Figure IV-12).
Lateral variability is probably as common as vertical
variability, particularly in lakes and ponds receiving inflow of
varying quality. Figure IV-13 illustrates the types of factors
that contribute to lateral variability in lake water quality. In
r~servoir systems, storm plumes can cause significant lateral
Davenport and Kelly (1984) explained the lateral variability
in chlorophyll a concentrations in an Illinois reservoir based on
water depth and the time period that phytoplankters spend in the
photic zone. Refer to Figure IV-3 for monitoring site locations,
arid note from Table IV-1 that sites 3 and 9 had significantly
higher annual mean chlorophyll a concentrations than all other
IV -12

, 0
, I
, I
, I
000 I

I ~f\f :
. "
~ b :
, ,
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. ,R.: I /\ :
I ? 0 : 0
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10 " " I ..' I I I \
, ,. o.
0' '.
1\,' P. .O,ft !f'
." P. I ..... .
o +"'.-r-8 , 'I 'I I ,
.0 II
30 ~
Figure IV-10. Phytoplankton chlorophyll a concentration in
Chautauqua Lake's northern basin (e-e) and southern basin (0-0),
1977. (SOURCE: Storch, 1986)

I- 15
10 15 20 25
Figure IV-11. Typical thermal stratification of a lake into the
epilimnetic, metalimnetic, and hypolimnetic water strata. (SOURCE:
Wetzel, 1975)
IV -14

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Figure IV-13.
Factors contributing to lateral differences in lake

Table IV~l. Comparison of means by site for chlorophyll a
concentrations (CAC) (ug/l) at Highland Silver Lake, May 1981
March 1984. Duncan's Multiple Range Test was used to compare
means for log transformed data. Means with same letter are not
significantly different.

Mean of
Log (CAC+1)
Mean (n)
1. 25
1. 25
Davenport and Kelly, 1984)
Std. Dev.
sites in the res~rvoir. A horizontal gradient of sediment,
nutrient, and chlorophyll a concentrations in St. Albans Bay,
Vermont, was related to mixing between Lake Champlain and the Bay
(Clausen, 1985). It is important to note that there is frequently
significant lateral and vertical variation in the toxicity and
contaminant levels of bed sediments (USEPA, 1987).
Despite the distinction made between mixed and stratified
lakes, there is considerable gray area between these groups. For
example, thermally stratified lakes might be assumed to be mixed
during periods of overturn, and laterally stratified lakes can
sometimes be treated as if the different lateral segments are
sublakes. In any case, it is important that the monitoring team
knows what parcel of water is being sampled when the program is
implemented. It would be inappropriate, for example, to assign the
attributes of a surface sample to the hypolimnion of a stratified
lake due to the differences in temperature and other parameters
between the upper and lower waters.
Estuaries can be very complex systems, particularly large ones
such as the Chesapeake Bay. Like lakes and streams, estuaries
exhibit temporal and spatial variability. Physically, the major
differences between estuaries and fresh waterbodies are related to
the mixing of fresh water with salt water and the influence of
IV -1 7

tides. These factors increase the complexity of
temporal variability within an estuary.
Short-term variability in estuaries is related directly to the
tidal cycles, which can have an effect on both the mixing of the
fresh and saline waters and the position of the freshwater-
saltwater interface (USEPA, 1982a). The same considerations made
for lakes regarding short-term variability of parameters such as
temperature, dissolved oxygen, and pH should also be made for
Temperature profiles such as those found in stratified lakeEi
can also change seasonally in estuaries. The resulting circulation
dynamics must be considered when developing monitoring programs.
The effects of season on the quantity of freshwater runoff to an
estuary can be profound. In the Chesapeake Bay, for example,
salinity is generally lower in the spring and higher in the fall
due to the changes in freshwater runoff from such sources as
snowmelt runoff and rainfall (USEPA, 1982a). Figure IV-14,
developed from Chesapeake Bay investigations, illustrates the
short-term temporal variability of salinity. levels in various
segments of the Bay.
Spatial variability in estuaries has both significant vertical
and lateral components. Typical estuarine circulation exhibits a
spktial pattern in which incoming tides push salt water into the
estuary while freshwater flow from rivers moves outward. Since
fresh water is lighter than salt water, it flows over the salt
water and displaces the lower saltwater flow shoreward. On
outgoing tides the saltwater mass is pulled outward and the
freshwater flow drops vertically and moves outward with the
saltwater flow (Cohen, 1990). Both small and large estuaries
(e.g., Chesapeake Bay, San Francisco Bay, puget Sound) exhibit this
pattern. Stratification during the summer creates vertical
variability during part of the year as well (USEPA, 1982a).
Freshwater and saltwater flows might also be diverted to opposite
shores of an estuary by a combination of tributary location, the
earth's rotation, and barometric pressure (Figure IV-15). In
addition, lateral variability in salinity can be caused by
different levels of mixing between saltwater and freshwater inputs.
For instance, in Puget Sound the numerous sills, inlets, channels,
and islands disrupt the natural estuarine circulation. Strong
mi'xing occurs around these features, and as a result the outward
freshwater flow-as much as two-thirds of it in place&-is mixed with
the deeper salt water and flows back into the Sound. Pollutants
cQntained in this water or bound to sediments carried in the fresh
water return to the Sound. The San Francisco estuary is
complicated in another way. The northern reach of the estuary
exhibits fairly typical estuarine flow, but the southern reach
receives only about one-tenth the amount of freshwater flow as the
northern reach. This quantity is too small to establish estuarine
flow or create a salinity gradient. Also, water stays in the
southern reach up to four times as long as in the northern reach.

SpriDg ~1i"Wy
in pans per tbousand
Figure IV-14. Chesapeake Bay salinity levels over time and space.
(SOURCE: USEPA, 1982a)

ICI'It'n4' $ IOTI'ITlO.. I

PY8'" ~......
....t- ta
w_,.~" ..,cr..
I !",,~ $11 WAT ~~ I

*Mign oressure over estuary
"o:':sl'\es" ocean \oIate" ~acj( i"lto
ocean. tnus reducing oenetratlon
ana mIxing of saLt water
I LOW Jlltsn'lc I

Figure IV-15. Physical
gradients in an estuary.
IV - 2 0

This has consequences for water quality because the southern reach
receives three times as much sewage effluent as the northern reach.
As noted for streams and lakes, the lateral and vertical
variation in the toxicity and contaminant levels of bed sediments
should be considered (USEPA, 1987).
Coastal Waters
Researchers and government agencies are collectively devoid of
significant experience in evaluating the effectiveness of nonpoint
source pollution control efforts through the monitoring of near-
shore and off - shore coastal waters. Our understanding of the
factors to consider when performing such monitoring is therefore
very limited. .
As for other waterbody types, it is important to understand
the hydrology, chemistry, and biology of the coastal system in
order to develop an effective monitoring program. Of particular
importance is the ability to identify discrete populations from
which to sample. For trend analysis it is essential that the
researcher be able to track over time the conditions of a clearly
identifiable segment or unit of coastal water. This may be
accomplished by monitoring a semienclosed near-shore embayment or
similar system. Knowledge of salinity and circulation patterns
should be useful in identifying such areas. Secondly, monitoring
should be focused on those segments or units of coastal water for
which there is a reasonable likelihood that changes in water
quality will result from the implementation of management measures.
Segment size, circulation patterns, and freshwater inflows should
be considered when estimating the chances for such water quality
Near-shore coastal waters can exhibit salinity gradients
similar to those of estuaries due to the mixing of fresh water with
salt water. Currents and circulation patterns can create
temperature gradients as well. Farther from shore, salinity
gradients are less likely, but gradients in temperature can occur.
In addition, vertical gradients in temperature and light might be
significant. These and other biological, chemical, and physical
factors should be considered in the development of monitoring
programs for coastal waters.
Ground Water
Aquifers are probably the least frequently monitored water
resources because of both the expense associated with drilling
wells and the "out of sight out of mind" approach to problem
finding. Today, however, ground water monitoring has become very
important because contamination of ground water drinking supplies
has been discovered in many areas across the United States. For
example, in the Big Spring area of Iowa, ground water is
contaminated with high nitrate levels and pesticides such as

atrazine, alachlor, cyanazine, and metolachlor (Hallberg et al.,
1984). In a nation where ground water withdrawals account for 35
percent of all public water supply use (more than 50 percent in 11
states), it is increasingly important to monitor the quality of
this resource (USGS, 1985, p. 120).
Ground water monitoring for NPS pollution studies serves
nunerous purposes, such as to determine the ground water component
of a hydrologic/chemical budget for a surface waterbody, to
document the impact of a pollution activity, to identify background
water quality, to identify trends and variations in water quality,
or to determine the effectiveness of land use or best management
Spatial and temporal variability in aquifers cannot be
generalized. Some aquifers respond to precipitation events very
quickly while others respond quite slowly. If the response rate of
an aquifer to outside influences, such as fertilizer applications
on agricultural fields, is not known, sampling at least weekly is
recommended. Otherwise, significant fluctuations in ground water
concentrations might be missed (Clausen et al., 1993).
For the purposes of this brief discussion, aquifers are
divided into two major types: (1) those with intergranular
porosity such as sands, gravels, sandstones, and silts, and (2)
those with solution porosity or fractured rock (Scalf et al.,
1981) . Both types of aquifers exhibit short- and long-term
temporal variability and vertical and lateral spatial variability.
The differences between the two types of aquifers largely relate to
flow patterns. In general, aquifers with intergranular porosity
have more predictable flow patterns than do fractured rock aquifers
(Scalf et al., 1981).
The selection of well locations is highly dependent on the
spatial variability of aquifer water quality. Factors that can
complicate well monitoring efforts include the presence of
confining beds (Figure IV-16), the possibility of multiple aquifer
systems (Figure IV-17), the effects of pollutant density on
pollutant transport, and changes in permeability (Figure IV-18).
Because of these complicating factors, hydrologic information
specific to the site to be monitored is needed to design a ground
water monitoring program. Only site-specific information can
create an accurate picture of the surrounding geology, which is
. essential to be certain that sampling locations are properly

, )
. .
. .. .'
. .
. .. .
. . . .
The water table is deep. Leachate percolates downward
under the landfill, forming a perched water table before
finally reaching the actual water table.
Figure IV-16. Permeable sand layer underlain by a clay layer.
(SOURCE: Scalf et al., 1981)

..'... ,.;:/i~~;:;;&\,::Th
. ''-';'.. ....;;~ ----

';:~ '~~~il!!~~!~i!I~~~~I~~
Leachate first moves into and flows with the ground water
in the upper aquifer. Some of the leachate eventually
moves through the confining bed into the lower aquifer
where if flows back beneath the landfill and away in the
other direction.
Figure IV-17. Two-aquifer system with opposite
(SOURCE: Scalf et al., 1981)
flow directions.

, I
\ :
\ I
\ I
. . ~ ......... '
,,:~.;~ J,'
,,:.""" ,
".... - ,~-:"'.; ~ ,

t jf~!

('.\ I
\ '.~
. . ~
;:.~;;..~.~", '-.-.
- -- ~...:.,..., -' ...t-liIIeCI
_t": . - - C......
lIMP -
Figure IV-18. Effect of permeability change on shape of pollution
plume. (SOURCE: Scalf et al., 1981)
IV - 2 5


Data Needs
Data needs are a direct function of monitoring goals and
objectives. Thus, data needs cannot be established until specific
goals and objectives are defined. Furthermore, data analyses
should be planned before data types and data collection protocols
are agreed upon. In short, the experimental approach should be
followed in establishing all monitoring programs. As defined by
Random House,' an experiment is "a test, trial, or tentative
procedure; and act or operation for the purpose of discovering
something unknown or of testing a principle, supposition, etc."
(Stein, 1980). Rarely will a monitoring program have a purpose
that does not fall within the above definition of an experiment.
The following discussion touches upon the types of information
that should be considered in nonpoint source monitoring programs.
It is impossible to recommend in advance a complete suite of
parameters to be monitored for all possible program objectives.
The monitoring group should select parameters based upon their
monitoring objectives and their particular situation.
Data Types
Many types of data may be required for nonpoint source
monitoring and evaluation depending upon the program and the
monitoring and evaluation goals and objectives. Adequate water
quality data are obviously required, but the form and scope of
needed water quality data should be determined as a function of
quantitative monitoring and evaluation objectives and planned data
analysis. .
In some cases, it may be more beneficial to use surrogate
measures instead of the parameters mentioned in the monitoring and
evaluation goals and objectives. In these cases, objectives for
the surrogates should be established which are consistent with the
overall monitoring and evaluation goals. For example, a program
goal may'be to improve the trophic state of a lake from eutrophic
to mesotrophic, with a monitoring and evaluation goal to document
this change. Surrogate measures for trophic state may be
phosphorus and chlorophyll-a. The corresponding surrogate program
goal may be to reduce phosphorus and chlorophyll-a concentrations
to levels deemed sufficient to change the trophic state to
mesotrophic. The monitoring and evaluation goal would then be to
document these changes in phosphorus and chlorophyll-a levels.
The key to using surrogate measures is that a reliable
relationship must exist between the true measure and the surrogate
measure. An example of poor surrogate selection is the unqualified
use of erosion rates as estimators of sediment delivery to water
resources. Without the existence of a reliable relationship
between these two measures (i.e., sediment delivery ratio), the
surrogate will produce misleading results.

Sherwani and Moreau (1975, p. 34) illustrate how
interparameter correlations can be used to optimize parameter
selection. In essence, one parameter value is used to estimate the
value for a correlated parameter. The authors noted that higher
order streams showed better interparameter correlations than lower
order streams.
Hydrologic Data
Hydrologic data are critical to many nonpoint source
monitoring and evaluation efforts. Due to the relationships
between flow parameters and pollutant characteristics, hydrologic:
data are almost always required in some form at some state 01:
nonpoint source monitoring and evaluation. It may be necessary to
establish watershed water budgets in order to determine thE~
location and magnitude of nonpoint source or background sources.
In.other cases, the extent of the floodplain may prove critical to
assessments of BMP control needs. For example, in the New York MIP
project it was discovered that flooded cropland was a much lager
source of phosphorus to Cannonsville Reservoir than was expected
(B~own, et ale 1986). As a result, nonpoint source control efforts
wo~ld have to be redirected to cover manure-spread cropland as well
as bainyard runoff which was the original focus of BM~
Biological Data
Biological data are very useful in evaluating impairment to
the water resource from nonpoint source impacts, because aquatic
communities integrate the exposure to various nonpoint sources over
time. An assessment of biological condition is crucial to the
judgment of a waterbody to maintain and protect a healthy aquatic
ecosystem. Monitoring of changes in the aquatic community over
time provides an understanding of the improvement due to BMPs and
allows a judgment of the effectiveness of various mitigativE~
measures. Biological survey approaches will differ depending upon
the water body-i.e., streams, rivers, lakes, wetlands, or estuaries.
3 .
precipitation Data
Precipitation data, including total rainfall, rainfall
intensity, storm interval, and storm duration have proven to be key
to successful interpretation of nonpoint source data in the NURP,
MIP, and RCWP studies. The Universal Soil Loss Equation (USLE) is
ba~ed on research showing that there is a direct linear
relationship between average annual soil loss and a rainfall runoff
factor (R) (Wischmeier and Smith, 1978). The R factor accounts for
the cumulative energies and intensities of a year's storms, plU:3
the erosive forces of runoff from thaw, snowmelt, and irrigation.
The erosion index found in the USLE is also used in several
nonpoint source models, including the Agricultural Nonpoint Source
Pollution Model (AGNPS) (Young, et al., 1985). A procedure derived
from the NURP program uses storm frequency and other factors to
determine recurrence intervals for in-stream pollutant

(USEPA, 1984a).
from urban nonpoint
source pollution
Land Use Data
Land use and land treatment data are important in monitoring
and evaluation efforts designed to test the effectiveness of
implementation programs. In RCWP, for example, it has been
discovered that traditional USDA reporting schemes may not provide
sufficient land treatment data for use in analyses relating BMP
implementation to water quality changes. . New approaches are needed
to report land treatment and land use in ways that are quantitative
and transferable. This problem was addressed and recommendations
were made in an RCWP workshop, but the issue was not resolved.
Topographic Data
Topographic data are also required for many nonpoint source
monitoring and evaluation efforts, particularly when soil erosion,
water runoff, and sedimentation are estimated with models. For
example, the USLE includes both slope length and slope steepness
factors (Wischmeier and Smith, 1978). AGNPS input includes a slope
shape factor, field slope length, channel slope, and channel side-
slope (Young, et ale 1985)..
Soil Characteristics Data
other data such as soil chemistry and soil physical
characteristics may be required for some monitoring and evaluation
efforts. Recent approaches to assessing the potential for ground
water contamination from nonpoint sources have emphasized the need
for data such as hydrologic soil group, soil organic carbon
content, depth to water, net recharge, aquifer media, and vadose
zone characteristics (Dean, et aI, 1984; Aller, et ale 1985).
Data Sources
Many of the data requirements for nonpoint source monitoring
and evaluation efforts can be met using nationally available data
sources. This section describes some of these data sources and
includes contacts for those interested in accessing the data.
There are likely very many other data sources available to nonpoint
source professionals-this guidance focuses only on some of the
major data sources made available to EPA or known to reviewers of
this document.
STOrage and RETrieval (STORET) System
The STOrage and RETrieval (STORET) system is one of the oldest
and largest water information systems currently in use. STORET
stores information on ambient, intensive survey effluent, and
biological water quality monitoring information. Although most
STORET information has been added since 1975, records go back to
1899. STORET has four information areas:

Water Quality System: WQS is the main component of
STORET and contains chemical and physical
information obtained during monitoring of waterways
within and contiguous to the united States. This
includes information for estuaries, streams, lakes,
rivers, ground water, canals, and coastal and
international waters.
Biological System: Bros contains information on
the distribution, abundance, and physical condition
of aquatic organisms in waters wi thin and
contiguous to the united States, as well as
descriptions of their habitats. Bros provides a
central repository for biological information and
analytical tools for data analyses.

Daily Flow System: DFS contains daily observations
of stream flow and miscellaneous water quality
parameters collected at gaging stations belonging
to the USGS's national network. The DFS contains
essentially the same information as the USGS Daily
Values File; the DFS provides an alternative source
for the information and simplifies linkages to
other, non-USGS water data bases.
Fish Kill File: The Fish Kill File tracks fish
kills caused by pollution that have occurred
throughout the united States. The kills are a
result of a variety of industrial, municipal,
agricultural, and transportation related
Currently about 800 organizations have submitted information
to. STORET. There are over 735,000 sampling stations in STORET and
more than 180 million parametric observations covering some 12,000
water quality parameters.
Many organizations submit information to STORET, including
federal, state, interstate, and international agencies. Users
submit new information in the appropriate format daily. STORET
data files are updated weekly. Each organization is responsible
for the information it submits to STORET; STORET is a user-owned
system. States submitting information follow quality assurance and
cdntrol procedures. All STORET data has been checked for invalid
data ranges or missing mandatory fields before being added to the
system. Although STORET software edits incoming data for errors
and inconsistencies, the owners of the data have the primary
responsibility for its content.
Bob King
Office of Wetland, Oceans, and Watersheds
U.S. Environmental Protection Agency
The Fairchild Building
499 South Capitol Street, SW, 4503F
Washington, DC 20460

(202) 260-7028
Water Quality Analysis system (WQAS)
The Water Quality Analysis Branch has developed several data
bases and procedures that operate under the umbrella of the Water
Quality Analysis System (WQAS). WQAS data bases are available on
the same mainframe as the STORET files, and many procedures
intrinsic to one system access and manipulate data from the other.
WQAS includes many data bases; the following data bases are a
sample of these that would be most useful in a nonpoint source
monitoring and evaluation study.
Association of State and Interstate Water Pollution
Control Administrators (ASIWPCA): Data covering water
quality impairments for 1972, 1982, and 1984.
CITY: Data on 53,000 cities in the united States and its
GAGE: Data on 36,000 stream gaging locations across the
United States
Reach File (RF): Data on stream reaches across the
united States. Information on RF3 streams is limited;
100 percent of all RF1 and RF2 streams are included.
Bob King
Office of Wetland, Oceans, and Watersheds
U.S. Environmental Protection Agency
The Fairchild Building
499 South Capitol Street, SW, 4503F
Washington, DC 20460
Phone: (202) 260-7028
National Water Information system (NWIS)
USGS is in the process of designing and developing a new
National Water Information System (NWIS). The goal of the NWIS
effort is to develop and implement a highly flexible hydrologic
data management and processing system; one that can be easily
changed and expanded in a rapidly changing technological
environment. The NWIS will replace the following two systems:
National Water Data Storage and Retrieval System
(WATSTORE): This system consists of several files
in which data are grouped and stored by common
characteristics and data collection frequencies.
The system also is designed to allow for the
inclusion of additional data files as needed.
Currently, files are maintained for the storage of
(1) surface water, quality-of-water, and ground
water data measured on a daily or continuous basis;
(2) annual peak values for stream flow stations:
(3) chemical analyses for surface and ground water
sites; (4) water data parameters measured more
frequently than daily; (5) geologic and inventory
data for ground water sites; and (6) summary data

on water use. In addition, an index file of sites
for which data are stored in the system also is
National Water Data Exchange System (NAWDEX):
NAWDEX is a national confederation of water-
oriented organizations working together to improve
access to water data. Its primary objective is to
assist ~sers of water data in the identification,
locations, and acquisition of needed data. NAWDEX
consists of member organizations from the water
data community. The members are linked so that
their water data holdings may be readily ~xchanged
for maximum use. It encompasses four major areas
of operation: (1) maintaining an internal data
center, including access to automated data
processing facilities for maintenance and use of
its information files; (2) indexing water data held
by participating organizations; (3) providing
facilities and personnel for responding to requests
for water data; and (4) formulating recommended
water data handling and exchange standards.

NWIS will be a single integrated system that will have thE~
functionality of current data systems plus expanded capability for
processing and managing additional chemical constituent, sediment,
bi0logical, and spatial data.
Tom Yorke, Chief
National Water Information
u.S. Geological Survey
437 National Center
Reston, VA 22092
National Stream Quality Accounting Network (NDSQamYUSGS
The National Stream Quality Accounting Network (NASQAN)
program, started in 1972, provides a nationally uniform basis for
assessing large-scale and long-term trends in the physical,
chemical, and biological characteristics of the nation's surface
waters. Water quality monitoring is carried out at the stations
which are generally located on major rivers at the downstream end
of the accounting unit.
Physical constituents monitored in freshwater and analyzed for
trends are pH, alkalinity, sulfate, nitrate, phosphorus, calcium,
magnesium, sodium, potassium, chloride, suspended sediment, fecal
cqliform bacteria, fecal streptococcal bacteria, dissolved oxygen,
arid dissolved oxygen deficit. The following radionuclides are al80
monitored at 46 sites, but have not been analyzed for trend8:
gross alpha, gross beta, radium-226, and uranium. Data collection
stations are maintained at selected locations to provide
standardized records on surface and ground water conditions. A
variety of automated instruments are used to measure and record

water conditions. Data are collected at 58 percent of sites and
quarterly at 42 percent of sites. Trace element collection is
quarterly and radionuclides are collected semiannually. Yearly
data summaries are available for each state.
Richard A. Smith, Hydrologist
Water Resources Division
U.S. Geological Survey
410 National Center
Reston, VA 22092
Phone: 703-648-6870
National Surface Water Survey (NSWS)
The National Surface Water Survey (NSWS) consists of two
parts: the National Lake Survey and the National Stream Survey.
The purpose of the National Lake Survey is to quantify, with know
statistical confidence, the current status, extent, and chemical
and biological characteristics of lakes in regions of the United
States that are potentially sensitive to acidic deposition.
The purpose of the National Stream Survey (NSS) is to
determine the percentage, extent, and location of streams in the-
united States that are presently acidic or have low acid-
neutralizing capacity and may, therefore, be susceptible to future
acidification, as well as to identify streams that represent
important classes in each region for possible use in more intensive
studies or long-term monitoring. The NSS provides an overview of
stream water chemistry in regions of the united states that are
expected, on the basis of previous alkalinity data, to contain
predominantly low acid-neutralizing capacity waters.
Variables monitored include: acid neutralizing capacity,
aluminum, base cations, conductance, major ions, metals, nitrate,
organics, pH, and sulfate. A randomly selected subset of lakes was
sampled using appropriate methods. The sample results were then
weighted to estimate the chemical compositions of lake populations
with known confidence. Uncertainties with time of sampling,
spatial variability, and population definition are included in
specific research projects to improve confidence in estimates. The
NSS employed a randomized, systematic sample of regional stream
populations and used rigorous quality assurance protocols for field
sampling and laboratory chemical analysis.
Dixon Landers
Environmental Research Laboratory
U.S. Environmental Protection Agency
200 SW 35th Street
Corvallis, OR 97333
Phone: 503-754-4423
National Coastal Pollutant Discharge InventorVS~NC1Hm~
The National Coastal Pollutant Discharge Inventory (NCPDI)
Program is a series of data base development and analytical

activities within the strategic Assessment Program for coastal and
estuarine areas of NOAA. The cornerstone of the program is a
co~prehensive data base and computational framework that has been
developed over the last nine years. The data base contains
pollutant loading estimates for all major categories of point"
nonpoint, and riverine sources located in coastal counties of thE!
200-mile exclusive economic zone that discharge to the estuarine,
coastal, and oceanic waters of the conterminous united states
(excluding the Great Lakes). The pollutant discharge estimates in
the NCPDI are made for the following base years for each coastal
East Coast - 1982,
West Coast - 1984, and
Gulf Coast - 1987.
The estimates can be considered to approximate pollutan't
di~charge conditions for a five-year period around the base year.
Estimates are made for nine major source categories and 17
pollutants. Source categories include:
point sources,
urban nonpoint sources,
nonurban nonpoint sources,
irrigation return flow,
oil and gas operations,
marine transportation operations,
accidental spill, and
dredging operations.
Pollutant estimates can be aggregated by county, USGS
hydrologic cataloging unit, or estuarine watershed. Pollutant
parameters include:
flow (wastewater flow or surface runoff),
.biochemical oxygen demand,
particulate matter,
nutrients (total nitrogen and phosphorus) ,
metals (arsenic, cadmium, chromium, copper,
mercury, and zinc),
petroleum hydrocarbons (oil and grease),
pesticides (35 compounds),
pathogens (fecal coliform bacteria), and
wastewater treatment sludges.
Estimates are based on a combination of computed methodologiE~s
and actual monitored observations. Estimates are seasonal (winter,
spring, summer, fall) for a base year. Updated discharge estimatE~s
for 1987for the coastal areas of the Gulf of Mexico and for 1989
for the East Coast are being prepared.
Daniel R. Farrow, Chief
Pollutant Sources Characterization Branch
National Oceanic and Atmospheric Administration
6001 Executive Boulevard, Room 220

Rockville, M 20852
Phone: 301-443-0454
Ocean Data Evaluation System (ODES)
The Ocean Data Evaluation System (ODES) is a menu-driven
system for storing and analyzing water quality and biological data
from marine, estuarine, and freshwater environments. The system
supports federal, state, and local decision makers associated with
marine monitoring programs. The system was designed to support
managers and analysts in meeting regulatory objectives through the
evaluation of marine monitoring information.
ODES contains over 2.5 million records of data from the
National Estuary Program, the Great Lakes National Program Office,
the Ocean Disposal Program, the 301(h) Sewage Discharge Program,
the National Pollutant Discharge Elimination system (NPDES)
Program, and the 403(c) Program.
Bob King
Office of Wetland, Oceans, and Watersheds
u.S. Environmental Protection Agency
The Fairchild Building
499 South capitol street, SW, 4503F
Washington, DC 20460
Phone: (202) 260-7028
Waterbody system (WBS)
The Waterbody System (WBS) is an automated data base of state
water quality assessment information. WBS facilitates collection,
storage, retrieval, and analysis of water quality assessment
information collected by the states to meet EPA's Congressional
reporting requirements under section 305(b) of the Clean Water Act.
The WBS contains information that helps program managers
report accurately and quickly on the water quality status of a
particular water body. It may also be used to target resource
expenditures and to set surface water program priorities. Under
the Clean Water Act, states submit information to EPA on several
types of surface waters affected by point or nonpoint source
pollution, lakes monitored under the Clean Lakes Program, and
surface waters requiring the assigning of total maximum daily loads
limits to restore or maintain their water quality.
WBS serves as an inventory of each state's navigable waters
that have been assessed for water quality and is sued as the basis
for the 305(b) report to Congress every two years. States assemble
available monitoring information and make judgments on water
quality before summary information can be entered into the system.
WBS stores the components and the results of the assessment. The
WBS is not designed to store, manipulate, or analyze raw monitoring

WBS is a voluntary program currently used by approximately 40
states, territories, and river basin commissions. the data base
consists of assessments rather than monitoring data and includes
many optional fields. Consistency is good within a state. Those
wishing to aggregate to a regional or national level should discuss
data characteristics with the WBS coordinator.
Office of Wetland, Oceans, and Watersheds
u.s. Environmental Protection Agency
The Fairchild Building
499 South capitol Street, SW, 4503F
washington, DC 20460
Phone: 202-260-3667
Pesticide Information Network (PIN)
, The Pesticide Information Network (PIN), maintained by EPA's
Office of Pesticide Programs, enables pesticide monitoring data
generated by a variety of sources to be routinely identified,
obtained, and utilized. PIN also provides federal, state, and
IOGal agencies with a means to sharing information and expertise on
pesticides. In addition, information in PIN is used to enhance the.
accuracy of pesticide risk assessments and risk/benefit regulatory
decisions regarding exposure and effects of pesticides under the
Federal Insecticide, Fungicide, and Rodenticide Act (FIFRA). PIN
is composed of three files:
The Pesticide Monitoring Inventory (PMI) is a
nationwide compilation of synopses of pesticide
monitoring projects conducted by federal, state,
and local governments as well as private groups.
PMI includes the location of the monitoring
proj ect, the pesticides involved, an abstract of
the project, and the name and address of a contact
person. PMI does not contain hard data or results;
these can be obtained from individual contact
persons for each project.
The Restricted Use Products (RUP) File is a
regulatory file that serves as an information
resource for states. Information provided includes
pesticide active ingredients, dates of restriction,
reasons for restriction, and all products that
contain the restricted active ingredients.
The Coordination File is a cross-referencing
chemical index of all synonyms for the active
ingredients listed in the PMI and RUP files.
Constance A. Hoheisel
Office of Pesticide Programs
u.s. Environmental Protection
401 M Street, SW, H7507C
Washington, DC 20460

Management System
The Environmental contaminant Data Management System (ECDMS)
is the cataloging, sample management, and data storage system for
residue data from field studies conducted by the USFWS. Data are
from sample matrices consisting of animal and plant tissues,
sediments, soils, and water. The system contains data on
pesticides, elements, PCBs, and other compounds.
The National contaminant Biomonitoring Program (NCBP) is
maintained by USFWS to document temporal and geographic trends in
concentrations of persistent environmental contaminants that may
threaten fish and wildlife. NCBP data is maintained by the ECDMS.
The NCBP is the USFWS segment of the National Pesticide Monitoring
Program, a multi-agency monitoring effort by the member agencies of
the Federal Committee on Pest Control. Since 1965, USFWS has
periodically determined concentrations of potential toxic elements
and selected organochlorine chemicals in fish and wildlife
collected from a nationwide network of stations. The NCBP is being
phased out with the implementation of the broader Biomonitoring of
Environmental Status and Trends (BEST) Program. -
In addition to organochlorine chemical residues, freshwater
fish, starlings, and waterfowl samples are analyzed for arsenic,
cadmium, copper, lead, mercury, selenium, and zinc. Composite
samples of whole freshwater fish are collected in replicate from
112 stations in major rivers throughout the united States and in
the Great Lakes. starlings are collected in replicate from 139
terrestrial sites in the conterminous 48 states. wings of mallards
and black ducks shot by hunters in the continental untied States
are collected to assess body burden of organochlorine compounds in
migratory birds. This monitoring program has continued at two- to
four-year intervals since 1965. The USFWS is in the process of
reviewing the NCBP and an agency initiative was approved for fiscal
year 1992.
James K. Andreasen
Division of Environmental contaminants
U.S. Fish and wildlife Service
4401 North Fairfax Drive
suite 330
Arlington, VA 22203
Phone: 703-358-2148
National Shellfish Register (NSR)
Classified shellfishing waters are monitored as an indicator
of bacterial water quality nationwide. Waters are classified for
the commercial harvest of oysters, clams, and mussels based on the
presence of actual or potential pollution sources and coliform
bacteria levels in surface waters. Each shellfish-producing state
classifies its waters in accordance with guidelines established by

the national Shellfish Sanitation Program.
classified shellfishing areas are defined by:
Approximately 2,000
location (nautical chart number, estuary, state, region);
classification (approved, prohibited" conditional
approved, restricted);
size; and
pollution sources (identified for all non-approved
areas) .
Trends in classification by region from 1966 to 1990 and by
selected estuaries in the northeast, southeast, Gulf of Mexico, and
Pacific from 1971 to 1990 are available. Areas that were
reclassified because of improved or diminished water quality are
distinguished from those that were reclassified as a result or
improved monitoring. Data also are collected on administration of
state programs, including:
identification of state agencies responsible for
monitoring waters, assigning classification, analyzing
water samples, etc.;
number of personnel;
number of sampling stations;
frequency of sampling; and
other factors that may influence classification.
Data are collected by questionnaire and followed by
interviews. Classifications are noted on 265 nautical charts.
Data were compiled in 1966, 1971, 1974, 1980, 1985, and 1990. The
next survey is scheduled for 1995.
Sharon Adamany, Environmental Analyst
National Oceanic and Atmospheric Administration
6001 Executive Boulevard
Rockville, MD 20852
Phone: 301-443-8843
National Status and Trends Database (NST)
Beginning in 1984, NOAA undertook the task of providing
information on the status and trends of environmental quality in
estuarine and coastal areas. The program defines the geographic
distribution of contaminant concentrations in tissues of marine
organisms and in sediments. Status and trends data are available
from the Mussel Watch and Benthic Surveillance for four major
elements, twelve trace elements, DDT and its metabolites, selected
chlorinated pesticides, selected PCB congeners, approximately 22
pcDlyaromatic hydrocarbons, and ancillary sediment and tissue
Samples have been collected since 1984 at about fifty Benthic
Surveillance sites and since 1986 at about 150 Mussel Watch sites.

Sediment samples are collected at all sites. At Benthic
Surveillance sites, benthic fishes are collected and their livers
excised and stored for subsequent chemical analysis. At Mussel
Watch sites, bivalve mollusks are collected for analysis. Data are
collected annually.
Thomas P. O'Connor
Ocean Assessments Division
National Oceanic and Atmospheric Administration
6001 Executive Boulevard
Rockville, MD 20852
Phone: 301-443-8655
National Climate Data Center (NCDC)
The National Climatic Data Center (NCDC) collects, processes,
and archives meteorological and climatological data from a global
network of stations. Records begin in the mid-19th century and
continue to the present. Climatic variables (e.g., temperature,
precipitation, solar radiation, storms, wind, and floods) are
summarized for both short-term and long-term periods of record.
Data are available in published form, on microfiche, or on magnetic
tape. Derived values relating to growing season and heating and
cooling degree days are also produced. Special statistical-
summaries of actual and derived values of meteorological elements
over the world's oceans as well as summaries used in the study of
air pollution are available.
For about four decades, NCDC has been receiving climatic data
from across the United States and around the globe. Principal
sources in the United states are the National Weather service
(NWS) , the Federal Aviation Administration, the U.S. Air Force, the
U. S. Navy, and the U. S. Coast Guard. The NWS' s Cooperative station
Network is comprised mainly of 10,000 volunteer observers and has
been recording daily records since the 1800s. As aircraft began to
fill the skies, information on the upper atmosphere was needed.
Balloon-borne instruments radioed data; radars began to probe the
clouds; rockets reached the fringes of the atmosphere; weather
satellites, both geo-stationary and polar orbiting, now
continuously watch and record the weather. Technical advancements
led NCDC to archive some of their data on CD-ROM's so that users
could look at a large amount of climatic data at one time. The
NCDC plans to archive new data sets using the latest technical
advances available. Observations are taken at varying intervals,
from every fifteen minutes to once per month. Collections are
daily or monthly depending on type and source of information.
National Climatic Data Center
Climate Services Division
Federal Building
Asheville, NC 28801-2696
Phone: 704-259-0682
Synoptic Rainfall Data Analysis Program (SYNOP)

EPA maintains a Synoptic Rainfall Data Analysis Program
(SYNOP) as a tool for summarizing and statistically characterizing
rainfall records. SYNOP summarizes hourly rainfall data by stornl
events, calculating for each event the volume (inches), duration
(hours), average intensity (inches per hour), maximum intensity
(inches per hour), time since the previous storm (hours),
antecedent rainfall (inches), the hours of missing data, and the~
hours that the meter did not read. SYNOP then uses these storm
event statistics to determine monthly and annual means and
coefficients of variation for the various storm parameters.
Dennis Athayde
u.S. Environmental Protection
401 M Street, SW, H7507C
Washington, DC 20460
Phone: 202-382-7112
Acid Deposition System (ADS)
The National Acid Deposition Program/National Trends Network
(NADP/NTN) was the first, and continues to be the only, United
States network to monitor precipitation chemistry on a national.
scale. The current network consists of 196 sites in the
conterminous united States, Hawaii, Puerto Rico, and American
Samoa. sites are located in predominantly rural areas to avoid the
localized influences of large point sources and major urban
centers. Nearly 14 years of continuous data are available from the
sites with the greatest longevity; many of these sites are
associated with the State Agricultural Experiment stations.
The primary objective of the NADP/NTN is the determination of
gepgraphical patterns of temporal trends in chemical deposition.
The program provides scientists, managers and policy makers with
weekly precipitation chemistry data and information on geographical
patterns and temporal trends in concentrations and deposition of
hydrogen, sulfate, nitrate, ammonium, calcium, magnesium, sodium,
potassium and chloride, and ortho-phosphate ions in precipitation.
Ftnal quality assured data are available to a multitude of data
users upon request, within six months of sample collection.
P~incipal constituents monitored in precipitation and analyzed for
t:r:ends are:
specific conductance,
hydrogen ions,
sulfate and nitrate ions,
ammonium and calcium ions, and
chloride, magnesium, sodium, and
potassium ions.
The NADP/NTN monitoring program has developed criteria and
protocols which ensure uniformity in siting, sampling method~;,
analytical techniques, data handling, and overall network
o~erations. Precipitation is collected by wet/dry precipitation

collectors and rain gages.
variables measured are:
Analytical methods for the chemical
field pH;
laboratory conductivity;
electronic detection of hydrogen (also reported as pH);
automated calorimetric detection of ammonium;
atomic absorption spectrophotometric detection of
calcium, magnesium, sodium, and potassium; and
ion chromatographic detection of sulfate, nitrate, and
Samples are collected weekly. Data from some sites are
available from 1979. The data is maintained on the Acid Deposition
System (ADS).
Ranard J. Pickering
U.S. Geological Survey
416 National Center
Reston, VA 22092
Phone: 703-648-6875
Major Land Uses in the united States (MLU)
For more than fifty years, the Economic Research Services
(ERS) and its predecessor agencies have estimated acreage and
maintained an inventory of the major uses of land in the United
States at intervals coinciding with the Census of Agriculture.
Estimates are made for major land use classes:
grassland pasture
forest land;
special use; and
.unclassified use.
and range;
Each major class is further classified by specified uses and
some by ownership. Land uses are also designated as agricultural
and nonagricultural. Agricultural land uses include:
cropland (cropland harvested, cropland failure, cultivate
summer fallow, and idle cropland);
grazing lands (cropland pasture and permanent pasture and
grazed forest land; and
miscellaneous agricultural uses (farmsteads, farm roads,
and farm lands).
Special uses include:
forest land not grazed;
intensive uses (highways
airports); and

extensive uses (national parks, state parks, wilderness
areas, federal wildlife areas, state wildlife areas,
national defense areas, and federal industrial
Unclassified other land uses include urban and other special
us~s not inventoried and other miscellaneous areas, such as
marshes, open swamps, bare rock areas, deserts, and tundra. Data
are analyzed for trends.
Data from the Bureau of the Census, agencies of the Department
of Agriculture, public land management and conservation
organizations, and other sources are assembled, analyzed, and
synthesized to estimate state, regional, and national land USE~
acreage. The major uses of land are inventoried every five years
coinciding with years in which the Census of Agriculture is
completed. The inventories generally have been comparable in
format and coverage since 1945. The series on "cropland used for
crops" dates back to 1909.
Arthur B. Daugherty, Agricultural Economist
Economic Research Service
U.s. Department of Agriculture
1301 New York Avenue, N.W., Room 408
Washington, DC 20005-4788
Phone: 202-219-0424
Agricultural Census (AgCensus)
The Agricultural Census (AgCensus) data base includes about
750 variables reported at the county level for 1978, 1982, and
1987. The census is scheduled for years ending in 2 and 7.
Agcensus variables include simple statistics such as the number of
farms, total acreage of farms, acreage of various major crops, and
total number of various livestock. It also includes such data as
the number and acreage of irrigated farms, the number and acreage
ot' farms irrigated by various sources, the number and acreage of
farms by farm size, commercial fertilizer and other agricultura.l
chemical expenditures, the number of farms and livestock by herd
size, the number and acreage of vegetable farms, and a subset of
these statistics for farms with sales greater than ten thousand
AgCensus does ont include pesticide application rates or even
the acreage to which specific pesticides are applied. Fertilizer
and manure application rates and acreage are also not reported.
Irrigation rates and farm management practices are likewise not
included in the data base.
Charles P. Pautier, Jr., Chief
Agriculture Division
Bureau of the Census
U.s. Department of Commerce
Washington, DC 20233
Phone: 301-763-1113

Forest Service
Information System
The Forest Service Range Management Information System
(FSRAMIS) collects and analyzes data on grazing in national forests
and grasslands. FSRAMIS provides grazing use statistical data.
Data on the number of grazing animals (cattle, horses and burros,
sheep and goats), animal unit month, and number of permittees are
reported at the national level and for each type of Forest Service
land, region, and state. Other variables measured include:
allotment condition,
improvement inventory
grazing capacity,
actual use, '
authorized use, and
unauthorized use.
and activity,
Data are analyzed for trends in ecological potential. Data on
grazing on the National Forest System lands are extracted from the
grazing permits. Data on free-roaming horse and burro populations
are estimated by census. Data are collected on cycles ranging from
annual to once every three to five years.
Robert M. Williamson, Director
Range Management Staff
u.s. Forest service
Department of Agriculture
P.O. Box 96090
Washington, DC 20090-6090,
Phone: 202-205-1460
Forest Inventory and Analysis Program (FIA)
The Forest Inventory and Analysis (FIA) program is responsible
for making and keeping current a comprehensive inventory and
analysis of the renewable forest and rangeland resources of the
united States. Initial inventory efforts began in the West in 1930
and, by'the 1960s, inventories were completed for all of the 48
conterminous states and many of the important forested states had
been re-inventoried. The inventory data and analysis provide trend
information on the extent, condition, ownership, and composition of
the nation's forests as well as information about wildlife habitat,
forage production, and other resource characteristics needed for
resource planning. At least 43 kinds of resource data are
collected for sample plots during the inventory, including:
land use,
land owners~ip,
forest type,
stand age,
stand size and volume
harvest history,
soils data,

. tree data (species, diameter
cull, etc),
other vegetation data, and
non-timber data.
at breast height, height,
These data are used to make estimates of forest land areas,
species composition, timber volume, and net annual timber growth,
removals, and mortality by forest type, state, region, ownership,
softwood and hardwood sawtimber species, productivity class,
diameter class, and other classifications. The volume of roundwood
pr6ducts harvested by material species group, region, and product:
are estimated. Estimates also are made of areas harvested or
otherwise disturbed, regenerated to forest, or cleared for other
use. Additional estimates of recreation use, wildlife values, sitE~
productivity, physiographic characteristics, and other items arE~
made. The data is maintained in three possible data bases:
National Resources Planning Act (RPA) Timber Database
Eastwide Forest Inventory Database
Forest Inventory and Analysis Database
Data are gathered using a two-phase sampling design, with th'e
fiFst phase involving ground measurements at sample plots, each-
covering one acre. Depending upon the extent to which sensing is
us~d, ground sample intensity ranges from one plot per 3,000 acres
to one plot per 10,000 acres. statewide timber inventory
information has been collected continuously for about fifty years.
In most regions of the united states, the third inventory cycle has
been completed and some areas have been inventoried as many as five
times. Each year, some fifty million acres are inventoried in the
conterminous untied states. Currently this rate of coverage
translates into an inventory cycle of twelve years for the nation.
James T. Bones
U.S. Forest Service
u.s. Department of Agriculture
P.O. Box 96090
Washington, DC 20090-6090
Phone: 202-205-1343
National Land Use and Land Cover Maps
As part of its National Mapping Program, the USGS produces and
distributes land use and land cover maps and digitized data. Land
use refers to human acti vi ties that are directly related to the
land. Land cover describes the vegetation, water, natural surfacE~,
and artificial constructions at the land surface. Associated maps
display information on political units, hydrologic units, census
county subdivision, and in some cases, federal land ownership.
Land use and land cover areas are classified into nine major
built-up land,
agricultural land,

forest land,
water areas,
barren land,
tundra, and
perennial snow
or ice.
Each major class is subdivided into several minor classes, for
37 minor classes total. For example, forest lands are further
classified as deciduous, evergreen, or mixed forest land, and water
is further classified as streams and canals, lakes, reservoirs, or
bays and estuaries. Remote sensing methods are used, including
satellite imagery, high-altitude imagery, medium-altitude remote
sensing, and low-altitude imagery. Data were collected in the late
1970s and early 1980s.
Richard L. Kleckner
Office of Geographic and
u.s. Geological Survey
590 National Center
Reston, VA 22092
Phone: 703-648-5741
Cartographic Research
Population Census Data (CENDATA)
The decennial census provides a comprehensive set of
population statistics for the united states. Basic demographic
characteristics are collected on a 100-percent basis. Social and
economic characteristics are collected from a large sample of all
households and persons in group quarters. The decennial census
provides demographic (e.g., age, race, sex, relationship), social
(e.g., education, migration, ancestry, language), and economic
(e.g., occupation, industry, income, place of work) characteristics
of the population of the united states, Puerto Rico, the Virgin
Islands, Guam, American Samoa, the Norther Marianas, and Palau.
Trend data are available from pervious decennial censuses. Basic
demographic data are collected from 100-percent of the population.
Social and economic characteristics are collected from a large
sample, approximately one-in-six in 1980 and 1990.
Contact: Philip N.
Census Programs
population Division
Bureau of the Census
u.S. Department of Commerce
Washington, DC 20233
Phone: 301-763-7890
National Resources Inventory (NRI)
For fifty years, SCS has been conducting periodic inventories
of the nation's soil, water, and related resources. The National
Resources Inventory (NRI), which is an extension and modification
of earlier inventories, provides data on the status, condition, and
trends of these resources of nonfederal land in the united States.

The many types of data collected by the NRI process are organized.
into eight general categories:
soil characteristics and interpretations (including'
agricultural land capability);
land cover;
land use (including irrigated and nonirrigated cropland,
grazed and ungrazed forest land, prime farmland, etc);
erosion (such as sheet and rill, wind, and ephemeral
land treatment (such as irrigation, tillage, and
conservation treatment needs;
vegetative conditions (such as wetlands, rangeland
condition and species, and pasture management); and
potential for conversion to cropland.
The NRI is a multi-resource inventory based on soils and
related resource data collected at scientifically selected randOIn
sample sites. The NRI sample design was developed by the Iowa
state University statistical Laboratory at Ames. It uses censu:;
area and point methods for data collection. Data collection
involves both field investigation and remote sensing. Data are.
collected on a five-year cycle. Recent surveys were conducted in
1977, 1~82, and 1987.
The 1987 NRI data were collected from nearly 300,000 sample
sites from all counties of the United states, except those in
Alaska, and in Puerto Rico and the Virgin Islands. Most of these
samples were part of the 1982 NRI which had nearly 1 million sample
sites. The 1987 NRI data has a high degree of reliability at the
state level and the 1982 NRI provides a high degree of reliability
at the mUlti-county level. Data estimates can be made by Major
Land Resource Areas (MLRA), SCS Administrative Areas, Water
Re'sources Council Aggregated Subareas, and other multi-county
. geographic subdivisions.
Jeff Goebel
Resources Inventory and Geographic Information
systems Division
soil Conservation Service
U.s. Department of Agriculture
P.O. Box 2890
South Agricultural Building, Room 6175
Washington, DC 20013
Phone: 202-720-4530
Ecoregion Maps
Ecoregions are defined by EPA to be regions of relative
homogenei ty in ecological systems or in relationships betweEm
organisms and their environments. Ecoregions of the united states
have been mapped to help water resource managers understand better
the regional patterns of ecosystem quality and the relative
importance of factors that may be determining this quality.

Specifically, the ecoregion framework can establish a logical basis
for characterizing ranges of ecosystem conditions or quality that
are realistically attainable. A national ecoregion map has been
prepared at a scale of 1:7,500,000 and regional maps are prepared
at a scale of 1:2,500,000. The maps are available in an ARC-INFO
format for use by individual users.
David Larsen
U.S. Environmental Protection Agency
Environmental Research Laboratory
200 SW 35th Street
Corvallis, OR 97333
Phone: 503-757-4601
National Wetlands Inventory (NWI)
In 1975, the (USFWS) established the National Wetlands
Inventory (NWI) to develop technically sound and comprehensive
information the characteristics and extent of wetland resources in
the united States. Status and trends information is available for
selected wetland types including estuarine wetlands, palustrine
wetlands, lacustrine wetlands, and deepwater habitats in the lower
48 states. In addition, statistical data are available for coastal.
waters and bay bottoms, coastal marshlands and mangroves, recent
changes in inland vegetated wetlands, recent changes in lacustrine
deepwater habitats, estimates of current annual wetland losses,
estimates of wetland losses by flyways, . states with significant
changes in wetland resources, indicators of development pressures
on wetland resources, and causes of wetland losses. The Emergency
Wetlands Resources Act of 1986 requires that updates of the wetland
status and trends be produced on 10-year cycle with reports due in
1990, 2000, 2010, etc. Data are collected continuously with
updates on a ten-year cycle. The 1990 update provides trend data
on wetlands losses and gains between the 1970s and the 1980s.
The wetland mapping phase of the proj ect has produced map
coverage for approximately 70 percent of the lower 48 states, 22
percent of Alaska, and all of Hawaii, Puerto Rico and .Guam.
Wetland status and trends information is designed to provide
statistical estimates on a national basis (lower 48 states). In
addition, regional intensification studies are available for the
Chesapeake Bay Region and the Central Valley of California. Other
statewide status information is available for the states of
Florida, Delaware, New Jersey, Illinois, Washington, Maryland, and
Connecticut. Status reports covering the coastal wetlands of
Alaska and the prairie Pothole Region (North Dakota, South Dakota,
Minnesota) are also available.
Thomas E. Dahl
National Wetlands Inventory
U.S. Fish and wildlife service
suite 101 Monroe Building
9720 Executive Center Drive
st. Petersburg, FL 3702-2440
Phone: 813-893-3624


The following, taken from Sherwani and Moreau (1975, p.
describes the need for water quality data:
3) ,
All phases of planning, development, and operation of a water
resource management system, including water quality control,
require the acquisition and processing of data to quantify existing
states of the system, to forecast future changes and trends, and to
predict responses of the system to interventions for development
and con trol. The kind of da ta required and their spa tial and
temporal resolution depend upon [the] nature of the problems and
[the] kinds of interventions under consideration. The word
moni toring has been defined as this acti vi ty of making" sys tema ti c
observations of parameters related to a specific problem, designed
to provide information on the characteristics of the problem and
their changes with time."
Before getting into specific monitoring guidance it is
important to note that these recommendations are just that,
recommendations. As stated by Sherwani and Moreau (1975, p. ix),
"there is no single specification of a [monitoring] network which
is optimal for all purposes." The researcher should tailor these
general guidelines to adjust for the specific objectives, water
resource characteristics, climate, financial resources, and other
factors unique to the area being monitored.
Samples and Sampling
Random House (Stein, 1980, p. 1165) defines a sample as "a
small part of anything or one of a number, intended to show the
quality, style, or nature of the whole." We collect environmental
samples for both economic and practical reasons; that is, we cannot
afford to inspect the "whole" and we usually have neither the time
and resources nor the capability to even try to inspect the
"whole." Besides, we often find that a sample or collection of
samples will provide sufficient information about the "whole" to
allow us to make decisions regarding actions which should or should
not be taken.
In a statistical sampling program, the "whole" is called the
"population" or "target population," and it consists of the set of
"population units" about which inferences will be made (Gilbert,
1987, p. 7). As an example, population units could be defined as
macroinvertebrate populations on square-meter sections of river
bottom, phosphorus concentrations in l-liter grab samples, or
hourly-mean flow values at a specific gaging station. Gilbert
(1987, p. 7) refers to the "sampled population" as the set of
population units directly available for measurement.

Sampling Objectives
Gaugush (1986, p. 189) states that lithe major objective in
sampling program design is to obtain as accurate or unbiased an
estimate as possible, and at the same time reduce or explain as
much of the variability as possible in order to improve the
precision of the estimates. II Accuracy is a measure of how close
the sample value is to the true population value, whereas precision
refers to the repeatability of sample values. Biased estimates are
those which are consistently higher or lower than the true
population value. According to Cochran (1977, p. 11), an estimator
is unbiased if its mean value, taken over all possible samples, is
equal to the population statistic which it estimates.

In the real world it is necessary to design sampling programs
which meet accuracy and precision requirements, while not placing'
unreasonable burdens on sampling personnel or sampling budgets. As
stated by Gaugush (1986, p. 190), budget constraints may force the
issue of whether sampling results will produce information
sufficient to meet the study objectives.
Gaugush (1986, p. 190-194) describes in some detail specific
points to consider in defining study obj ecti ves. He notes that
IIsampling is facilitated by specifying the narrowest possible set
of, objectives which will provide the desired information. II First,
he recommends that the target population be defined as a key step
in limiting the variability encountered in the sampling program..
As an example, in a watershed impacted by nonpoint sources, the
target population could be defined as storm-event, dissolved
phosphorus concentrations at the inlets to all impoundments. This
specificity focuses the sampling program better, eliminating the
need to monitor at upstream and in-lake sites, and during baseflow
conditions. The definition also specifies the water quality
parameter of interest. Note that both spatial and temporal limits
should be established in defining the target population. As a
fUFther refinement, the researcher may define the population units
as the dissolved phosphorus concentrations in half-hour, composite
samples taken during all storms (II storms II as defined by the
re'searcher) .
The next step, according to Gaugush (1986, p. 192), is to
decide whether parameter estimation or hypothesis testing is the
primary analytic goal. This choice will have an impact on the
sampling design. As an example, Gaugush points out that balanced
designs are desirable for hypothesis testing, whereas parameter
estimation may require unbalanced sample allocations to account for
the spatial variability of variable levels. Hypothesis testing is
likely to be used in program evaluation (e.g., water quality before
and after pollution controls are implemented), whereas parameter
estimation can be applied in assessments when determining pollutant
loads from various sources.
Finally, Gaugush (1986, p. 193) recommends that exogenous
variables and sampling strata be defined. Exogenous variables are
used to explain some of the variability in the measured parameter

of interest. As an example, total suspended solids (TSS)
concentration is typically a covariate of total phosphorus (TP)
concentration in watersheds impacted by agricultural runoff.
Measurement of TSS may help increase the precision of TP estimates.
Sampling Error and Variability
Gilbert (1987, p. 10-13) discusses five general sources of
variability and error in environmental studies:
Environmental variability
Bias, precision, and accuracy
Statistical bias
Random sampling errors
Gross errors and mistakes
The author describes environmental variability as "the variation in
true pollution levels from one population unit to the next." This
can be caused by several factors including distance to the
pollutant source; nonuniform distribution of the pollutant due to
physical, biological, or chemical influences; buildup or
degradation over time; and temporal and spatial variation in
background levels. Gilbert (1987, p. 11) notes that existing
information on environmental variability can be used to "design a
plan that will estimate population parameters with greater accuracy
and less cost than can otherwise be achieved."
Accuracy, precision, and measurement bias are described above
(Section III.C.1.b.). Gilbert (1987, p. 11) uses an illustration
to point out that high accuracy can only be obtained when
measurement bias is low and precision is high. Cochran (1977, p.
12 -15) provides a simple, yet convincing, demonstration of the
impact of bias on the probability of estimation errors.
Random sampling errors (e.g., variability in sample means for
different random samples from the same population) arise from the
environmental variability of population units (Gilbert, 1987, p.
12) . By def ini tion, random sampling error is zero if all (N)
population units are measured, but will never. be zero if N is
infinitely large (Gilbert, 1987, p. 12).
Gross mistakes can occur at any point in the process beginning
with sample collection and ending with the reporting of study
results (Gilbert, 1987, p. 12). Adherence to accepted sampling and
laboratory protocol, combined with thorough quality control and
data screening procedures, will minimize the chances for gross
Monitoring Approaches
General Approaches
Reviewers of three general types of monitoring designs for
documenting water quality changes related to best management

practice (BMP) implementation have concluded that (Spooner et al.,
1985) :
Monitoring above and below an implementation site is
generally more useful for documenting the severity of a
nonpoint source than for documenting BMP effectiveness.
Time trends may be helpful, but variables associated with
land treatment, hydrology, and meteorology should be
accounted for to increase the likelihood of successful
documentation of water quality-BMP relationships.
Paired watershed designs show the greatest potential for
documenting improvements from BMP implementation due to
the ability to control for meteorologic and hydrologic
The paired watershed approach is currently being used in the
St. Albans Bay, Vermont RCWP project (Clausen, 1985). In this
study, two small watersheds received proper manure management
during a two-year calibration period, followed by a period in which
one watershed received winter-spread manure. This is an
interesting approach in that BMPs were removed from instead of
applied to a watershed after the calibration period. The
anticipated analytic result in using the paired watershed,design is
a demonstrated water quality change attributable to management
differences because all other key factors are very similar.

, Data from the Rock Creek, Idaho RCWP were collected in
upstream-downstream pairs. These paired data were utilized in
regressions of water quality against time. The downstream
copcentrations (below NPS) were adjusted for upstream
concentrations (above NPS) , transformed, and then regressed against
time as a continuous variable (Spooner et al., 1986). Results of
this approach were used to indicate decreasing pollutant
cohtributions from NPS. This example illustrates uses of both
upstream-downstream monitoring and time trends.
Erlebach (1979, p. 7) has described a systematic approach to
monitoring surface water quality trends associated with urban,
iddustrial, and agricultural developments in a river basin. The
steps in this approach are:
identify developments which may impair or change water
assign priorities to areas of concern and select study
examine background data and literature to assess gaps in
required information and develop a conceptual model
perform a basin reconnaissance to confirm background
assessment, to determine logistic requirements, and to
select sites and parameters

propose and implement coordinated pilot studies to
develop a monitoring approach, to determine spatial,
short term, and seasonal variations in relevant
parameters of water quality and quantity and to
investigate relationships between parameters
design and implement a trend monitoring program to
investigate future needs for remedial action or to show
that remedies are effective.
Richards (1986) has used Monte Carlo models to determine the
best of seven sampling strategies for estimating tributary loads.
Applying the bias and precision statistics from the Monte Carlo
simulation to datasets covering five parameters for three rivers,
the researcher found that bias and precision of loading estimates
are affected by the frequency and pattern of sampling, the
calculation approach used, watershed size, and the parameter being
monitored. Richards concludes that flow-stratified sampling and
calculations using the Beale Ratio Estimator provided the most
precise results in the study. A further point made is that initial
sampling should be intense such that sampling theory calculations
can then be used to adjust the program.
Meals (1987, personal communication) notes that flow-
proportional sampling is not possible unless the stage-discharge
relationship is known. His experiences in nonpoint source
monitoring of agricultural watersheds in Vermont has led him to
conclude that researchers should use time-based sampling, even
after a stage-discharge relationship is established. In addition,
Meals recommends a greater emphasis on runoff events versus
baseflow conditions, particularly where budget limitations are
In these days of increasing M&E needs and relatively small M&E
budgets it is extremely important for researchers to design
efficient M&E programs. The menu of parameters selected for a
monitoring program should be tied directly to the monitoring
objectives. It is often the case that parameters in addition to
those of prime interest are monitored because these other
parameters are cheap to monitor and may provide some useful
information for purposes not yet outlined. This is generally
reasonable, but the researcher should:
Anticipate these undefined purposes such that the extra
parameters are monitored in a manner that truly does
yield useful information (e.g., support statistical
analyses) .
Make sure that the extra cost associated with additional
parameters does not preclude necessary expansions and/or
extensions of the monitoring and evaluation program for
the parameters of prime interest.

Sherwani and Moreau (1975, p. 24) indicate that parameter
selection can be governed by (1) water use requirements, (2) water
quality standards, (3) type of pollutant source, and (4) the other
constituents normally present in the waterbody. For enforcement
purposes, the parameters measured should be those specified in
water quality standards. For use support analyses, additional
parameters may be required since a broader definition of water
quality is applied. Both Sherwani and Moreau (1975, p. 27) and an
EPA Interagency Task Force (USEPA, 1981) recommend key parameters
to be measured for various designated uses.
Parameter selection should reflect the NPS M&E objectives and
data analysis plans. For example, if the objective is to monitor
the condition of salmon spawning areas, then parameters such as
streambank undercut, embeddedness, and vegetation overhang may bE~
important (Platts et al., 1983). If the goal is to assess the
impact of NPS controls in terms of standards violations, then the
parameters selected should be only those required for the analysis
of standards violations. If the M&E plan involves data
normalization or grouping prior to data analysis then the parameter
list should include those parameters used in normalization and/or
grouping. Some analyses may require discrete variables, whereas
others may use continuous variables; these issues should be
addressed in choosing parameters to monitor.
Both surface and ground water monitoring require that samplinq
sites are characterized sufficiently for meaningful data
interpretation. In the case of ground water monitoring, thi:3
information includes the aquifer tapped by a well, the depth of the
well, the type of well construction, and the well elevation (USGS,
1977, p. 2-1). For surface water sites the relevant information
may include waterbody name, river reach number and milepoint,
location, prevailing winds, shading, bottom sediment, elevation,
slope, stream width and depth, lake depth, etc.
Water level measurements should be included in all ground
water studies. These measurements are used, among other things,
to: (1) indicate the directions of ground water flow and areas of
recharge and discharge, (2) evaluate the effects of manmade and
natural stresses on the ground water system, (3) define the
hydraulic characteristics of aquifers, and (4) evaluate stream-
aquifer relations (USGS, 1977, p. 2-1).
The reader is referred to Section
discussion of data types or parameters.
Sherwani and Moreau (1975, p. 34) illustrate how inter-
parameter correlations can be used to optimize parameter selection.
In essence, one parameter value is used to estimate the value for
a correlated parameter. The authors noted that higher orde:r
streams in North Carolina showed better inter-parameter
correlations than lower order streams. In addition to inter-
parameter correlations, the authors recommend principal components
and factor analysis as a means for identifying the most important

parameters and clusters of related parameters (Sherwani and Moreau,
1975, p. 37).
Sampling Methodology
In the context of this NPS M&E Guidance, the purpose of
sampling is to obtain information sufficient to describe selected
characteristics of a system over pre-defined temporal and spatial
limits. The scope and quality required of these descriptions are
a direct function of the M&E objectives. For example, objectives
which incorporate hypothesis testing will. usually require more
extensive data bases than objectives which entail only general
assessments of water quality. Hence, the sampling methodologies
required to meet different M&E objectives for the same waterbody,
and especially for different waterbodies, may differ considerably.
This may seem to be a statement of the obvious, but all too often
sampling programs are established with insufficient consideration
of the match between data needs and the data to be collected.
As stated earlier, the target population is the set of
population units about which inferences are to be made. Following
the steps outlined by Gaugush (1986, p. 190 -194), researchers
should define the target population and population units before
establishing the sampling program. While this step in the process
ensures that the "right stuff" is being sampled, it does not
address other sampling issues such as "when," "where," and "how
much" to sample. Researchers should design their sampling programs
to develop data bases describing the "right stuff II in such a way
that statistical and other planned analyses can be performed in
support of the M&E objectives. That is, the sampling program
should provide "representativf!!" and "sufficient" data.
The question of whether the data are sufficient is addressed
in subsequent sections of this guidance. The representativeness of
collected data is discussed in considerable detail in section
III. A., but warrants some additional comments as follow.
Site location and sampling frequency are often considered
sufficient to describe the "where" and "when" of sampling programs.
While this is certainly true to a large extent, these two factors,
taken alone, do not describe fully where and when samples are
collected. Additional considerations include the depth of sampling
and the surface or ground water stratum in which the sampling depth
belongs, the origins of the aliquots (s) taken in each sample
bot tle, the time - frame over which measurements are made, etc.
These additional considerations fall under the heading of "sample
type" in this guidance. Site location and sampling frequency are
components of "sampling design," and sample type and sampling
design are taken in combination as the overall "sampling
In order for the data analyst to interpret sampling results
appropriately, the sample type, sampling design, and target
population must all be identified explicitly. It should be clear
from the descriptions of the sampling methodology and target

population whether the data collected are representative of the
target population.
- Examples of sample type classifications include instantaneous
and continuous; discrete and composite; surface, soil profile, and
bottom; time-integrated, depth-integrated, and flow-integrated; and
biological, physical, and chemical. Several existing guidance
manuals (USEPA, 1981; Scalf et al., 1981; Brakensiek et al., 1979;
USGS, 1977; USEPA, 1978b; USEPA, 1987a; Platts et al., 1983; and
Shelley, 1979) and other reference materials (Wetzel and Likens,
1979) describe these various sample types and the equipment used to
collect them. Therefore, this document focuses on sampling
designs, with only a few illustrative examples of sample type
selection. All samplinq desiqns in this quidance are based oq
probability samplinq.
The selection of an appropriate sampling design for nonpoint
so~rce M&E efforts can be a very complicated and frustratinsr
experience for the researcher dabbling in statistics. It is hiqhl~
recommended that all researchers consult with a qualifiec!
statistician for quidance in desiqninq statistically-based samplinq
Simple random sampling
In simple random sampling, each unit of the target population
has an equal chance of being selected. For example, if the target:
population is the macroinvertebrate population found on lOa-square
meters of river bottom, and the population units are one-square
meter sections of river bottom, then each unit would have a one
percent chance of being sampled under a random sampling program.
To select ten one-square meter sections for analysis, the
in:vestigator could first number each section (i.e., 1-100), and
then use a random number table to identify the first ten sections
to be sampled. In some cases, sampling with replacement is
possible (e.g., fish surveys), but in many cases sampling without
replacement is the only practical option (e.g., collecting aliquots
of stream water) .
, Gilbert (1987, p. 26-43) and Cochran (1977, p. 18-45) both
address many aspects of simple random sampling. Included in these
, texts are estimation of the mean and total for sampling with and
without replacement, equations for determining the number of
samples required for both independent and correlated data, and the
impact of measurement errors.
Stratified Random Sampling
In stratified random sampling, the target population is
divided into separate groups called" strata" for the purpose of
getting a better estimate of the mean or total for the entire
population" (Gilbert, 1987, p. 21). Simple random sampling is then
used within each stratum.

Stratification involves the use of categorical variables to
group observations into more homogenous units to reduce the
variability of observations within each unit. Cochran (1977, p.
127-131) provides equations and examples to show how to define
strata. Much of the introductory discussion in this guidance
document (Section III .A.) is intended to illustrate the
opportunities and needs for creating strata for improving sampling
programs and data analyses and interpretations. Strata are useful
when the combined data show greater variability than the separate
Stratified sampling is generally used in efforts to estimate
parameters (Gaugush, 1986, p. 195). Stratified sampling results
can be used to determine either a combined mean or a combined total
population estimate (Gaugush, 1986, p. 200). The combined estimate
of the population mean is the mean of the weighted strata means
(weighted by stratum sample size). However, if proportional
allocation is used (i.e., the sampling fraction is the same in all
strata), then the sample is "self-weighting" (Cochran, 1977, p.
91) .
The sum of the. strata estimates is the total population
estimate (Gaugush, 1986, p. 200). The population variance estimate
is the weighted sum of the strata variances (Gaugush, 1986, p.
200) .
As an example, stratified random sampling could be used to
monitor water quality in streams below irrigation return flows.
Based on a knowledge of irrigation and precipitation patterns for
the watershed, the researcher could divide the year into two or
more homogeneous periods. Within each period random samples could
be taken to characterize the average concentration of a particular
pollutant. These random samples could take the form of daily,
flow-weighted composite samples, with the sampling dates randomly
Cluster Sampling
Another sampling design described by Gaugush (1986, p. 204-
205) is cluster sampling. In cluster sampling, the total
population is divided into a number of relatively small
subdivisions, or clusters, and then some of these subdivisions are
randomly selected for sampling (Freund, 1973, p. 453). For one-
stage cluster sampling, these selected clusters are sampled totally
(Gaugush, 1986, p. 204). In two-stage cluster sampling, random
sampling is then performed within each cluster (Gaugush, 1986, p.
204) .
Gaugush (1986, p. 205) states that" analysis of cluster
samples requires the estimation of variance at two levels, the
between-cluster variability and the within-cluster variability. The
total variability is a recombination of these two levels." Still,
Gaugush believes that the difficulty associated with analyzing
cluster samples can be more than compensated for by the reduced
sampling requirements and cost.

Cluster sampling is applied in cases where it is more
practical to measure randomly selected qroups of individual units
than to measure randomly selected individual units (Gilbert, 1987,
p. 23). An example of one-stage cluster sampling is the collection
of all macroinvertebrates on randomly selected rocks within a
specified sampling area. The stream bottom may contain hundreds of
rocks with thousands of organisms attached to them, thus making it
difficult to sample the organisms as individual units. However, it
is often possible to randomly select rocks and then inspect every
organism on each selected rock.
Multi-stage Sampling
Two-stage sampling involves dividing the target population
into primary units, randomly selecting a subset of these primary
units, and then taking random samples (subunits) within each of the
selected subsets (Gilbert, 1987, p. 22). All of the random samples
fr0m the subunits are measured completely. Two- stage cluster
sampling, described above, is one form of two-stage sampling.
Cochran (1977, p. 274-285) describes two-stage sampling in
great detail and presents methods for determining the mean and
variance in two-stage sampling with units of equal size. In his
discussion, Cochran (1977, p. 279) notes that if all population
units are sampled, then the formula for estimating the variance is
the same as that used to estimate the variance for proportional
stratified random sampling. This means that two-stage sampling is
a type of incomplete stratification, with the population units
treated as strata.
Three-stage sampling would involve measuring randomly selected
subunits within each of the subunits selected in two-stage sampling
(G~lbert, 1987, p. 71). The reader is referred to Gilbert (1987,
p. 71-87) and Cochran (1977, 285-288) for a more complete
discussion of three-stage sampling and compositing, including
fo~mulas for estimating the population mean, variance of the mean,
and total.
Double Sampling
Double sampling or two-phase sampling involves taking a large
preliminary sample to gain information (e.g., population mean or
frequency distribution) about an auxiliary variate (x.) in the
context of a larger sampling survey to make estimateslfor some
other variate (y.) (Cochran, 1977, p. 327). This technique can be
used for stratiftcation, ratio estimates, and regression estimates
(Cochran, 1977, p. 327).
Double sampling for stratification requires a first sample to
estimate the strata weights and a second sample to estimate the
strata means (Cochran, 1977, p. 328). The reader should consult
Cdchran (1977, p. 327-344) for further explanation, equations, and
examples of double sampling for stratification, ratio estimates,
and regression estimates.

Gilbert (1987, p. 23) discusses a use of double sampling in
which two techniques are used in initial sampling, and subsequent
sampling is performed using only the cheaper or simpler technique.
The initial sampling is used to establish a linear regression
between the measurements from the two techniques. This regression
is then applied to the subsequent measurements made with the
cheaper technique to predict the measurement result which would
have been obtained with the better, more expens i ve technique.
Gilbert (1987, p. 106-117) describes double sampling in much more
detail, and provides illustrative examples.
3.6. Systematic Sampling
A commonly used sampling approach is systematic sampling,
which entails taking samples at a preset interval of time or space,
using a randomly selected time/location as the first sampling point
(Gilbert, 1987, p. 23).
Systematic sampling is used extensively in water quality
monitoring programs, usually because it is relatively easy to do
from a management perspective. According to Gaugush (1986, p.
203), "[i] n systematic sampling the first sample placement is
generally decided at random within an initial region, and
subsequent samples are taken at some constant distance or time from
the first."
Cochran (1977, p. 205) points out that the difference between
systematic sampling and stratified random sampling with one unit
per stratum is that in systematic sampling the sampled unit occurs
in the same relative position within each stratum while in
stratified random sampling the relative position is selected
Cochran (1977, p. 207) also states that when a population
(N=k8n) is divided into k large sampling units for systematic
sampling, then" [a] systematic sample is a simple random sample of
one cluster unit from a population of k cluster units." For
example, if one daily sample is taken each week in the year, then
k=7 and n=52. That is, the systematic sampling can begin at one of
seven days (randomly selected), with a total of 52 units (i.e., 52
weeks) per systematic sample. By randomly choosing Tuesday, for
example, the entire systematic sample (or cluster unit) has been
randomly selected.
Cochran (1977, p. 229-231) recommends systematic sampling for
the following situations:
The ordering of the population is essentially random or
it contains at most a mild stratification.
Stratification with numerous strata is employed and an
independent systematic sample is drawn from each
Subsampling cluster units.

Sampling populations with variation of a continuous type,
provided that an estimate of the sampling error is not
regularly required.
Systematic sampling is generally inappropriate for hypothesis
testing due to violation of the assumption of random sampling. The
importance of this violation will vary with the situation.
Estimation can, however, be achieved through systematic sampling,
but the impact of this sampling design on the bias and precision of
estimates should be explored. Quantitative procedures for
estimating the population mean and variance from systematic
sampling data are presented by Gilbert (1987, p. 96-99).
3 .7.
Sampling for Regression Analysis
Regression analysis is used to predict variable values based
on a mathematical relationship between a dependent variable and one
or more independent variables (Gaugush, 1986, p. 208). Gaugush
points out that regression analysis requires that at least one
quantitative independent variable be used, whereas parameter
estimation and hypothesis testing can be performed for groups or
classes (i.e., only the variable tested needs to be quantitative).
Gaugush (1986, p. 208-211) discusses sampling to support
regression analyses in terms of relating variables to either a
spatial or a temporal gradient, the latter being for trends over
time. Some key points made in this discussion with respect to
gradient sampling are:
The gradient variable is treated as a covariant to the
variable of interest.
If the relationship is linear, only two points need to be
sampled; the extreme points are preferred.
Whenever the relationship is known, relatively
sampling points are needed along the gradient.
samples may then be used as replicates.
Whenever the relationship is not known, more sampling
points are needed along the gradient. More replicates
are also needed to test the proposed model.
It is usually acceptable to place sampling points equal
distances from each other along the gradient. However,
the investigator should be careful not to fall in step
with some natural phenomenon which would bias any data
S0me key points
sampling are:
this discussion with respect
to time
Time can be used either as a covariate or as a grouping
variable. Grouping by time may be desirable when
changes in the variable of interest are either small

over time or occur only during short periods with long
periods of little or no change.
Considerations in using time as a covariate are similar
to those above for gradients, but (a) time is usually
only a surrogate for other variables that truly affect
the variable of interest, and (b) the relationship with
time is likely to be complex.
If time is to be used as a covariate, relatively frequent
sampling will be needed, with some replication within
sampling periods. Random sampling within the periods is
also recommended.
Comparison of Sampling Strategies
Estimation of the Mean
Gilbert (1987, p. 89) states that systematic sampling will, in
many cases, "yield more accurate estimates of mean concentrations"
than simple random or stratified random sampling plans. Gaugush
(1986, p. 204) suggests that systematic sampling may be useful in
defining strata for stratified random sampling designs.
Cochran (1977, p. 221) used environmental data sets in
comparing systematic sampling to stratified random sampling in
estimating the mean, with the result that systematic sampling was
superior to stratified random sampling with one or two data per
stratum. Gilbert (1987, p. 95) reports that systematic sampling is
equivalent to simple random sampling in estimating the mean if the
target population has neither trends nor strata nor correlations
among population units. .
Freund (1973) notes that estimates based on cluster sampling
are generally not as good as those based on simple random samples,
but they ~re better per unit cost.
Cochran (1977, p. 214) found that stratified random sampling
provides a better estimate of the mean for a population with a
linear trend, followed in order by systematic sampling and simple
random sampling. For populations exhibiting a linear trend,
Gilbert (1987, p. 96) recommends the use of a weighted estimate of
the mean to improve the estimate of the mean derived from
systematic sampling. Cochran (1977, p. 216) also recommends using
weighted means, but specifies that "all internal members of the
sample have weight unity (before division by n) but different
weights are given to the first and last members." He also notes
that centrally located samples could be used as another option for
improved estimates of the mean.
Gilbert (1987, p. 96) notes that estimates of the mean for
correlated populations are better for stratified random sampling
than for simple random sampling. However, the relative quality of
the estimate for systematic sampling depends on the sampling

Estimation of Variance
Cochran (1977, p. 99) states that "stratification nearly
always results in a smaller variance for the estimated mean or
tot'al than is given by a comparable simple random sample." He goes
on to note (p. 100) that under optimum allocation of stratified
random samples, the variance is decreased relative to simple random
samples because both the differences among the stratum means and
the effect of differences among the stratum standard deviations are
Estimates of variance from systematic samples may differ from
that determined from random samples. Cochran (1977, p. 213) notes
that "on the average the two variances are equal." However,
Cochran (1977, p. 213) also states that for any single finite
po~ulation for which k (number of sampling units) is small, the
variance from systematic sampling is erratic and may be smaller or
larger than the variance from simple random sampling.
Gilbert (1987, p. 100) notes that assumptions about the
population are required in estimating population variance from a
sinqle systematic sample of a given size. However, there are
systematic sampling approaches which do support unbiased estimation
of population variance, including multiple systematic sampling,
systematic stratified sampling, and two-stage sampling (Gilbert,
1987, p. 96). In multiple systematic sampling more than one
systematic sample is taken from the target population. Systematic
stratified sampling involves the collection of two or more
systematic samples within each stratum.
Table VI-1 summarizes the conditions under which each of six
probabilistic sampling approaches should be used for estimating
me~ns and totals (after Gilbert, 1987, p. 20).
Examples of Sampling Methodology
The following examples are offered to illustrate
relationship between M&E objectives and sampling methodology.
Objective: Determine the annual loading of phosphorus
(P) from a watershed with no point sources.
Sampling methodology: Assuming that the majority of P
is delivered under high flow conditions, the researcher
should perform flow-proportional sampling during events.
This, of course, assumes that a stage-discharge rela-
tionship has been established. Vertical and horizontal
concentration and flow profiles should be assessed to
determine the need for transect and/or depth-integrated

Table VI-1. Applications of Six Probability Sampling Designs to
Estimate Means and Totals (after Gilbert, 1987)
Samplinq Desiqn
conditions for Application
Simple Random Sampling
population does not contain major trends,
cycles, or patterns of contamination.
Stratified Random Sampling
Useful when a heterogeneous population can be
broken down into parts that are internally
Multistage Sampling
Needed when measurements are made on subsamples
or aliquots of the field sample.
Cluster Sampling
Useful when population units cluster together
and every unit in each randomly selected
cluster can be measured.
Systematic Sampling
Usually the method of choice when estimating
trends or patterns of contamination over space.
Also useful for estimating the mean when trends
and patterns in concentrations are not present
or they are known a priori or when strictly
random methods are impractical.
Double Sampling
Useful when there is
relationship between
and a less expensive
a strong linear
the variable of interest
or more easily measured
Determine the extent to which bacterial
contamination precludes swimming at a lake
Sampling methodology: USEPA (1978, EPA-600/8-78-017,
p. 29) recommends .sample collection at locations and
times of heaviest use, with daily sampling in the
afternoon. Weekends and holidays of highest use should
receive special attention.
For estuaries USEPA (1978, EPA-600/8-78-017, p. 29) sug-
gests sample collection at high tide, ebb tide, and low
tide "in order to determine the cyclic water quality and
deterioration that must be monitored during the swimming
season." EPA states that composite samples should not
be collected for bacterial examination (1978, EPA-600/8-
78-017, p. 6). Surface sampling by hand or by sampling
devices, several of which are described by USEPA (1978/
EPA-600/8-78-017), are recommended.

Determine seasonal concentration
distributions for a tributary site in an
agricultural watershed.
Sampling methodology: As stated this objective is too
general to determine the sample type required. No
mention is made of the vertical and/or horizontal gra-
dients which may exist. Assuming that average spatial
concentration is needed, samples can be taken at the
depth and location at which the average concentration is
shown to occur (this may require initial intensive sam-
pling at the site). Since stream depth and width vary
with flow, allowances should be made to adjust the sam-
pling point as needed to accommodate changes in stream
flow (this may require that intensive sampling is per-
formed at two or more flow conditions to establish the
different "average" sampling points needed) .
Random samples or stratified random samples can be
collected as discrete or composite samples depending upon
the averaging time selected. As stated by Sherwani and
Moreau (1975, p. 13), "[t]he appropriate length of the
averaging interval is determined by the type of
parameter." For seasonal concentration distributions
it may be appropriate to use weekly, daily, hourly, or
instantaneous samples, depending upon the parameter and
the stated objectives.
The above objective is insufficient to determine the
desired averaging period. A refinement may be to de-
termine seasonal distributions of hourly ~ concentra-
tions. In this case, hourly composite samples would be
It should be clear from the above three examples that
objectives must be explicit in order to lead to the development of
a satisfactory M&E program. The examples above only address the
relationship of objectives to sampling methodology, but the
implications are similar for other aspects of a complete M&E
Site Location
Site location and establishment are discussed in several
existing monitoring guides and texts (USEPA, 1978b; USGS, 1977;
Ponce, 1980b); Wetzel and Likens, 1979; Brakensiek et al., 1979;
USEPA, 1981). Few differences exist between NPS site location
strategies and the approaches discussed in these documents. Within
any given budget, site location is a function of water r~source
type, M&E objectives, and data analysis plans. Additional
considerations in site selection are site accessibility and
landowner cooperation in data collection efforts (e.g., farm
management records). It is strongly recommended that NPS
monitoring stations be located near USGS gaging stations due to the

extreme importance of obtaining
estimating pollutant loads.
Once the number of measurements needed is estimated the number
of stations and the frequency of measurement at each station can be
determined. Sherwani and Moreau (1975) provide an example in which
collection of 100 samples could entail either sampling at 8
stations for a year or sampling at one station for 8 to 9 years.
This analysis assumes that the stations are all representative of
the conditions to be monitored. It also assumes that the CVs for
the parameters of interest do not change over time. This may not
be a good assumption for NPS M&E since parameter CVs will probably
change over time due to implementation of control practices.
Two techniques are offered by Sherwani and Moreau (1975, p. 56-
60) for selecting station locations. These methods are the
gradient location technique and the inter-station correlation
technique. The former uses parameter decay rates as the key factor
in site placement, whereas the latter seeks to maximize the
information content derived from all sites by minimizing the
information content common to all sites. Both approaches require
data that may not be available before monitoring has begun. The
authors conclude that it may be wise to collect more data initially
in a monitoring program. This information can be used to evaluate
and revise the program as needed.
The following overall site location guidance is taken from NURP
monitoring guidance (Shelley, 1979, p. D-22 to D-27) which
summarizes much of the information generated by a panel of federal
and state monitoring professionals (USEPA, 1975).
For overall background and problem assessment the following
locations are recommended for the chemical and physical
sampling of the water column. Biological and sediment stations
should also be established at these locations, as appropriate.
At critical locations in water quality limited areas.
Stations should be located within areas that are known or
suspected to be in violation of water quality standards,
ideally at the site of the most pronounced water quality
degradation. The data from these stations should gage the
effectiveness of pollution control measures being required
in these areas.
At the major outlets from and at the major or significant
inputs to lakes, impoundments, estuaries, or coastal areas
that are known to exhibit eutrophic characteristics.
These stations should be located in such a way as to
measure the inputs and outputs of nutrients and other
pertinent substances into and from these water bodies.
The information from these stations will be useful in
determining cause/effect relationships and in indicating
appropriate corrective measures.

,At cri tical locations wi thin eutrophic or potentially
eutrophic lakes, impoundments, estuaries, or coastal
areas. These stations should be located in those areas
displaying the most pronounced eutrophication or
considered to have the highest potential for
eutrophication. The information form these stations, when
taken in combination with the pollution source data, can
be used to establish cause/effect rela tionships and to
identify problem areas.
At locations upstream and downstream of major population
and/or industrial centers which have significant waste
discharges into flowing surface waters. These stations
should be loca ted in such a way tha t the impact on wa ter
quality and the amounts of pollutants contributed can be
measured. The information collected from these stations
should gage the relative effectiveness of pollution
control activities.
Upstream and downstream of representative land use areas
and morphologic zones within the area. These stations
should be located and sampled in such a manner as to
compare the relative effects of different land use areas
(e.g., cropland, mining area) and morphologic zones (e.g. t
piedmont, mountain) on water quality. A particular
concern for these stations is the evaluation of nonpoint
sources of pollution and the establishment of baselines of
water quality in sparsely populated areas.
At the mouths of major or significant tributaries to
mainstem streams, estuaries, or coastal areas. The data
from these stations, taken in concert with permit
monitoring data and intensive survey data, will determine
the major sources of pollutants to the area's mainstem
water bodies and coastal areas. By comparison with other
t~ibutary data, the relative magnitude of pollution
sources can be evaluated and problem areas can be
At representative sites in mainstem rivers, estuaries,
coastal areas, lakes, and impoundments. These stations
will provide data for the general characterization of the
area's surface waters and will provide baselines of water
quali ty against which progress can be measured. 'The
purpose of these stations is not to measure the most
pronounced areas of pollution, but rather to determine the
overall quality of the water. Biological monitoring will
be a basic tool for assessing the overall water quality of
an area.
In major water use areas, such as public water supply
intakes, commercial fishing areas, and recreational areas.
These stations serve a dual purpose: the first is public
heal th protection and the second is for the overall
characterization of water quality in the area.

Determining the presence and accumulation of toxic
substances and pathogenic bacteria and their sources are
primary objectives of these stations.
Sediment sampling sites should be located in sink areas as
determined by intensive surveys, reconnaissance surveys, and
historical data. A major concern of sediment monitoring will
be to assess the accumulation of toxic substances, and
locations for sediment sampling should be chosen with this in
mind. Sediment mechanics and the hydrological characteristics
of the water body must be considered.
In general, biological
established as follows:
1 .
At key locations in water bodies that are of critical
value for sensitive uses such as domestic water
supply, recreation, and propagation and maintenance of
fish and wildlife.
In major impoundments
Near the mouths of major rivers where they enter an
At locations in major bodies potentially subject to
inpu ts of con taminan ts from areas of concen tra ted
urban, industrial, or agricultural use.
At key locations in water bodies largely unaffected by
man's activities.
For purposes of biological monitoring, a station will normally
encompass areas, rather than points, within a reach of river
or area of lake, reservoir, or estuary adequate to represent
a variety of habitats typically present in the body of water
being monitored. Unless there is a specific need to evaluate
the effects of a physical structure, it is advisable to avoid
areas that have been altered by a bridge, weir, within a
discharge plume, etc. Thus, biological sampling stations may
not always exactly coincide wi th water column or sediment
To the extent possible, all monitoring stations should be
loca ted in such a manner as to aid cause/effect analyses. Some
station requirements may be such that, with careful station
siting, one particular stations could meet the criteria of a
number of types of sta tions. Caution should be exercised,
however, to avoid compromising the worth of a station for the
sake of false economy. In general, the quality of a monitoring
program is not judged solely by the number of stations. A few
critically located stations may be extremely valuable, while
a large number of randomly selected stations may yield

meaningless data. Resource constraints will limit the total
number of stations.
The Rural Clean Water Program (RCWP) 'includes several examples
of NPS M&E strategies. Two project strategies are described here
to illustrate slightly different approaches utilized under one
overall program with common goals for all projects. In a simple
sense, two of the program goals are to document receiving water
quality improvements resulting from agricultural NPS control
efforts, and to document the water quality effects of specific
agricultural pollution control practices.
The Idaho RCWP project had as its major focus the control of
sediment from irrigation return flows (Martin, 1984, p.6). Two
sets of monitoring stations were utilized for (1) ambient and (2)
intensive monitoring (Figure VI-1). The following describes the
stations and their purposes (Martin, 1984, p. 10-11):
S-3 :
near mouth - integrates all pollution sources flowing
into Rock Creek and measures the pollutant load that
goes into the Snake River (RM 0.75). Water quality,
benthic macroinvertebrates and fisheries data being
at poleline Road
fisheries monitoring
(RM 3.75) .
a benthic invertebrate and
site as well as wa terquali ty
above Highway 93 - below the confluence of the high
agricultural priority drains and city of Twin Falls
urban runoff (RM 7.3). Water quality, benthic
macroinvertebrates and fisheries data being collected.
at Twelvemile above the influence of Twin Falls
urban area and the high priori ty drains (RM 13.5).
Wa ter qual i ty, ben thi c macroinvertebra tes, and
fisheries data being collected.
at 3500 East Road a benthic invertebrate
fisheries monitoring site only (RM 21.1).
near Rock Creek townsite - measures. the quality of the
natural surface water above the irrigation tract (RM
30.3). Water quality, benthic macroinvertebrates, and
fisheries data being collected.
Twin Falls Main
irrigation tract.
Canal source of wa ter for the
Water quality data collected only.
Intensive monitoring stations were placed on irrigation drains
to track changes in sediment load and associated pollutants as
close to their source and the solutions (BMPs) as possible. In
this way, changes in water quality due to the RCWP program could be
more easily and quickly detected. Nineteen stations were located
in six subbasins (Figure VI-I). Stations measure the source of


.. ,""5e:",

.... S7~::AM S7A71QNS

sea I e
2 )
? ~,

Figure VI-1. Map of the Rock Creek Rural Clean Water Program study
area, Twin Falls County, Idaho. (SOURCE: Martin, 1984)

water to the subbasins (7-1, 5-1, 4-1, 4-3, 2-1, and 1-1), the
input of the subbasins to Rock Creek (7-7, 7-4, 5-2, 4-2, 4-3, 2-2,
and 1-2), and key intermediate sites (7-2, 7-3, and 7-6).
Addi tional stations were added in other subbasins as they were
needed (2-3, 2-4, and 10-1).
The St. Albans Bay, Vermont RCWP project utilized a four-level
M&E program to meet three objectives (Vermont RCWP Coordinating
Committee, 1986, p.III-1):
To document changes in the water quali ty of specific
tributaries within the watershed resulting from
implementation of manure management practices.
To measure the changes in the amount of suspended sediment
and nutrients entering St. Albans Bay resul ting from
impl emen ta tion of wa ter qual i ty managemen t programs wi thin
the watershed.
To evaluate trends in the water quality of St. Albans Bay
and the surface waters within the St. Albans Bay watershed
during the period of the St. Albans Bay RCWP Wa tershed
Monitoring sites for all four levels of M&E are shown in Figure
VI-2. The Levell Bay Sampling is designed to determine long-term
water quality trends in St. Albans Bay over the life of the project
(Vermont RCWP Coordinating Committee, 1984, p. IV-1). The Level 2
Tributary Sampling is designed to determine the long-term water
quality trends for the major tributaries including the Bay and the
St. Albans City wastewater treatment plant (Vermont RCWP
Coordinating Committee, 1984, p. IV-1). The Level 3 monitoring is
directed toward evaluating the effect of best manure management
practices on the quality of surface runoff from individual fields,
while Level 4 is designed to supplement the Level 2 monitoring by
sampling additional tributaries to St. Albans Bay and to isolate
sub-units within the Level 2 subwatersheds (Vermont RCWP
Coordinating Committee, 1984, p. IV-3).
Additional monitoring efforts include meteorological
monitoring, biological monitoring, land use monitoring, wetland
sampling, bay and wetland sediment sampling, and a bay circulation
study. More about the St. Albans Bay monitoring plan will be
discussed under sampling frequencies and approaches.
These two examples should point out the similarities between
site location for NPS M&E and the traditional site locations
recommended by the National Water Monitoring Panel (USEPA, 1975).
Clearly, in order to locate stations effectively the researcher
Have clear, quantitative, M&E objectives.
Understand the watershed/water body to be monitored.


#. ~IYIL 2
..A.. ~IYIL 3
l::.. UYIL .
. "'CIP

Figure VI-2. St. Albans Bay watershed, Franklin County~ Vermont,
sampling locations. (SOURCE: Vermont RCWP Coordinating Committee,

Know something about the locations of and pollutant
transport from point and nonpoint sources.
Sample Size and Allocation
The issue of sample size is important from several
perspectives, including (1) statistical and/or modeling uses of the
monitoring data, (2) logistics of sample collection, and (3) cost.
For these reasons it is important to estimate early in an M&E
effort the number and frequency of samples required to meet M&E
objectives within budget constraints.
Simple Random Sampling
As discussed by Reckhow (1979, pp. 286-293), Cochran (1963)
determines the number of random samples required to achieve a
desired level of precision as:
n =
t2 . S2
(1 )
= number of samples
= Student's t value
s' = population variance estimate, and
= desired precision in units of parameter.
Reckhow concludes that "random sampling design is specified by the
variance estimate, the precision, and the sampling program cost (or
number of samples)."
To estimate the population variance,
Cochran's (1963) four information sources:
Existing information on the same population or a similar
Informed judgment, or an educated guess.
A two-step sample. Use the first-step sampling results to
estimate the needed factors, for best design, of the
second step. Use data from both steps to estimate the
final precision of the characteristic(s) sampled.
A "pilot study" on a "convenient" or "meaningful"
subsample. Use the results to estimate the needed
factors. Here the results of the pilot study generally
cannot be used in the calculation of the final precision,
because the pilot sample often is not
representative of the entire population to be sampled.

Stratified Random Sampling
For stratified random sampling, the equation is (Reckhow, 1979,
p. 290):
n. w. - (CV)x. - (x.) 
1 1  1  1 (2)
    - (x,) 
n Z::w. - (CV)x.  1 
 1  1   
total number of samples
number of samples in stratum i
(mean) of characteristic x in stratum i,
a weight reflecting the size (number of units, for
example) of stratum i, and
= coefficient of variation (standard deviation div-
ided by the mean) of characteristic x in stratum i.
Reckhow (1979, p. 291) reiterates Cochran's (1977, p. 98) rules for
determining the composition of a stratified random sampling design.
He states that a larger sample should be taken in a stratum if the
stratum is:
more variable
(CV) .
larger (w, x), and
less costly to sample.
Gaugush (1986, p. 196) presents a general equation for sample
allocation in a random sampling program. This equation takes into
account the size of the strata, the variance of the strata, and the
cost of sampling the strata to arrive at proportional allocations.
The equation can be simplified if the size, variance, and/or cost
are the same across strata. If strata are not needed the equation
reduces to Equation 1: The general equation is:
n. = n- (
N1 -a1/lc1
+ N2-a2/lc2 + ...
+ N - a /Ic
s s s
(3 )
= the number of strata
= the stratum number (i = 1, 2 ... s)
= the size of the ith stratum
= the standard deviation of the ith stratum
= the cost of sampling the ith stratum -
= the total number of samples to be allocated
= the number of samples allocated to the ith stratum

The reader is referred to Gaugush (1986, pp. 194-200) for further
discussion and illustration of this sample allocation formula.
Cochran (1977, p. 119-124) offers methods for determining
optimum sample allocation in cases where more than one item
(parameter) is being sampled. For example, initial survey results
may indicate that the optimum sample allocation for conductivity
measurements is different from that for total phosphorus. Cochran
(1977, p. 119-124) provides examples where optimal, compromise, and
proportional allocations are compared.
Cluster Sampling
Cochran (1977, p. 233-272) discusses in great detail single-
or one-stage cluster sampling for clusters of either equal or
unequal sizes. Cochran (1977, p. 234-237) provides equations for
determining the optimal population unit size using the relative
sizes of possible population units, the variance among the
population unit totals, and the relative cost of measuring one
population unit. He notes that many factors come into play when
determining optimal population size, including cost versus unit
5.4. Multi-stage Sampling
Gilbert (1987, p. 58-69) discusses and illustrates the use of
two-stage sampling for determining the mean and total in
environmental monitoring efforts. The author provides equations
for estimating the number of samples (primary units) and subsamples
for two conditions: (1) prim~ry units of equal size and (2) primary
units of unequal size.
Gilbert (1987, p. 71-87) shows how to use composite samples of
both equal- and unequal-sized units to estimate the mean and total
values for the target population. The author also provides
equations for calculating the number of composites and composite
subsamples needed.
Double Sampling
Gilbert (1987, p. 109-117) provides methods for estimating the
number of samples needed to determine the mean and total for the
target population. These methods address fixed cost, fixed
variance, and stratified double sampling. A case study is provided
to illustrate the use of the sample allocation equations.
5 . 6 .
Systematic Sampling
Gilbert (1987, p. 90-94) discusses systematic sampling along
a line (space or time) and over space. In sampling along a line,
the author notes that the starting point should be randomly
selected, and subsequent sampling points should be spaced at
regular intervals from the starting point. Procedures are
presented for selecting sample points from either a fixed sample
size or a fixed sample interval.

Gilbert (1984, p. 92) cautions that any periodic variation in
the target population should be known before establishing a
systematic sampling program. It is highly likely that sampling
intervals equal to or multiples of the target population's cycle of
variation will result in biased estimates of the population mean.
Cochran (1977, p. 218) states that systematic samples can be
designed to capitalize on a periodic structure if that structure
can be characterized sufficiently. A simple or stratified random
sample is recommended, however, in cases where the periodic
structure is not well known (Cochran, 1977, p. 218).
5 . 7 .
Sampling for Regression Analysis
According to Gaugush (1986, p. 210), the number of samples
required when time is used to create strata should reflect the
desired precision. If stratified random sampling is used, then
Equations 2 and 3 should be appropriate. If time is used as a
covariate, then the time cycle (e.g., annual) should be subdivided,
with sample replicates placed randomly within the subunits
(Gaugush, 1986, p. 210).
6 .
Sampling Frequency
Sherwani and Moreau (1975, p. 61) have stated that the desired
frequency of sampling is a function of several considerations,
the response time of the system
expected variability of the parameter
half-life and response time of constituents
seasonal fluctuation and random effects
representativeness under different conditions of flow
short-term pollution events,
the magnitude of response, and
variability of the inputs.
NOTE: While this guidance focuses on nonpoint source pollution, it
is important to note that effluent from wastewater treatment plants
can show considerable fluctuation in both quantity and quality
throughout the day and has a weekly cycle (Sherwani and Moreau,
1975, p. 62).
Sherwani and Moreau (1975, p. 67) state that for a given
confidence level and margin of error, the frequency of sampling is
proportional to the variance. Since the variance of water quality
parameters may differ considerably over time, the frequency
requirements of a monitoring program may vary depending on the time

of the year. Sampling frequency will need to be greater during
periods of greatest variance.
- One approach to determine sampling seasons is to plot variance
over time, dividing the year into periods of relatively constant
variance (Sherwani and Moreau, 1975, p. 68). Sampling frequency
requirements can then be determined for each period.
The authors calculate the longest acceptable sampling interval
using Equation 4 (Sherwani and Moreau, 1975, p. 73).
(4 )
(1/n1 + 1/n2)~

where t is Student's t value for the level of confidence desired
(d.f.=n -1), d is the specified precision (in parameter units if
normal ~istribution), n1 and n2 are the number of observations per
year, and S is the standard deviation of the larger number of
observations (n1)' To use this equation, data must already exist
for a sampling program with shorter sampling intervals than for the
desired program (i. e., the equation is useful for decreasing
sampling frequency from n1 to ~, but should not be used for
increasing sampling frequency). FOr example, daily sampling would
result in 365 samples (n~) with a corresponding standard deviation
(S) for the parameter or interest. The minimum number of samples
per year (i.e., the longest sampling interval) is then calculated
as n2 for a desired confidence (t) and precision (d) with Equation
S .
The following is taken from Sherwani and Moreau (1975, p. 69)
to illustrate the effect .of parameter selection on sampling
The sampling interval of a constituent should be related to
the temporal behavior of the constituent that is being measured.
Here, the dichotomy between a conservative and non-conservative
substance is qui te useful. The conservative substances have
relatively long half-lives in the sense that they are not degraded
or their rates of uptake by organisms are low. They are
transported relatively unchanged in form over long distances.
Problems caused by these substances in a natural aquatic system are
generally those tha t resul t from build-up over rela ti vely long
periods of time. Their instantaneous concentrations are less
important than their long-term average concentrations. For
conservative substances, monitoring can be carried out over
relatively coarse intervals of time. For some constituents annual
averages may be sufficient; for others, seasonal or monthly
averages may be necessary to characterize the mass flux through the
Non-conservative substances are characterized by relatively
short half -li ves. The adverse effects of these substances are

realized over short intervals of time and space. The temporal
coverage can be limited to critical periods. Mean annual
concentrations of these substances are of little value in water
quality management. The half-lives of non-conservative
constituents may be small relative to the time of travel through
the basin, especially under low-flow conditions.
Sherwani and Moreau (1975, p. 71) discuss the serial
correlation between parameter values taken over time and warn
against wasting monitoring funds on too frequent sample collection.
However, they also note that a sufficient number of samples is
needed "to describe adequately the significant information in the
high frequencies."
Noting that most water quality parameters exhibit a periodic
structure, Sherwani and Moreau (1975, p. 71) state that "the least
favorable sampling interval is equal to the period or an integral
mul tiple of a period." They say that the best case occurs when the
sampling interval is an odd multiple of half-period. As an example
for a weekly cycle, they recommend that sampling is staggered such
that every week day is equally represented.
In both random sampling and stratified random sampling Reckhow
(1979, p. 288) points out that systematic sampling is acceptable
only if "there is no bias introduced by incomplete design, and if
there is no periodic variation in the characteristic measured." He
goes on to say that such systematic sampling is even better if the
starting point is based on a randomly selected day, site, and/or
depth, with systematic sampling from then on.
When time is used as a stratification variable, the samples
within the time strata should be randomly allocated, with the
number of samples reflecting the desired precision (Gaugush, 1986,
p. 210). If time is used as a covariate, the annual cycle should
be subdivided, with sample replicates randomly placed within the
subunits. Gaugush (1986, p. 210) reports that "monthly sampling is
usually adequate to detect the annual pattern of changes with
time." More frequent sampling would be required for the detection
of short-lived phenomena.
Finally, two-stage sampling incorporates systematic sampling
within a randomly-selected subset of the population primary units.
For example, if the target population is the average annual
pollutant concentration in a stream, then the primary units could
be daily average concentrations (n=365). A subset of these daily
concentrations (e.g., n=24) could be selected at random for further
systematic sampling of hourly concentrations (four hourly
composites per day). Thus, 96 hourly composite samples would be
taken for calculation of the population mean and variance. Four
systematic, hourly samples would be taken on each of 24 different
days, with the hour for the first sample determined randomly,
followed by three more hourly samples taken every sixth hour. For
example, if hour six (6:00 AM) was selected randomly as-the first
hour, then hourly composite samples would also be taken at noon,
6:00 PM, and midnight.

Ground Water Monitoring
Ground water monitoring and evaluation is addressed in a
peripheral manner in this NPS M&E guidance. Other documents
address ground water resources, subsurface sampling, and ground
water data analysis in much greater detail (USGS, 1980; Scalf et
al., 1981; USEPA, 1987a; Everett, 1980), and should be reviewed by
those investigating ground water contamination from NPS. The
following are general comments taken from these very useful
Data Needs
As for surface water, the data to be collected is determined
by the objectives of the study. It is recommended that II [b]efore
the field is ever visited, a thorough search should be made of
files and the literature for pertinent information II (USEPA, 1987a,
p. 22). The types of information to be collected include: soil,
geologic, topographic, county, and state maps; geologic cross
sections; aerial photographs; satellite imagery; location of
pumping centers and discharge rates; well logs; climatological and
stream discharge records; chemical data; and the locations of
potential sources of ground water contamination.
Most of the above data sources are the same as those discussed
for surface waters, however, the applications of the data may be
quite different. For example, soil information can be used lito
evaluate the potential for movement of organic and inorganic
compounds through the unsaturated zone II (USEPA, 1987a, p. 23).
Aerial photographs and satellite imagery are helpful in locating
potential drilling sites and indicating the presence of faults or
Well logging is the description of collected samples and
factors involved in drilling the sampling wells (USGS, 1980, p. 2-
80) . The types of well logs include geologic, lithologic,
driller's, construction, drilling rate, and fluid loss. These logs
are essential in ground water investigations, providing information
on types and characteristics of rocks in the subsurface, drilling
conditions, well construction details, and water levels (USEPA,
1987a, p. 23).
The USEPA (1987a, p. 109) recommends candidate parameters to
be measured for both detective and assessment monitoring programs.
Scalf et al., (1981, p. 87) provide a summary of sampling methods
and well construction considerations, keyed to the nature of the
monitored pollutant. As is the case for surface water monitoring,
the parameter lists for ground water monitoring programs should be
tailored to match the objectives of the M&E effort.
Site Location
Ground water research has shown that II it is impossible to
prescribe standard locations for sampling points that would be
applicable to all sitesll (Scalf et al., 1981, p. 7). Furthermore,

" [t] he
of the
110) .
placement and number of wells will depend on the complexity
hydrologic setting and the degree of spatial and temporal
needed to meet the goals of the program" (USEPA, 1987a, p.
The importance of investigating existing data sources cannot
be overemphasized with regard to site location. For example,
water-level data can be used to develop contours for use in
selecting sampling sites (Scalf et al., 1981, p. 6). Background
sampling is recommended to help situate wells and/or define
sampling points. In addition, when sampling to track pollutant
plumes, "it is extremely important to locate subsequent monitoring
wells one at a time, sample, and base succeeding well locations on
results of previous. sampling" (Scalf et al., 1981, p. 11).
While it is sometimes possible to consider surface water
monitoring to involve only two dimensions, it is always important
to consider three dimensions when locating ground water monitoring
sites. Four general categories reflecting the depth of monitoring
are the land surface, the top soil, the vadose zone, and the zone
of saturation (Everett, 1980, p. 130). Considerations made in
sampling from each of these depth categories are discussed in
detail in several documents (Everett, 1980i USEPA, 1987ai Scalf et
al., 1981i USGS, 1980).
3 .
Sampling Frequency
It is generally recommended that monthly, seasonal, or annual
sampling is sufficient for most ground water monitoring programs.
However, more frequent sampling may be required in very shallow
aquifers or under conditions of rapidly changing water quality
(USGS, 1980, p. 2-88).
It is important to note that irrigation, precipitation,
drainage control devices, and other natural and artificial events
may influence the water level and/or ground water quality in such
a way that storm-event, weekly, or some other unique sampling
frequency may be needed to track ground water quality adequately.
Example Monitoring Programs
Below are three examples of nonpoint source monitoring
programs which are considered by many NPS experts to be good
programs for the objectives they address. These examples should
not be copied indiscriminately for use in every other similar
watershed, but should only be used as references for designing good
monitoring programs for similar situations. Furthermore, cost will
be a maj or factor in determining the scope and intensity of a
monitoring program, so these examples should be put into a cost
perspective. The St. Albans Bay, Vermont monitoring and evaluation
program was funded at $1.6 million over eleven years (1980-1990),
a price well beyond reach for many watersheds of similar size
(33,344 acres) (Smolen et al., 1986, p. 35).

St. Albans Bay, Vermont RCWP Project
The monitoring and evaluation objectives for St. Albans Bay
have already been given under Section III.C.2.a. The complete
monitoring strategy is given below (Vermont RCWP Coordinating
Committee, 1984, p. IV-l to IV-II) .
Site Locations
The moni toring strategy for the St. Albans Bay Watershed
includes long-term water quality monitoring, related long-term
monitoring, and short-term intensive studies:
Long-Term Water Quality Monitoring
Bay Sampling
Levell monitoring is designed to determine long-term water
quality trends in St. Albans Bay over the life of the project.
Four sampling locations are located in St. Albans Bay (Figure VI-
2) :
Station 11:
Station 12:
Station 13:
Station 14:
Outer Bay
Inner Bay
Off Bridge
Level 2:
Trend Stations
Level 2 moni toring is designed to determine the long- term
water quality trends for the major tributaries including the Bay
and the St. Albans City wastewater treatment plant. Six continuous
monitoring stations are located throughout the watershed (Figure
VI - 2) :
Station 21:
Station 22:
Station 23:
Station 24:
Station 25:
Station 26:
Jewett Brook
Stevens Brook
Rugg Brook
Mill River
St. Albans Wastewater
Stevens Wetland
Treatment Plant
Level 3:
Mobile Monitoring
Level 3 monitoring is designed to evaluate the effect of best
manure management practices on the quality of surface runoff from
individual fields. Two continuous monitoring stations are located
in the headwaters of the Jewett Brook subwatershed (Figure VI-2):
Station 31: Larose ditch - below site
Station 32: Larose ditch - above site

Level 4:.
Random Sampling
Level 4 moni toring is designed to supplement the Level 2
monitoring by sampling addi tional tributaries to St. Albans Bay and
to isolate sub-units within the Level 2 subwatersheds. Randomly
timed grab samples are collected at four locations (Figure VI-2):
Station 41:
Station 42:
Station 43:
Station 44:
Jewett Brook
Stevens Brook
Guayland Brook
Mill River
Related Long-Term Monitoring
Meteoroloqical Monitorinq
Precipitation and other climatological data are being
collected in the St. Albans Bay Watershed at four locations (Figure
VI-2) :
P-3 :
St. Albans Radio Station
Dunsmore Farm
Franklin Ford Tractor
LaRose Farm
Bioloqical Monitorinq
The monitoring of biological characteristics is being
conducted in St. Albans Bay and in Bay tributaries. Bay biological
monitoring is conducted at the Levell stations (Figure VI-2).
Tributary biological monitoring is conducted at five locations
(Figure VI-2):
21: Jewett Brook
22: Rugg Brook
23: Mill River
22A: Stevens Brook
22B: Stevens Brook
above STP outfall
below STP outfall
Land Use Monitorinq
A cooperative program has been developed to collect land use
and agricultural activity information from each farm in the
watershed. Both baseline information and daily field log data are
collected. These data are then input to a computerized Geographic
Information System (GIS).
Short-Term Intensive Studies
Wetland Influences
Stevens Brook wetland has been sampled to determine the
effects of the wetland on water entering St. Albans Bay from point
and nonpoin t sources. Fifteen sampling s ta tions are loca ted wi thin

the wetland along the brook channels. Station 26 serves as a
continuous monitoring of the wetland outlet.
Bav and Wetland Sediments
Fifteen sampling stations have been located wi thin the Bay and
contiguous wetland to determine the chemical and physical
properties of the sediments. Six of these stations have been used
for wi thin-year temporal studies. Sediment phosphorus release
studies have also been conducted at these sites.
Bav Circulation
Wind, water current, and concentration data have been
collected in St. Albans Bay to determine the effect of bay
circulation on water quali ty. A model has been developed to
predict phosphorus concentrations in the Bay under different
loading rates and meteorological conditions.
Parameters Monitored
Long-Term Water Quality Monitoring
Table VI-2 lists the parameters monitored for each level of
the long-term monitoring.
Related Long-Term Monitoring
Table VI-3 lists the parameters monitored for each of the
related long-term monitoring efforts.
Short-Term Intensive Studies
Table VI-4 lists the parameters monitored for each of the
short-term studies.
Data Collection Schedule
Table VI-5 summarizes the frequency and type of sample
collected for the long-term water quality monitoring. However, as
indicated in Table VI-6, not all stations are operational each year
of the project. .
Sampling and Analytic Techniques
The sampling years for each monitoring level are summarized in
Table VI-6. The methods used to determine each water quality
parameter are given in Table VI-7.
Bellevue, Washington NURP Project
The Nationwide Urban Runoff Program (NURP) was designed in
such a way that each project met minimum monitoring requirements to
support national analyses. Thus, the monitoring programs were very
similar for all NURP projects. The Bellevue, Washington monitoring

Table VI-2. Long-Term Monitored Parameters for Each Level in the
St. Albans Bay Watershed.
Levell - Bay Monitorinq
Total Suspended Solids
Volatile Suspended Solids
Total Phosphorus
Total Kjeldahl Nitrogen
Nitrite + Nitrate - Nitrogen
Level 2 - Subwatershed Trend Stations
Total Suspended Solids
Volatile Suspended Solids
Total Phosphorus
Total Kjeldahl Nitrogen
Nitrite + Nitrate - Nitrogen
Chlorophyll a
Fecal Coliform
Fecal Streptoccoccus
Dissolved Oxygen
Secchi Disc
Fecal Coliform
Fecal Streptococcus
Dissolved Oxygen
Level 3 - Mobile/Field Monitorinq Stations
Total Suspended Solids
Volatile Suspended Solids
Total Phosphorus
Level 4 - Random Grab Samplinq
Total Suspended Solids
Volatile Suspended Solids
Total Phosphorus-
Total Kjeldahl Nitrogen
Nitrite + Nitrate - Nitrogen
Total Kjeldahl Nitrogen
Nitrite + Nitrate - Nitrogen
Fecal Coliform
Fecal Streptococcus
Dissolved Oxygen

Gilbert, R.O. 1987. Statistical Methods for Environmental Pollution
Monitoring. Van Nostrand Reinhold Company, New York, 320 pp.
Snedecor, G.W. and W.G. Cochran. 1980. Statistical Methods, 7th ed.
The Iowa State University Press, Ames, Iowa, 507 pp.
Ward, R.C., J.C. Loftis, and G.B. McBride. 1990. Design of Water
Quality Monitoring Systems. Van Nostrand Reinhold Company, New
York, 231 pp.
Available Software
Many statistical methods have been computerized in easy-to-use
software that is available for use on personal computers.
Inclusion or exclusion in this section does not imply an
endorsement or lack thereof by the U.S. Environmental Protection
Agency. Specialized software includes SAS, Statistica, and
Statgraphics that cover a wide range of statistical and graphical
support. Numerous spreadsheets, data base management packages, and
other graphics software can also be used to perform many of the,
needed analyses. In addition, the following programs, written
specifically for environmental analyses, are also available:
SCOUT: A Data Analysis Program, EPA, NTIS Order Number PB93-505303.
Aroner, Environmental Engineer, P.O. Box 18149, Portland, OR 97218.
WQSTAT, Jim C. Loftis, Department of Agricultural and Chemical
Engineering, Colorado State University, Fort Collins, CO 80524.
Exploratory Analysis
The first step of data analysis is exploratory. The purpose
of this step is to perform a preliminary assessment of the data and
"develop a feeling" for the data. This section describes
approaches for data inspection, data stratification, data
normalization, and tests of assumptions. If the data analyst is
familiar with the data set, data inspection and stratification is
fairly straightforward and usually intuitive. Data normalization
involves the process of transforming data into a usable form and
assumption testing includes evaluating hypothesis about the
statistical characteristics of the data. The last portion of this
section discusses probability distributions in detail and is
considered optional reading.
Data Inspection
Researchers generally agree that data inspection is necessary
before data analyses are performed on a data set (Gaugush, 1986;
Spooner et al., 1986, p. 3). Gaugush (1986) recommends graphical
displays as a means for inspecting data as follows:
It is good practice in statistical analysis to begin with a
study involving graphical displays of the data. That is,

The other type of trend commonly tested for is monotonic or
gradual changes at a single station. In this case, observations
are typically taken on a regular basis (e.g., weekly, monthly,
quarterly) . The Seasonal Kendall test is recommended for
hypothesis testing.
Determining only the existence of a trend is sometimes not
sufficient for decision makers. It is also necessary to estimate
the magnitude of the trend. The Seasonal Hodges-Lehman estimator
is recommended for estimating the trend magnitude when comparing
two or more random samples. The Seasonal Kendall slope estimator
is recommended when estimating the magnitude of monotonic trends.
Extreme Values
The most effective means for summarizing extreme values is to
compute the proportion (or frequency) of observations exceeding
some threshold value. This can be accomplished by plotting a time
series with the threshold value or dividing the number of
excursions by the total number of observations. A common analysis
would be to compare the proportion of excursions from one year or
station to the proportion of excursions from another year or
station. A test for equality of proportions can be performed or
the confidence limits on proportions can be compared.
The evaluation of extreme values related to nonpoint source
moni toring and other ran- induced impacts (e. g., combined sewer
overf lows (CSOs)) may require greater care. For example, when
evaluating the number of overflows in a year or comparing storms,
it is important to make sure that the data are comparable. This
may result in selecting portions of data.sets for analysis. It is
also important to make sure that length of record is appropriate.
Recommended Reading List and Available Software
Recommended Reading List
Over the last 20 years, considerable effort by researchers and
practitioners has gone into the development of improved statistical
methods for analyzing environmental data. Nonetheless, there is
probably no single reference that fully covers all of the issues
that the data analyst must consider when selecting methods for
analyzing environmental data. The following list provides a
summary of selected references that provide more details about a
wider variety of issues and are strongly recommended for those who
need a more in-depth discussion than can be provided in this
chapter. .
Chambers, J.M., W.S. Cleveland, B. Kleiner, and P.A. Tukey. 1983~
Graphical Methods for Data Analysis. Duxbury Press, Boston,
395 pp.
Conover, W.J. 1980. Practical Nonparametric Statistics,
Wile, New York, 493 pp.
2nd ed.

Changing Conditions
One of the most frequently asked questions related to the
evaluation of monitoring is whether conditions have improved or
degraded. The approaches used to select monitoring station
locations range from random sampling to fixed stations (see Section
VI.A.3). Both types of monitoring designs can be used to evaluate
trends. In random sampling, each location along a st'ream has an
equal probability of being selected and is common to intensive
surveys. Random sampling (and variations) is generally most
appropriate when estimating means and totals if there is a low
likelihood of major patterns of contamination or trends. Fixed
station sampling is commonly based on additional knowledge about
where impairments are likely to be or is based on professional
In the case of random sampling, data are typically collected
in a "before and after," "upstream/downstream," or "reference and
test site" setting. The resulting data usually come as two or more
sets of random samples. In the case of upstream/downstream
sampling, the upstream sampling locations typically represent a
reference or background condition, whereas the downstream locations
typically represent impaired (targeted) conditions. The goal might
be to determine whether there is a significant difference in
phosphorus concentrations between the background and impaired
(targeted) areas. If so, it might be possible to infer that
significant phosphorous loadings occurred between the two
locations. Similarly, when performing a biological assessment the
goal would be to determine whether there is a significant
difference in the biological metric between the reference and test
(targeted) sites.
In either case, at least two random samples have been
collected. The Mann-Whitney test is recommended for comparing two
random samples when the distribution of the data is unknown or
sufficiently nonnormal. The Student's t test. can be used when the
data are normally distributed. (Several researchers have
demonstrated that the Student's t test can be successfully applied
when the data are not normally distributed and might be more
powerful under selected circumstances.)
The Kruskal-Wallis test (an extension of the Mann-Whitney
test) is recommended for when there are three or more random
samples. For example, numerous biological surveys are initiated by
collecting data during the spring, summer, and fall. The
hypothesis might be to determine whether there is a significant
difference in key biological indexes between the different seasons
(index periods) .
A special case of random sampling is when the random samples
from one population (e.g., the upstream location) are paired with
random samples from the second population (e.g., the downstream
location) . This situation is referred to as paired or matched
sampling. The Wilcoxon signed rank test is recommended for paired

Table VIII-2. Methods for Routine Data Analysis
(adapted from Ward et al., 1990).

METHOD (P = parametric, N = nonparametric)

Box-and whiskers
plots (B.1)
Time series
plots (B.1)
Annual box-and-
whiskers plots
(B. 1)
Time series
plots (B.1)
Time series
plots with
excursion limit
(P) Sample mean (or
geometric mean) and
sample standard
deviation (or geometric
standard deviation) with
confidence limits (C.1,

(N) Sample median and
interquartile range with
confidence limits (C.1,

(N) Seasonal Hodges-
Lehman estimator
(P) Linear,regression
(D.3. 4)

(N) Seasonal Kendall
slope estimator (D.3.4)
(P,N) Proportion
(frequency) of
Excursions (E.3)
Two random samples

(P) Student's t test

(N) Mann-Whitney test
Matched samples

(P) Paired t test (D.2.3.1)

(N) Wilcoxon signed rank
test (D.2.1.2)

Three or more random
(P) ANOVA (D.2.4.1)

(N) Kruskal-Wallis test
(P) t-test for significance
of slope (D.3.4)

(N) Seasonal Kendall test
(P) Test for equality of
proportions (E.3)

(N) Confidence limits on
proportions (E.3)

(N) Tolerance intervals
(E. 3)

Site Selection
Sampling Frequency Determination
Recommendations for Selecting Statistical Methods
Information goal assessment typically involves the evaluation
of the average, changing, and extreme conditions of environmental
variables (Ward and Loftis, 1986). This section provides
recommendations for selecting statistical methods that can be
applied on a routine basis (Table VIII-2, adapted from Ward et al.,
1990) . In some instances, more appropriate methods might be
available depending on the specific information needs. One
decision facing many data analysts is the selection of parametric
versus nonparametric methods. For routine analyses, nonparametric
methods are recommended. Nonparametric tests also have underlying
assumptions and violation of these assumptions can lead to
incorrect conclusions about the collected data.
Average Conditions
What is the quality of water? What were the phosphorus
loadings from the last storm? To answer these types of questions
the data analyst is typically faced with describing the average
conditions. Measures of central tendency and spread are the most
common measures of average conditions. As suggested in Section
VIII.A.3, using the mean, geometric mean, or median is recommended
for summarizing the central tendency and the standard deviation,
geometric standard deviation, and interquartile range are
recommended measures of spread or dispersion. Since these
parameters are only point estimates, the uncertainty should also be
indicated by reporting parameter estimates with confidence limits.
The selection of the mean (and standard deviation) versus the
median (and interquartile range) is sometimes a subjective
decision. If the data are symmetrically distributed, either set of
parameters is acceptable. Data that are not symmetrically
distributed (skewed) should typically be summarized with the median
and interquartile range. The geometric mean and standard deviation
are most appropriate when the data typically range over a couple
orders of magnitude. The presentation of geometric means is also
called for in some regulations such as those for coliform bacteria.
In many cases, simple graphical displays such as time series or
box-and-whiskers plots will convey more information than tables of
numerical results. .

monitoring program. How quickly must information be presented to
information users? To what kind of information and how much
information do the decision makers respond favorably? At a
minimum, the data analyst should prepare example report formats to
be approved by the decision makers, keeping in mind that "a picture
is worth a thousand words." In all cases, the goal should be to
present clear and accurate information that is not subj ect to
misinterpretation. Ward et al. (1990) present an example outline
of what might be considered in an expectations report (the data
analyst should modify this outline to suit:
Evolution of Water Quality Management Program
Geographical/Hydrological Setting
Water Quality Problems
Water Quality Laws
Management Program Structure
Management Procedures
2. '
Information "Expected" by Management Program
Implications of the Law Establishing the Program
Legal Goals
Management Powers and Functions
Directly State Monitoring Requirements
Information Needs of Management Operations
Water Quality Criteria
Water Quality Standards
Enforcemen t
Construction Loans
,Water Quality Assessment
Ability of Monitoring Systems
Narrative Information
Numerical Information-Data
Graphical Information
Statistical Information
Average Conditions
Changing Conditions
Extreme Conditions
Water Quality Indices
Wa ter
Suggested Information Expectations for
Management Information Goal(s)
Definition of water Quality
Monitoring System Goal(s)
Information Product of Monitoring
Monitoring System
Resulting Monitoring Network Design Criteria
Variable Selection

Central   Sample mean         P C .1.1
tendency Sample median      N C.1.1
    Sample geometric mean    P C.1.1
    Box-and-whiskers plot    G B.1
Spread   Sample standard deviation   P C.1. 2
    Range, maximum-minimum    P,N C.1. 2
    Interquartile range     N C.1. 2
    Box-and-whiskers plot    G B.1
Distribution Histogram         G B.1
shape   Percentiles         N C.2.3
    Sample skewness      P C.1. 3
    Sample kurtosis      P C.1. 4
    Chi-squared test      P B.5.2.3
    Kolmogorov-Smirnov test    N B.4.1.4
    Shapiro-Wilk test      N B.4.1.3
Seasonal Time series  plots      G B.1
variation Seas. box-and-whiskers plot   G B.1
    ANOVA          P D.2.4.1
    Kruskal-Wallis test     N D.2.4.2
Serial   Sample autocorrelation    P B.4.4
correlation Spearman's rho      N B.4.4
Key to Method Type:           
P = Parametric N = Nonparametric G = Graphical
Table VIII-l. Methods for characterizing
data (adapted from Ward et al., 1990).
6 .
Develop consensus as to an agreeable formulation of
information expeGtations and related monitoring system design
This process is typically performed as an iterative process
that involves the technical staff and the decision makers who
developed the monitoring objectives. To develop an information
expectation report, the data analyst may need to have formal
meetings, develop questionnaires, and conduct interviews to learn
what the managers need. In some cases this iterative process might
require modifying or redesigning the monitoring program. The data
analyst should remember that complete consensus might not be
When developing. an information expectation report,
presentation of results should be selected depending on
audience reviewing the information and the objectives of

they often result in less reliable observations and less
information for a given data set. The presence of data limitations
also increases the' complexity in applying standard statistical
methods (and using commercially available software). Section
VIII.G describes data record limitations in more detail and
provides suggestions for performing routine data analyses that
minimize the impact of such limitations.
Common statistical characteristics include location (central
tendency), variability (scale or spread), distribution shape,
seasonality, and serial correlation. While these characteristics
do not cause computational problems, they can violate the
underlying assumptions of statistical methods. "All statistical
methods which produce probability statements, such as confidence
intervals, are based on assumptions about the data used in the
analysis" (Ward et al., 1990). Common assumptions include
distribution shape, seasonality, correlation, and applicability of
a linear model. Table VIII-1 presents a variety of methods for
characterizing data that are helpful for selecting appropriate
statistical methods and providing a general understanding of water
quality data. Sections VIILB and VIILC provide a detailed
discussion of each data characteristic and method.
Communicating Results
Ward et al. (1990) point out that "one of the most important
and difficult tasks [is to identify] what information is to be
produced by the monitoring effort." It is particularly critical to
ensure that policy makers and other stakeholders have bought into
the type of information that a monitoring program can produce and
that realistic monitoring program expectations are developed. Ward
et al. (1990) identify key steps to ensure that realistic
expectations are placed on the monitoring program and the
associated data analysis:
Perform a thorough review of the legal basis for the
management effort and define the resulting "implications" to
Review administrative structure and procedures developed from
the law in order to define information expectations of
management staff.
Reviewability of monitoring program to supply information.
Present information expectation report to all users of the

statistical inference: estimation
(Remington and Schork, 1970).
. In estimation, summary statistics are computed from sample
information to make a reasonable conclusion regarding the value of
an unknown parameter. For example, the sample mean and standard
deviation can be used to estimate a range within which it is likely
that the population mean falls. This sort of estimation can be
useful in developing baseline information, developing or verifying
models, estimating the NPS contributions in a total maximum daily
load (TMDL), or determining the load of a single NPS runoff event.
Means, percentages, proportions, and variations are all parameters
that can be estimated (Freund, 1973). This chapter addresses many
of these parameters, and includes numerous examples.
In the broad arena of environmental management and protection,
it is more the rule than the exception that monitoring and
evaluation are performed for the purpose of making decisions
regarding remedial and/or preventive actions. For example,
confidence intervals for the mean concentration of a pollutant
before and after an NPS control program might tell very little
about the success of the program. Granted, if the means were so
different that the confidence intervals had no overlap it would be
reasonable to state that a change has occurred (note that a cause
and effect relationship can not be established with water quality
data alone). However, if the confidence intervals overlapped, a
very likely scenario, what could be said about changes in water
quality? Statistical tests would need to be performed which
establish rules for deciding whether a change occurred and whether
this change is significant. This type of statistical analysis
falls under the general category of hypothesis testing.
Characteristics of Environmental Data
The statistical methods selected must match the type of
environme~tal data collected and the decisions to be made.
Although summarizing the mean annual dissolved oxygen concentration
along an impaired stream might provide an indication of habitat
quality, evaluating the 10m or 15m percentile during summer months
over the same time period might have a greater impact on subsequent
management decisions. Environmental managers and data analysts
must collectively determine which statistical methods will result
in the most useful information for decision makers. As a result,
any data analysis protocol should include a suite of techniques to
meet the monitoring and evaluation objectives.
The selection of statistical methods is further complicated by
the presence of data attributes (Harcum, 19~0). Two main types of
attributes are commonly found in environmental monitoring: data
record limitations and statistical characteristics. Common data
record limitations include missing values, changing sampling
frequencies over time, different numbers of samples during
different sampling periods, measurement uncertainty, censored data
(e.g., "less-thans"), small sample sizes, and outliers. Data
limitations are, for the most part, human-induced attributes, and.

This chapter provides detailed information on the statistical
analysis of environmental monitoring data. The first section of
this chapter is intended for both the manager and data analyst.
The goal of this section is to acquaint the reader with key
concepts and issues related to data analysis. This section also
provides recommendations for selecting statistical procedures for
routine data analysis and can be used to guide the reader in
selecting additional portions of the chapter for more detailed
The organization of the remainder of this chapter follows the
normal progression of a typical statistical analysis: exploratory
analysis, summary statistics, trend testing, extreme events, and
advanced procedures. The final section of this chapter has been
specifically designed to address special issues related to
environmental monitoring such as how to treat missing values,
outliers, and censored data (e.g., "less-thans").
Purpose of Data Analysis
Data analysis begins at the monitoring program design phase.
Those responsible for monitoring should specifically identify the
reasons for monitoring and the methods to be used for analyzing the
collected data. Preliminary assessment of the specific reasons for
monitoring (i.e., what will the project leaders try to say based on
the data collected?) is critical to the success of any monitoring
and evaluation program. Chapter II provides an overview of
commonly encountered monitoring objectives.
Once goals and objectives have been clearly established, data
analysis approaches can be explored. Usually, monitoring data by
themselves do not provide the necessary information to support
decision making. This chapter provides guidance for selecting and
applying statistical methods. By selecting and applying suitable
methods, the data analyst responsible for evaluating the data can
prevent the "data rich-information poor syndrome" described by Ward
et al. (1986). .
Estimation and Hypothesis Testing
Ponce (1980b, p. 6) states that monitoring objectives "should
be specific statements of measurable results to be achieved within
a stated time period." He notes that monitoring obj ecti ves "should
be specific enough so that the [data analyst] can convert them into
statistical hypotheses which can be tested with the data obtained
from the water quality monitoring program." MacDonald et af.
(1991) state that "statistics [provide] the scientific basis and
procedures for studying numerical data and making inferences about
a population based on a sample of that population (Mendenhall,
1971; Sokal and Rohlf, 1981)." There are two major types of


Table VII-JOe. Selected biomonitoring program components, Vermont Department of Environmental
Conservation (Vermont DEC). [Contact: Steve Fiske, 802-244-4520]
Region of State Entire state; Entire state; Entire state 
 hiQh gradient low gradient  
Site Selection riffles woody debris representative of 
  macrophytes reach; mix of riffle, 
  boulders run, pool 
Sample Gear Rectangular kick net Rectangular kick net electro-shocking 
 18" x 8" (460,200 mml 18" x 8" (460,200 mm)  
 500 ,um mesh 500 ,um mesh  
 2 min timed 2 min sample; all substrate 1-3 upstream passes
Sampling Method composite; 30 see in ea of 2 materials are hand into blocknet or vert 
 points in slow area; 2 points in scrubbed drop instream 
 fast area   
 preserve in field; subsample preserve in field total count 
Sub-sampling and gridded tray 1/4 sample and min subsample gridded tray  
Enumeration 300 animals (technique allows density  
  estimate for site)  
Taxonomic Level specified in protocols; family- protocols list taxonomic species 
genus-species, depending on level and key to be used  
 all samples archived; replicate all samples archived; same person 
 samples always collected; two replicate samples always conducts collection 
QA Procedures people check pick; two people collected; two people and taxonomy 
 trained in each taxonomic order check pick; two people  
  trained in each taxonomic  
 includes substrate composition, includes substrate qualitative or ,
 embeddedness, periphyton composition, quantitative transect 
Habitat cover type, canopy cover, embedded ness,  method; depth, 
Assessment immediate riparian zone info periphyton cover type, velocity, substrate 
 ave. stream velocity, depth canopy cover, immediate  
  riparian zone info ave.  
  stream velocity, depth  
 also record temperature, pH,  have modified the 181
 alkalinity, cond and  to fit Vermont's 
 characterization of site,  wadable streams 
Comments elevation, DO; also will be   
looking at stream low flow   
 characteristics and surficial and   
 bedrock geology and land use   
 cover to help differentiate sites   
 as "ecotype"; set biocriteria for   
 individual metrics   

Table VII-lOco Selected biomonitoring program components. Montana Department of Health and
Environmental Sciences (Montana DHES). [Contact: Steve Trallis/Bob Bukantis. 406-444-2406]

ReQion 01 State entire
Site Selection riffles
Sample Gear D-frame (12") net
SamplinQ Method travellinq kick across riffles 1-2 diaqonal collections (time and distance recorded)
Subsampling and 300-organism subsample in laboratory
Taxonomic Level qenus/species
QA Procedures replication on selected sites and proiects
Habitat Assessment follows RSP habitat assessment approach
Comments lab processinq done by outside contractors
Table VII-lOd. Selected biomoniroring program components. North Dakota Department of
Environmental Health (North Dakota DEH). [Contact: Mike Ell, 701-221-5214]
ReQion 01 State not developed as of current date Red River
Site Selection  25 sites to date; randomized selection;
 but dictated by access loqistics
Sample Gear  electrofishing; shore-based longline
Sampling Method  minimum of 100 meters; 20 times river
  width on wide rivers
Subsampling and  not applicable
Taxonomic Level  lowest positive taxon
QA Procedures  10 percent repeat sampling
Habitat Assessment  based on RSPs
Comments planned to be started next year in development

Table VII-lOb. Selected biomonitoring program components. Florida Department of Environmental
Protection (Florida DEP). [Contact: Russ Frydenborg, 904-487-2245]
 Presence or absence of major productive habitats at each sampling location is
 established during preliminary reconnaissance. Habitats include: riffles, snags,
Habitat Selection aquatic vegetation, leaf packs, undercut banks/root systems, leaf mat, rocky outcrops, 
 muck/silt, sand. Major habitats sampled equally; Group of minor habitats treated as a
 sinale major habitat.
Sample Gearl Standard 0 frame dip net (0.3 meter width 600 micron mesh), wide mouth jars,
Preservative formalin.
Sampling Method 20 jab dip net sample, composite sample across habitats. Individual jabs are
approximatelv 0.5 m makina a total comoosite of 3 m2.
Subsampling and Entire sample in gridded pan (5 X 3 cm grids), randomly select grids (1n2 of sample),
Enumeration remove contents,. sort into taxonomic groups, continue until a minimum of 100
oraanism are counted: a arid's entire contents must be sorted.
Taxonomic level Lowest taxonomic level (aenus or soeciesL
 Replicate sampling for 10% of samples collected on an annual basis have not been
QA Procedures implemented but are planned. Resorting of 10% of samples. Field crew undergo
 periodic trainina.
Habitat Assessment Field data sheet, 7 visually-estimated habitat parameters, weighted equally.
Physical/Chemical characterization field data'sheet
 Stream classification factors for establishing reference conditions based on Ecoregion
 and subecoregion. Site selection factors: Availability of least impaired and reference
Comments sites, specific monitoring issues, accessibility and safety, compatibility of habitat.
 Standard operating procedures and report describing state-wide non point source
 proqram preoared bv Florida DEP and suooort contractors.

Table VII-lOa. Selected biomonitoring program components, Delaware Department of Natural
Resources and Environmental Conservation (DNREC). [Contact: John Maxted, 302-739-4590]

 Stable habitats that are 5% of the 100 meter assessment area. Habitats
Habitat Selection include: Snags, Submerged macrophytes, banks/root systems, and riffles.
 Sampled in proportion to representation.
Sample Gear/ Standard aquatic D-frame dip net (0.3 meter width & 700-900 micron mesh),
Preservation Sieve bucket (600 micron mesh), 70% ethanol, storage containers (1-2 liter).
 20 jab method, a single jab consists of thrusting the net into a productive
 habitat for a distance of approximately 1 meter. 20 jabs composited across
Sampling Method habitats (6.2 m2). Samples are cleaned by running stream water through the
 net then transferring to a sieve bucket for further cleaning. Transferred, to a
 storaae container and preserved in 70% ethanol.
Subsampling and Preserved samples returned to the lab for processing. Subsampling to 100-
Enumeration organism level.
Taxonomic Level Currently at family level. Investigating efficacy of doing genus-level
 Same as RSPs (Plafkin et al. 1989), habitat assessments are evaluated by
QA procedures all investigators while reviewing the slides and field notes, Field investigators
 must have proper trainina.
Habitat Field data sheet: 7 parameters numerically scored (1-20) similar to RSPs;
Assessment documents other physical and water quality data.
Comments Standard operating procedures in draft form and prepared by Mid-Atlantic
Coastal Streams Workaroup.

Table VII-9. Summary of the primary technical issues related to biological monitoring for nonpoint
source evaluations.
 Biomonitoring for Nonpoint-source Evaluations
 Sampling is conducted over a stream reach, such that a composite of different
Sampling habitats or different parts of a habitat is created. Natural biological heterogeneity
Areal is accounted for by sampling a relatively large area. Fish sampling may extend
Size from 100 yards to 20 or 30 times. the stream width. Benthic sampling may extend
over several riffles or a composite of habitats taken from a 100-yard length of
 Replication at a site is important to evaluate within-site variability. However,
 several samples taken at a single ~ite would be pseudoreplication if used to
Replication evaluate effects of impacts, such as nonpoint source pollution. Sites from
different streams and watersheds are considered replicates to assess status or
 condition of regions or watershed basins. Monitoring can be accomplished with
 sinqle larqe samples that sufficiently represent the stream reach under study.
 Gear can be as rigorous and quantitative as a program deems necessary.
Sampling However. gear must efficiently sample the targeted assemblage and specified
Gear habitat and be maintained in good operational condition. Electrofishing is the
preferred gear for fish assemblages. Most state agencies have selected a kick
 seine or D-frame and artificial substrates are used for periphvton.
 The investigator must find a compromise between selecting a sampling period
 that is representative of the biological community and one that reflects the worst-
Biological case conditions of pollutant stress. Seasonality is an important consideration
Index Period because the taxonomic and functional feeding group compositions change
naturally throughout the year in response to emergence and reproductive cycles.
 The optimal biological index period will vary throughout the United States. Some
 states. such as Florida. have more than one index period for samplinq.

- L  I-      
 I I   "  I ' I
Figure VII-6. Trend in biological condition (based on the multimetric ICI) of the Cuyahoga River at
Independence, Ohio (river mile 15.6) (Ohio EPA 1992).
gradient streams, and benthic macro invertebrates
multihabitats in low gradient streams.

sampling will allow assessment of all watersheds over che 5-year
Repeated sampling of monitoring and reference sites over
time, along with adequate characterization of bioassessment
method precision, can yield significant management information as
demonstrated by the Ohio EPA bioassessment program. Since 1977,
Ohio EPA (19921 has used assessments of the benthic
macroinvertebrate assemblage to document changes in the
biological condition of a waterbody. Figure VII-6 illustrates
annual results or biological assessments using the Invertebrate
Community Index (ICI) (Ohio EPA 1992) over a 14-year period in
the Cuyahoga River. A 95 percent confidence interval of t4 ICI
units was determined based on analysis of intra- and inter-site
variance in ecoregional reference scores. The graph demonstrates
several features including a general improvement in water quality
over time. Furthermore, certain apparent changes in score
between 1977 and 1980 are in fact illusory since the confidence
intervals overlap. Thus, actual trends can be statistically
differentiated from random changes in the data over time.
Overview or Some State Programs
Biological monitoring programs of five states are
highlighted as an overview of technical program components (Table
VII-9). The Delaware Department of Natural Resources and
Environmental Conservation (DNREC) led the Mid-Atlantic Coastal
Streams (MACS) workgroup in adapting the RBPs to low-gradient
streams. The MACS workgroup consists of technical staff from
biomonitoring programs of Delaware, Maryland, Virginia, and North
Carolina (MACS 1993 (draft)). They were able to determine that
the most appropriate method for obtaining a representative sample
of benthic macroinvertebrates from low-gradient, sandy-bottomed,
coastal plain streams was a multihabitat approach. The approach
uses a standard D-frame net and samples the most dominant habitat
types from a lOa-meter reach in proportion to their frequency.
The Delaware DNREC samples approximately 300 sites on an annual
basis using this approach (Table VII-lOa). The Florida
Department of Environmental Protection has adopted this method
for its nonpoint source monitoring program (Table VII-lab) and
has established reference conditions. The State of Montana,
Department of Health and Environmental Sciences, uses a different
approach for its higher-gradient streams, which are generally
cobble-bottomed. They have adapted a traveling kick method
(Table VII-lOci for macroinvertebrates and is developing
reference conditions. The health of the fish assemblage is the
primary biological monitoring indicator for che North uakota
Department of Environmental Health (Table VII-lad). They are
planning to further develop its monitoring program to include
benthic macroinvertebrates. The State of Vermont, Department of
Environmental Conservation, does three types of sampling (Table
VII-10e): fish, benthic macroinvertebrates from riffles in high

Delaware Coastal Plain Data
35 ~ \

~ i

30 - \

25 ~ \

20 '- \
; \
15 '- i

10 ~


Box VIlA. (cominued)
Comparison 01 Populations
Pariwise Comparison 01 Two Sites
I , I ,
Percent Difference in Index Scores
, , I

Determining the appropriate sampling effort: An example using DNREC
data from the Mid-Atlantic Coastal Plain Ecoregion
Most environmental monitoring programs are designed to avoid detecting a problem
or noncompliance that, in reality, does not exist. These false positives are called
Type I errors. It is traditional to accept a five percent probability of false positives
as occurring (see page VIII-47 for further discussion). The probability of false
negatives (Type II error, failing to detect a problem that does exist), is evaluated
through power analysis. A power analysis provides an estimate of the number of
measurements (sample size) required to detect a change for a given significance
level (usually, oc = 0.05), with the power typically set at 80 percent. Power analysis
requires prior knowledge of, or rational assumptions on, the statistical properties of
the data, in particular, the nature of the variability associated with them. Two types
of variance used in power analysis: variance of total bioassessment scores among
all reference sites, and variance among total bioassessment scores within a site.
Maxted and Dickey (1993), as part of their non point source biological monitoring
program, produced replicated bioassessment data from 23 sites. Total
bioassessment scores were developed for each using an RSP - type approach for
normalization of six metrics: (i) Taxa richness, (ii) EPT index, (iii) percent EPT
abundance, (iv) percent Chironomidae abundance, (v) percent dominant family, and
(vi) family biotic index.
The sampling error takes into account the natural variability among multiple sites;
measurement error is the variability observed among multiple samples at the same
site, that is, it tells us how well we are characterizing the site. The power analysis
estimated the number of samples required for a given percent difference in total
bioassessment score. Using the sampling error, it estimated, that in order to detect
a 20 percent difference in the index value (between a population of reference sites
and a population of test sites) a minimum of eight reference and eight test sites
(subjected to NPS pollution) should be sampled (solid line in accompanying figure).
Power analysis using the measurement error indicates that three repeated
measurements at each site are necessary to detect a 20 percent difference in total
bioassessment score (broken line in the accompanying figure).

Box VII-4.

A bioassessment method that has substantial intra-site
variability will have reduced statistical power resulting in a
greater number of sampling sites to distinguish a given level of
impairment. Similarly, a very heterogeneous population of
ecoregional reference sites, with widely ranging bioassessment
scores, will a~so yield reduced statistical power.
An example of power analysis is shown for the Delaware
coastal plain screams in which the benthic macroinvertebrate
community was the biomonicoring indicator used to detect status
and trends of water quality (Maxted and Dickey 1993; Box VII-4) .
The power analysis graph shows a steep decline in the number of
monitoring sites necessary as percent difference in assessment
score (between reference and monitoring sites) decreases. In
other words, if one is interested in detecting a relatively small
difference in assessment score between the reference and
monitoring sites, or alternacively, one wants to detect a
relatively small change in assessment score over time with a high
degree of confidence, then a greater number of monitoring sites
within a strata (i.e., stream order, urban versus agricultural)
will need to be sampled.
The Prince George's Councy case study reviewed earlier
illustrates how this power analysis example was used to determine
the number of monitoring sites needed to obtain meaningful
biomonitoring data. A d~sign consideration was that impairment,
as defined by a 50 percent reduction of the reference condition,
be detected with 80 percent probability of detection, and 95
percent confidence that observed differences are significant.
Power analysis (Text Box VII-4) revealed that a sample of two
sites on a stream class could be used to detect a difference of
50 percent using bioassessment procedures in coastal plain
streams. Assessment of a single watershed can be done by
sampling at least two sites of each stream order present in the
watershed. Most of the 41 watersheds in this county are third
order coastal plain streams. Therefore, an average of six sites
per watershed, or approximately 246 sites, should be sampled for
an assessment of all watersheds. This represents approximately
25 percent of th~ total population of stream segments in the
The above considerations lead to the target sampling design
of 25 percent of stream segments. Because county-wide assessment
is one of the goals of this program, selection probability was
kept at 25 percent. The sampling rule used in this program is at
least 25 percent of stream segments in each stream order are
selected in each watershed. For example, one segment is selected
if there are one to four segments of a given order in the
watershed; two segments are selected if there are five to eight,
and so on. The probability that a watershed will be included in
sampling thus varies slightly among watersheds, and this
probability is used as a weighting factor in county-wide
assessmenc and estimation. Given an annual sampling effort of
approximately 50 probability sites per year, a 5-year rotation of

, Reference score decreases
! over time. Monitoring site A
. increases in score over time
(improves) while Monitoring
site B decreases slightly (i.e.,
continues to show impairment.
: Monitoring Site~.///-'A/o.-

i ---'

. ------.:::~ --
. Reference score decreases
: over time. Monitoring site
. generally tracks the reference
condition and shows
over time.
-... -
-... --
en :....
i Reference score is fairly stable
i over time. Monitoring site is
i initially similar to the reference
- - - - - - , condition and then shows
- - - - - . impairment over time.
Monitoring Site ---------;
Figure VII-5. Some trends that might be observed during the course of a biological monitoring program.

a biological monitoring nonpoint source program is accomplished,
in part, by using a comparative analysis of reference site and
monitoring site data. Figure VII-5 illustrates some possible
trends that could be observed in a biological monitoring program.
These types of data can be analyzed in a variety of ways as
described in C0apter VIII, Section 2 and in Green (1993) and
Smith et al. (1988).
Acc~rate characterization of trends in biological data over
time depends on the degree to which sources of variability in the
data are defined and characterized. In general, there are two
major sources of variability: natural and experimental. Natural
sources or variation include seasonal effects such as species
life cycles, natural disturbances such as floods and fires, and
microhabitat differences among sites or over time. Experimental
sources or variability include collection method and gear
variation. The previous discussion of biological assessment
methods in this chapter addresses many of the common natural and
experimental sources of variability. The use of a well-defined
and appropriate field collection method, for example, reduces
experimental sou~ces of variability. Incorporation of a
population of eco~egional reference sites into a biological
monitoring design serves as a control for natural sources of
variability over time, in addition to providing a sound data
assessment framework. An apparently downward trend for certain
sites in watersheds over time, for example, may be open to
interpretation if the same trend is observed in reference sites
(Figure VII-5). Repeated sampling during the same index period
over time also provides some control for natural sources of
Although natural sources of variability are not often
amenable to characterization, experimental or method-sources of
variation can and should be defined. Factors such as precision
and sensitivity of the assessment scores are achieved by
collecting and analyzing multiple samples from the same site
using consistent procedures and by sampling and analyzing samples
from multiple sites that are similar, particularly ecoregional
reference sites. One of the results of this method
characterization process is the ability to define statistical
power of a sampling and bioassessment method. Statistical power
is the degree to which a Type 2 error has a given probability of
occurrence. Put simply, this is the probability of assessing a
site as unimpaired when in fact it is impaired; or concluding
that there is no trend or change in water quality over time when
in fact there has been a change.
Defining the statistical power of a given bioassessment
method allows cne to rigorously determine the number of sites
necessary in a monitoring program to detect a given level of
impairment, or a certain trend over time, with a known degree of
confidence. A power analysis achieves this objective by
constructing an empirical relationship between the number of
sites or measurements observed and the resultant difference in
assessment score detected between the reference and test sites.

sites. ,~hese data allow estimation of annual variation and
trends in the biological characteristics of the reference sites.
These escimaces are critical for determining biological status of
test sites.
Forcy-one watersheds have been identified to address status
and trends for the county. Site selection is in two stages. In
the firsc stage, a set of watersheds are selected randomly. In
the second stage, stream segments within the selected watersheds
are chosen at random for sampling. In each year of the
monitoring program, a set of six to ten watersheds are selected
(depending on size), and approximately 45 stream segments of
those wacersheds are sampled. After 5 years, all watersheds in
the councy will have been sampled and in the sixth year the
program will return to the originally sampled watersheds. An
estimate of status can be made for each watershed every 5 years.
Status of streams county-wide can be estimated from the first
year on. The first year's estimate will be based on a small
sample of wacersheds and segmencs, and will have greater
uncertai~ty than estimates developed in later years.
Prior knowledge of land use in che county was applied to
stratify watersheds and sites. Urbanization is known to affect
stream hydrology, water quality, habitat, and biota, and the
northern watersheds of the county are urban and suburban, being
close to Washington, D.C. Therefore, Prince George's County was
divided (stratified) into northern and southern watersheds so
that in any given year, an equal number of watersheds would be
selected in the more urban north and in the more rural southern
Monitoring Trends in Biological Condition
Two separate factors affect our ability to distinguish
trends over time in biological monitoring. The first factor,
common to any trend analysis, are those sources of variability
inherent in the measurements obtained from the monitoring sites.
A signifi~ant challenge is distinguishing random changes in
biological monitoring data over time from actual trends. Chapter
VIII, Section 2 outlines statistical considerations regarding
this issue and Figure VIII-33 illustrates several common types of
data patterns that may be obtained over time in a water quality
monitoring program. One of the solutions to this challenge is to
have either a long time series of data or to have a sufficient
number of monitoring sites (probabilistic, targeted, or
integraced design) so that the data can be statistically
A second factor affecting the ability to detect trends in a
biomonitoring program is the observed relationship between
reference site data and monitoring site data over time. This
factor is somewhat unique to biomonitoring programs because a
biological assessment at any given time is dependent on data from
two sources: the population of reference sites and the
monitoring sites. Thus, an accurate interpretation of trends in

Case Study
Development of an Integrated Biological
Monitoring and Assessment Program
in Prince George's County, Maryland'
Prince George's County, Maryland, immediately east of Washington, DC, is
developing a biological monitoring program to assess the status and trends in
ecological condition and their physical habitat quality in county streams. Program
goals include:
Document and monitor the biological status and trends of county streams.
Integrate data from biological, chemical, and physical monitoring programs
to make a comprehensive assessment of the county's stream resources.
Use biological monitoring data to identify and characterize impairment to the
ecological system.
further public education in environmental problems through a component of
the biological monitoring program tailored for lay-person involvement.
Evaluate the effectiveness of environmental management and mitigation
The program design includes both probabalistic and targeted elements that will
allow specific questions to be addressed at three spatial scales: county-wide,
watershed-wide, and stream-specific. There are approximately 100 sampling
locations that have been selected for the initial year of monitoring (1995). In two
separate sampling periods (early spring and fall), there will be approximately 50
probability sites, 20 known problem sites, 20 reference sites, and another 15 sites
that will be for either confirmation of volunteer monitoring results or quality control
The sampling units are stream segments between confluences. Segments are
sampled at accessible points. Sampling is two-stage: for the first stage,
watersheds are selected randomly so that one-fifth of the watersheds in the county
are sampled in anyone year and all watersheds will be sampled in the fifth year of
the program. The second stage is random selection of stream segments within
watersheds, stratified by stream order, so that sampling effort is allocated
optimally among three stream orders.
Box VII-3.
. Used by permission of: Watershed Protection Branch. Department of Environmental Resources. Prince George's Couney. Maryland.

geographic area of concern. NPDES permits, urban storm water
sites, timber harvest areas, rangeland, row crop farming,
construction sites, and Superfund sites are all examples of known
stressor sites. Upscreamjdownstream sampling stations, before-
and-after site a~teracions, or recovery zones (sampling at
established distances from sources) are types of sampling
locations for known stressor sites. Ecologically sensitive sites
that mayor may ~ac be affected by stressors might also be chosen
as targeted sites.
Integrated Network Design
Integrated ~etwork design consists of integrating multiple
monitoring subprograms to effectively meet various monitoring
objectives and improve the applicatibility of data. An emerging
biological monitoring program in Prince George's County,
Maryland, is used here at a useful example demonstrating the
design componencs reviewed above (Box VII-3) .
Prince George's County is interested in assessing the status
and trends of biological stream resources in the county with
known confidence. Assessment levels include county-wide,
watershed-wide, and stream-specific. Biological assessment,
based on sampling benthic macroinvertebrates, is used as the
indicator of stream condition. Judgement of ~mpairment or
nonimpairment results from comparison to reference conditions
(see Section VII-D). Two major components of this program are
volunteer monitoring of selected sites and nonvolunteer
monitoring of probability-based and targeted sites. The
volunteer sites serve for public education and some initial
screening of stream conditions. Those sites monitored by the
nonvolunteer program are intended to provide unbiased estimates
of biological status of streams throughout the county, trends in
their condition, problem identification, evaluation of management
activities (e.g., restoration, BMP installation, chemical
controls, and altered land use practices), and data for eventual
establishment of cause-and-effect associations.
Three types of sites are monitored in this program to
address the county's multiple goals: targeted sites, reference
sites, and probability sites. Each site type addresses specific
questions on stream status in Prince George's County. Targeted
sites are sampled semiannually during two program index
period&-Spring and fall. Annual sampling allows estimation of
intra- and interannual variation in the measured variables and
indices, and allows estimation of trends after several years of
monitoring. After the first 2 or 3 years of monitoring, the data
will be reevaluat:ed to determine if sampling at: longer intervals
(for example, every other year) is sufficient to detect trends.
Data from targeced sites can document the decline or recovery of
streams subject to specific stresses and will allow assessment of
restoration and mitigation efforts.
A set of 15 to 20 reference sites (having over 50 percent
forest cover) are monitored semiannually as are the targeted

Table VII-8. Waterbodv stratification hierarch v
Population of Stieams and Rivers' Lakes l'J Reservoirs I' 2 Estuaries; Wetlands' Groundwater T
Operational cnannel segment (Le.. self-contained basin self-contained basin self-contained basin transect transect
Sampling Unit a length of river  (hydrologically isolated  uplana or deep 
(SU) channel Into-whiCh no  from other basins I   water coundaries 
 tributanes flowi     
Strata lor higher ecoreglon ecoreglon ecoregion blogeograpnlc wetland svstem tYpe ecoregion
stages!    province (marine. estuarine. 
comprising SUs     riverine. lacustrine, 
 watershed size/surface area of size/surface area of watershed watershed watershed
  lake (km') reservoir (km')  recharge. discharge 
   {watershed arealbasin  or 00111 
   surface areal   
 streammver cnannel lake hydrology hydrology (water level watershea area (km') class I based on aquifer type
 (ordinal/areal) (retention time. ftuctuation/ diawoown:  vegetative type: (unconfined (water
  thermal stratihcation) retention time  substrate and tabte] aquifers.
   stratihcation)  flooding regime: conhned (artesian
     hvdrooeriod) weln aquifers)
 segment cnaracteristic water characteristic water zones (tidal basin, flooding regime aquifer matenal type
  quality (natural quality (natural depth. salinity) water chemistry (sedimentary rock:
  conditions I  conditionsl  soli type man: unconsolidated
     rock. etc. \
 characteristic water     hydraulic ConductMty
 quality (natural     (homogenous.
 condltionsl     heterogenous.
      isotTooic. anisotroDic)
Habitats within macrOhaoitat  longitudinal zone   depth zone
SUs (pooVriffle: shorezone  (riverine: transitional:   
 vegetation: submerged  lacustrine: tailwaters   
 aquatic macrophytes)  [may be more riverine   
   but always associated   
   with damsl)   
  depth zone depth substratelhabltat subsystem (subtidal. temperature
  (eulittoral -   intertidal. tidal. lower 
  profundal)   perennial. upper 
     intermittent. littoral. 
 miaohabitat substrate! substrate! microhabitat  substrate! 
  microhabitat   microhabitat 
. Frissell et al. 1986; . Gerritsen et al. 1994 (Draft]; - Wetzel 1975;
, Thornton et al. 1990; 5 Day et al. 1989; 6 Cowardin et al. 1979; , Heath
watersheds, the watersheds may be further stratified to ensure
inclusion of an even distribution of land use types (e.g.,
subwatersheds having different levels of urban development) .
Waterbodies can be further stratified by section or segments.
For instance, streams should be stratified by stream order
(first, second, third, etc.; Strahler [1957]), or specific
sections of a bay or lake may be identified as separate strata.
(3) Select sampling sites. Sampling units or sites within each
stratum (or other delineation as dictated by the general design)-
are randomly selected. This approach provides a basis for making
general statements about the condition of the entire stratum,
including sites not sampled.
2 .
Targeted Site Selection
In a targeted site selection
based on the location of known or
(stressors), planned point source
design, sites are selected
suspected perturbations
controls, or BMPs in the

As a :arget population is recognized to consist of groups
that each ~ave internal homogeneity (relative to other groups),
it can be stratified to minimize within-group variance and
maximize a~ong-group variance (Gilbert 1987). Table VII-8
summarizes a waterbody stratification hierarchy for streams and
rivers, lakes, reservoirs, estuaries, wetlands, and groundwater.
With the exception of estuaries, the highest-level strata would
be ecoregions and subecoregions. Biogeographic provinces (e.g.,
Virginian and Louisianian Provinces used in the EMAP-Estuaries
program as described by Weisberg et al. (1993) are more
appropriate as the highest stratification level for estuaries
because or the relatively large size of their watersheds and the
fact that :hey are influenced directly by marine processes.
Depending on the waterbody, subsequent stratification levels
may vary i~ number and may be quite different across waterbodies
at a given level in the hierarchy. For example, a state or
regional ~onitoring program designed to assess the status of
biological communities in streams might need to be stratified to
the level of segments, whereas monitoring to assess the efficacy
of specifi~ stream restoration measures might need to be
stratified to the macro- or microhabitat level. If data
collected by a particular design are so variable that meaningful
conclusions cannot be drawn, post-stratification of the dataset
may be re~~ired. If stratification to the level of microhabitat
is needed, it may indicate that the sampling and analysis methods
used at higher levels are inappropriate or inadequate.
Process of Randomized Sampling Site Selection
probabilistic sampling designs require the random selection
of sampling sites within the basic design (e.g., simple random,
stratified random, multi-stage; Chapter VI, Section 3). There
are three major steps involved in selecting sampling sites using
a probabilistic design:
(1) Identify the level of site classification. Monitoring
program objectives will dictate the geographic extent at which
monitoring is to be done, for instance state-wide, county-wide,
within an ecoregion, or within a watershed. This level of site
classification should be identified initially.
(2) Stratify the site classes. A sampling design appropriate to
the monitoring objectives must be selected. For probabilistic
designs, simple random sampling is not usually the optimal
method. It can produce clusters of sampling sites that may not
be representative of the larger scale area of interest (e.g.,
Hurlburt 1984). Therefore, some sort of stratification is
preferred for ensuring a dispersed distribution of site
locations. Stratification can begin at an ecoregion site
classification level and proceed to more specific levels of
resolution as necessary to meet project objectives (Table VII-8) .
If there are clear clusters of differing land use among

T bl VII 7 C
a e - ompanson 0 pro a a IStIC an targete momtonng eSlgns.
    AdvantaqeS    Disadvantaqes
Probabilistic . Unbiased estimates of status for a valid . Small scale problems will not
D.esign   assessment on a scale larger than that  necessarily be identified
    of the sample location    unless the waterbody or site
        happens to be chosen in the
   . Can provide large scale assessment of  random selection process
    status and trends of resource or  
    geographic area that can be used to . Cannot track restoration
    evaluate effectiveness of environmental  progress at an individual site
    management decisions for watersheds,  or site-specific management
    counties, or states over time.  goals.
   . Stratified random sampling can improve . Stratified random sampling
    sampling efficiency, provide separate  requires prior knowledge for
    data on each stratum. and enhance  delineating the strata
    statistical test sensitivity by separating  (MacDonald et al. 1991)
    among-strata variance from within-strata  
 Targeted . Systematic sampling along a stream or . A targeted design will not yield
 Design   river can be an efficient means of  information on the condition of
    detecting pollution sources (Gilbert  a large scale area such as the
    1987).    watershed, county, state, or
   . Identifies small scale status and trends  
    of individual sites that can be used to . It cannot specifically monitor
    assess potential improvements due to  changes from management
    restoration projects and other  activities on a scale larger
    management activities    than site-specific.
   . Contributes to understanding of . Resource limitations usually
    responses of biological resources to  make it impossible to monitor
    environmental impact.    effects of all pollutant sources
        using a targeted design.
       . Systematic sampling can
        result in biased results if there
        is a systematic variation in the
        samoled oooulation.
b b I" .
d .
Assessments of waterbodies and subsequent monitoring often occur
at the watershed scale within which both targeted and
probabilistic sites could be selected. A probabilistic design
would yield information on the watershed scale as well as on the
site- or stream-specific scale; these locations mayor may not be
impaired. The targeted design would ensure that known problem
sites or sites of special interest are evaluated and their
response over time is assessed.
Assessment on a small geographic scale may be whole stream,
river, bay, or a segment (reach) of the water body. A targeted
sampling design applies to monitoring waterbodies within a
watershed that are exposed to known stressors. Known
disturbances, such as point sources, specific NPS inputs, or
urban stormwater runoff can all be targeted for small-scale
assessments. It is at this scale that the effectiveness of
specific pollution controls, BMP installation/implementation,
natural resource management activities, or physical habitat
restoration can be monitored.

three types of network
designs depending on
the objectives of the
targeted, or integrated
design. Objectives
that are site-specific,
such as determining
whether biological
impairment exists at a
given site, are
addressed using a
targeted monitoring
design (Table VII-7) .
Objectives that address
questions of large-
scale status and
trends, for example,
require a probabilistic
design. For many
nonpoint source
objectives (see Chapter
2), an integrated network monitoring design is most appropriate.
Monitoring performed at different spatial scales can provide
different types of information on the quality and status of water
resources. Conquest et al. (1994) discuss a hierarchical
landscape classification system, originally developed by Cupp
(1989) for drainage basins in Washington state, that provides an
organizing framework for integrating data from diverse sources
and at different resolution levels. The framework focuses on
river and stream resources at its higher resolutions, but could
be modified for other waterbody types such as lakes and wetlands.
In its simplest form, the nested hierarchy consists of five
Network Design refers to the array, or network. of sampling sites
selected for a monitoring program; usually taking one of two
. Probabilistic Design Network that includes sampling sites
selected random Iy in order to provide an unbiased
assessment of the condition of the waterbody at a scale
above the individual site or stream; can address questions at
multiple scales.
. Targeted Design Network that includes sampling sites
selected based on known existing problems, knowledge of
upcoming events in the watershed, or a surrounding area that
will adversely affect the waterbody such as development or
deforestation; or installation of BMPs or habitat restoration
that are intended to improve waterbody quality; provides
assessments of individual sites or reaches.
An Integrated Design combines these two approaches and
incorporates multiple sampling scales and monitoring objectives.
Valley segments
Habitat complexes (e.g., stream
Habitat units (e.g., riffle).
Assessments of waterbodies on a large scale such as an
ecoregion, subregion, state, or county provide information on the
overall condition of waterbodies in the respective unit.
Appropriately-designed probabilistic sampling can provide results
such as the percentage of waterbodies in a geographic area that
are impaired (status), or, if the sampling is repeated at regular
intervals, an assessment of the trends in the percentage of
impaired waters. Probabilistic site selection is most
appropriate for an unbiased estimate of the status and temporal
behavior of waterbodies on a large geographic scale.

discusses appropriate electrofishing techniques for
bioassessment. Other sources for sampling method discussions are
Allen et al. (1992), Dauble and Gray (1980), Dewey et al. (1989),
Hayes (1983), Hubert (1983), Meador et al. (1993), and USFWS
(1991) .
Leng~h and Weight Measurements
Leng~h and weight measurements can provide
growth, standing crop, and production of fish.
commonly used length measurements are standard
length, and total length. Total length is the
often used.
Age may be determined using the length-frequency method,
which assumes that fish increase in size with age. However, this
method is not considered reliable for aging fish beyond their
second or third growing season. Length can also be converted to
age by using a growth equation (Gulland, 1983).
Annulus formation is a commonly used method for aging fish.
Annuli (bands formed on hard bony structures) form when fish go
through differential growth patterns due to the seasonal
tempera~ure changes of the water. Scales are generally used for
age determination, and each species of fish has a specific
location or. the body for' scale removal that yields the clearest
view for identifying the annuli. More information on the annulus
formation method and most appropriate scale locations by species
can be found in Jerald (1983) and Weatherley (1972).
estimations of
The three most
length, fork
measurement most
2 .2.
Fish External Anomalies
The physical appearance of fish usually indicates their
general state of well-being and therefore gives a broad
indication of the quality of their environment. Fish captured in
a biological assessment should be examined to determine overall
condition such as health (whether they appear emaciated or
plump), occurrence of external anomalies, disease, parasites,
fungus, reddening, lesions, eroded fins, tumors, and gill
condition. Specimens may be retained for further laboratory
analysis of internal organs and stomach contents if desired.
Biomonitoring Program Design
The design of a biomonitoring program (similar to other
types of monitoring programs), will depend ultimately on the
goals and objectives of the program. Several of the objectives,
identified in Chapter 2 of this document, can be directly
addressed using a properly designed biomonitoring program. These
objectives may differ in spatial and temporal scales, thereby
requiring different monitoring designs as reflected in
differences in the site selection process, number of sites
sampled, and time and frequency of sampling. The sampling design
used in nonpoint source biological monitoring consists of one of

square-meter kicknet or a long-handle D-frame. The former is
typically used at sites that are considered to be in higher
gradien~ (riffle-prevalent) streams (Plafkin et al., 1989) i the
latter ~s used primarily in coas~al plains streams and is
standardized as the 20-jab method (MACS, 1993 [draft]). In both
of these methods, organisms are dislodged from their substrate by
the sampler and captured in a net. Passive collection approaches
include the Hester-Dendy multiplate sampler and rock baskets.
These are considered artificial substrates. They are placed in
the stream or stream bottom and left for a standardized amount of
time. Upon retrieval, the invertebra~es are removed from the
sampling unics in the laboratory. For further information on
sampling methods, see Klemm et al. (1990).
Fish Sampling
Fish surveys should yield a representative sample of the
species present at all habitats within a sampling reach that is
representative of the stream. Sampling reaches should ensure
that generally comparable habitats will exist at each station.
If comparable physical habitat is not sampled at all stations, it
will be difficult to separate degraded habitat from degraded
water quality as the factor limiting the fish community (Klemm et
. At least two of each of the major habitat types (i.e.,
riffles, runs, and pools) should be incorporated into the
sampling as long as they are typical of the stream being sampled.
Most species will be successfully sampled in areas where there is
adequate cover, such as macrophytes, boulders, snags, or brush.
Sampling near modified sites, such as channelized stretches
or impoundments, should be avoided unless it is conducted to
assess the impact of those habitat alterations on the fish
community. Sampling at mouths of tributaries entering larger
waterbodies should also be avoided because these areas will have
habitat characteristics more typical of the larger waterbody
(Karr ec al., 1986). Sampling station lengths range from 100 to
200 meters for small streams and 500 to 1000 meters for rivers.
Some agencies identify their sampling reach by measuring a length
of stream that is 20-40 times the stream width.
Fish are generally identified to the species or subspecies
level. For biological assessments of the entire assemblage, the
gear and methods used should ensure that a representative sample
is collected.
Fish can be collected actively or passively. Active
collection methods involve the use of seines, trawls,
electrofishing equipment, or hook and line. Passive collection
can be conducted either by entanglement using gill nets, trammel
nets, or tow nets, or by entrapment with hoop nets or traps. For
a discussion on the advantages and limitations of the different
gear types, see Klemm et al. (1992). The Index of Biotic
Integrity (IBI) emphasizes active gear, and electrofishing is the
most widely used active collection method. Ohio EPA (1987)

Raw data
Example of transforming benthic macroinvertebrate data into biological metrics
Taxa Number FFG TV
Oligochaeta 2 col 8
Valvata 4 ser 6
Fossaria 3 col 6
G yrau/us parvus 15 scr 8
Pisidium 32 fil 8
Hydracarina 1 pre 6
Caecidotea 6 col 6
Hyaffela azteca 35 Col 8
Arthrop/ea 2 fil 3
Ame/etus 34 col 0
Amphinemura 1 shr 3
Anabo/ia 4 shr 5
Neophy/ax 2 scr 3
A noma /agrionl/ sc hn ura 1 pre 9
Hygrotus 1 pre 5
Hydrobius 1 pre 5
Sialis 3 pre 4
Nymphuliella 1 shr 5
Diptera 1 fil 8
Culicodes 1 pre 2
Similium 40 Iii 6
Prosimilium 4 Iii 2
Chrysogaster 1 col 10
M%philus 1 shr 4
Pseudolimnophia 1 pre 2
Bittacomorpha 1 col 8
Ptychoptera 2 col 8
Orthocladiinae 20 col 5
T anypodinae 15 pre 7
Chironominae 2 col 6
Calculated Metrics

Box VII-2. (continued)
Taxa Richness
Hilsenhoff Biotic Index
EPT Index
Percent Domin~nce
Percent Pisidium
Percent Simuliidae
Percent Isopoda
Percent Diptera
Percent EPT
Percent Filterers (fil)
Percent Collectors (col)
funcitonal feeding group
tolerance value



Example of transforming benthic macroinvertebrate data
into biological metrics
The data prese(1ted here are from a single sampling event at one site in New England. They are
a 200-organism subsample of organisms collected with the 20-jab method (MACS 1993 [draft])
for low gradient streams. The eleven metrics calculated from the data are described below.
Taxa Richness - the number of distinct taxa in the sample.
Hilsenhoff Biotic Index - measures the abundance of tolerant and intolerant individuals in a
sample by the following formula: HBI = Lx~J n, where XI is the number of individuals in the ith
species, tl is the tolerance value of the ith species, and n is the total number of species in the
EPT Index - the number of taxa in the insect groups Ephemeroptera (mayflies), Plecoptera
(stoneflies), and Trichoptera (caddisflies).
Percent Dominance - the number of individuals in the numerically most dominant taxon as a
proportion of the total sample [(Number individuals in dominant taxon / Total individuals in
sample) x 100].
Percent of Total Samole - (1) Pisidium, (2) Simuliidae (= Prosimulium + Simulium), (3) Isopoda
(= Caecidotea), (4) Diptera. (5) EPT (= mayflies, stoneflies, caddisflies), (6) filters FFG, and (7)
collectors FFG.
Box VIl-2.
within a range of stream sizes, is the most representative of the
stream type or class under investigation, and is likely to
reflect anthropogenic disturbances within the watershed.
Suitable habitat alternatives to riffles for sampling benthos
include snags, downed trees, submerged aquatic vegetation beds,
emergent shoreline vegetation, and the most prevalent substrate.
The RBPs recommended by EPA specify that a subsample of 100
organisms be used for a biological assessment; however, several
states use 200-300 organisms. Agencies should evaluate the level
of subsampling required to meet their objectives. The level of
taxonomic identification should be specified in the study design
and is determined by the study objectives. Identification to the
species level gives the most accurate information on pollution
tolerances and sensitivities, though some metrics or analytical
techniques might require identification only to the order,
family, or genus. Verification of taxonomic identifications is
critical and can be accomplished by (1) comparing specimens with
a reference specimen collection or (2) sending specimens to
taxonomic,experts familiar with the group in question.
Benthic macro invertebrates can be collected actively or
passively. Two of the more commonly used active methods use a

Table VII-6, Scoring criteria for the metrics as determined by the 25th percentile of the metric values
for the two aggregated subecoreoions for Florida streams
Metric Stream  Panhandle   Peninsula 
 Score 5 3 1 5 3 1
# of Total Taxa  ~31 16-30 0-15 ~27 14-26 0-13
EPT Index  ~7 4-6 0-3 -- ~4 0-3
# Crustacea + Mollusca Taxa  n -- -- -- ~4 0-3
% Dominant Taxon  -- s20 >20 n s37 >37
% Dietera  n s38 >38 -- s32 >32
% Crustacea + Mollusca  n -- n n > 16 0-15
Florida Index  > 18 0-8 0-8 ~7 4-6 0-3
% Filterers  ',12 0-6 0-6 ~8 4-7 0-3
% Shredders  n ~0-9 0-9 -- ~ 13 0-12
Ranoe of Aooreoate Score   7-29   9-33 
habitat types. Decisions on the habitats selected for sampling
should be made with consideration of the regional characteristics
of the streams. For instance, high-gradient montane streams are
best sampled from the cobble substrate of riffles for
macro invertebrates, whereas low-gradient coastal streams lack
riffles and are appropriately sampled from snags and shorezone
vegetation. These two different stream types might be sampled
with different methods, during different times of the year, or
with different biological index periods. The seasonal
variability of the biota and stream environment are key factors
that determine the proper index period. Established sampling
protocols that are part of existing monitoring programs should be
considered for NPS bioassessment. However, current and/or
historical sampling approaches should be evaluated to determine
whether they will provide the required data to 'address the
program objectives.
Sampling a single habitat, such as riffles, limits the
variability inherent in sampling natural habitats. This can
produce a more repeatable characterization of the biological
condition of a stream because sampling bias is reduced, whereas
sampling multiple habitats must be carefully standardized to
reduce investigator bias and to control for sampling efficiency
If the biological assessment strategy is to sample a single
habitat, the most representative stable habitat conducive to
macroinvertebrate colonization should be chosen. The most
suitable habitat choice will vary regionally. The key is to
select one habitat that supports a similar assemblage for benthos

Table VII-4. (continued)
benthic metrics

Shannon-Weiner Diversity Index


Index of Community Integrity
Category ICI. RBp. RBpe ID OR WA B.IBr
A     X  
A    X   
A    X   
A = Community structure
B = Taxonomic composition
C = Individual condition
D = Biological processes
'Invertebrate Communiry Index. Ohio EPA (1987).
"Rapid Bioassessmen! Protocols. Barbour et al. ( 1992) revised from PlatKin et al. (1989)
'Rapid Bioassessmen! Protocols. Shackelford ~ 1988).
"Rapid Bioassessmen! Protocols. Hayslip (1993); ID = Idaho. OR = Oregon. W A = Washington.
~Note: these metrics in !D. OR. and W A are currently under evaluation)
'Benthic Index of Biotic Integrity. Kansas et al. (1992).
Table VII-5. Scoring criteria for the core metrics as determined by the 25th percentile of the metric values
from the Middle Rockies - Central EcoreQion. Wvoming.
Metric Stream  Elevation> 6,500 ft.   Elevation < 6,500 ft. 
 Score 5 3 1 5 3 1
EPT Taxa  >14 14-8 <8 >18 18-10 <9
% PlecoDtera  >7% 7%-4% <4% -- -- --
% EDhemeroDtera -- -- .. >22% 22%-11 % <11%
% Chironomidae <36% 36%-68% >68% >6% 6%-4% <4%
Predator Taxa  >5 5-3 <3 <12% 12%-39% >39%
% Scrapers  >5% 5%-3% <3% >7 7-4 <4
MHBI  <4.3 4.3-4.8 >4.8 >8% 8%-5% <5%
BCI  >74 74-42 <42 <3.7 3.7-4.7 >4.7
CTOD  <99 99-112 >112 >79 79-46 <46
Shannon H  >3.5 3.5-1.8 <1.8 -- -- --
% Multivoltine  <48% 48%-57% >57% .- -- ..
% Univoltine  >40% 40%-20% <20% .. .. --
% Coliector.Filterers .- -- -- <2.6% 2.6-23.2 >23.2%
Range 01 Aggregate  11-55   9-45 

Table VII-4. Examples of metric suites used for analysis of macro invertebrate assemblages.  
 Alternative Metric       
 benthic metrics Category ICI. RBp. RBpe ID OR WA B.IBr
1. Total No. Taxa A X X X X X X X
 % Change in Total Taxa Richness A    X X X 
2. No. EPT Taxa B X X  X X X 
 No. Mayfly Taxa B X      X
 No. Caddisfly Taxa B X      X
 No. Stonefly Taxa B       X
 Missing Taxa (EPT) B   X    
3. No. Diptera Taxa B X      
 No. of Chironomidae B    X  X 
4. No. Intolerant Snail and Mussel Species B       X
5. Ratio EPT/Chironomidae Abund. B    X X X 
 Indicator Assemlage Index B   X X X  
 % EPT Taxa B    X   
 % Mayfly Composition B X      
 % Caddis fly Composition B X      
6. % Tribe Tanytarsini B X      
7. % Other Diptera and Noninsect Composition B X      
8. % Tolerant Organisms B X      
 % Corbicula Composition B       X
 % Oligochaete Composition B       X
 Ratio HydropsychidaelTricoptera B  X   X  
9. % Ind. Dominant Taxon A  X  X X X 
 % Ind. Two Dominant Taxa A       X
 Five Dominant Taxa in Common A  X X  X  
 Common Taxa Index A   X    
10. Indicator Groups B    X  X 
11. % Ind. Omnivores and Scavengers D       X
12. % Ind. Collector Gatherers and Filterers D       X
 % Ind. Filterers D    X  X 
13. % Ind. Grazers and Scrapers D    X   X
 Ratio Scrapers/Filterer Collectors D    X X X 
 Ratio Scrapers/(Scrapers + Filterer D  X     
14. % Ind. Strict Predators D       X
15. Ratio ShredderslTotallnd. (% shredders) D  X  X  X 
16. % Similarity Functional Feeding Groups D  X X    
17. Total Abundance A    X   
18. Pinkham-Pearson Community Similarity Index A  X     
 Community Loss Index A     X X 
 Jaccard Similarity Index A    X   
19. Quantitative Similarity Index (Taxa) A  X X    
20. Hilsenhoff Biotic Index B  X  X X X 
 Chandler Biotic Score B    X   

Tabk VII-3. (continued)         
    Metric  New  Central Colorado Western Sacramento- 
Alternative 181 metrics Category Midwest England Ontario Appalachia Front Range Oregon San Joaquin Wisconsin
8. % Insectivorous cyprinids D X       
 % Insectivores D  X    X  X
 % Specialized insectivores D    X X   
 # Juvenile trout D       X 
 % Insectivorous species D X       
9. % Top Carnivores D X X X     X
 % Catchable salmonids D      X  
 % Catchable trout D       X 
 % Pioneering species D X       
 Density catchable wild trout D       X 
10. Number of individuals A X  X X X X X X'
 Density of individuals A  X      
11 . % Hybrids C X X      
 % Introduced species C     X X  
 % Simple lithophills C X       X
 # Simple lithophills species C X       
 % Native species C       X 
 % Native wild individuals C       X 
12. % Diseased individuals C X X X X X X  X
Note: X = l11etric IISed in region. Many of Ihese variations are applicahle elsewhere.       
'Melric suggested hy Moyle or Hughes as a pruvisi()nal replacemellll11elric in small western salmunid streams.      
'Excluding individuals of tolerant species.         
Taken frum Karr cl al. (1<)86), Hughes and Gal11n1<1I1 (1<)87). Ohio EI'A (1<)87), Miller et al. (1<)88), Sleedmall (I<)X8), and Lyoos (1')1)2).    

Tahk VII-3. Fish IBI metrics used in various regions of North America.      
   Metric  New  Central Colorado Western Sacramento- 
Allernative 181 metrics CateQorv Midwest EnQland Ontario Appalachia Front RanQe OreQon San Joaquin Wisconsin
1. Total number of species A X X  X X  X 
 # Native fish species A X  X   X  X
 # Salmonid age classes' A     X X  
2. Number of darter species B X   X X   
 # Sculpin species B      X  
 # Benthic insectivore species B        
 # Darter and sculpin species B X X      
 # Salmonid yearlings (individuals)" B  X    X X 
 % Round-bodied suckers B X       
 # Sculpins (individuals) B       X 
3. Number 01 sunlish species B X    X   X
 # Cyprinid species B      X  
 # Water column species B  X      
 # Sunlish and trout species B   X     
 # Salmonid species B       X 
 # Headwater species B X       
4. Number 01 sucker species B X X    X  X
 # Adult trout species' B      X X 
 # Minnow species B X    X   
 # Sucker and catfish species B   X     
5. Number 01 intolerant species B X X   X X  X
 # Sensitive species B X       
 Presence 01 brook trout B   X     
6. % Green sunfish B X       
 % Common carp B      X  
 % White sucker B  X   X   
 % Tolerant species B X       X
 % Creek chub B    X    
 % Dace species B   X     
7. % Omnivores 0 X X X X X   X
 % Yearling salmon ids'  0     X X  
't:7''''T"'''T" '""""'"

Western ',;------~
!j ~
Oregon:' . ! ---

"C---' -un

;' \- I ~J ' ~

/' i,,': - \ j --------~
//' ~;. , : ~ !--
/ \ ' I:
acramento \- ,-J ;' :
an Joaquin " ,( I':~
"\ /) . :
._~. ' i i '------ I I.
,'. f ~~~
~ ,,; \ \
"\. \ I \
'-. ~, !-,~\

'-"\ r'~~\ ~\ \

\,~ Wisconsin ~
New Englan
Colorado Front
Ran e
Figure VIlA. Regions in which various fish IBI metrics (see Table VII-4) have been used.
correlation between the two for a particular ecoregion.
Obviously, the more correlative data that are collected, the more
useful they will become in interpreting sampling data, that is,
in separating water quality and habitat quality effects as they
relate to biological condition. The ability to separate the two
influences is important for determining the expected or potential
improvement in biological condition from water quality
improvement programs (e.g., point or nonpoint source pollution
control) (Barbour and Stribling, 1991).
When sampling multiple habitats, it is important to
establish consistency in sampling procedures. Sampling protocols
should be standardized and the same level of effort should be
applied at each sampling station. Because differences in gear
efficiency and techniques may affect results, standardized
sampling is needed if direct comparisons are to be made between
and among stations or among data from a single station at
different times.
Benthic Macroinvertebrate Sampling
Stream environments contain a variety of macro- and
microhabitat types including pools, riffles, and runs of various
substrate types; snags, and macrophyte beds. Relatively distinct
assemblages of benthic macro invertebrates inhabit various
habitats (Hawkins et al., 1993), and it is unlikely that most
sampling programs would have the time and resources to sample all

ABUNDANCE (intolerance)  

Figure VII~3. Organizational structure of attributes that can serve as metrics.
Sampling Considerations
The large influence that small environmental factors, such
as amount of sunlight or presence of woody debris in a water body,
can have on aquatic communities means that even though there
might not be easily-distinguished boundaries between habitats,
such as those between riffles and pools, the biota inhabiting
them are often taxonomically and biologically distinct (Hawkins
et al., 1993). The distribution of benthic fauna in lakes and
streams is also heterogeneous because of variable requirements
among species for feeding, growth, and reproduction, which are
satisfied for different species by different substrata, water
chemistry, and inputs of woody debris (Wetzel, 1983). This leads
to a patchy, nonrandom distribution of animals.
Because of the influence that habitat has on biological
communities, sampling similar habitats at all sampling stations
is important for data comparability and for data interpretation
(Plafkin et al., 1989). Collection of habitat quality data each
time biological data are collected helps to establish the

Figure VII-3 i~lustrates a conceptual structure for the
attributes calculated or measured for a biological assemblage
during a biological assessment. Generally, the biological
assemblage at a si~e can ~e characterized by metrics organized
into four classes: community structure, taxonomic composition,
individual conditio~, and biological processes. These are
described below.
Community structure (A) is characterized by measurements of the
variety of taxa and the distribution of individuals among taxa.
Taxa richness is the number of distinct taxa in a sample and
reflects its diversity. The relative abundance of each taxon is
a comparison of the number of individuals in one taxon to the
total number of individuals in the sample. Dominance is
calculated as the percent composition of the dominant taxon
within the total sample. It indicates balance within the
Taxonomic composition (B) refers to the types of taxa in the
sample. Sensitivicy is the number of pollution-tolerant and
intolerant species in the sample. The presence of exotic and
nuisance species is also noted because they can play important
ecological roles and indicate stressed conditions.
Individual condition (C) is more easily measured with fish than
in benthos and periphyton; it refers to the presence or absence
and frequency of diseases and anomalies. Contaminant levels in
the tissues of individuals can also be measured. .
Biological processes (D) occurring at the sample site are
indicated by measurements of species that perform specific
functions within the community. For instance, the functional
feeding groups (e.g., detritivores, filter feeders) indicate the
primary source of energy for the biological system.
Numerous biological metrics have been tested in various
regions of the country (Figure VII-4), primarily for fish and
benthos. Summaries of those used have recently been presented in
tabular form (Gibson et al., 1994; Barbour et al., 1995) and are
reproduced.in Tables'VII-3 and VII-4. The letter (A, B, C, D)
following each metric or group of metrics in Tables VII-3 and
VII-4 indicates to which category of metric listed above it (or
they) belong. Examples of metrics that have been tested and have
had scoring criteria established are those for the montane region
of Wyoming (Table VII-5) and the plains streams of Florida (Table
VII-6). Box VII-2 explains five common metrics and presents
sample data and calculated values for each of the metrics.
Readers should calculate the metrics themselves to be certain
that use of the data for metric calculation is understood.

Limited Effort
Focus on commun~ies
and populations. 4 levels
01 Impairment detected
Figure VII-2. Selection and application of the different tiers of RBP depend on monitoring objectives.
whereas RBP III involves identification to the lowest practical
level, generally genus or species. These data are used to
calculate or enumerate a variety of values, or metrics. Each
reflects a different characteristic of community structure and
has a different range of sensitivity to pollution stress (Plafkin
et al., 1989). Appropriately developed metrics can be used to
draw conclusions about different aspects of the biological
condition at a site, and measurements of multiple metrics in a
biological assessment will yield a more accurate representation
of the overall biological condition at a site. Gray (1989)
stated that the three best-documented biological responses to
environmental stressors are a reduction in species richness, a
change in species composition to dominance by opportunistic
species, and a reduction in the mean body size of organisms.
Though the last type of biological response (change in mean body
size) may be well-documented, it is rarely used in the more
common bioassessment protocols because the level of effort for an
accurate interpretation can be prohibitive.

T bl VII ') F
f h
.ct b'
I (PI flc"
I 1989)
a e - -. Ive tIers 0 t e rap! lOassessment proroco s a In et a. 
.Level or   Organism Group Relative Level of Effort Level of Taxonomyl Level of Expertise
 Tier       Where Performed Required
I   benthic invertebrates low; 1-2 hr per site (no order, familylfield one highly- trained biologist
    standardized samolinq)   
    benthic invertebrates intermediate: 1.5-2.5 hr per family/field one highly-trained biologist
II     site (all taxonomy performed   and one technician
      in field) .   
    benthic invertebrates most rigorous: 3-5 hr per site genus or species/ one highly-trained biologist
 III     (2-3 hr of total are for lab laboratory and one technician
 IV   fish low: 1-3 hr per site (no not applicable one highly trained biologist
     fieldwork involved)   
    fish most rigorous; 2-7 hr per site species/ field one highly trained biologist
V     (1-2 hr per site are for data   and 1-2 technicians
" ~aytlies. stOnellies. and caddisflies. respectively.
approaches and are useful for setting priorities for more
intensive s~udy. RBP IV is a screening technique used to survey
persons knowledgeable about the fish in an area. It is not
described here; for further information about RBP IV, consult
Plafkin et al. (1989).
Selection of appropriate organisms and protocols for
biological assessment depends on the objectives of the monitoring
study (Figure VII-2). RBP benthic protocols have been applied in
freshwater streams and wadable rivers, and their applicability is
presently limited to these water bodies. Fish RBP protocols have
been used in freshwater streams and larger rivers and are
applicable to both. RBP-type methods for fish and invertebrates
have been adapted for use by many states and federal agencies and
are in use across the country (Southerland and Stribling, 1995).
The Multimetric Approach for Biological Assessment
Accurate assessment of biological condition requires a
method that integrates biotic responses through an examination of
patterns and processes from the organism to ecosystem level (Karr
et al., 1986). The rapid bioassessment protocols (Plafkin et
al., 1989) discussed above make use of an array of measures that
individually provide information on diverse biological attributes
and, when integrated, provide an overall indication of biological
The raw data collected during a biological survey consist
entirely of taxonomic identifications and numbers of individuals
within each taxon. The level of identification-whether to
family, genus, or species-depends on the method being used. For
instance, RBP II involves identification to the family level,


/// Referenc~,,-
/ Sites '-.,
", Acceptable? /'~

'" "",~///
I Reference Sites
No Reference Sites
I Where

"natural" sites
I ~~bn,"
expectations :


"~I Biological I
: Integri1y
: Expectation I
---'..-- ---
More Than;
Minimally :
Disturbed :
Ecological I
Modeling I
.~--..----.- .
, No 'natural" !
sites exist. '
select best :
: (may requirei
: sampling 0111
: sites), I
; No "natural" ,
, sites exist.
select best '
: (may require!
sampling all
! sites). :
I i

Upper Tail
Use (1) nelghbortng site
classes. (2) expert
consensus. or (3)
composite of "best'
ecologicai information
I Intertm I
i Expectation i
: I
, I
i HypOtret1cal I
: Expecta1lon I
Figure VII-I. Approach to establishing reference conditions (Gibson et al. 1994).
The five protocols differ in the level of effort, taxonomic
level, and expertise required to perform them, and in the
applicability of the data obtained (Table VII-2). More intensive
bioassessments (RBPs III and V) give the most useful information
for trend analysis and establishment of a baseline for problem
diagnosis. RBPs I and II are less intensive bioassessment

would not be considered candidates for reference sites because
chey are not representative of the norm of the region.
Reference conditions are established for ecologically
homogeneous regions. Ecoregion boundaries delineated by Omernik
(1987) are appropriate in many cases for the establishment of
regional bounqaries for reference condition applicability.
Omernik used the perceived patterns of four combined causal and
integrative factors-land use, land surface form, potential
natural vegetation, and soils-to delineate 76 ecoregions in the
conterminous United States. The size of each ecoregion is a
function of its within-region homogeneity relative to between-
region variation. The ecoregion concept is useful for water
quality management because waterbodies within ecoregions are
relatively homogeneous and can therefore be managed similarly.
Omernik (1987, 1995) found that hydrologic units such as
river basins cannot be used to accurately delineate ecoregions,
but that within an ecoregion there may be separate watersheds or
subwatersheds. Therefore, surveys and monitoring conducted in
several watersheds are strengthened by the ecoregion framework.
Characteristics other than ecoregion are also helpful in
classifying sites. For example, the Wyoming Department of
Environmental Quality (DEQ) found that elevation distinguishes
stream classes within the Middle Rockies Ecoregion. EPA's
Biological Criteria: Technical Guidance for Streams and Small
Rivers (1994) describes the process for classifying sites and
selecting reference sites.
In a landscape that is heavily altered by agricultural
activity, silviculture, industrial-commercial development, or
urbanization, undisturbed streams or reaches might not exist, and
reference conditions might need to be determined based on best
professional judgement of that which is likely attainable,
historical records, or another means of estimation. The most
appropriate approach to establishing reference conditions is to
conduct a preliminary resource assessment to determine the
feasibility of using reference sites (Figure VII-i). If the use
of reference sites is not an alternative because "natural" sites
do not exist and "minimally impaired sites" are unacceptable,
then some form of simulation modeling might be the best
alternative. Biological attributes can be modeled from
neighboring regional site classes, expert consensus, and/or a
composite of "best" ecological information. Such models might be
the only viable means of examining significantly altered systems.
The expectations derived from these models should be regarded as
hypothetical or temporary until more reliable information is
Rapid Bioassessment Protocols
EPA has recommended a set of rapid bioassessment protocols,
or RBPs, that use benthic macroinvertebrate and fish communities
to assess biological condition in streams and wadable rivers.

region created f~om information gathered at multiple reference
sites. The reference condition accounts for natural variability
in the biological communities within a region because it is
established using data from reference sites from different
streams in the region. Between-region differences in reference
conditions can be large, so reference conditions established for
a particular ecoregion should be used for the interpretation of
data from that region. For instance, reference conditions for a
mountainous region should not be
used as a basis for analyzing
sites monitored in a lowland
plains area.
The overall goal of
establishing a reference
condition is to describe the
natural potential of the biota
for the waterbody and habitat
types characteristic of the
region, independenc of the extent
of human degradacion. Reference
conditions account for
environmental variability and
thus minimize background "noise"
as a factor when making comparisons among reference and monitored
sites. As described above, comparison of the biological
communities and physical habitats at monitored sites to the
appropriate regional reference condition indicates the degree and
possible cause of biological impairment. For instance, if the
habitat at a monitored site appears to be in good condition but
the benthic macroinvertebrate or fish species differ from those
of the reference condition, poor water quality resulting from
point or nonpoint source pollution might be responsible. If
habitat degradation is noted and the biological condition is
impaired, physical habitat restoration might be necessary to
improve the biological condition. Refer to the summary of the
Process of Metric Selection, Validation, and Development of
Reference Conditions in Box VII-1 (p. VII-11) for a step-by-step
explanation of the process of developing reference conditions.
A reference condition can be formulated from historical data
sets, from extrapolation from ecological or other information, or
from multiple reference sites (Gibson et al., 1994). However,
the availability of candidate reference sites, the preferred
approach, dictates which method might be most appropriate. There
are two primary criteria for selecting candidate reference sites:
minimal impairment and representativeness (Gibson et al., 1994).
The minimal impairment criterion acknowledges that pristine sites
are nonexistent in a region and are not likely to become
available. Sites with the least amount of impairment, therefore,
are used as reference sites. The representativeness criterion
refers to the requirement that reference sites be representative
of a particular region or class of sites. Surface waters that
are unique in some way or unusual within the particular region
Reference site - a specific location on a
waterbody that is minimally impaired and
is representative of the expected
ecological integrity of other localities on
the same waterbody or nearby
Reference condition - a set of selected
measurements or conditions of minimally
impaired waterbodies characteristic of a

Step 5. Scoring of Metrics. Develop bioassessment scoring criteria for each of the core
metrics, within each site class. Using scoring criteria, normalize metrics.
Metrics vary in their scale; they are integers, percentages, and ratios. Prior to developing an
integrated index for assessing biological condition. it is necessary to normalize the core metrics
via a transformation to unitless scores. This is accomplished by selecting the lower quartile of
the range in reference metric values, which assumes that only the upper 75% of the reference
values are representative of natural conditions for the site class. Therefore, the upper 75% of
the values are given the highest score, and the remainder of the range is bisected to give
progressively lower scores. The figure below demonstrates this approach.
Middle Rockies - Central Ecoregion
30 r'"
75th %ile-
25th %ile-
10 t
o '
1 .
Site Class
Assignment of unitless scores (5, 3, 1)
to reference metric values
Step 6. Index Development. Following development of scoring criteria for all metrics, score
metric values from all sites, reference and impaired, and sum bioassessment points. The
reference condition is the distribution of total bioassessment scores from multiple reference site
representing an individual site class.
The index is a means of integrating information from the various measures of biological attributes
(or metrics). In monitoring, the "tracking" of an index value that integrates all of the core metrics
will enable an interpretation of improvement or degradation of the biological assemblage.
Aggregation of metric scores simplifies management and decision making so that a single index
value is used to determine whether action is needed.
Box VII-I. (continued)

Step 4. Determination of Core Metrics. Calculate metrics based on biosurvey data (see Box
VII-2, page VII-27). Compare value range of each candidate metric from reference sites to those
from impaired sites. Metrics become part of the core analysis if the data show them able to
discriminate between reference and impaired sites.
Core metrics are those remaining following initial candidate metric screening that will discriminate
between good and poor quality ecological conditions. or will provide a basis for monitoring
changes over time. Metrics that use the relative sensitivity of the monitored assemblage to
specific pollutants or stressors, where these relationships are well-characterized, can be useful
as a diagnostic tool. Discriminatory ability of metrics can be evaluated by comparing the
distribution of each metric at a set of assumed reference sites with the distribution of the same
metric values from a set of known impaired sites within each site class. This is done to calibrate
the metrics. If there is minimal or no overlap between the distributions, then the metric can be
considered to be a strong discriminator between reference and impaired conditions. The
following two figures, (a) and (b), graphically demonstrate the difference between strong and
weak metrics.
"''- Rodnq
! 26
~ 20 _d
E ,.
~ 8
::r:: Min-Mu
CJ 25~75%
a _VIIIuo
~ 2
(a) Strong metric: Percent Total Sample as Stoneflies
Middle Rodde8 . Cenlral Ecareglon. Wyomng
BenIhc Metrtca
a 92
11 88
';; 80
~ 76
8 72
I 68
11. 64
 0  I
a a I
::r: Mi~
o 25~75%
C Median vatue
b Weak metric: Percent Contribution of 10 Dominant Taxa
Box VII-I. (continued)

The Process for Metric Selection, Validation, and Development
of Reference Conditions
Step 1. Candidate Metric Selection. List all metrics that are relevant to the biological
communities being used for assessment of a site or waterbody.
Metrics allow the investigator to use meaningful indicator attributes in assessing the status of
communities in response to perturbation, or to monitor trends in the health of the communities.
All metrics that have relevancy to the assemblage under study and will respond to the targeted
stressors are potential metrics for consideration. For example, the number of taxa as a
measure of diversity can be identified for various groups of organisms that are relatively
sensitive to environmental change (i.e., mayflies, darters, diatoms, etc.); the relative
dominance of a single taxon is informative of a pollutant situation: an imbalance in trophic
structure is suggestive of an adverse effect on food source.
Step 2. Reference Site Selection. Select candidate reference sites from maps and other
available information and confirm through reconnaissance. Sites are confirmed through the
existence of non-degraded physical habitat and the absence of known contaminant sources.
Assuming that reference sites are available (See explanation in text (p. VII-10) if reference
sites are not available), candidate sites are selected to represent the "natural" condition within
a region or area. These sites should be representative of:
Extensive, natural, riparian vegetation
Natural channel structures typical of region .
Natural hydrograph (typical flow patterns and discharges)
Absence (or minimal presence) of sources of perturbation
These sites can be identified from existing GIS or landuse maps and confirmed through site
Step 3. Site Classification. Determine site classes based on mapped information or
regional water quality characteristics such as, e. g., ecoregion or subecoregion, gradient,
alkalinity, and hardness.
The purpose of site classification is to partition the variability within each biological metric to
enhance the ability to discriminate impairment from non-impairment, or to improve the
interpretation of change in monitoring. Physicochemical aspects, e.g., ecoregions, alkalinity,
pH, elevation, drainage area, etc. are analyzed to derive site classes. Then, the biological
metrics are used to confirm site classes and partition variability.
For example, the number of taxa in a set of reference sites might range between 10 and 40
species. However, in ecoregion A, the number of taxa is between 10 and 25 to represent a
natural community. In ecoregion S, the number of species range between 20 and 40. The
classification of sites by ecoregion, in this case, allows for a better understanding of natural
variability than a universal compositing of all reference sites.
Box VII-l.

the evaluation of biological communities. (as is done by Ohio EPA
and Delaware DNREC) .
The habitat assessment phase of
composited reference site bioassessment is
not different from that of the screening-
level bioassessment approach. Refer to
that section (C.l) for a description of
what is involved.
The biota collection phase for
composited reference site bioassessment is
similar to that of a screening-level .
bioassessment, but involves the collection
of additional samples to detect subtle
differences in NPS pollution impacts. Specimen identification is
generally done in the laboratory to the genus or species level.
This level of detail allows for a more accurate analysis of
community structure and biological condition. Data analysis
using genus- and species-level identifications can provide
information on the generic cause of impairment (nutrient
enrichment, toxic pollutants, or habitat degradation). To gain
this level of insight, however, it is necessary to be able to
distinguish the effects of NPS pollution impairment from natural
variability of the populations being
sampled. Reference condi.tions must be
established for this purpose.
Additionally, area- or region-
specific metrics must be established
before the composited reference site
bioassessment approach can be used
effectively. During the process of
establishing reference conditions for an
area, metrics specific to the area are
selected and calibrated. Box VII-l
describes the development of metrics and
associated reference conditions in a
step-by-step manner.
Reference Sites and Conditions
Biogeography - the
geographic distribution of
plants and animals that
results from a combination
of their evolutionary
history, mobility, and
ability to adapt to
changing conditions
Metric - an enumerated or
calculated term representing
some aspect of biological
assemblage structure,
function, or other measurable
feature and which changes in a
predictable way in response to
environmental (including
human) influences
In biological assessment, macroinvertebrates and fish are
commonly used as indicators of the condition of biological
communities. Comparisons are made between macroinvertebrates and
fish found at undisturbed sites and those found at monitored
sites to determine how closedly they resemble one another. The
undisturbed, or reference sites, are aquatic habitats that are
assumed to fully support natural biological communities. The
greater the difference is between reference and monitored sites,
the more disturbed the monitored sites are considered to be. The
disturbance responsible for the difference might be a habitat
change, pollution, or some other stress.
A reference condition is a composite characterization of the
natural biological condition in an ecologically homogeneous

paired-site approach is that the control and treatment
populations do respond similarly to environmental parameters
(Skalski and McKenzie, 1982). It is this similarity of response
that enables one to detect changes due to the treatment. If
control and treatment populations are chosen that respond
differently tQ environmental factors, then the effect of the
treatment cannot be determined. Identification of specimens to
the genus o~ species level should be sufficient to determine
significant changes in biological communities at pairs of sites.
Some laboratory work may be necessary or desirable to be certain
that accurate identifications have been made.
Pretreatment sampling establishes the pattern of changes at
the control and treatment sites. Skalski and McKenzie (1982)
recommend that the proportional abundance of populations of
macroinvertebrates at control and treatment sites be the
paramete~ used to determine any change attributable to the
treatment. Further discussion of monitoring program design and
data analysis for the paired-site approach can be found in
Skalski and McKenzie (1982) and Richards and Minshall (1992).
Composited Reference Site Bioassessment
Composited reference site bioassessment is an approach
wherein biological communities at monitored sites are compared to
"reference" biological communities, or reference conditions,
which represent biological communities in unimpaired or
minimally-impaired waterbodies in the region of interest.
Reference conditions are discussed in greater detail below. The
approach is useful for ranking sites according to the degree by
which they differ from the unimpaired status, which is equated
with the degree of impairment at the monitored site. The
composited reference site approach integrates characteristics
among broad geographical areas and watersheds and thus is a more
comprehensive assessment and monitoring approach than the paired-
site approach. It also requires the greatest amount of time,
specialized expertise, and field and laboratory effort to
perform, largely because in order to conduct a composited
reference site biological assessment and monitoring program, it
is necessary to initially establish a reference database for the
region in which monltoring will be conducted.
Biological sampling for the composited reference site
approach is conducted at each of the reference sites on a
periodic basis, which can vary from region to region. Once a
composite of reference sites has been established, monitoring can
be conducted on a randomly-selected subset of the reference
sites, and thus, reducing the intensity of monitoring. All
monitoring of reference sites and assessment sites (unknown
condition) is done within a specific index period, which reduces
temporal variation. This approach can include more than one
index period (as in the Florida nonpoint source program) but is
usually based on a single index period established to optimize

whether che biota at a site are moderately or severely impaired
using this approach, but sUDsequent sampling is often necessary
to confirm any findings. ~~e mosc useful application of this
approach is for problem idencification or screening and for
secting pollution abatemen~ priorities. Florida DEP has
developed a b~ological screening cool, the BioRecon, that is used
for this purpose in their ~onpoint source pollution concrol
paired-site approach
The paired-site approach for biological monitoring involves
the use of control and treacment sites for the detection of
changes in biological condi~ion. It is useful for the detection
of changes due to changes in water quality, habitat quality, or
land use features. A key element of the approach, as the name
implies, is the simultaneous monitoring of sites that are not
affected by the changes for which the monitoring is being
conducted (concrol sites) and separate sites that are affected by
a "treatment" (treatment si~es), '.'lhich might be BMP
implemencation or another form of NPS pollution control. To
provide reliable and. valuable data, the control and treatment
sites must be as similar as possible. "Similarity" in this
context means chat the biological populations to be monitored at
both the control and treatment sites must respond similarly to
changes in environmental parameters (Richards and Minshall, 1992;
Skalski and McKenzie, 1982). Paired sites can be similar
watersheds within a region or separate sites within a watershed
that are located upstream and downstream from a nonpoint source
of pollution.
Habitat assessment is as important in the paired-site
approach as it is in the other biological assessment approaches.
Because of the influence of surrounding landscape features on
aquatic biota, control and treatment sites that are influenced by
the same habitat features should be chosen. This implies that
the hydrologic characteriscics (flow, waterbody type, channel
width, etc.) of the waterbodies in which the control and
treatment sites are located, surrounding land use, slope and soil
type, and riparian vegetation should be as nearly identical as
possible. For the same reasons, similar habitats should be
sampled at the control and treatment sites. Type of substrates,
locations in the streams (e.g., center or edge of stream), and
nature of surrounding aquatic vegetation and debris should be
nearly identical. All habitat features should be thoroughly
investigated prior to the final selection of the control and
treatment sites to be monicored to ensure their similarity.
Determination that the biota at control and treatment sites
respond similarly to enviroTh~ental factors is extremely important
and usually requires separate sampling before any treatment is
introduced at the treatment sites. It is important that the
biota at control and treatment sites vary similarly both
spatially and temporally, and a critical assumption of the

The first element of the screening-level approach, as with
all biological assessment approaches, is a habitat assesement.
The instream habitat should be inspected for the amount of
ewDeddedness, type of bottom substrate, depth, flow velocity,
presence of scoured areas or areas of sediment deposi~ion,
relative abundance of different habitat types (pools, riffles,
runs), presence of woody debris, and aquatic vegetation. If
conducting the assessmen~ in a stream, record whether the stream
channel has been altered. If the assessment is in a lake,
reservoir, or pond, determine whether artificial bottoms or
shorelines (beach sand, cement) have been installed. The
riparian habitat must also be inspected for the amount of
riparian cover, evidence of bank erosion, areas where livestock
enter to water, and proximity of altered land uses (e.g.,
residential, agricultural, silvicultural, or urban). Determine
the width of any natural vegetation buffer areas. The
surrounding land use should be noted as a percentage of each type
(e.g., 40 percent agriculture, 40 percent wooded, 20 percent
residential) .
The biological sampling portion of the streamside
bioassessment is relatively simple. No laboratory work is
involved, and it can be conducted by a person with a basic
knowledge of aquatic biology. Macroinvertebrates should be
collected from differen~ instream habitats, with data from each
habitat kept separate. Calculations of relative abundance and
number of orders/families represented are 'then made.
Calculations of basic community structure can also be made if
specimen identifications are sufficiently detailed to allow
determination of the functional feeding group the organisms
occupy. Sample calculations of relative abundance and community
structure are presented in Box VII-2 (page VII-27). Different
functional feeding groups dominate in different habitats
(filterers and scrapers dominate in riffle/run habitats whereas
shredders dominate areas with large amounts of woody debris), so
these calculations require that distinct habitats be sampled.
Samples 'of invertebrates from woody debris of all types should be
taken, including sticks, twigs, leaves, needles, etc. Freshly
fallen debris will generally support a less representative
macrobenthos than debris that is at least 50 percent decomposed.
A reference collection of biological organisms, usually
available at a museum or university, should be used to positively
identify any specimens whose identification is in doubt. A
reference collection is a collection of preserved specimens of
organisms from an area that is the same or similar to that where
monitoring is done.
Since a screening-level bioassessment is done without the
benefit of comparison to unimpaired sites, a judgement of
biological condition is made based solely on the presence or
absence of indicator taxa, dominance of nuisance or sensitive
taxa in the sampled habitats, or evenness of taxonomic
distribution. A trained biologist will be able to determine

The aspects of habitat structure mentioned above (channel
morphology, floodplain size and shape, etc.) should be inspected
during habitat assessment. The aspects are separated into
primary, seconda~y, and tertiary groupings corresponding to their
influence on small-, medium-, and large-scale aquatic habitat
features (Plafkin et al., 1989). The status or condition of each
aspect of habita~ is characterized as falling somewhere on a
continuum from optimal to poor. An optimal condition would be
one that is in a natural state. A less than optimal condition,
but one that satisfies most expectations, is suboptimal.
Slightly worse is a marginal condition, where degradation is for
the most part moderate and severe in some instances. Severe
degradation is characterized as a poor condition. Habitat
assessment field data sheets (see Plafkin et al., 1989) provide
narrative descriptions of the condition categories for each
parameter. Habitat can be assessed visually, and a number of
biological assessment methods incorporate assessments of the
surrounding habitat (Ball, 1982; Ohio EPA, 1987; Plafkin et al.,
1989; Platts et al., 1983).
The relationship between habitat quality and biological
condition is generally one of three types: (1) the biological
community varies directly with habitat quality-water quality is
not the principal factor affecting the biota; (2) the biological
community is degraded relative to the potential of its actual
habitat-water quality degradation is implicated as a cause of the
biotic condition; and (3) the biological community is elevated
above what actual habitat conditions should support-organic
enrichment in the water or alteration of energy source is
suspected as a cause (Barbour and Stribling, 1991). A clear
distinction between impacts due to watershed (i.e., large-scale
habitat), stream habitat, and water quality degradation is often
not possible, so it is difficult to determine with certainty the
extent to which biological condition will improve with specific
improvements in either habitat or water quality.
Overview or Biological Assessment Approaches
Screening-level or Reconnaissance Bioassessment
The simplest bioassessment approach that can be used to
obtain useful information about the status of an aquatic
community and condition of a site is a screening-level, or
reconnaissance, bioassessment (USEPA, 1994, Plafkin et al.,
1989). This type of survey can be done inexpensively and with
few resources. If conducted by a trained and experienced
biologist with a knowledge of aquatic ecology, taxonomy, and
field sampling techniques, the results of screening-level
bioassessment will have the greatest validity. This
bioassessment method is most often conducted using benthic
macroinvertebrates and is described in detail in Plafkin et al.
(1989) and by the U.S. Environmental Protection Agency (USEPA
1994) .

a e - enera stren2:t s an ImitatIOns a 10 02:lca momtonn2: an assessment approac es.
Properly developed methods. metrics, and reference Development of regional methods, metrics. and reference
conditions provide a means to assess the ecological conditions takes considerable effort and an organized and
condition of a wateroodv   well-thought-out desiqn 
Simpler bioassessments' can be relatively inexpensive and Rigorous bioassessment can be expensive and requires a
easilv performed with minimal traininq  hiqher level of traininq and eXDertise to implement
Bioassessment indicates the cumulative impacts of Biological assessment information does not provide
multiple stressors on biological communities. not only information on sources of pollution or cause-effect
water quality    relationships 
Biological communiiy condition reflects both short- and There may be a lag time between pollution abatement or BMP
long-term effects    installation and community recovery, so monitoring over time
      is required for trend detection 
Biological assessment data can be interpreted based on The optimal season for biological sampling season varies
regional reference conditions where reference sites for the regionally, and sampling during multiple seasons may be
immediate area beinq monitored are not available required in some areas 
Bioassessments involving 2 or more organism groups at Biological assessment does not distinguish between the
different trophic levels provide a reasonable assessment effects of different stressors in a system impacted by more
of ecosystem health   than one stressor 
:ommunities to exist. Habitat quality encompasses the three
:actors habitat structure, flow regime, and energy source.
{abitat structure refers ,to the physical characteristics of
3tream environments. It comprises channel morphology (width,
iepth, sinuosity); floodplain shape and size; channel gradient;
Lnstream cover (boulders, woody debris); substrate types and
iiversity; riparian vegetation and canopy cover; and bank
3tability. Flow regime is defined by the velocity and volume of
vater moving through a stream. Energy enters streams either as
:he input of nutrients in runoff or ground water, as debris
(e.g., leaves) falling into streams, or from photosynthesis by
~quatic plants and algae.
These three factors-habitat
structure, flow regime, and energy
source-are interrelated and make stream
:nvironments naturally heterogeneous,
Nherein habitat structural features that
jetermine the assemblages of
nacroinvertebrates can differ greatly
Nithin small areas-or microhabitats-or
Ln short stretches of a stream. For
Lnstance, woody debris in a stream
~ffects the flow in the immediate area,
~rovides a source of energy, and offers
~rotection to aquatic organisms. Curvature (sinuosity) in a
stream affects currents and thereby deposition of sediment on the
Lnner and outer banks. Rocks and boulders create turbulence,
Nhich affects dissolved oxygen levels; deep, wide portions are
~reas of lowered velocity where material can settle out of the
Nater and increased decomposition occurs.
T bl VII I G
fb' I
Microhabitat - in streams, any
small-scale physical feature
contributing to the texture of the
habitat such as the type and
structure of substrate particles;
submerged, emergent, or
floating aquatic vegetation; algal
growths; snags and woody
debris; or leaf litter

assessments (including reference conditions and metrics, which
are discussed later). Establishing these protocols can require
intensive training and a considerable level of effort, and
~herefore can be quite expensive. Also, detailed biological
assessments require some knowledge of the aquatic communities
specific to the region where the assessments are being conducted.
The biological assessment methods and the means of interpreting
the results from assessments are not available for many habitats
and regions of the country. Establishing a biological assessment
and monitoring program, therefore, can require significant
amounts of time, staff, and money.
Establishment of a biological assessment program is further
complicated by the fact that for a given biological community,
one season may be most appropriate for sample collection. It is
often not known which season is best for obtaining reliable data,
or whether it might be necessary in a particular region to take
samples during one optimal season per year or during multiple
seasons. Annual variations in the status of biological
communities at any given time of year, for instance due to the
severity of winter, also complicate data interpretation. The
seasonality element of a biomonitoring program is best determined
with some well-designed investigative preliminary sampling.
?inally, there can often be a lag between the time at which
a toxic contaminant or some other stressor is introduced into a
waterbody and a detectable biological response. As such,
biological monitoring is not appropriate for determining system
response due to short-term stresses such as storms. Similarly,
there is often a lag time in the improvement of biological
communities following habitat restoration or pollution problem
abatement. The extent of this lag time is difficult if not
impossible to predict. Other factors also determine the rate at
which a biological community recovers, e.g., the availability of
nearby populations of species for recolonization following
pollution mitigation and the extent or magnitude of ecological
damage done during the period of perturbation (Richards and
Minshall, 1992). In extreme cases, a biological community might
not recover following pollution abatement or habitat restoration.
Both the possibility of the failure of a biological community to
recover from perturbation and unpredictable lag times before
improvement is noticeable have obvious implications for the
applicability of biological monitoring to some NPS pollution
monitoring objectives. Table VII-l summarizes the strengths and
limitations of the biomonitoring approach.
Habitat Assessment
Habitat assessment is an important component of biological
assessment and monitoring. As mentioned in the introduction, the
quality of the physical habitat is important in determining the
structure of benthic macroinvertebrate and fish communities.
Habitat quality refers to the extent to which habitat structure
provides a suitable environment for healthy biological

Some NPS pollutanc ~~puts such as wet-weather runoff of
urban contaminants or sediment are highly variable in time, and
biological monitoring can De a useful approach for monitoring
this type of NPS impact. Biological monitoring can be used to
assess the overall impacc of multiple stressors, although it
might not proyide informac~on abouc the relative magnitude of
each stressor.
Knowledge of the nacural physical habitat and biological
communities in an area is importanc for interpreting biological
assessment data. Biological and habitat data collected from
numerous sites that are in good or near-natural condition can be
used to determine the cype of biological community that should be
found in a particular aquatic habitat. In areas where natural
conditions do not exist (due to past disturbances), historical
data or the best professional judgment of knowledgeable experts
can somecimes be used to decermine the expected natural
condition. This nacural condition has been referred to as
reflecting biological incegrity, defined by Karr and Dudley
(1981) as "the capaDility of supporting and maintaining a
balanced, integrated, adaptive community of organisms having a
species composition, diversity, and functional organization
comparable to that of the natural habitat of the region." Highly
detailed biological assessments are comparisons of biological
conditions at a test sice co the expected natural community and
are thus a measure of the degree to which a site supports (or
does not support) its "ideal" or potential biological community
(Gibson et al., 1994). Other levels of biological assessment
involve comparisons of impacted sites to control sites, the
latter being sites that are similar to monitored sites but which
are not affected by the stresses that affect the monitored sites
(Skalski and McKenzie, 1982). paired-watersheds or upstream-
downstream approaches are examples. A knowledge of the natural
condition is still valuable for accurate data interpretation when
control sites are used (Cowie et al., 1991).
Limitations of Biological Assessment
Although biological assessment is useful for detecting
impairments to aquatic life and assessing the severity of the
impairments, it is not necessarily a measure of specific
stressors. Thus, ic usually does not provide information about
the cause of impairment, i.e., specific pollutants or their
sources. Certain biological indicators do provide information
about the types of stress affecting a biological community.
However, if stress to a stream community is chemical, chemical
monicoring in addition to biological monitoring is required to
determine the actual pollutants and their sources responsible for
biological or water quality impairments. Chemical monitoring and
toxicity tests are also necessary to design appropriate pollution
control programs.
A detailed biological monitoring program requires the
development of sampling and analysis protocols for biological

and excessive sediment loading-and thus provide an overall
measure of the aggregate impact of the stressors. While
biological communities respond to changes in water quality more
slowly than water quality actually changes, they respond to
stresses of various degrees over time. Because of this,
monitoring changes in biological communities can be particularly
useful for detersining the impacts of infrequent or low-level
stresses, such as highly variable NPS pollutant inputs, which are
not always detected with episodic water chemistry measurements.
Improvements in waterbody condition after the implementation of
best management practices (BMPs) can sometimes be difficult to
detect, and biological assessment can be useful for measuring
such improvements. Biosurvey techniques useful for detecting
aquatic life impairments and assessing their relative severity
are discussed below.
A small number of factors are often key in determining the
structure of a community and its response to stress, e.g., type
of substrate, or the riparian vegetation that provides organic
material to the stream, regulates temperature, and provides bank
stability (National Research Council, 1986). Landscape features
such as soil type, vegetation, surrounding land use, and climate
also have a well-documented influence on water chemistry and
hydrologic characteristics. Finally, water quality, as
influenced by landscape features and anthropogenic sources of
pollutants, has a direct effect on aquatic biological
The quality of the physical habitat is an important factor
in determining the structure of benthic macroinvertebrate and
fish assemblages. The physical features of a habitat include
substrate type, amount of debris in the waterbody, amount of
sunlight entering the habitat, water flow regime (in streams and
rivers), and the type and extent of aquatic and riparian
vegetation. Even though there might not be sharp boundaries
between habitat features in a stream, such as riffles and pools,
the biota inhabiting them are often taxonomically and
biologic~lly distinct (Hawkins et al., 1993). Habitat quality is
assessed during biological assessment and is a measure of the
extent to which the habitat provides a suitable environment for
healthy biological communities.
Natural biological communities are generally diverse,
comprising species at various trophic levels (e.g., primary
producers, secondary producers, carnivores) and levels of
sensitivity to environmental changes. Adverse impacts from NPS
pollution or other stressors such as habitat alteration can
reduce the number of species in a community, change the relative
abundances of species within a community, or alter the trophic
structure of a community. Biological surveys of select species
or types of organisms that are particularly sensitive to
stressors, such as fish, periphyton, or benthic
macroinvertebrates, take advantage of this sensitivity as a means
to evaluate the collective influence of the stressors on the
biota (Cummins, 1994).

Biological monitoring, as described here, consists of
assessiTIg the condition of the physical habitat and specific
biological assemblages, typically benthic macro invertebrates and
fish, ttat inhabit the aquatic environment. In the true
definition of the term, biological monitoring includes toxicity
testing, fish tissue analyses, and single population surveys
conducted over time. However, for purposes of this document, the
definition of biological monitoring is limited to the concept of
community-level assessments.
This chapter discusses the rationale
behind using biological monitoring as part
of a nonpoint source (NPS) monitoring.
program, gives basic guidance on conducting
biological assessments, provides biological
monitoring program design considerations,
and discusses ways in which biological
assessment data can be used to detect trends in NPS impacts.
Numerous texts and papers have been written on biological
monitoring methods (see references), but methods and means of
interpreting the results from them are still under development
for many habitats and regions of the country. Many state
agencies, such as Ohio Environmental Protection Agency (EPA),
Delaware Department of Natural Resource and Environmental Control
(DNREC), Florida Department of Environmental Protection (DEP),
Connecticut DEP, and New York Department of Environmental
Conservation (DEC), are incorporating biological monitoring into
ongoing and new monitoring programs. The methods for biological
monitoring are thereby being improved, and this in turn is making
biological assessment a more widely accepted and applicable tool
for monitoring programs.
Biological survey approaches differ depending on the
waterbody, i.e., stream, river, lake, estuary, or wetland. EPA
is currently developing bioassessment survey methods appropriate
for use in these different waterbody types.
Rationale and Strengths
of Biological
The central purpose of
assessing biological condition is
to determine how well a waterbody
supports aquatic life.
Biological communities integrate
the effects of different
pollutant stressors-such as
excess nutrients, toxic
chemicals, increased temperature,
Community - any group of
organisms of different
species that co-occur in
the same habitat or area
Biological assessment - an evaluation of
the biological condition of a waterbody
using biological surveys and other direct
measurements of biota in surface waters
Biological monitoring - multiple, routine
biological assessments over time using
consistent sampling and analysis methods
for detection of changes in biological





Monitorino .ell,
(.itft lQ numbe,.)
Precipilolion Gog.
Runoff Gooe
$p, in, (.ilh lD. numbe,)
Te,tace Oullel Pipe
Figure VI -10. Field site 2, Lancaster County , Pennsylvania.
(SOURCE: Pennsylvania RCWP Coordinating Committee, 1984)

Field Site 2:
. . . The planned schedule, approach, and data collection are
similar to those for field si te 1 (Table VI -12) . The only
significant difference is that data collection will concentrate
on nutrients at field site 2; nutrient management BMPs are
planned for this component, so current sediment and pesticide
levels are not expected to change...
Table VI-12.
Monitoring plan for field site 2.
1984 - 1986 PRE-BMP
1984 BMP
1986 - 1988 POST-BMP


Pennsylvania, 1984)
The location[s] of the data collection facilities [at this
field site] are shown in Figure VI-10. Field site 2 is in a
carbonate area and will be monitored for two years for pre-BMP
moni toring. . .

(f) f-'-
.. <:
Table VI-11.
Monitoring plan for field site 1.
1982 - 1984 PRE-BMP
1984 - 1985 BMP
1985 - 1987 POST-BMP




Pennsylvania, 1984)

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Table VI-10.
Monitoring plan for small watershed site.
1982 - 1985 PRE-BMP
1985 - 1986 BMP
1986 - 1988 POST-BMP


Pennsylvania, 1984)
.. . One gage, four additional base-flow sites, and all the
ground water sites are located in the eastern end of the basin
where BMF implementation is projected to be greatest (Figure
VI - 8) . . .
Field Site 1:
.. .In addition to the same data that is being collected at the
small watershed site (with the exception of base-flow data),
data are being obtained from lysimeters (Table VI-II).. . The
locations of the data collection facili ties at [one of the
field sites] are shown in Figure VI-9

::J '"Ij
ro 1-'-
:s ~
o ti
ti ro
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ro rt
::J 1-'-
::J 0
(f) ::J
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at rea. gage
carbonate area
noncarbonate area
baae-flow aite
ground-vater alte

Table VI-9.
Monitoring plan for
Pennsylvania, 1984.)
1982 - 1983
1985 -:- 1986
1988 - 1989





... [The 43 ground water sites] include 42 private domestic, and
farm wells and one spring... .Of the 43 ground water sites, 33
are located in carbonate rocks (Figure VI-7). This difference
in geology [carbonate vs. noncarbonate areas] plays an
important role in the quality of water. The areas having the
highest levels of nutrients, sediment, pesticides, and bacteria
in water consistently coincide with areas underlain by
carbonate rocks. This is probably due to the greater number
of farms in the carbonate areas and the greater permeability
of the carbonate rocks. Because of the grea ter problems in the
carbonate areas, the regional network, as well as the other
three monitoring components, are concentrated in the carbonate
Small Watershed Site:
. . . In addi tion to ground water, surface water,
precipitation data, data on nutrients in soils and manure
are being collected [at this site] (Table VI-lO). Also,
detailed land-use data are being collected.

components consist of intensive monitoring on a field scale.
[Both field sites are on farms].
All four components are designed to permit the comparison of
water quality before and after the implementation of BMPs. As
such, they include pre-BMP and post-BMP monitoring periods.
Al though the basic strategy is the same, each component
addresses a slightly different problem (Table VI-8). All four
components address the problem of nutrients in ground water and
surface water; three address the sediment problem in surface
water; and two address the pesticide problem in ground and
surface waters.. .Because the single most important source of
water quality problems appears to be the excess of nutrients,
nutrient management BMPs are emphasized in most of the
monitoring components.
Table VI-8.
Specific problems to be addressed for each monitoring
(SOURCE: Pennsylvania, 1984.)
Reqional Network (188 MI')



100 ACRES)
Regional Network:
The monitoring schedule for the regional network consists of
three one-year monitoring periods: (1) a pre-BMP period; (2)
an early post-BMP period; and (3) later post-BMP period (Table
VI-9)... The quality of ground and surface waters, as well as
precipitation, is being monitored.

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precipi ta tion in up to the three rain gages,
stages for computing discharge.
(4 )
up to two
For the City's street sampling task various vacuu, hose and
gulper attachment combinations were tested. Relative air flows and
suction pressures in the hose were monitored for different test
set-ups. Both one- and two-vacuum configurations and 1.5 inch
hoses in lengths varying from 10 to 35 feet were tested, along with
a Vacu-Max uni t. The standard "reference" system was two vacuums
and a 35-foot hose. The best suction and higher air velocities
were observed with two vacuums and short hose lengths (10 feet),
but the short hose length would require that the vacuums be
dismounted from the truck at each subsampling location. The longer
hose, with the'two vacuums, was judged adequate, and resulted in
great cost and time savings. .
A pick-up
consisting of
and wand, and
The truck had
truck was used to cary the equipmen t componen ts ,
a generator, tools, fire extinguisher, vacuum hose
two wet-dry vacuum units during sample collection.
warning lights, including a roof-top flasher unit.
Two industrial vacuum cleaners (2 -hp) wi th one secondary fil ter
and a primary dacron filter bag were used. The vacuum units were
heavy duty and made of stainless steel to reduce contamination of
the smaples. The two 2-hp vacuums were used together by using a
wye connector at the end of the hose. This combination extended
the useful length of the 1.5 inch hose to 35 feet and increased the
suction. A wand and a gulper attachment were also used.
Alternate streetsweeping in the Lake Hills and Surrey Downs
basins, using the unswept basin as a control, was described
earlier. The other control being evaluated is a unique, small,
short-term detention basin at 148th St. The storm sewer system
consists of a main trunk line parallet to the street, which is fed
by short laterals that connect to catchbasins in 148th Avenue and
in adjacent lands. The sewer has a complex system of gates and
valves in five junction boxes that permit the storm water to be
backed up into five grassy swales which serve as detention basins.
Conestoga Headwaters, Pennsylvania RCWP Project
The following are the key elements to the ground water
monitoring program of the Pennsylvania Rural Clean Water Program
(Pennsylvania RCWP Coordinating Committee, 1984, p. 24-26).
There are four components to the monitoring strategy and they
include three scales or levels of monitoring (Figure VI-6).
The first component, the regional network, consists of general
moni toring on a regional scale and incl udes the en tire 188
square-mile area. The second component involves more detailed
monitoring in a small watershed area of about 5.8 square miles
(Little Conestoga Creek basin). The third and fourth

record the dimensions of each catch basin. Sediment volume could
then be calculated from a measurement of sediment depth.
Some experimental design work was done in 1979 and early 1980
to determine the concentrations of some pollutant constituents.
Grab samples of supernatant and sediment were taken from selected
catch basins in each study area and submitted to a contract lab for
chemical analysis. During 1980, two complete catch basin
inventories were made,. recording sediment depth, and thus mass
loading in the system. Monthly inventories are scheduled for 1981.
Since December, 1980, spot checks of fifteen to twenty-five
selected catch basins in each study area have been made after each
significant storm event. This information, along with storm and
street loading data should allow characterization of flushing and
deposition within the sewerage system.
For the toxicant inventory portion of the study, stormwater
runoff samples are collected as flow proportioned composites using
Manning S300T automated samplers ---all teflon and glass contact
surfaces acti va ted by ul trasonic flowmeters, except for the
volatile samples which are collected as grabs early in the storm
events. Samplers and containers are cleaned between events
according to USEPA protocols using "Micro" brand soap and nitric
acid,. the hydrochloric acid and methylene chloride rinses are not
used. Deionized distilled water blanks are taken through each
sampler before use and have proven to be completely clean of
organic and metal contaminants. Street surface dust samples are
collected as described above using a stainless steel vacuum and PVC
flexible hose. No special cleaning protocal has been applied to
the vacuum. Some sample contamination could occur from the PVC
hose, but no functional alternatives [have] been found for
collecting the dust samples. Interstitial water samples from the
stream-bed in Kelsey Creek are collected through aluminum
standpipes set in the stream gravel, using a Manning S3000T sampler
to draw the water up from the perforated base of the standpipe.
This sampling is in conjunction with the "Ecological Impacts of
Stormwater Runoff in Urban Streams" project of the Universi ty of
The equipment used by the City of Bellevue at the Lake Hills
and Surrey Downs si tes for flow-weighted composi te stormwa ter
monitoring consists of a Manning composite samples (S-3000), a
Manning flowmeter with an ultrasonic stage sensor (UF-1100) and a
12 volt power converter. The samplers were factory modified for
priority pollutant sampling. All surfaces contacting the sampler
are either glass or teflon.
For the USGS sampling effort at Lake Hills, Surrey Downs and
148th St., a walk-in instrument shelter was constructed near the
mouth of each catchment for housing a data recording system and
sample control and collection system. A digi tal paper punch
recorder records: (1) clock time, (2) a number code which indicates
if a sample was taken by the automatic sampler, (3) accumulated

The 148th Avenue catchment contains 4,960 feet of 148th Avenue,
a four-lane, divided arterial street, and some adjacent land with
sidewalks, apartments, parking lots, office buildings, and grassy
swales that can be used as detention basins. A little over one-
fourth of the catchment area is taken up by the 148th Avenue street
USGS sample collection and management procedures are
essentially the same at all three sites. A digital paper punch
recorder records: (1) clock time, (2) a number code which indicates
if a sample was taken by the automatic sampler, (3) accumulated
precipitation in up to three rain gages, and (4) up to two stages
for computing discharge. Data are recorded at 5-minute intervals
whenever the gage exceeds a [preset] threshold or whenever there is
measurable precipitation. Precipitation is measured with tipping-
bucket rain gages. Three gages are operated for the Surrey Downs
catchment and two each are operated for the Lake Hills and 148th
Avenue catchments. Rainfall and dry deposition quality samples are
collected at one location in each catchment. Discrete runoff
samples are taken during storms for defining the temporal variation
of water quality during storm hydrographs. Samples are taken at a
preset time interval (5 to 50 minutes) once the stage exceeds a
preset threshold.
The procedures and techniques used by Bellevue for collecting
composite flow and proportional stormwater runoff samples are as
follows. The sampler is triggered at pre-determined increments of
flow by the flowmeter (300 and 500 cubic feet, the former to obtain
more subsamples when small events were expected). The flowmeters
use an ultrasonic transducer to sense relative stage. Stage is
converted to discharge by a programmed microprocessor in the
flowmeter and presented on a circular flow chart as a percentage of
maximum rated flow. The microprocessor is programmed from a
stage/discharge rating developed by the USGS. Storm samples are
removed from the samplers as soon as possible after storms,
typically within two or three hours. Samples are kept on ice until
pH, conductivity and turbidity are measured in-house. Subsamples
are preserved and sent to a contract lab in Seattle for the
remaining chemical analysis.
To obtain street surface particulate samples the Ci ty of
Bellevue used the following procedures. Because the street
surfaces were more likely to be dry during daylight hours
(necessary for good sample collection), collection did not begin
before sunrise nor continue after sunset, unless additional
personnel were available for traffic control. Subsamples were
collected in a narrow strip about six inches wide (the width of the
gulper) from one side of the street to the other (curb-to-curb).
In heavily traveled streets wher traffic was a problem, some
subsamples consisted of two separate half-street strips (curb-to-
crown) .
To carry out the catch basin sampling tasks, all catch basins
in each study area were surveyed for location, length, size and
slope of pipes, and depth of catchment. Another survey was done to

IIDCIIt ......
- -
, --
L 10lNO
. ..... -......... - ....., ..... - ... - ......
. ........
Figure VI-5.
Bellevue sampling sites.
USEPA, 1982c)

.To evaluate methods of transfering the data to ungaged
watersheds in other regions.
-Monitoring activities took place in three catchment areas
(Figure VI-5) (USEPA, 1982c, p. G27-7): (1) Surrey Downs, (2) Lake
Hills, and (3) 148th Avenue. Three groups participated in the
monitoring efforts: the USGS, the City of Bellevue, and the
municipality of Metropolitan Seattle (Metro). Objectives of the
monitoring activities included:
To define pollutant hydrographs for each of the
catchments during approximately 12 storms per year.
To determine the effectiveness of street cleaning
equipment for various levels of effort under the actual
conditions encountered.
To describe the quantities and characteristics of sewerage
system particulates in the study area.
To obtain a continuous mass balance relationship between
total runoff yields and all the sources of urban runoff
To analyze samples for the 129 EPA toxic or "priori ty"
The following, taken from NURP project summaries (USEPA, 1982c,
pp. G27-14 to G27-16), describes in some detail the sampling
approaches and equipment used to meet the monitoring objectives.
Two of the three study catchments, Surrey Downs and Lake Hills,
are single-family residential areas of similar size. These two
basins are used to investigate the effectiveness of street sweeping
for reducing the amount of pollutants in storm runoff. The third
catchment, 148th Avenue, consists mainly of a divided 4-lane
arterial street. The data from this site are used to investigate
the effects of detention basins on the quality of runoff.
The area comprising the Surrey Downs catchment consists of
single family homes and the Bellevue Senior High School. Slopes in
the basin are generally moderate, with the exception of the steep
slopes on the west side. Surrey Downs is relatively isolated from
neighboring communities by the general lack of easy vehicular
access and convenient "short cuts'" through this residential
The Lake Hills catchment contains single family residences and
the St. Louise Parish Church and School. Al though there are
relatively isolated residential areas within the catchment, two
through-streets, which carry more traffic than a typical
residential street, cross the area.


- -
. -
Figure VI-4.
Bellevue stream systems.
(SOURCE: USEPA, 1982c)

~ ,~~-----------

~ ''\..~ J.uASH'HC'T'Ofif

Qq!:J ~ I
) , ~~ ~~
program is described to illustrate the type of monitoring used in
Bellevue (25 square miles, 1982 population about 75,000) is
located in the puget Sound lowlands on the west side of the Cascade
Mountains and immediately east of Lake Washington (Figure VI-3)
(USEPA, 1982c, p. 827-4). Land use is primarily residential and
mean annual precipitation, mostly rain, is about 42 inches.
The land surface in Bellevue is mostly hilly, with moderate
slopes predominant. Drainage is carried by a system of totally
separate storm sewers, open channels and streams largely to the
west into Lake Washington through Mercer Slough (Figure VI -4)
(USEPA, 1982c, p. 827-6). Some drainage flows east into Lake
Sammamish through Phantom Lake and another stream.
12) :
The project objectives were as follows (USEPA, 1982c, p. 827-
To apply uniformly, in selected drainage basins, a variety
of management practices which are available to and
achievable by local units of government.
To improve standard practices and operations by varying
the frequency and manner of application, developing
management programming methods and al tering moni toring and
inspection practices for greater responsiveness to water
quality needs.
To test, analyze and document the impact of local
management practices on storm water quali ty, isolating
causal factors and their impacts on water quali ty and
evaluating and developing functional relationships between
the quantity and quality of runoff and the hydrologic and
cultural characteristics of the basins involved.
To develop, test and document methods of source control of
common urban storm water pollutants.
To document. temporal changes in storm runoff and
constituent concentrations within several drainage basins
of differing land use.
To develop and documen t means of incorpora ting
management practices into the institutional
operational framework of local government agencies.
To expand the toxic metals, sediment, herbicides and
pesticides and other data base for various land use
categories, contributing to the data base of storm water
quality modeling efforts nationally.
To develop methods for estimating storm and annual loads
of water quality constituents from unsampled watersheds in
each urban-study area, and

Table VI-7.
Methods of Water Quality Analysis
Method of Analvsis Reference
Dissolved Oxygen
YSI 51B meter
Method 150.12
Method 360.12
Orion 399A meter
Method 120.1
Turbidity cool, 4C Hach
Turbidimeter (NTU) 1
Total Suspended Solids cool, 4C
103-105C filtration
YSI 33 S-C-T meter
Method 180.12
Method 160.22
Method 160.42
Volatile Suspended
4C Filter ignition
at 550C
Total Phosphorus
acid (pHs2)

Orthophosphatel cool, 4C Ascorbic acid Method 365.22

Nitrate + Nitrite-Nl cool, 4C Cd-Cu reduction Method 353.32
acid (pHs2) sulfanilamide
cool, 4C Persulfate digestion
Method 365.22
acid (pHs2)
cool, 4C Boric Acid
Method 350.2
Total Kjeldahl
cool, 4C Macro-digestion with
acid (pHs2) sulfuric acid
Bremner 1965
Chemical Oxygen
Demand acid (pHs2)
4C Potassium dichromate
ternational Corp.
Fecal Strep-
4C Membrane filtration
Method 909A3
Method 909C3
Fecal Coliform
4C Membrane filtration
~ Filtration through glass fiber filter.
3 USEPA, 1974.
American Public Health Administration,

Tab~e VI-6. Years of Sampling for Each Monitoring Level in the St.
Albans Watershed
Long-Term Monitoring
1 2
LEVEL 1:. Bay Sampling
Sta. 11
Sta. 12
Sta. 13
Sta. 14
Trend Stations
Sta. 21
Sta. 22
Sta. 23
Sta. 24
Sta. 25
Sta. 26
Mobile Sampling
Sta. 31
Sta. 32
Random Sampling
Sta. 41-44

Table VI-5.
Water Quality Sampling Schedule for the St. Albans
~ Season
grab Oct. - Apr.
May - July
Aug. - Sept.
pH, 02'
2 - 4 8 hr.
and 1-72 hr.
3 Larose
composite All
composite All
May - Feb
Mar. - Apr.
20 days (average)

Table VI-3. Related Long-Term Monitored Parameters in the St.
Albans Bay Watershed.
Meteoroloqical Monitorinq
Continuous precipitation
Continuous streamflow
Continuous temperature (Level
Wind speed and direction (Bay
3 only)
Bioloqical Monitorinq
Fish species and abundance
Benthic invertebrates
Use Monitorinq
Land use - field by field, activity dates
Livestock - type, number, housing, dates
Manure management - type, capacity, fields, dates
Fertilizer - type, amount; field, dates
Pesticide/agrichemicals - type, amount, field, dates
Milkhouse - type, disposal
Barnyard - size, paving, use schedule
Drainage - type, fields
Soils, topography, streams, farm and watershed boundaries
Table VI -4 :
Monitored Parameters for the Short-Term Intensive
Wetland Influences
Dissolved Oxygen
Total Suspended
Volatile Suspended Solids
Total Phosphorus
Total Kjeldahl Nitrogen
Nitrate + Nitrite - Nitrogen
Bav and Wetland Sediments
Redox potential
Grain size distribution
% organic matter
Total phosphorus
NH4Cl phosphorus
NH4AC phosphorus
NaOh phosphorus
HCl phosphorus
Bav Circulation
Total phosphorus
Wind speed and direction
Water velocity and direction

Defore descriptive statistics are calculated from a data set,
and before analyses such as correlation, analysis of variance,
or linear regression are performed, it is wise to look at
various displays of the raw data. The graphs recommended for
this task [time series, histograms, stem and leaf displays,
box plots, and scatter plots] are useful in identifying the
need to edit or transform the data prior to conducting the
statistical analysis. . Most procedures in statistics (e.g.,
regression analysis, hypothesis testing) derive summary values
(e.g., mean and standard deviation) from a data set. Thus, if
the inferences drawn from the statistical procedures are to be
valid for the entire data set, it is important that the
summary statistics represent the entire data set. The
graphical displays help guide the choice of any necessary
manipulations of the data set and the selection of appropriate
statistics to summarize the data.
The reader is referred to Gaugush (1986) or Chambers et al.
(1983) for more detailed discussions regarding these graphical
displays. of data. Based on an inspection of the data, the analyst
should be able to make a qualitative assessment of seasonality,
variance homogeneity, distributions,. data gaps, unusual sampling
patterns, the presence of censored data, and a general
characterization of the available data. All of these features may
have an influence on the type of statistical analyses to be
performed. By using graphical methods to examine the data, the
data analyst can more appropriately select appropriate methods.
Figures VIII-1 to VIII-4 illustrate various graphical displays
of dissolved oxygen (DO) data for a monitoring station in the
Delaware River at Reedy Island, Delaware. Each figure reveals
different features of the data. The DO time series plot (Figure
VIII-1) demonstrates a seasonal nature to the data. In this case
the time series includes data over a 10-year time span. Similar
plots can also be made over shorter time periods such as intensive
data collection during a storm event. In the case of a storm
event, the investigator may plot precipitation and runoff volume
together with pollutant concentrations. It is also apparent from
Figure VIII-1 that data are collected more frequently in the summer
months. Inspection of the raw data show that DO was typically
sampled twice a month during the summer, once a month during the
spring and summer months, and less often during the winter months.
It is also clear that since the summer of 1984, the DO has not
dropped below 5.0 mg/L.
Figures VIII-2 and VIII-3 are a DO histogram and stem and leaf
plot, respectively. These figures demonstrate that most of the
observations fall between 6.0 and 10.0 mg/L. The difference
between these plots is that the stem and leaf plot displays the
actual data rather than a bar. In typical applications the analyst
might display histograms from several stations or different
groupings of data.
Figure VIII-4 is a box and whisker plot. For each month along
the. horizontal axis, the box indicates the middle 50 percent of the

::J 10
~ 8
:i 6
C 4
Figure VIII-l. Dissolved oxygen concentrations from 1980 through
1989 for the Delaware River at Reedy Island, Delaware using a time
series plot.

rJ) 25
~ 20
~ 15
~ 10
o. '" 0 '" 0  0  0           
 '" '" '" 0 '" 0 '" C! ~ 0 '" 0 '"
 .. on on .,; .,; ,...: ,...: .; .; .,; .,; c;j ~ cO cO ~ (OJ
 " .;, " .;, " .;, " .;, " .;, "   ~   
 .. .. on on .,; .,; ,...: ,...: .; .; .,; .;, " .;, .n. " .;, ,,
 .,; c;j c;j cO cO (OJ
        DISSOLVED OXYGEN (MGIL)       
Figure VIII-2. Dissolved oxygen
1989 for the Delaware River at
concentrations from 1980 through
Reedy Island, Delaware using a

4 35689
5 02344455577789
6 000012223333334444445555555667778888899
8 000012223333444555566677799999
9 00001222223345556667777899
11 14566
12 00148
13 1
413 = 4.3 MG/L
Figure VIII-3. Stem and leaf plot of dissolved oxygen
concentrations from 1980 through 1989 for the Delaware River at
Reedy Island, Delaware.

~ 10
~ B
UJ 6
~ 4
Figure VIII-4. Box and whisker plot of dissolved oxygen
concentrations from 1980 through 1989 for the Delaware River at
Reedy Island, Delaware.

data. The lower and upper ends of the box represents the 25~ and
75~ percentiles, respectively. The horizontal line inside the box
represents the 50~ percentile or median. Depending on the
convention used, the whiskers extending from the box represent the
range of the remaining observations. In this case, the short
horizontal lines at the end of the whiskers represent the minimum
and maximum observations for a given month. Some software packages
use different rules for creating the whiskers (Chambers et al.,
1983) and the analyst should be aware of these differences when
mixing and matching analyses from different packages. The expected
seasonal nature of DO is strongly depicted in Figure VIII-4
confirming the suspicions developed from visual inspection of
Figure VIII-I. This figure also allows the analyst to evaluate how
much variability there is in the data. It may be interesting to
note, for example, that in November the lower and upper 25 percent
of the data (represented by the whiskers) are drastically different
lengths while the whiskers (and the box) for August appear
symmetric. In this case, DO was plotted as a function of month.
Similar plots as a function of year could also have been made with
these data.
If the analyst is comparing biological metrics, it may be
appropriate to summarize the data by station classification.
Figure VIII-5 is a box and whisker plot of mean abundance per grab
from the Louisiana Province of the Environmental Monitoring and
Assessment Program (EMAP) for 1991 and 1992. Based on visual
inspection, it appears as though mean abundance per grab between
large rivers (LR) and small rivers (SR) might be similar. A
statistical test is required however. In other cases, it may be
helpful to plot water quality data as a function of other
explanatory variables such as flow. Figure VIII-6 is an example of
total suspended solids measured at a storm sewer in Denver,
Colorado as a function of instantaneous flow. Depending on the
nature of the source loading, the correlation between pollutant
concentrations and flow may be positive (as in Figure VIII-6) or
could be negative. Typically, a negative correlation (decreasing
concentrations with increasing flows) are indicative of constant
pollutant sources (e.g., traditional point sources).
Figure VIII-7 is a scatter plot of orthophosphate for several
stations along the Delaware River. In addition to the seasonal
cycles during each year, some unusually high values on September
23, 1991 can be observed. In this particular case, the analyst
should be alerted to the potential of erroneous data. In this
case, one potential cause may be due to unit conversions. The data
were stored as mg/L of P; however, another set of units for
orthophosphate is mg/L of PO.. If one were to multiply the data
collected on September 23, 1991 by one-third (approximate
conversion from PO. to P) the data will fall in line with the rest
of the observations. Ideally, the analyst would go back to the
original data to determine what type of error occurred and perform
corrective action. These types of errors also occur while
converting data from ppm to ppb, converting from wet to dry weight
basis, normalizing for organic carbon, etc. Data visualization is
a good method picking out gross errors; however, cannot be relied

ffi 1200
c.. 1000
~ 800
~ 600
w 400
Figure VIII-5. Box and whisker plot of mean abundance per grab
from 1991 through 1992 for the Louisiana Province of the
Environmental Monitoring and Assessment Program (EMAPt,

U; 1 000
Q 100
      ...  ~  
     I . ~  .~  
  .  ' .. M    
     I I    
   I  I I    I
   I  I  I  I 
Figure VIII-6. Bivariate scatter plot of total suspended solids
and flow at 36m Street storm sewer in Denver, Colorado.

~ 0.30
~ 025
w .
35 0.20
:r: 0.15
!Ii! 0.10
C 0.05
..      ..   
.    .  .. .
. .      .. .  
..     .....  
... . . ......  
....   .. .......  
.....   ...... ....  
.-- . ..... .......  
.... I -.... . .. . .  
... .... . ..    
.. ...  .    
1990 1991  1992 1993 1994
Figure VIII-7. Time series plot of dissolved orthophosphate from
1989 through 1994 for portions of the Delaware River.

upon for more subtle errors. The likelihood of correcting data
errors goes down significantly with time.
B.2 - Data Stratification
An important component in data analysis is data
stratification. Lumping measurements over a period of time has
limited use in water quality evaluation, unless the period of time
is defined in more specific terms and directly related to the
source of the identified problem. This is particularly true when
comparing the effectiveness of management measures. If the
implemented management measure is designed to reduce pollutant
loadings during storm events, lumping baseflow and storm event data
together for analysis masks the effectiveness of the management
In urban areas the periods should be set to correspond to the
pollutant of concern and urban activities. Depending on the
monitoring objectives, it may be necessary to consider periods of
activity and non-activity. If phosphorus is the pollutant of
concern, periods that correspond to lawn maintenance activities and
spring flush should be considered. If sediment is the problem,
then periods that correspond to the construction season should be
considered. For irrigated agriculture, two periods should be \
established to correspond to irrigation time and non-irrigation
In non-irrigated agricultural settings the periods selected
should conform to the normal agricultural management pattern of the
watershed. These periods should be based on amount of surface
covered, precipitation patterns, and the timing of land and/or
water management activities. Alberts et al., (1978) used this
concept to examine seasonal losses of nitrogen and phosphorus in
Missouri during three periods:
fertilizer, seedbed, and establishment period (March-June)
reproduction and maturation period (July-October).
residue period (November-February).
Some variation in period length from year to year can be
expected due to the climate's impact upon agricultural activities.
There must be enough flexibility within your data analysis to
account for this variation.
Once temporal stratification has been completed, and if
sufficient data are available, the water quality variable being
examined can be categorized by initiation/transport mechanism. For
a sediment related problem, three categories have been devised
(Davenport, 1983) related to the principal detachment process of
.sediment particles:
Baseflow (no rainfall or overland runoff to the stream). This
consists of non-precipitation induced flow and is considered

as the normal day-to-day flow (Viessman et al., 1977)".
Sediment concentrations are dependent upon available material
in the channel network and the carrying capacity of the
Rainfall and snow-melt runoff. This category consists of
runoff events whose rainfall is less than Wischmeier and
Smith's (1965) definition of a storm and snow-melt. Sediment
concentrations are dependent upon flowing water detachment or
re-entrainment of previously detached soil particles, together
with sufficient overland flow to transport them to the stream
Event. This consists of rainfall-runoff events whose rainfall
characteristics meet Wischmeier and Smith's definition.
Sediment concentrations are dependent upon the detachment of
soil particles due to the impact of raindrops and flowing
water detachment or re-entrainment of previously detached soil
particles, together with overland flow to transport them to
the stream network.
Data categorized by detachment category can then be examined
in terms of resource management systems implemented to control the
various types of detachment. It is to be noted that data
stratification results in smaller data sets. You must check these
new data sets for normality before performing any statistical
analyses upon them. It is also important to note that due to the
smaller data set size the differences between data sets must be
pronounced to be significant.
Data Normalization
Data normalization is the process or technique used to convert
data into a production value; i.e., a rate. The normalization of
data results in the factoring out of inherent factor(s) of the data
base that are related to the data collection or generation process.
Data normalization is most commonly utilized in comparison of
loading data.

The most common normalization of data are time period (kg/yr),
unit area (kg/ha), or combination of unit area per time period
(kg/ha/month) basis. The other maj or type of normalization is
related to parameter generation or transport factors such as
rainfall and runoff; examples are kg/cm of precipitation or kg/I'
of streamflow.
Data normalization is extremely useful in evaluating the
impact of implementation acti vi ties, source control, and
determination of implementation priorities. An example of raw and
normalized data is provided in Tables VIII-3 and VIII-4.

Table VIII-3. Raw data by time period. The watershed is 20 ha and
has three consecutive years of pre- and post-implementation
sediment loading, precipitation, and runoff data.
Sediment loading
48 kg
120 em
15 l'
implementation of terraces and conservation tillage
Sediment loading
45 kg
180 em
18 l'
Table VIII-4. Normalized data. The watershed is 20 ha and has
three consecutive years of pre- and post-implementation sediment
loading, precipitation, and runoff data.
1970-1973 average annual loading 16 kg/year
 average annual loading 0.10 kg/em/year
 average annual loading 1. 07 kg/1'/year
1974-1978 average annual loading 15 kg/year
 average annual loading 0.08 kg/em/year
 average annual loading 0.83 kg/1'/year
Review of Table VIII-4 indicates that there has been a 20
percent reduction in sediment generated per centimeter of rainfall
and a 22 percent reduction in annual loading. This indicates that,
irrespective of flow' and precipitation, sediment loading has
decreased. Based on this exploratory analysis, a more detailed
frequency analysis would be required to test for statistical
Another useful normalization of data is converting or
summarizing storm event data. The flow-weighted mean concentration
(FWMC) and time-weighted mean concentration (TWMC) are calculated
as (EPA, 1990)
FWMC = (Sum of CiTiQJ
/ (Sum TiQJ
TWMC = (Sum of CiTJ / (Sum T,)

concentration of the ith sample,
time period for which the ith sample is used to
characterize the concentration, and
instantaneous discharge at the time of the ith sample.
Ci =
T; =
Q, =
The numerator of Equation 8.1 is equal to the total loading.
Figure VIII-8 presents a summary of the rainfall, runoff, and total
nitrogen data collected from a storm event in Florida. Runoff
(1,780 ft3) from this 0.2 inch storm lasted for approximately 2.4
hours. The total runoff volume and precipitation depth can be
computed by integrating the respective curves in Figure VIII-8 or
directly from the data. The nitrogen concentrations are typical of
a "first-flush" in which the concentrations are higher during the
early part of the runoff. The raw nitrogen are provided in Table
VIII-5 together with the example calculations for calculating total
loading and flow-weighted mean concentration. .
Table VIII-5. Total nitrogen runoff concentrations for a single
storm event in Florida.
1. 30
1. 85
1. 64
1. 30
1. 08
SUM of TiQi
SUM of CiT;Q;
= 2080.44 FT3
= 2768.23 MG-FT3/L (=78.40 grams of TN)
Flow-weighted mean concentration = 2768.23 / 2080.44 = 1.33 MG/L
The first column in Table VIII-5 is the time since the
beginning of the storm. The fourth column is the time interval
represented by each sample. For example the first entry of 540
seconds is computed as (0.24 hours 0.09 hours) . 3600
seconds/hour. The value of 0.24 is one-half way between 0.20 and
0.28 hours. Using conversions, the total loadings of nitrogen for
this storm are 78.40 grams. Using Equation 8.1, the FWMC for total
nitrogen is 1.33 mg/L. Because different analysts use different

 0.7  .          2.5 
 0.6  .     TOTAL RUNOFF = 1,780 CU. FT.   
3:             2.0-
o 0.5             a
u..         FLOW-WEIGHTED MEAN   ~
a:     .    
0              Z
z 0.4      CONCENTRATION = 1.33 MG/L   1.50
o              ~
~     .         a:
t:: 0.3      .      !Z
c..      .   1.0 w
(j         0
w              z
a: 0.2             0
c..              0
 0.0.           0.0 
  0 C\J .". to CX) q ~ ~ ~ CX! 0  
  a a a a a N  
Figure VIII-B. Precipitation, runoff, total nitrogen,
phosphorous from a single storm event in Florida.
and total

conventions for analyzing storms, it is important that the analyst
exercise care when comparing the storm summaries computed by
different analysts.
Equation 8.3 provides an approach for estimating the event
mean concentration (EMC):
Sum (T;+, - T;)
. 0.5 .
(C;Q, + C;+IQi+')
Sum (Ti+, - TJ
. 0.5 .
(Q; + Q;+I)
Table VIII-6 demonstrates the use of this equation using the same
storm event presented in Figure VIII-8 and Table VIII-5. The first
three columns of Table VIII-6 correspond to Table VIII-5. The next
four columns correspond to intermediate calculations needed for
Equation 8.3. For example, the values of 0.11, 0.000, 0.342, and
0.14 in the first data row are computed from 0.20-0.09, 0.00 .
0.000, 0.14 . 2.44, and 0.00+0.14, respectively. The last two
columns correspond to intermediate calculations for the numerator
and denominator of Equation 8.3, respectively. 'Finally, the EMC
can be calculated as 0.6722 / 0.4981 or 1.35 mg/L as shown in Table
Table VIII-6. Total nitrogen runoff concentrations for a single
storm event in Florida and example calculations for the EMC.
TIME FLOW  TN Ti+' Ci.Q, C,+,. Q;+  Num.  Den.
(HRS) (CFS)  (MG/L) -T;   Qi+1 Qi+1     
0.09 0.00  0.00 0.11 0.000 0.342 0.14  0.0188 0.0077
0.20 0.14  2.44 0.08 0.342 0.663 0.44  0.0402 0.0176
0.28 0.30  2.21 0.09 0.663 0.654 0.60  0.0593 0.0270
0.37 0.30  2.18 0.08 0.654 0.291 0.60  0.0378 0.0240
0.45 0.30  0.97 0.08 0.291 0.353 0.68  0.0258 0.0272
0.53 0.38  0.93 0.09 0.353 0.595 0.88  0.0427 0.0396
0.62 0.50  1.19 0.06 0.595 0.981 1. 03  0.0473 0.0309
0.68 0.53  1. 85 0.09 0.981 1.115 1. 21  0.0943 0.0545
0.77 0.68  1. 64 0.08 1.115 0.754 1. 26  0.0748 0.0504
0.85 0.58  1. 30 0.12 0.754 0.414 1. 02  0.0701 0.0612
0.97 0.44  0.94 0.16 0.414 0.233 0.68  0.d517 0.0544
1.13 0.24  0.97 0.17 0.233 0.140 0.37  0.0317 0.0315
1. 30 0.13  1. 08 1.11 0.140 0.000 0.13  0.0779 0.0722
2.41 0.00             
         SUM  0.6722 0.4981
The event mean concentration = 0.6722 / 0.4981 = 1. 35 MG/L 
Tests of assumptions
In section VIII. A, the need to evaluate test assumptions was
discussed. Ponce (1980) outlined the basic assumptions when using
parametric statistical tests as:

The observations are independent.
The distribution of the population is known.
The variances of the populations being compared are
of known ratio.
equal or
He also states that parametric statistical tests require that the
Were collected in a random manner.
Have error variation independent
distributed, and homogeneous.
Have variance components which are additive.
This section describes tests which Gan be used to determine
whether or not a data set satisfies some of the assumptions and
requirements of parametric tests. Researchers are referred to
statistics texts such as Snedecor. and Cochran (1980) for further
information regarding tests of assumptions.
Tests of normality
Remington and Schork (1970) state that "the consequences of
violating the assumption [of normality] vary from relatively mild
in the case of inferences on means to relatively severe for
inferences on variances." The following tests can be used to
determine whether a data set satisfies the normality assumption.
Remington and Schork (1970)
of skewness (a3) such that:
recommend a standardized measure
E (x. -x) 2
n - 3
E (x. -x)
a =
m =
m =

The approach used in testing for normality using a measure of
skewness is that a non-normal distribution may be skewed, whereas
a normal distribution is not skewed. Sample sizes as small as n=25
can be tested for skewness at confidence levels of 0.05 or 0.01
using the table in Appendix F. The calculated value of aJ is
compared with the appropriate critical value in the table; if aJ is
greater than or equal to the critical value then the hypothesis
that the observations are a random sample from a normally
distributed population is rejected (Remington and Schork, 1970).
Otherwise, the hypothesis is accepted.

Using the mean abundance per grab data from Figure VIII-5 for
large rivers (LR) and small rivers (SR), selected statistics were
computed and are summarized in Table VIII-7. Selected statistics
are also calculated for log-transformed data. Using Equation 8.4,
a3 for large rivers is equal to (465. OE+06/77) / (1. 5E+06/77) II or
2.22. The critical value from Appendix F for a sample size of 77
is approximately 0.44 (0.05 confidence level). Therefore, it is
assumed that the data do not come from a normally distributed
Table VIII-7. Selected summary statistics for mean abundance per
grab from 1991 and 1992 for the Louisiana Province of the
Environmental Monitoring and Assessment Program (EMAP) from large
rivers (LR) and small rivers (SR).
  LR SR log(LR} log(SR}
Number 77 42 77 42
Sum  10,416.07 5,098.00 144.34 68.53
Mean  135.27 121.38 1. 87 1. 63
Variance 20,295.22 39,031.80 0.31 0.52
St. Dev. 142.46 197.56 0.55 0.72
E Ix;-xl 7,701.40 4,994.28 32.92 23.83
L:' (x;-x) 2 1.5E+06 1.6E+06 23.24 21.46
E (x;-x) 3 465.0E+06 942.5E+06 -10.38 -7.50
E (xi-x) 4 258.1E+09 736.8E+09 24.11 31.37
The SAS Institute (1985a, Basics) calculates sample skewness
n - 3 3
n/(n-1} (n-2) .. E1 (x. -x) /s
1= 1
Skewness values using this statistic can range from negative to
positive infinity, with a value of 0 for normal distributions.
Using the intermediate calculations provided in Table VIII-7, the
sample skewness for large rivers is 77/(76 . 75) . 465. OE+06/
142.463 or 2.17.
Both Remington and Schork (1970) and the SAS-Institute (1985a)
caution that the test for skewness is only a partial indica~or of
normality. With small samples 25) the test is particularly
unreliable. That is, because of the small sample size, very large
departures of normality are required before statistical tests will
reject the null hypothesis of normality.
Using Fisher I S measure of skewness (8,) Cochran (1963) proposed
a general rule for determining how large n must be to allow safe
use of the normal approximation in computing confidence limits for

the mean. This rule is used most effectively for distributions
with positive skewness which is most common for environmental data.
n > 25G12
where G1 is
G =
N - 3
8L: (x. -x)
NS3 i=l
Applying Equations 8.6 and 8.7, G1 can be computed as 2.09 for the
large river data from Table VIII-7 and therefore more than 109 (=25
8 2.092) samples are needed. The example data set only contains 77
samples. Therefore, there are not sufficient data to allow safe
use of the normal approximation in computing confidence limits for
the mean.
The test for kurtosis is as limited as the test for skewness
since it measures only one attribute of normality and requires
large samples for meaningful results. Remington and Schork (1970~
recommend the following to measure kurtosis:
L:lx. -xl
. 1 1
g =
where I x; - xi is the absolute value of x; - x. For a normally
distributed population g would be 0.7979, with smaller and larger
values indicating leptokurtic and platykurtic distributions,
respectively. (Probability distributions are discussed in section
B.5 in more detail.) The table in Appendix G permits upper or
lower one-sided kurtosis tests of the hypothesis that the
observations are a random sample from a normally distributed
population (Remington and Schork, 1970). If the calculated value
of g falls outside of the values in the table for the selected
level of confidence then there is evidence of non-normal kurtosis.
The SAS Institute (1985a)
calculates sample kurtosis as:
Kurtosis =
(n-I) (n-2) (n-3)s
- 4 3 (n-I) (n-I)
E (x. -x) -
1. (n-2) (n-3)
Measures of kurtosis using this statistic range from -2 to positive
infinity with a value of 0 for normal distributions. Using the
intermediate calculations provided in Table VIII-7 and Equation
8.9, the sample kurtosis for large rivers is 5.8.

Shapiro-Wilk W test
The Shapiro-Wilk W test can be used to test the distribution
of a data set for sample sizes of less than or equal to 50 (SAS
Institute, Inc., 1985a). This test uses the W statistic which is
"the ratio of the best estimator of the variance to the usual
corrected sum of squares estimator of the variance" (SAS Institute,
Inc., 1985a). The null hypothesis for this test is that the data
set is a random sample from a normal distribution. Values of Ware
greater than zero and less than or equal to one. The null
hypothesis is rejected with small values.
Anderson and McLean (1974) recommend this test for normality
and note that it is superior to the Kolmogorov-Smirnov and chi-
squared tests in detecting non-normality over sample sizes ranging
from 10 to 50. The following procedure for using the test is
adapted from Anderson and McLean (1974) and Gilbert (1987):
Order the n observations as xl S x2 s ...
Compute d = L: (x. - x) 2 .
s x .
Compute k.
If n is even, k=n/2.
If n is odd, k=(n-1)/2.
b = L: a. (x . 1 - x.)
. 1 1 n-1+ 1
1= .
(8.10 )
where the values of a. appear in Appendix H.
Compute W = b2/d.
Compare W to the quantile given in Appendix I. If W is
less than the ,quantile, rej ect the null hypothesis of

For further information regarding this test the reader is
encouraged to consult statistics texts (Gilbert, 1987, p. 158) and
the publication by Shapiro and wilk (1965). Table VIII-8 presents
the mean abundance per grab data for small rivers in a format ready
for analysis. The results for step 2 are provided in Table VIII-7.
Since there are 42 observations, k is equal to 21. The first
column in Table VIII-8 indicates the value of i for each row in the
table. The second column corresponds to the values of ai from
Appendix H. The third and fourth column, Xi and Xn-i+1f represent the
raw abundance data. The third column represents the first half of
the observations and the fourth column represents the last half of
data in reverse order (e.g., 923.33 is the largest sample
observation). The fifth and sixth columns correspond to the log-
transformed data from columns 3 and 4. For example, log(0.67) is
equal to -0.17. The last two columns provide intermediate
calculations associated with Equation 8.10 (e. g., ai (Xn-i+1 - Xi)) for
the raw and log-transformed data, respectively.
6 .

Table VIII-8. Example analysis of the Shapiro-WilkW test using
mean abundance per grab data for the Louisiana Province of the
Environmental Monitoring and Assessment Program (EMAP) from 1991
and 1992 for small rivers.
1. 67
Applying Equation 8.11,
1. 36
1. 40
1. 41
1. 44
1. 46
1. 52
1. 57
1. 64
1. 70
1. 73
log Intermediate
Xn,;+1 Calculations
1. 96
1. 96
1. 94
1. 88
1. 82
1. 77
1. 77
1. 21
1. 23
W = 1/1.6E+06 x 972.132 = 0.59 for raw data
W.= 1/21.46 x 4.562 = 0.97 for log-transformed data
Summing the last two columns results in completing the
computations for Equation 8.10. The W statistic may now be
computed using Equation 8.11 as shown, in Table VI I 1- 8. From
Appendix I, the quantile for 42 observations (95 percent confidence
level) is 0.942. As a result, it can be concluded that the raw
data are not normally distributed and the log-transformed data are
normally distributed. In other words, the data are lognormally
Kolmogorov-D statistic
The Kolmogorov-D statistic is one of a class of goodness-of-
fit statistics referred to as EDF (empirical distribution function)
statistics (Stephens, 1974). When compared to other EDF
statistics, Stephens (1974) found that the D statistic was inferior
to other EDF statistics such as the Cramer-von Mises statistic and

the Anderson-Darling statistic, but still roughly comparable to the
W statistic (above). The reader is referred to advanced statistics
texts and a publication by Stephens (1974) for more detailed
discussion. The SAS Institute (1985a) uses this test statistic
instead of the Shapiro-Wilk W statistic for sample sizes greater
than fifty. The major reason for not using the W statistic for n
greater than 50 is that Shapiro-Wilk coefficients (Appendix H) are
not available for these larger sample sizes (Stephens, 1974).
The Kolmogorov-D statistic tests the sample data against a
normal distribution with mean and variance equal to the sample mean
and variance, i.e., a comparison of the actual sample distribution
against what the sample distribution would be if it was normal. A
D statistic is computed and tested against critical values provided
by Stephens (1974). Ponce (1980a) and Spooner et al. (1986) apply
this test to actual data using SAS (Statistical Analysis System)
. procedures. Ponce notes that both the Kolmogorov D and Shapiro-
Wilk W tests are also available in SPSS (Statistical Package for
the Social Sciences) .
Graphic method
Ponce (1980a) recommends a graphic method for testing the
distribution of a data set. In this method one simply plots the
data in a cumulative manner on arithmetic graph paper; for
continuous data you will have to select intervals and plot interval
frequencies. The cumulative frequency can be plotted on normal
probability graph paper. To test for normality using this method
one then compares the resulting plots against the examples plotted
on probability graph paper in Figure VIII-9 (Ponce, 1980a, p. 28).
What does the researcher do when the sample data set fails to
pass the normality tests? There are several options (including
proceeding in violation of the normality assumption--which is not
always so bad), but the one most appreciated by statisticians is to
perform data transformation. According to Gaugush (1986, p. 30),
data transformations may: .
Straighten (linearize) a nonlinear relationship between
two variables.
Reduce skew (achieve symmetry) in a data set for a single
Stabilize variance (create constant variance)
particular variance across two or more data sets.
It is generally agreed that log transformations are the most
useful for water quality and hydrologic variables (Spooner et al.,
1986; Gaugush, 1986; Ponce, 1980a; USEPA, 1983b). Ponce (1980a)
states that log transformations are particularly useful when the
data are skewed to the right. Gaugush (1986) agrees with Ponce
because "the effect of a log transformation is to stretch out data

 % %  
 0.01   0 
  Normal Equal mixture of two normal  
c 99.99   50 
~     "
i     ~
...     ~
~ SO.    c
4)    CD
.~     ~
a;     '<
"5 0.01   0 
~  Skewed to left Skewed to right  
 99.   50 
 0.01   0 
  PI.~urtic Leptokurtic  
Figure VIII-9. Examples of several frequency distributions and
their respective cumulative frequency distributions. (SOURCE:
Ponce, 1980a)

on the left side of a plot and to pull in data on the right side of
a plot." Ponce (1980a) says that the transformation to use when
zero values exist in the data set is the log(x+l). This eliminates
all zeros; there should be no negative numbers either, but this is
unlikely in water quality investigations (an example of an
exception is redox potential) .
The reader is encouraged to study the examples of log
transformations presented by Ponce (1980a) and USEPA (1983b).
Additional information regarding possible transformations is
provided by Snedecor and Cochran (1980, p. 287-292). After the
data have been transformed it makes sense to take another look at
them before proceeding with statistical analyses. As stated by
Spooner et al. (1986), the transformed data should be tested for
normality to determine if the transformation is adequate. The
example analysis provided in section B.4.1.3 (see Table VIII-8)
demonstrates that the log-transformed data were normally
distributed while the raw were not normally distributed.
Tests of equal variance
Using the F distribution we can test the assumption of equal
variance of two populations based upon the two sample variances
(s 2 and sb2) (Freund, 1973). In this test F is equal to the ratio
ofa the two sample variances, s 2/ S 2 or Sb 2/ s 2. The null
hypothesis in this test is that th~ raio is I, and he alternative
hypothesis is that the ratio is not 1. The calculated F statistic
is compared versus critical F values (Appendix E) which are based
upon the sample sizes (n and nb) and the selected level of
significance (a). The folfowing equation is used to calculate the
region of rejection for the test (Winer, 1971, p. 40):
Pr ~
s 2
> F 8(n-l
I-a a'
nb -1) I
(8.12 )
Recalling the data from Table VIII-7, the F 'statistic can be
computed as 39,031.8/20,295.22 or 1.92 with 41 and 76 degrees of
freedom. Using Appendix E, the critical F value (95 percent
confidence level) is approximately 1.56. Therefore the null
hypothesis is rejected and variances of the mean abundance per grab
from large and small rivers have different variances.
Tests of constant variance of the residuals
The fQllowing taken from Spooner et al. (1986) describes tests
for constant variance:
The assumption of constant variance of the residuals can [also
be] tested. There are many diagnostic tools available. In
the case where the Y variable is regressed on a continuous X
variable, the two most common methods are: 1) the plot of the
residuals vs. the predicted Y values, and 2) the plot of the

residuals vs. their X values. For constant variance and
constant mean of the residuals, both of these plots should
look like a "constant horizontal band." For residuals that
are calculated from ANOVA-type [analysis of variance]
analyses, equality of variance tests between the groups should
be performed (Snedecor and Cochran, 1967, p. 196-198). . A
rough estimate is that variances need to differ by a factor of
two to be considered statistically significant.
when the residuals do not exhibi t constant variance, then
several common transformations should be used. Logarithmic
transformations are used when the standard deviation in the
original scale is proportional to the mean of Y (i. e. ,
constant CV). Square root transformations are used when the
variance is proportional to the mean of Y. Wi th da ta tha tare
percentages, or proportions (between the values of 0 and 1),
the variances at 0 and 1 are .small. The ARCSIN of the square
root of the individual values is a common transformation which
helps spread out the values near 0 and 1 to increase their
variance (Snedecorand Cochran, 1967).
Tests of randomness
Freund (1973, p. 382) describes a test of randomness in which
the total number of runs (u) above and below the median are
analyzed. A run is a string of values all above or all below the
median. In this test, the median is determined, all values are
placed in chronological order, and each value is assigned an "a" if
it is above the median and a "b" if it is below the median. For
example, the following is a series of sample values:
5, 5, 6,
9, 1, 7,
9, 13,
11, 12
12, 2, 3, 2, 8, 14, 13, 11, 20,
4, 6,
The median for this set of values
values in terms of "a" and "b" is:
(n=21 )
is 8.
The series of
b, b, b,
a, b, b,
a, a,
a, a
a, b, b, b,
omit, a, a, a,
a, b, b,
The number of runs (u) in the example data set is 8. Note that in
this test all values equal to the median are omitted. Also, the
number of values above (n,) and below (n2) must each be ten or more
to allow use of the following statistics. For n, and n2 less than
10 special tables are required (Freund, 1973).
The test statistic is:
u - Jl
z =

 2n1n2 + 1   (8.14)
Jl =   
 n1 + n2    
 12n1n2(2n1n2 - n1 - n ) 
  2 (8.15)
a I   
u \ I (n1 + n2) 2 (n1 +   1)
 n2 -
Using the example data set above:
(8 - 11)/2.1764
Using a level of significance (a) of 0.05 in a two-tailed test, the
z values (a/2) are 1.96 and -1.96 (Appendix B). Since -1.38 falls
within this range we accept the null hypothesis that the sample is
Spearman's rho is another common test for evaluating
correlation. If the data does not have ties, the following
equation is recommended (Conover, 1980):
n [ n + 1 ] [ n + 1]
E R(X.)- --- R(Y.)----
i=l 1 2 1 2
p =
n (n2-1) /12
where R(') is the rank of the data. If there are ties in the data
set, the following equation should be used:
R(X.) R(Y.) -
1 1
n [ n:l r
[ i~l R IX/ - n [ n:l n. 5 [ i~l R IY i) 2 -
(8.17 )

n [ n:l n. 5
p =
Table VIII-9 presents an example analysis using the same data as
above. The first two columns correspond to the chronological order
of sampling and the observations, respectively. The first column
could also correspond to another variable such as rainfall while
the second column could correspond to runoff. As a result, the
first column may not always be ordered. R(~) and R(~) correspond
to the ranks of ~ and~, respectively. If observations are tied,
they are assigned the average of the associated ranks. For

example, an observation of 5 is the 6'" and 7'" smallest observations.
As a result, R(~=5) is equal to 6.5.
Table VIII-9. Example application of
evaluating independence.
Spearman 1 S rho
test for
R (X,)
R (Y,) R (Xi) R (Yi)
n[ n:1 r " 21 (22/2)' " 2,541
Applying Equation 8.17,
p =
2,661 - 2,541
(3,307.5-2,541)U (3,311-2,541)U
= 0.156
The last three columns provide intermediate calculations
necessary to apply Equation 8.17. The test statistic is computed
as 0.156. Using Appendix S, the appropriate quantile (95 percent
confidence level) is 0.3688. The null hypothesis is accepted that
the data are independent.
The analyst may also use the correlation coefficient, r. when
the analyst is comparing a time series of data such as that
displayed in Figure VllI-1, r is referred to as the autocorrelation
coefficient. Salas et al. (1980) provides the formula for the
autocorrelation coefficient as:

(x, - x)
(x'+k - x)
r. =
(x, - X}2
Anderson (1941) gave the limit
-1 t 1.96 (n-k-1)U
r. =
(8.19 )
for the 95 percent probability levels where n is the sample size.
'The correlation coefficient ranges from -1 to 1. Values close
to 1 mean that there is a strong positive correlation (e.g., high
values follow high values). Values close to-1 mean that there is
a strong negative correlation (e.g., high values follow low
values) .
To apply Equation 8.18 to the dissolved oxygen data from
Figure VIII-1, some preprocessing is necessary. Due to the lack of
data in December, January, and March, these data are dropped from
the analysis. Therefore, there nine seasons (i.e., months). In
addition, only the first observation from each month and year are
used. Figure VIII-10 presents the autocorrelation coefficient
(correlogram) calculated for lags 1 through 20. The figure shows
a strong cyclic pattern that repeats every 9 lags. This
corresponds to the number of months used in the analysis. There is
also a very strong correlation at lag 1 which suggests that there
is a tendency for the dissolved oxygen in the following month to be
similar to the current months dissolved oxygen data. The negative
correlation at lag 4 suggest also suggests a strong correlation
with data 4 months apart.
Probability Distributions (optional reading)
Before discussing probability distributions, it is important
to review some of the central concepts upon which our statistical
analyses'are based. The f91lowing definitions describe briefly
some of the terms that will be used in the following sections
(Remington and Schork, 1970, p. 98-109):
A random variable is a quantity that takes various values or
sets of values with various probabilities.
A tablet graph, or mathematical expression giving the
probabili ties wi th which a random variable takes different
values or sets of values is called the distribution of the
random variable.

u: 0.50
(,) 0.25
o 0.00
g -0.25
        I- -      -  
'I-, '"     -' I- -     i- - -' l-
 f- . ~     - I- -     - - - t-
'f- "- - r- I- - I- -  t- ,.-- I- - - - f-
 I- (- I-- - I- I-- I- I-- -  - I- I- I- - I- l-
 ,d-+-    4- -+- 4- -+- '"       
, 4-    -+- 4- 4- 4- -+- 4- I...;-
o ...
... ...
Figure VIII-10. Autocorrelation (correlogram) for dissolved oxygen
data from 1980 through 1989 (March~November) for the Delaware River
at Reedy Island, Delaware.

The' distribution of a statistic over all random samples of
size n from an underlying population is called the'samplinq
distribution of the statistic for random samples of size n.
The standard deviation of the sampling distribution of a
statistic for random samples of size n is called the standard
error of the statistic.
A simple random sample of size n from a population of size N
is a sample selected in such a way that every group of n
different units has the same probability of being selected as
the sample.
Suppose a population is divided into subpopulations or strata.
If a simple random sample is selected from each of these
strata; the aggregated sample is called a stratified random
As stated by Ponce (1980a) theoretical probability density
functions can be used as models for samples from a population.
Thus, by utilizing selected sample statistics in conjunction with
a probability density function we can make generalizations about
the population from which the sample was taken. Freund (1973)
noted that "whenever possible, we try to express probability
functions by means of formulas which enable us to calculate the
probabilities associated with the various values of a random
variable." The sum of probabilities across all values must equal
1, and the probability of any value must be either positive or
Ponce (1980a) stated that if a sample can be fitted to a
theoretical probability density function, then we can estimate
errors of the population parameters, compare temporal and spatial
changes in frequency, and examine the effect of environmental
factors and management practices. What are these theoretical
probability density functions?
Discrete data distributions
For discrete data there are the binomial and Poisson
distributions (Ponce, 1980a). The binomial distribution is
. appropriate for data sets in which there are two possible outcomes
(e.g., heads or tails, true or false, success or failure). Freund
(1973) determines the probability of getting x successes in n
independent trials with:
f(x) = npx(l - p)n-x
for x = 0,
1, 2,
..., n
(8.20 )
where p is the constant probability of a success
individual trial. For more information about
distributions consult a statistical text such as
referenced in this manual.
for each
the ones
Freund (1973) noted that binomial probabilities with a large
n and a small p are often approximat~d with~

(np) x -np
f(x) =
for x = 0, I, 2, 3,
(8.21 )
where x! is factorial notation and e is "approximately" 2.71828.
This equation describes the Poisson distribution. Remington and
Schork (1970) replace np with the mean of the distribution (~) i
thus, while the binomial distribution requires knowledge of nand
p, the Poisson distribution requires only knowledge of ~. The
reader is again referred to statistics texts for additional
Continuous data distributions
Ponce (1980a) refers to the normal, t, chi-square, and F
distributions as the most important theoretical probability density
functions for continuous or measured data. The following
discussion is intended to introduce the reader to the t, chi-square
and F distributions while devoting more attention to the normal
distribution. The t, chi-square, and F distributions will be
discussed in further detail in subsequent sections.
Normal distribution
The normal distribution plays a major role in most statistical
analyses performed by researchers. Most of the descriptive and
inferential statistics we use are based on the assumption of a
normally distributed sample data set. Remington and Schork (1970)
explain the importance of the normal distribution in terms of its:
convenient mathematical properties leading directly to
much of the theory of statistics available as a basis for
.availability as an approximation to other distribution
direct relationship to sample means from virtually any
4 .
application to many random variables that
approximately normally distributed or can
transformed to approximate normal variables.
either are
be easily
The graph of a normal distribution is a bell-shaped curve that
extends indefinitely in both directions (Freund, 1973). Figure
VIII-II illustrates the single peak or mode at x=~ and the sYmmetry
about x=~ (Remington and Schork, 1970). Figures VIII-12 and VIII-
13 show that changes in ~ and a, respectl vely, will alter the
normal distribution, which can have an unlimited number of
different appearances. It should be noted that the normal
distribution is completely determined by its mean and standard
deviation (Freund, 1973). The equation for the normal curve is
(Ponce, 1980a):

Figure VllI-11.
Schork, 1970)
,,-. "
A normal distribution.
(SOURCE: Remington and

Figure VIII-12.
distribution while
Schork, 1970)
The effect of changing ~ in the normal
keeping a constant. (SOURCE: Remington and


-1/2 (x-p./a) 2
y =

where y is the frequency of observations of a given x, 7r is 3.1416,
e is 2.71828, p. is the population mean, and a is the population
standard deviation.
Due to the unlimited number of possible normal distributions,
a convention was decided upon for defining the standard normal
curve. Hence, as shown in Figure VIII-14, the standardized normal
distribution is a bell-shaped curve with a mean (p.) of zero and a
variance (a 2) of one (Gaugush, 1986). To create this standard
normal distribution, the z statistic was defined as (x-p.)/a
(Remington and Schork, 1970). Substituting z into the above
equation and using a standard deviation (a) of 1, we obtain:
. e
(8.23) .
y =

In Figure VIII-14 the z-scale shows the number of standard
units from the mean of zero. For the standard normal curve 68.3
percent of the observations lie within plus or minus one standard
unit (z=l and z=-l) of the mean, while 95.5% of the observations
lie within two standard units (z=2 and z=-2) of the mean (Ponce,
1980). Tables such as that in Appendix B can be used to calculate
the area under the curve (probability) for other values of z. This
table can be used for normal distributions where the mean is not 0
and the standard deviation is not one by converting x values into
z values as described above for the z statistic (Freund, 1973). To
calculate the area between (i.e., the probability that a random
variable will assume a value between) any two values of x, one
simply has to convert the x values to z values (using p. and a),
determine the areas corresponding to the z values (Appendix B), and
add (one z positive, one z negative) or subtract (each z positive)
these areas. For further discussion of the normal and standard
normal distributions consult statistics texts; Ponce (1980a)
demonstrates applications of the normal distribution.
In the above equation for the standard normal distribution we
used the population mean (p.) and the population stand~rd deviation.
What do we do when we don't have population statistics, i.e., when
we have only sample statistics? The logical approach is to use our
sample statistics to approximate the population statistics.
To understand how to apply sample statistics in estimating
population statistics it is first useful to discuss sampling
distributions. The following two theorems provide nearly all we
need to know about the sampling distribution of the mean (Freund,
1973) :

Figure VIII-14.
      z - scale
~-3~  ~-~ ~ ~." ~ . 3"
I I I I I I I-Kale
-3 -2 -I 0 2 3 
Change of scale.
(SOURCE: Freund,

For random samples of size n from a population having the mean
~ and the standard deviation a, the (theoretical) sampling
distribution of x has the mean ~ =~, and its standard deviation
is given by x

or a
a. I (N - n) / (N - 1 )
(8. 24)
depending on whether the population is infinite or finite of size
N. If n is large, the (theoretical) sampling distribution of the
mean can be approximated closely with a normal distribution.
Taking this a step further, if n is large (greater than 30), the
sampling distribution of the z statistic can be approximated
closely with the standard normal distribution (Freund). The need
for use of the t-distribution arises when one attempts to estimate
the error associated with using x to estimate ~, a subject to be
discussed in more detail in subsequent sections. For this
application we must know the population standard deviation (a), but
only have an estimate, namely the sample standard deviation (s).
The equation used to estimate the error associated with an estimate
of the mean involves the quantity
t = I""
S / In
(8.25 )
which does not follow the standard normal distribution (Remington
& Schork, 1970). Instead, it follows the t-distribution (Figure
VIII-15) which depends solely on the sample size as reflected in
the number of deqrees of freedom (n-1) (Freund, 1973). The t-
distribution is similar to the normal distribution in that it is
symmetrical, has a mean of zero, and approximates the normal curve
as n gets large (>30). However, as shown in Figure VIII-15, the
peak is not as high and the tails are larger than for the standard
normal curve. Appendix C is a table of t values to be used in
calculations using the t statistic.
Chi-square distribution
The chi-square distribution (Figure VIII-16) is commonly used
to estimate the confidence intervals for the standard deviation (a)
of a population with a normal distribution based upon a sample
standard deviation (s). The equation for the chi-square (X2)
statistic is (Freund, 1973):
X2 =
(8.26 )
where (n-1) is the mean of the distribution and is referred to as
the number of degrees of freedom. As the equation indicates, this
distribution does not include negative numbers. Calculations using

Normal dl$tributlOl'l
----- , dlslribullOl'l(4deqr... of freedom)
Figure VIII-15. Standard normal distribution and example of t-
distribution. (SOURCE: Freund, 1973)

Figure VIII-16.
o .
Chi-square distribution.
(SOURCE: Freund, 1973)

the chi-square distribution will be discussed in subsequent
sections; Appendix D is a table of values for this distribution.
F distribution
The F distribution (Figure VIII-17) is a continuous
distribution which represents the sampling distribution of the
ratio of the sample variances (s 2) of two normal distributions
(Freund, 1973). The F distribution depends upon two parameters
called the numerator ,(n,-l) and denominator (n2-1) degrees of
freedom (Remington and Schork, 1970). The F distribution is
similar to the chi-square distribution in that both contain no
negative numbers and both are positively skewed. Applications of
the ,F distribution will follow; Appendix E contains F values.
Summary (Descriptive) Statistics
Rather than present every data element within a data set, the
data analyst usually summarizes the major numeric characteristics
of the data set with a few descriptive statistics. As stated by
Freund (1973, p.3) descriptive statistics "includes any treatment
designed to summarize, or describe, important features of a set of
data without going any further; that is, without attempting to
infer anything that pertains to more than the data themselves." In
the case of water quality monitoring we almost invariably use
descriptive statistics of samples to formulate conclusions
regarding populations. Thus, the analyst carries the investigation
a step further by making generalizations which go beyond the data.
A conclusion concerning a population of observations made on the
basis of a sample of observations is called a statistical inference
(Remington and Schork, 1970, p. 91). This section describes
methods that can be used to characterize the average conditions.
Sections VIII. D and VIII. E describe methods for characterizing
changing and extreme conditions, respectively.
A point estimate is a single number representing the unknown
parameter (Freund, 1973). Such point estimates for central
tendency could be the mean, median, mode, or geometric mean from a
sample. The sample standard deviation and interquartile range
could likewise be used as point estimates of spread or variability
of the population. This manual recommends summarizing data using
the sample mean, median, geometric mean (if applicable), standard
deviation, and the interquartile range (25m percentile subtracted
from the 75m percentile) for characterizing average conditions in
most situations.
The use of point estimates is warranted in some cases, but in
NPS analyses point estimates should be coupled with an interval
estimate because of the large spatial and temporal variability of
NPS pollution. In estimating the true population mean and standard
deviation from anyone sample or combination of samples we have to
account for the uncertainty associated with use of sample
statistics. As stated by Freund (1973), "point estimates do not
tell us anything about the intrinsic reliability or precision of
the method of estimation which is being used." This manual

Figure VIII-17.
Reject null
F distribution.
(SOURCE: Freund, 1973)

recommends that at a minimum, the data analyst should provide
confidence intervals for the point estimates of central tendency
(i.e., mean or median).
After the methods for point estimates and confidence intervals
have been implemented, the data analyst may be discouraged with
interval estimates that are too large to allow for effective
environmental management. This section concludes with a discussion
on sample size calculations. This analysis is usually performed
during the monitoring program design; however, it is sometimes
necessary to modify an existing program in order to achieve the
desired monitoring objectives.
Point Estimation
Central Tendency
The central tendency of a data set. is the most important
statistic and it is widely used (Gaugush, 1986, p. 21; Ponce,
WS1980a, p. 5). Remington and Schork (1970) emphasize that it is
important to realize that measures of central tendency apply to
groups rather than to individuals. The mean, median, and mode are
the three major measures of central tendency. The arithmetic mean
is the sum of the observations divided by the number of
observations (n). The median (i. e., 50'" percentile or middle
quartile) is the middle value when all observations are ordered by
magnitude. The median is the horizontal line inside the box of a
box and whisker plot. When there is an even number of
observations, the median is the arithmetic mean of the two middle
observations.' The mode is the most frequently occurring value in
the set of observations.
Comparison of these measures of central tendency reveals that
the mean is sensitive to extreme values, whereas the median is not
(Remington and Schork, 1970). When the data are symmetrically
distribut~d, the mean and median are comparable. In the case of
nonpoint source pollution where storm events generate very large
pollutant loadings it is clear that the mean and median event may
be very different. It is important that the data analyst considers
the ramifications of relying on just one of these statistics when
reporting results . This manual recommends that when presenting
tabular information, the mean and the median should be computed.
Other measures of central tendency include the midrange,
geometric mean, harmonic mean, and weighted mean (Remington and
Schork, 1970). The midrange is the arithmetic mean of the smallest
and largest values and, like the mean, is influenced by extreme
values. Gilbert (1987) also describes the trimmed mean and the
winsorized mean for when there are censored (e.g., non-detects) in
the data set.

The geometric mean of n observations is the nth root of their
product. It can also be calculated as the antilog of the means of
the logarithms of the individual observations (natural or base 10) .
All observations must be positive to calculate this statistic.

Gaugush (1986) states that the geometric mean is "a reasonable
measure of central tendency for a set of data that exhibit a
lognormal distribution." It is common to report the geometric mean
for coliform data.
log (x.)
Geometric mean = antilog
(8.27 )
The harmonic mean is "the reciprocal of the arithmetic mean of
the reciprocals of the observations" (Remington and Schork, 1970).
Freund (1973, p. 46) refers to the harmonic mean as n divided by
the sum of the reciprocals of the n numbers. It has become common
practice to estimate the harmonic mean flow for performing chronic
risk assessments.
Harmonic mean =
(8.28 )
The weighted mean is a mean for which all observations do not
have equal importance. For example, when we want to determine the
overall mean of several sets of data on the basis of their
individual means and the number of observations in each we
calculate the weighted mean as the sum of the products of the
individual means and number of observations divided by the overall
sum of the observations (Freund, 1970, p. 42). In this case the
number of observations is the weight variable (w.). This may occur
when the monitoring program has used a stratified sampling strategy
and the strata have different sample sizes.
w. .x.
l l
Weighted mean =
(8.29 )
The trimmed mean is a useful estimator of the mean when the
data are sYmmetrically distributed and it is necessary to guard
against erroneous data or when censored observations are present
(Gilbert, 1987). (Censored observations are results that are
presented as less-than or not-detected.) The trimmed mean is equal
to the arithmetic mean after equal proportions of the smallest and
largest observations are dropped from the analysis. Research has
suggested that for sYmmetric distributions, no more than 50 percent
of all data should be dropped (Hoaglin et al., 1983). If the data
are not sYmmetric, then no more than 30 percent of the data should
be dropped (Mosteller and Rourke, 1973).

The Winsorized mean can be computed by estimating the mean
after substituting an equal proportion of the smallest observations
with the next largest observation and the largest observations with
the next smallest observation. Gilbert (1987, p. 180) provides
detailed instructions on how to compute the associated standard
deviation and confidence limits.
C.l. 2
Measures of dispersion or measures of variation describe
extent to which the data are dispersed, spread out, or bunched
(Freund, 1970, p. 63). The measures of dispersion described in
this manual are the range, variance, standard deviation, and
interquartile range.
The range of a set of observations is simply the difference
between the largest and smallest values~ Ponce (1980, WSDG-TP-
00001, p. 6) argues that the range should only be considered as a
rough estimate of dispersion due to its dependence upon extreme
values. Remington and Schork (1970, p. 30) agree and point 'out
that the range is also dependent upon the number of observations in
a sample (larger samples have a greater chance of containing
extreme values), an undesirable characteristic for a measure of
variability. Gaugush (1986, p. 26) states clearly that "the range
should not be relied upon as the sole indicator of variability."
The variance (S2) is the sum of the squares of the deviations
from the mean divided by n-1 (Freund, 1973, p. 67). Deviations
from the mean are the differences between individual observations
and the arithmetic mean of all observations. The standard
deviation (s) is the square root of the variance (Remington and
Schork, 1970, p. 34). For a normal distribution, about 68 percent
of the data are within z one standard deviation of the mean.
r: (x. - x) 2
. 1 1
Variance = S2 =
n - 1
Standard deviation = s
In cases where it is necessary to compare standard deviations
(e.g., comparing the precision of measurements) we need a measure
of relative variation. Freund (1973) recommends the coefficient of
variation (CV) as the "most widely used measure of relative
variation. " The CV is defined as: .
CV = 100 (six)
CV = 100 (alp,)
(8.31 )
Freund (1973)
dispersions of
states that the CV can be used to
two or more sets of data that are
compare the
measured in

different units. The analyst should be careful in presenting the
results for the CV, since some analysts do not multiply by 100.
The interquartile range is a robust (changes little if any
particular observation is deleted from the sample) alternative to
the standard deviation (like the median is to the mean) for
situations where the standard deviation is not an appropriate
measure of dispersion (Gaugush, 1986, p. 26). It is the difference
between the observation at the upper quartile, Q3' and the
observation at the lower quartile, Q,. The upper quartile is the
observation value for which 75 percent of the observation values
are lower, and the lower quartile is the value for which 25 percent
of the observation values are lower.
To compute a quartile, the data must be ordered from smallest
to largest observation. Then compute p (n+1) where p corresponds to
the quartile (as a fraction), either 0.25 or 0.75 and n is the
number of observations. For n equal to 9, the lower quartile is
equal to the 2.5m ordered observation or the interpolated value
between the second and third observation. Similar to the CV, the
coefficient of quartile variation can be used to compare different
data sets. .
Q3 - Q,
v = 100
(8.32 )
Q3 + Q,
C.1. 3
Skewness is a measure of the symmetry of a distribution
(Remington and Schork, 1970, p. 219). The normal distribution is
only one of many symmetric distributions (Figure VIII-18). A
positively and negatively skewed distribution are shown in Figure
VIII-19. Section B.4.1.1 provides computational formulas for
C .1.4
The kurtosis of a distribution describes its peakedness
relative to the length and size of its tails (Remington and Schork,
1970, p. 223). It has been argued, however, that kurtosis measures
tail heaviness, not the peakedness of a distribution (SAS
Institute, Inc., 1985a, p. 741). The normal distribution is
considered to have intermediate kurtosis (mesokurtic). Flat
distributions with short tails have low kurtosis (platykurtic),
while distributions with sharp peaks and long tails have high
kurtosis (leptokurtic). These types of distributions are shown in
Figure VIII-20. Section B.4.1.2 provides computational formulas
for kurtosis. .
Interval Estimation
In taking random samples from a fixed population the sampler
be obtaining fixed values for sample parameters (mean,

Figure VIII-18. Some examples of
(SOURCE: Remington and Schork, 1970)

positi".I" ......d
Figure VIII-19. Examples
Remington and Schork, 1970)
".,.ti..I, s"...d

pi .tyk urt i c
Figure VIII-20. Symmetric distributions
(SOURCE: Remington and Schork, 1970)

standard deviation, etc.) that fall within a fixed distribution of
sample parameter values (Remington and Schork, 1970). In
estimating the true population mean and standard deviation from any
one sample or combination of samples we have to account for the
uncertainty associated with use of sample statistics.
Interval Estimation for the Mean
To estimate the confidence intervals for the mean, it is necessary
to estimate the standard deviation of the sample mean:
or a
= . I(N-n) / (N-l)
(8.33 )
function of the sample standard
and whether the population is
The standard deviation is
deviation, the sample size
infinite or finite of size N.
For large n (>30), the sampling distribution of the mean can be
approximated closely with the normal curve (Freund, 1973). Thus,
by knowing the sample mean and population standard deviation we can
make an interval estimate for the population mean. By using the
above equation, the confidence interval can be computed as:
~ = x Z za/2 . 7n
where z~/ is the statistic from the standard normal curve
(Appendi~~). Figure VIII-21 illustrates how values of z and the
confidence (I-a) of the interval estimate are related (Freund,
1973). By selecting a desired confidence level "(0.90, 0.95, and
0.99 are the most common) for the estimate, a z value from Appendix
B (column C) is defined.
We can obtain a value of x from the sample, but the standard
deviation of the population is generally unknown. Hence, the above
equation applies only to the confidence interval for the mean of a
normal distribution with known variance (Remington and Schork,
1970) .
When the population variance is not known we have to use the
sample variance (s 2) as a substitute. Thus, the confidence
interval for the mean of a normal distribution with unknown
variance can be determined as (Freund, 1973, p. 255):
~ = x Z ta/2 .
(8. ~5)
where t y /2 is determined by the sample size and the desired
confiden~e (I-a) for the interval estimate (Appendix C). Because
one additional statistic (i.e., standard deviation) was estimated
from the data, the degrees of freedom used in Appendix C is equal

Figure VIII-21.
Normal distribution.
(SOURCE: Freund, 1973)

to the n-1. For large sample sizes the value of ta/2 approaches
za/2 in Appendix B.

. The following example of setting confidence limits for the
population mean is based upon an example given by Ponce (1980,
00001, p. 48-49).
Fifty-four (54) samples were collected to determine the fraction of
water collected (i.e., the split) by a water and sediment sampler
for plot and field studies (Dressing et al., 1987). The data were
tested and found to be normally distributed with a mean split of
D.0265 and a standard deviation of 0.0040. Determine the 95 and 99
percent confidence limits for the population mean, ~.
For the 95 and 99 percent confidence limits, a/2 is equal to
0.025 and 0.005, respectively. The t-value is then estimated
by interpolation between the values for 50 and 60 degrees of
freedom (Appendix C) using the columns to.97S and t09'1H
respectively. We estimated t-values of 2.0061 and 2.6726.
The 95 percent confidence interval about the mean may then be
estimated as
~ = X I t.025(53)8s/ln
~ = 0.0265 I 2.00618(0.0040//54) = 0.0265 I 0.0011
0.0254 < ~ < 0.0276
There is a 95 percent chance that the population mean, ~, will
be covered by the interval 0.0254 to 0.0276.
The 99 percent confidence interval about the mean may then be
estimated as
.~ = X I t.005(53)8s/ln
~ =.0.0265 I 2.67268(0.0040/154)
= 0.0265 I 0.0015
0.0250 < ~ < 0.0280
There is a 99 percent chance that the population mean, ~, will
be covered by the interval 0.0250 to 0.0280.
Interval estimation for the standard deviation
The chi-square distribution is used to estimate
intervals for the standard deviation of a normal
Referring to Figure VIII-16, we establish the
confidence interval for the standard deviation
distribution as (Freund, 1973, p. 290):
the conf idence
small sample
of a normal

[ J1/2 [ J1/2
(::1108' < a < (::1108'
(1/2 . 1-(1/2
(8.36 )
Note that since the chi-square distribution is asymmetric the above
inequality requires a different chi-square value for each end of
the confidence interval, i.e., values for (1/2 and (1-(1/2).
Remember that 1-(1 is the confidence level for the estimation
For large samples (n~30) Freund (1973) notes that the sampling
distribution of s approximates a normal distribution with a mean of
a and a standard deviation of a/f2n. Thus, for large samples the
following formula may be used (Freund, 1973, p. 291):
< /1 <
1 + a/2
1 - (1/2
Note that the confidence limits for the variance can be obtained by
squaring the confidence limits for the standard deviation
(Remington and Schork, 1970).
Interval estimation for the median and quartiles
Although several approaches exist to estimate confidence
levels for any percentile, many rely on assuming a normal or
lognormal distribution. The approach presented here (Conover,
1980, p. 111) for more than 20 observations does not rely on these
assumptions. Conover (1980) provides a procedure for smaller
sample si::o;es.
Order the data from smallest to largest observation such that
xI S ... S x, S
. .. S X. S
. .. S x, S ... S Xn
where X. corresponds
median = Xo.",) .
to the
(e.g. ,
Compute the values of r' and s' as
r' = np
- Zal2
(np (l-p) ) os
(np(l-p) )OS
s' = np
+ Za/2
Za12 is
selected from Appendix B.
Round r' and s' up to the next highest integers rand s. The
1-(1 lower and upper confidence limits for Xp are x, and x"

Compute the 90 percent confidence interval for the median dissolved
oxygen data presented in Figure VIII-3.
From Figure VIII-3, the median observation can be computed as
7.6 mg/L. There are 182 observations. Note that Figure VIII-
3 already presents the raw data from smallest to largest
r. and s. may then be computed as
r. = np
- Z./2
= 182 x 0.5 - 1.645 (182 x 0.5 x 0.5)U
= 79.9
s. = np
+ Z"'2
(n p ( 1 - p) ) ",
= 182 x 0.5 - 1.645 (182 x 0.5 x 0.5)''-'
= 102.1
rand s are therefore 80 and 103, respectively. From Figure
VIII-3, x.". and XIOJ can be estimated as 7.3 and 8.0 mg/L,
Sample Size Calculation
A natural extension of Section C.2 is to estimate the number
of samples needed estimate the mean within a prescribed relative
error, dr when the observations are independent (Gilbert, 1987).
n = (z.12 CV / dr) 2
(8.38 )
d -
r -
Ix - fJ. I / fJ.
(8.39 )
Table VIII-10 summarizes the sample sizes required for estimating
the true mean for a variety of CV and relative error. The analyst
can use these formulas for suggesting modifications to an existing
monitoring program if the current relative errors are too large.

Table VIII-10. Sample Sizes Required for Estimating the True Mean
(after Gilbert, 1987).     
Confidence Relative  Coefficient of Variation 
Level Error     
(l-a) d, 0.10 0.50 1. 00 1. 50 2.00
0.80 0.10 2 42 165 370 657
 0.25  7 27 60 106
 0.50  2 7 15 27
 1. 00   2 4 7
 2.00     2
0.95 0.10 4 97 385 865 1,537
 0.25  16 62 139 246
 0.50  4 16 35 62
 1. 00   4 9 16
 2.00    3 4
Trend Testing
Evaluating the effectiveness of controls and changing
environmental conditions is one of the key objectives of monitoring
programs. For this reason statistical analysis of monitoring data
usually involves hypothesis testing for trends. In general, there
are two basic types of trend testing: step and monotonic. Step
trends are typically evaluated when comparing at least two
different sample populations such as site and reference biological
data or one sample population to an action level. Monotonic trends
are evaluated when the analyst is investigating long-term gradual
changes over time.
Hypothesis Testing
The null hypothesis (Ho) is the root of hypothesis testing.
Traditionally, null hypotheses are statements of "no change," "no
effect," or "no difference." Remington and Schork (1970) prefer
the term "tested hypothesis" since these hypotheses can take the
form of expected changes, effects, or differences. The alternative
hypothesis. (Ha) is the counter to the null hypothesis,
traditionally being statements of change, effect, or difference.
That is, upon rejection of Ho stating no change we would accept the
Ha of change. We could, however, state an Ho of the type "change
of at least 10 percent" with an Ha of the type "no change of at
least 10 percent." The choice is left to the researcher.
The following are examples of hypotheses formulated by
participants in the joint USDA/USEPA Rural Clean Water Program
(RCWP) (Jamieson, 1986):
Best Management Practices (BMPs) will reduce total suspended
solids (TSS) concentrations to 25 mg/L.

BMPs will reduce phosphate
implementation levels.
by 50
from pre-
Reduced surface application of fertilizer will not reduce
nitrate (NO,) concentrations in the soil profile.
For further discussion of basic concepts in hypothesis testing the
reader is encouraged to consult text books such as winer (1971) and
Snedecor and Cochran (1980).
Type I and II Errors
Regardless of the statistical test selected for analyzing the
data, the analyst must select the significance level of the test.
That is, the analyst must determine what error level that is
acceptable in the analysis. There are two types of errors in
hypothesis testing:
Type I The null hypothesis (Ho) is rejected when Ho is really
Type II The null hypothesis (Ho) 1S accepted when Ho is really
Table VIII-11 summarizes these two error types, with the
magnitude of Type I errors represented by a and the magnitude of
Type II errors represented by~. The probability of making a Type
I error is at most equal to the level of significance (a) of the
test. winer (1971) emphasizes that the probability of making a
Type I error is "controlled by the level of significance." In most
cases, managers or analysts will define 1-a to be in the range of
0.90 to 0.99 (e.g., a significance level of 90 to 99 percent)
although there have been environmental applications where 1-a was
set to 0.80. .
Table VIII-11.
Errors in Hypothesis Testing
 State of affairs in the population
  Ho True   Ho False  
Reject Ho Type I error (0')  No error (l-P)
Accept Ho No error (1-0')  Type II error (P)
 "Signif. level"      
Type II error "depends in part upon the significance level and
in part upon which one of the possible alternative hypotheses is
actually true." He notes that each alternative hypothesis has an
associated Type II error of different magnitude.

The power of a test (1-~) is defined as the probability of
rejecting the tested (null) hypothesis when it is false (Remington
and Schork, 1970). This probability of correctly rejecting Ho
should be as close to unity as possible, meaning that ~ should be
It is evident that there can be tradeoffs between minimizing
a (m~ximizing the probability of accepting a true Ho) and
minimizing ~ (maximizing the power). Remington and Schork (1970)
state that, in general, for a fixed sample size, a and ~ vary
inversely. For a fixed value of a, we can reduce ~ by increasing
the sample size.
Figure VIII-22 illustrates the relationship between a and ~
using a one-tailed test that will be discussed later. Note that as
a is decreased (fixed sample size) from 0.10 to 0.01 the area of
overlap between Hal and the acceptance region for 0 (i.e., ~)
increases. As tne alternative hypothesis distribution moves
farther away from Ho (i.e., move from Hal to Ha2) ~ decreases.
D.l. 2
One-sided Versus Two-sided Tests
Depending on the type of null hypothesis, it is appropriate to
select either a one- or two-sided test. For example, if the
analyst knew that TSS could only go down as a result of BMP
implementation then a one-sided test could be formulated.
TSS(Post) = TSS(Pre)
TSS(Post) < TSS(Pre)
Alternatively, if data have been collected in a pre- and post-
BMP implementation and the analyst does not know whether TSS will
go up or down then a two-sided test is necessary.
TSS(Post) = TSS(Pre)
TSS(Post) ~ TSS(Pre)
When the researcher selects a one-sided test instead of a two-
sided test there is an increase in the power with respect to Ha
(Winer, 1971). That is, a corresponding one-sided test is more
powerful, and therefore desirable, than a two-sided test given the
same a and sample size. The manager and analyst should take great
care in selecting one- or two-sided tests. '
Selection of Nonparametric Procedures
The statistical methods discussed in this manual include
parametric and nonparametric procedures. Parametric procedures
assume that the data being analyzed have a specific distribution
(usually normal). These methods involve population parameter
estimation and hypothesis testing and are appropriate when the
underlying distributions are known and can be analyzed
analytically. For data with unknown distributions, nonparametric
methods might have to be used since these methods do not require

A c~ept fit,
Rt!jec t Ht)
( ().)
/~I ii-~
IIccept Ho
Heju,t HfI
I. ~
l b) 1i'IiC ~
I/q -';11 ~
Accept HD
Rejec t Ho
, (c..) l/'fIe"",+
Figure VIII-22.
v. "c.
Relationship between a and ~.
. VIII-66

that the data have a defined distribution; thus, these are often
referred to as distribution-free methods.
- Theoretically, nonparametric methods and distribution- free
methods are different. In NPS analyses, however, nonparametric
methods often stand for all distribution-free methods, and thus the
terms "distribution-free statistics" and "nonparametric statistics"
are used interchangeably. A more detailed discussion on the scope
of nonparametric methods is provided by Hipel (1988).
Nonparametric methods can also handle special data commonly
found in the NPS area, such as missing and censored data. Missing
data can occur when an automatic sampling station is out of order
for a short period of time, when samples are improperly handled, or
when an error occurs in the laboratory analysis. Censored data are
those without an exact numerical value, such as a value of "less
than 10 ug/l" or "below detection limit." Censored data often
appear in laboratory reports when the concentration being analyzed
is lower than the detection limit or higher than the allowable
range for a particular type of laboratory equipment or procedure.
Missing 'and censored data can cause problems in parametric methods
because these methods often require all data with numerical values.
In this case, nonparametric methods can be used because they often
deal with the ranking of the data, not the data themselves. For
example, for data "below detection limit," any value that is less
than the smallest value of all the data being analyzed can be"
assigned. This assignment does not affect the ranking of the data
even though the exact value of the "below detection limit" is
While nonparametric methods have several advantages, they are
not as powerful as the parametric methods when the assumptions of
the parametric procedure are met. Thus, when the underlying
distributions of the data being analyzed are known or can be
transformed to the form in which standard theory can be applied,
parametric methods might be preferred. As a matter of fact, to
improve the analytical power, nonparametric methods are often
modified to include more assumptions and requirements. This makes
the nonparametric methods more powerful, and the difference between
nonparametric and parametric methods becomes small (Hipel, 1988).
Step Trends
One-sample tests
Student's t-test
Using the TSS hypothesis formulated by the RCWP participants
from above, a one-sided hypothesis is developed to evaluate the
post-implementation mean TSS concentrations as compared against a
hypothesized value of 25 mg/L (Gaugush, 1986). A formalized
statement of hypotheses would be:
J1 = 25
J1 < 25

In this case we are using the mean TSS concentration as the
best measure for evaluation. We have also chosen to assume that
any change in TSS is due solely to BMPSi this will not be true in
most cases as will be shown in subsequent sections. Note that we
are stating the alternative hypothesis (Ha) such that we can apply
a one-sided test since we care specifically about whether the TSS
lS lower than 25 mg/L.
Data from the Highland Silver Lake RCWP project will be used
to evaluate the above null hypothesis. The TSS data shown in Table
VIII-12 are from May 21, 1981 through October 31, 1984. The period
before March 16, 1983 will be called the pre-implementation period
and the period after April 12, 1983 will be called the post-
implementation period for this analysis.
Table VIII-12.
Highland Silver Lake TSS Data for Site 1
TSS (mg/L)
TSS (mg/L)
9/ 3/81
10/ 6/81
11/ 5/81
12/ 8/81
4/ 8/82
6/ 7/83
10/ 5/83
n = 31 mean = 24.77 s = 14.93 median = 20
n = 16 mean = 29.38 s = 16.15 median = 23
n = 15 mean = 19.87 s = 12.17 median = 14
Before testing Ho with a statistical analysis we must inspect
the data and test the assumptions of randomness and normality. We
will perform these tests separately on the pre-implementation and
post-implementation data sets. Using the SAS Univariate procedure
(SAS Institute, Inc., 1985a), stem and leaf, boxplot, and normal
probability plots were generated for the two data sets (Figures
VIII-23 and VIII-24) .
The values for skewness (0.82) and kurtosis (-0.42) indicate
that there is positive skew (compare stem and leaf plot versus
Figure VIII-19) and low kurtosis (leptokurtic) in the pre-BMP
sample distribution. The Shapiro-Wilk W statistic (0.893) and
associated probability (0.063) show that the null hypothesis that

< (j)
H 1-'-
H 3
I 'D
01 f-'
I.D (j)
Std Dev
Num -= 0
Sgn Rank
Sum Wgts
Std Mean
Pr>: T I
Num > 0
 '"Ij      Moments    
 to N      15 Sum Wgts   15
 s:: Mean    19.86667 Sum    298
 Ii Std Dev  12.17061 Variance 148.1238
 CD Skewness  0.697811 Kurtosis -0.99379
 <: USS     7994 CSS  2073.733
 H CV    61.26147 Std Mean 3.142439
 H T:Mean=O  6.322054 Pr>:T:  0.0001
 H Num - = 0    15 Num > 0   15
 I M(Sign)   7.5 Pr>=:M:  0.0001
 .t> Sgn Rank   60 Pr>=:S:  0.0001
  W:Normal  0.877487 Pr
the sample is from a normal distribution can be rejected with 93.7
percent confidence. In other words, there is only a 6.3 percent
chance that a lower W value could be obtained if the sample was
indeed taken from a normal distribution. Hence, we rej ect the
assumption of a normal distribution and take the alternative
hypothesis that the distribution is nonnormal.
The values for skewness (0.70) and kurtosis (-0.99) indicate
that there is also positive skew and low kurtosis in the post-BMP
sample distribution. The Shapiro-Wilk W statistic (0.88) and
associated probability (0.044) show that the null hypothesis that
the sample is from a normal distribution can be rejected with 95.6
percent confidence. We also rej ect the assumption of a normal
distribution for the post-BMP data set.
Taking the logarithm (base 10) of each data point for the pre-
BMP and post-BMP data sets, we again ran the SAS Univariate
procedure to see if the assumption of normality would be
appropriate for the log-transformed data set. The output plots and
statistics are shown in Figures VIII-25 and VIII-26. Note that the
skewness (0.10) is much less pronounced, but the kurtosis (-1.09)
is more negative for the transformed pre-BMP data set. The higher
W statistic (0.951) and associated probability (0.493) indicate
that we cannot reject the hypothesis that the transformed data are
normally distributed.
For the log-transformed post-BMP data set the skewness (0.072)
is also reduced and the kurtosis (-1.23) more negative than for the
raw data set. The W statistic (0.939) and associated probability
(0.367) indicate that we cannot reject the hypothesis that the
transformed data are normally distributed. In fact, there is a
63.3 percent probability that a lower W statistic could be obtained
if the sample is from a normal distribution.
To test the randomness of the data sets, we used the test
proposed by Freund (section VIII.B.4.4). Since the test requires
only the number of runs and the number of values above and below
the median it doesn't matter whether the raw or transformed data
are used. Using the raw data in Table VIII-12, the number of runs
for the pre-implementation data set is 6 while for the post-
implementation data set there are 9 runs. The resulting z
statistics for the pre-implementation and post-implementation data
sets are 1.5526 and 0.8971, respectively. We cannot reject the
null hypothesis that the samples are random (a=0.05) for either
data set, but we did not use the special tables needed for n1 and
n2 values less than 10 (Freund, 1973). Without having special
tables (probably a common situation), we do a further test on the
overall data set (pre- and post- combined) and obtain a z statistic
of 0.0276 which is well within the 95 confidence levels we seek
(z=1.96). This result, combined. with the results for the tests on
the two data subsets is sufficient to conclude that we are working
with random samples.
Satisfied that we now have randomly sampled, normally
distributed data sets (after log-transformations), we can perform

<: 0
H Ii
H 3
H (j)
I 0,
tV 'd
Std Dev
Num -= 0
Sgn Rank
Sum IJgts
Std Mean
Num > 0
<: 0
H :3
H (()
H P..
-.....] '"d
w 0
 . 1-'-
N 15 Sum Wgts 15
Mean 1. 21969 Sum 18.29535
Std Dev 0.273571 Variance 0.074841
Skewness 0.072331 Kurtosis -1.22633
USS 23.36244 CSS 1.047777
CV 22.42956 Std Mean 0.070636
T:Mean=O 17.26731 Pr>:Ti 0.0001
Num -= 0 15 Num > 0 15
M(Sign) 7.5 Pr>=:M' 0.0001
Sgn Rank 60 pr>=:s! 0.0001
W:Normal 0.939469 Pr
the one-sample hypothesis test using the post-BMP data set. As
shown in Figure VIII-26 the mean of the log-transformed post-BMP
data set is 1.21969 and the standard deviation is 0.273571. The
log of the hypothesized value (25 mg/L) is 1.3979. Using the t-
statistic (section VIII.B.5.2.2) we determine whether or not the
post-BMP TSS concentration is less than or equal to 25 mg/L. The
one-sided t-statistic is calculated using Equation 8.25:
t =
1.21969 - 1.3979
t = -2.53
The schematic representation of this test is shown in Figure VIII-
27, where the critical t value (-1.761) for the one-sided test
(n=15, d. f . =14, a=O. 05) is taken from Appendix C. Our t value
falls to the left of the critical value so we reject the null
hypothesis. In turn, we accept the alternative hypothesis that the
post-BMP TSS concentration is less than 25 mg/L.
The power of this test can be computed using the noncentral ~
distribution with respect to various alternative hypotheses (Winer,
1971). The statistic t' is defined as (Winer, 1971, p. 21):
t' = t + <5.(a2/s2)~
= (/J.'-/J.)./n/a
and <5 is called the noncentrality parameter.
the log-transformed data from our one-sample
(/J.=1.3979, /J.'=1.21969, s=0.273571, n=15), we
estimate of a) <5 using Equation 8.41 as:
Using the t test and
hypothesis test above
calculate (using s as
<5 = (1.21969-1.3979) (/15/0.273571)"
= -2.5229
Consulting the table ~or a=0.05 in Appendix J, we find that ~ (the
type II error associated with Ha) is approximately 0.23 (f = d.f.
= 14). Thus, the power with respect to Ha is 0.77. .
Wilcoxon Signed Rank Test
Alternatively, if the log transformation
normally distributed data, the analyst could
analyze the raw data using the wilcoxon Signed
VIII-13 shows the calculations used to evaluate
did not result in
have selected to
Rank test. Table
the hypotheses
/J. ~ 25
/J. < 25
For convenience the post-implementation data are sorted from
smallest to largest observation. The difference, d;, is computed

Figure VIII-27.
~j('f' I
H. I
ACC8'r H.
t. -I. '"
.;I( Ill' .,IL
One-sided t-test.

as 25-TSS;. For example, the first entry is equal to 25 - 6 or 19.
The third column is the absolute value of the difference, Idil. The
last column is the rank of the I di I. The test statistic, T, is
normally distributed and is given by Conover (1980) as
L Rank I d; I 
T =  (8.42)
[~1  J"S
 2 '
Table VIII-13. Nonparametric evaluation of post-implementation
data using the Wilcoxon Signed Ranks test.  
     Id;1   *
TSS (mg/L) di=25-TSS;   rank I di I
6  19 19  15
7  18 18  14
  10  15 15  11
  10  15 15  11
  11  14 14  9
  12  13 13  8
  14  11 11  6.5
  14  11 11  6.5
  16  9  9  5
  22  3  3  1*
  30  -5  5  -2*
  32  -7  7  -3.5*
  32  -7  7  -3.5*
  40  -15 15  -11*
  42  -17 17  -13
* = Assign the negative of the rank if ~ is negative
Sum of rankld;I' = 54 Sum of rankldil' = 1237
where the rank is assigned a negative value if d. is negative. T
is equal to 54/11237 or 1.54. Since 1.54 is le\;s than 1.64, we
reject the null hypothesis that the mean concentration is less than
25 mg/L. El-Shaarawi and Damsleth (1988) provides a modified
version of the wilcoxon Signed Rank test for use with serially
correlated data.
In this case, the t-test and wilcoxon Signed Rank test result
in different conclusions. We propose that the results from the t-
test (Section VIII.D.2.1.1) are more appropriate for this example
since all of the assumptions of the parametric test were met. Had
we elected to perform the analysis in spite of assumption
violations, we would have-selected the results from the Wilcoxon

Signed Rank test as being more appropriate. That is, if all
assumptions are met, parametric procedures are more powerful
(Section VIII.D.1.3) than their nonparametric alternative.
Two-sample tests
Student's t-test
Suppose that we now wish to compare the pre-BMP and post-BMP
data sets to see if the BMPs have had an effect on TSS levels in
Highland Silver Lake. Remembering the simplifying assumptions made
earlier, we can use these two data sets in a one-sided hypothesis:
 Ho: TSS(Post) = TSS(Pre)  
or Ho: TSS(Post) - TSS(Pre) = 0
 Ha: TSS(Post) < TSS(Pre)  
or Ha: TSS(Post) - TSS(pre) < 0
Note that in this case we test the Ho that the post-BMP TSS
equals the pre-BMP TSS concentration with an Ha that post-BMP TSS
is lower. We would interpret this in a very simple sense as a test
of whether the BMPs have worked; other factors must be considered.
We could also have set this up as a two-sided test where Ha would
simply be:
TSS(Post) ~ TSS(Pre)
TSS(Post) - TSS(Pre) ~ 0
We test this Ho using a one-sided t-test. Both the pre-BMP
and post-BMP data sets are random samples and normal when log-
transformed. However, the two-sample t-test also requires that the
variances of the two populations are equal (Gaugush, 1986). Since
a major effect of many NPS control practices is to reduce the
occurrence of large loading events, it is very likely that these
practices will have an effect on the variance of NPS loads. For
this and. other reasons equal' variance should be tested, not
assumed. Thus, we perform' an F test of the assumption of
homogeneity of variance before proceding with the t-test. It
should be noted, however, that Winer (1971) notes that the t-test
is robust with respect to moderate departures from homogeneous
Since we are using the log-transformed data (Figures VIII-25
and VIII-26) we must use the variance of the transformed data in
the F test. The resulting F statistic is computed from Equation
F = 0.075/0.057 = 1.32
The variances are substituted into equation 8.12 so that the
F statistic is greater than unity to account for the fact that the
F tables in Appendix E cover only the right side of the curve. The
critical F value from Appendix E (f1=14, f2=15, a/2=0.025) is 2.86.

We compare 1.31 versus 2.86 and accept the null hypothesis of equal
Satisfied now that our data meet all of the assumptions
required of the two-sample hypothesis test, we can test the null
hypothesis that the pre-BMP and post-BMP mean log-transformed TSS
concentrations - are the same. The two-sample t statistic is
(Remington and Schork, 1970):

(Xl -x2) - Llo

Sp8/(1/n1 + 1/n2)

where s is the square root of the pooled variance which is defined
by: p
t =
(8.43 )
S 2 =
(n1-1)8s12 + (n2-1)8s22
(n1-1) + (n2-1)
(n1-1)8s12 + (n2-1)8s22
(n1 + n2 -2)
(8.44 )
The difference quantity (Ll ) can be any value, but in our case we
test for a difference of ~ero. Using the above transformed data
for pre-BMP (n1=16, variance=0.057087, mean=1.407) and post-BMP
conditions (n2=15, variance=0.074812, mean=1.21969), we calculate
the pooled variance:
(16-1) (0.057087) + (15-1) (0.074812)
(16 + 15 - 2)
= .06564
t statistic:
(1.407 - 1.21969) - 0
t =
= 2.034
Comparing this t statistic in a one-tailed test versus the t
value from the table (a=0.05, d.f.=n1+n2-2=29) in Appendix C we
find that the 2.034 exceeds the table value of 1.6991. - We
therefore reject the null hypothesis and say that the post-BMP mean
log-transformed TSS concentration is lower than the pre-BMP level,
i.e., the BMPs worked (given earlier assumptions). Note that if we
had used a two-tailed test we would have accepted Ho (t=2.0452).
Remington and Schork (1970, p. 210-214) give test statistics
for other cases in which we are testing the difference between
means. These cases and corresponding equations are given below
(Table VI I I -14). Ponce (198 Oa) contains examples of several of
these cases.

Table VI I I -14. Summary of parametric tests used to evaluate
difference between means (Remington and Schork, 1970).
Case 1: Difference Between Means When Variances Are Known
(test statistic is standard normal distribution)

Null Test Statistic Assumptions
independent, random
sample~ of size n1
and n from two
normafly distributed

2: Difference Between Means When Variances Are Unknown
Equal (test statistic is Student's t distribution with
n1+n2-2 degrees of freedom)
(x -x ) - ~
t = 2 2 0.5
(a 1/n1 + a 2/n2)
Ho: fl1-fl2 = ~o

independent, random
samples of size n1
and n from two
normafly distributed
populations with
equal variances

Difference Between Means When Variances Are Known and
(test statistic is approximately Student's t-see below
for degrees of freedom)

Test Statistic
(X -x ) - Ll-
t = 2 2 0.5
(s 1/n1 + s 2/n2)
Test Statistic
fl1-fl2 = ~o
t =
(x -x ) - ~
1 2 0
sp(1/n1 + 1/n2)0.5
Case 3:
fl1-fl2 = ~o
, (s 1/n1 +
df = 2 2
(s 1/n1)
2 2
s 2/n2)
2 2
(s 2/n2)

independent, random
samples of size n1
and n from two
normafly distributed
populations with
unknown and
presumably unequal
.n1 + 1
n2 + 1
df = df' - 2

Case 4: Pairing-The Mean Difference (test
Student's t distribution with n-1 degrees

Ho Test Statistic
fld = ~o
fld = fl2 - fl1
t =
d - ~
/ 0.5
sd n
statistic is
of freedom)


random sample of size
n paired differences
from a normally
populations of

The above test showed that the difference between pre-BMP and
post-BMP log-transformed TSS concentrations is not zero, but it
would be useful to describe in more detail what the difference
really is. One way to describe this difference more completely is
to determine the confidence interval about the difference. The 95%
confidence interval for equal variance conditions can be calculated
by (Winer, 1971):

(post-pre)-t8s !(1/n1+1/n2) s ~ s (post-pre)+
p 0 t8s !(1/n1+1/n2)
For t=2.05 (a=.025, d.f.=29) this becomes:
(1.21969-1.407) - .18876 s ~
s (1.21969-1.407) + .18876
-0.18731 - .18876 s ~
s -0.18731 + .18876
-0.3761 s
s 0.0014
Note that this interval includes 0, a result of the fact that if we
had used a two-tailed test above we would have accepted Ho.
Since we have selected the one-tailed test
determine the one-tailed confidence interval as:
we will
(post-pre) - t8sp!(1/n1+1/n2) s
where t = 1.6991
(1.21969-1.407) - .1564 s
-0.3437 s ~
This difference in the means of log-transformed data can be
translated into TSS concentration data by taking into account the
fact that the difference of two logs is simply the ratio of the
antilogs. So, using the one-sided confidence interval above for
the difference between log-transformed pre-BMP and post-BMP means,
we can express the actual difference in TSS concentrations as:
antilog(-0.3437) s TSS(post)/TSS(pre)
0.453 s TSS(post)/TSS(pre)
TSS(post) s 0.4538TSS(pre)
rearranging and solving for the difference in terms of TSS(pre) ,
Difference ~ 0.4538TSS(pre) - TSS(pre)
Since the mean TSS(pre) concentration is 29.38 mg/L this becomes:

Difference ~ -16.07 mg/L
In other words, there is no more than a 16 mg/L reduction in mean
TSS from the pre-BMP to the post-BMP periods. Using the two-tailed
test, we would say that the difference is between 17 and 0 mg/L
TSS. .
The power of this test with respect to Ha can be estimated
using the noncentrality parameter (Equation 8.41) and by
approximating a with the pooled variance (Winer, 1971). Assuming
that the difference between the means is actually 5 mg/L
(10g=0.69897), the noncentrality parameter is (Winer, 1971):
{) =
0.69897 - 0
0.2562/(1/16 + 1/15)
= 7.59
From Appendix J we find that ~ is (d.f.=29=f, a=0.05) less than
0.01, so the power is greater than 0.99. If we were to select an
Ha with a difference of 15 mg/L (10g=1.1761) the resulting
noncentrality parameter would be 12.8, and the power would again be
greater than 0.99. For an Ha with a very small difference (0.5
mg/L, 10g=-0.3010) the noncentrality parameter would be negative
3.27 and the power would be about 0.94. This group of scenarios
for Ha emphasizes the point made earlier that for a given situation
(n, a) an increase in the difference between Ha and Ho parameters.
(e.g., mean) results in an increased power of the test with respect
to Ha.
Mann-Whitney (Wilcoxon's Rank Sum) Test
The Mann-Whitney test can also be used to evaluate the one-
sided hypotheses
TSS(Pre) s TSS(Post)
TSS(Pre) > TSS(Post)
wilcoxon (1945) first introduced this test for equal-sized samples.
Mann and Whitney (1947) modified the original Wilcoxon's test to
apply it to different sample sizes. In NPS data analyses, this
test can be used to compare data obtained from different
10cation8-cQr for example, whether the BOD, concentration at one
location in the stream is different from that at other location. .
The test can also be used to compare data collected at two
different periods of time at the same location (before and.after a
management practice) .
The Mann-Whitney test accomplishes the same objective as the
Student's t-test. The Student's t-test requires that the two
populations be normally distributed, whereas Wilcoxon's rank sum
test requires only that the two populations have the same
distribution, no matter what the distribution.
.The test statistic can be computed from the following equation
which allows for ties (Conover, 1980)

N + 1
T - n
[ nm
E R.2-
. 1 1.
nm (N+l)
- T =
4 (N-l)
] 0.5
n =
m =
number of samples in first random sample
number of samples in second random sample
n + m,
Sum of ranks for first random sample, and

rank for the ith ordered sample.
(e.g. ,
(e.g., post-
N =
T =
Table VI I I -15 has been prepared showing the intermediate
calculations using the same TSS data presented earlier. First, all
observations from the pre- and post-implementation are sorted
together and ranks assigned. Note that ties are assigned the
average rank.
Table VIII-IS. Nonparametric evaluation of post-implem~ntation.
data using the Mann-Whitney test.   
  Pre- Post-  Pre- Post-
  Implementation  Implementation
 Rank TSS (mg/L) Rank TSS (mg/L)
 1  6 17 21  
 2  7 18  22
 3.5  10 19 25  
 3.5  10 20.5 30  
 5.5 11  20.5  30
 5.5  11 22.5  32
 7.5 12  22.5  32
 7.5  12 24 35  
 9 13  25 37  
10.5  14 26  40
10.5  14 27.5 42  
12.5 16  27.5  42
12.5  16 29 48  
 15 20  30.5 60  
 15 20  30.5 60  
 15 20     
Sum of ranks for pre-impI2mentation, T = 302.5
Sum of ranks squared, ER. = 10409.5
Applying Equation 8.48 yields

31 + 1
302.5 - 16
T =
[ 16. 15
] 0.5
10409.5 -
T1 = 46.5/25.26 = 1.84

. T 1 is normally distributed and Appendix B can be used to
determlne the appropriate quantile. Since the hypothesis was one-
sided and we wish to use an C1. equal to 0.05, the appropriate
quantile from Appendix B is 1.645. T1 is greater than 1.645 and we
rej ect the null hypothesis. The post - implementation mean TSS
concentration is less than the pre-implementation mean TSS
The Hodges-Lehman estimator (Hodges and Lehmann, 1963) can be
used as a nonparametric estimator of the difference between the two
samples. To compute the Hodges -Lehman estimate, the analyst
compute the difference between all nand m observations. Using the
data in the above example, there are 16.15 or 240 differences to
compute. The Hodges-Lehman estimator is the median of these
differences or 8 mg/L.
Conover (1980) provides an approach
confidence limits for the difference.
determines the value w '/2 statistics for
Appendix T. Then k mayC1.be calculated as
for estimating the
First, the analyst
nand m samples from
k = wC1./2 - n(n+1)/2
(8.49 )
The upper and lower confidencet~imits on the difference between the
two samples is equal to the k smallest and largest differences.
Using the data from above where n=16 and m=lS, w 2 is equal to 207
from Appendix T. Applying Equation 8.49, k is ~qual to 71. From
the 240 differences computed for the Hodges-Lehman estimator, it
can be said that the confidence interval is -1 s difference s 19
Matched sample tests
Paired observations are a series of data collected as pairs
at a given time or location. For example, if BODS is sampled at
two stream locations at a regular time interval, the result each
time is a pair of BODS data. Several statistical tests are
available for comparing paired observations, depending on the study
obj ecti ves . I f samples are taken for total nitrogen and total
phosphorus concentrations regularly at the same location, a pair of
data for each sample collected is obtained.
For the BODS data at two locations, we may want to know
whether location 1 has a higher or lower concentration of BODS than
location 2, or whether the BODS concentrations at the two locations

are the same. In this case, the paired t-test or the Wilcoxon
Signed Rank test are good candidates.
For the paired total nitrogen and phosphorus concentrations,
we may want to compare whether there is a correlation between the
two sets of concentration data. In other words, is there a
tendency for hJgh total nitrogen concentration to occur with a
higher total phosphorus concentration, or are the two
concentrations unrelated? Spearman's test is a good test to answer
such questions. The Kendall tau test is similar to Spearman's test
and could be used; however, has found most of its applications in
time series data discussed in Section VIII.D.3. .
Paired t-test
The null hypothesis and test statistic is presented in Table
VIII-14, Case #4.
Wilcoxon Signed Rank Test
The Wilcoxon Signed rank
VIII.D.2.1.2 of this chapter.
Sign Test
The sign test is the oldest and simplest test among the tests,
discussed here. It compares paired data to test whether one data
set presents higher values than the other or whether the two sets
are the same. The data being analyzed consist of paired
. observations (Xl, YI), (X2, Y2) . . . . (Xi, Yi),... (Xm, Ym), where m is
the number of pairs. Generally, we want to know whether the sets
X and Y have the same mean. The assumptions and test procedures
are summarized in the box on the next page.
Table VIII-16 presents water samples collected daily at two
locations from the same stream and analyzed for BODS and the
intermediate calculations used for the sign test. In this case, we
want to test the hypothesis that there is no difference in BODS
concentrations between the two locations.
Construct hypothesis.
Ho: BODS concentrations are the same at the two locations.
Ha: BODS concentrations are different at the two locations.
(This is a two-sided test) .
Use confidence level a = 0.05.
Take the difference between the BODS of location 2 and
location I and assign a sign to it, as indicated in column 4
of Table VIII-16. If the two data are equal, assign a "tie."
From the table, calculate the number of pairs with a "+" sign
(B=8) .

Sign Test - Procedure
. The variables in each pair of data (Xi, Yi) are mutually independent.
The measurement in each pair of data is at least ordinal. That is, the pai'r can be
compared and assigned a "+", "-", or "tie" sign.
The pairs (Xi, Yi) are internally consistent. That is, . if the probability for" +" is
greater than" -" for one pair of data, it is also true for all pairs of data.
Test Steps
1. Construct test hypotheses.
. Null hypothesis (Ho): the median of the population of all possible difference is zero.
In other words, there is the same likelihood that Xi is greater than Yi as Yi is greater
than Xi.
. Alternative hypothesis (Ha): Select one of the following:
a. Two-sided test: Either Xi is more likely greater than Yi, or vice versa.
b. One-sided test 1: Xi is more likely greater than Yi.
c. One-sided test 2: Xi is more likely less than Yi.
2. Compute the following:
. The difference for each pair (Yi - Xi) and assign a sign to it if (Yi > Xi), the pair is
assigned a "+", if (Yi < Xi), a "-" sign is assigned. A "tie" is assigned if Xi = Yi.
Let B equal to the number of pairs that have a "+" sign, and let n equal the total
number of pairs with either a "+" or "-" sign (ties are excluded).
3. Compute the total number of pairs that have a "+" sign.
4. Draw conclusion.
a. Two-sided test: From Appendix P, find out the I and u values for the corresponding
significant level (alpha) and n. Reject Ho and accept Ha if B ~ u or B < 1-1
b. One-sided test 1: Multiply the alpha by 2 and use the new alpha and n to find out u
in Appendix 1. If B ~ u, reject Ho and accept Ha.
c. One-sided test 2: Multiply the alpha by 2 and use the new alpha and n to find out I
in Appendix 1. Reject Ho and accept Ha if B < 1-1. .

Table VIII-16. Sign test for comparing daily BODS concentrations
at two locations.
Conc. at Conc. at Sign of
Location 1 Location 2 Difference
( mg /1) (mg/l) 
29  19  +
22  20  +
10  5  +
26  24  +
12  15  
32  24  +
23  25  
11  23  
32  32  tie
27  30  
28  20  +
23  16  +
18  33  
35  25  +
20  20  tie
Calculate the
(n=lS-2=13) .
From Appendix P, using n=13 and alpha=O. OS,
Since B$l-l and B~u, Ho cannot be rejected.
the BODS concentrations at location 1 are not
of location 2 at the 0.05 confidence level.
we find 1=3, u=ll.
So we conclude that
different from those
Spearman's Test
Spearman's test is used to detect whether there is a
correlation between the paired data; that is, whether the two data
in the pair are independent, or when one datum in the pair is high
and the other datum tends to be high (or low). The procedure for
Spearman's Test is summarized in the box on the' next page. This
test can be used in NPS data analysis to find the cause for a
certain pollutant in the river. Suppose we observe that when a
location has high nitrogen concentration, the phosphorus
concentration at the same location is also high, and when the
nitrogen concentration is low, the phosphorus concentration is also
low. We also know that fertilizers with nitrogen and phosphorus
are applied to upstream lands and it is likely that the nitrogen
and phosphorus come from the applied fertilizer. On the other
hand, if the concentrations of nitrogen and phosphorus are
unrelated, we might suspect that the nitrogen is coming from
sources other than fertilizer applications.
A monitoring program was designed to see whether there is a
correlation between the total nitrogen and total phosphorus
concentrations. Water samples were collected and analyzed on a

Spearman's Test - Procedure
.1. Arrange ranks.
For n number of paired data (Xl, Yl), (X2, Y2).. ..(Xn, Yn), let R(Xi) be the rank of Xi among X I to Xn, with
the smallest num~er being rank I and the largest number being rank n. In the same manner. let R(Yi) be (the
rank of Yi among YI to Yn. In case of ties, assign the average value of the rank that would have been assigned
if there were no ties. For example, if rank 6, 7, and 8 have the same value, assign 7 to all three ranks.
2. Compute the Spearman's p value.
If there are no ties or moderate number of ties,

6L [R (Xi) -R (Yi) ] 2
p=l- i.1 =1- 6T
n en2-1) n (n2-1)
where T is the entire sum of square of difference hetween the two ranks. If there are many ties,

L [R(X;)-R(Yi)]-n(n+1)2
~I 2

[tReXi)2-n( n+1)2 [tReXi)2-n( n+1)2
i.1 2 i.1 2
where n is the number of paired observations.
3. Construct hypothesis.
Ho: There is no correlation between Xi and Vi.
HI: Use one of the following
a. Two-sided test:
There is a correlation between Xi and Vi; that is, either a large Xi value tends to pair with a large Yi
value or a large Xi value tends to pair with a small Yi value.
b, One-sided test I:
A large Xi value tends to pair with -a large Yi value, and a small Xi value tends to pair with a small
Yi value.
c. One-sided test 2:
A large Xi value tends to pair with a smaller Yi value, or vice versa.
4. Draw Conclusion.
From Appendix Q, obtain the quantile for the corresponding confidence level and n.
For two-sided test:
get two quantile values, wi and w2, from Appendix 2. Use p= 1-(alpha/2) for wi and p=alpha/2 for w2.
(For example, if n=20, alpha=0.05, wi =0.4451 based on p=0.975, w2=-0.4451, based on the equation
provided in footnote of the table.) If r> w I or r < w2, then reject Ho and accept Ha.
For one-sided test I:
use p= I-alpha and n to get w. For example, if n=20 and alpha=0.05 p=0.95, and w is 0.3789. Reject
Ho if r>w.
For One-sided test 2:
obtain w using the same procedure as one-sided test I, reject Ho if p < w.

monthly base for one year. The total nitrogen and total phosphorus
concentrations are listed in columns 2 and 3 of Table VIII-17. The
objective is to determine whether higher phosphorus concentration
tends to pair with higher nitrogen concentration.
Table VIII-17." Spearman's
phosphorus correlation.
for total nitrogen
and total
Month Total Total R R
N P (N;) (PJ
Jan 2.31 0.21 2 2.5
Feb 2.13 0.29 1 1
Mar 3.05 0.2 4 7
Apr 3.67 0.35 7 4
May 4.5 0.36 9 8
Jun 4.98 0.45 11 10
Jul 5.14 0.49 12 12
Aug 4.91 0.48 10 11
Sep 3.45 0.32 6 6
Oct 4.10 0.39 8 9
Nov 3.11 0.31 5 5
Dec 2.52 0.21 3 2.5
[R(Ni) -R(Pi)] 2
1. 0 ,
Arrange data ranking. "
The ranking of total nitrogen and phosphorus are made
columns 4 and 5 of Table VIII-17.
Calculate A value.
Since there is only one tie in the data, Equation 8.50 can be
used. The square of difference between the two ranks is
calculated in column 6 of Table VIII-17.
_1- 6(23.0) 0 08
p- 12 (122-1) = .
Construct hypothesis.
Ho: There is no correlation between total nitrogen and total
phosphorus concentrations.
Ha: Higher total nitrogen concentration tends to pair with
higher phosphorus concentration. (This is a two-sided test.)
Use a=0.05 as the confidence level for the test.

Draw conclusion.
From Appendix Q, using p=1-0.05=0.95 and
w=0.4965. we cannot reject Ho because p
The basic assumptions made in using ANOVA are (Remington and
Schork, 1970, p. 284):
1. Each sample is a random sample from the corresponding
population, and observations from different populations
are independent.
2. The measurement variable X is normally distributed in
each of the k populations.
3. The populations all have the
(homoscedasticity) .
same variance
An additional assumption stated by Ponce (1980a, p. 74) is that
"the treatment (group) and environmental effects are additive. II
Ponce goes on to note that if the error terms for each variate are
not independent the F-test of significance can be "seriously
impaired." He also states that "the assumption of homogeneity of
variances is very important in the ANOVA because each sample
variance is considered to be an estimate of the same parametric
error variance." Tests for homogeneity of variance are discussed
in section VIII-B.4.2.
It should be noted that an ANOVA and its F test do not lead to
the inference that all means are different from each other
(Gaugush, 1986, p. 116). A significant F test simply indicates.
that differences exist, but additional tests (e. g., tests for
differences among means) are needed to answer questions about
particular means and differences among means. Gaugush describes
two tests for differences among means, the Bonferroni method and
Scheffe's method (Gaugush, 1986, p. 135). The reader is encouraged
to seek statistics texts which discuss these and related methods
since this guidance addresses them in a very limited fashion.
One-way analysis of varlance
Fixed Effects - Model I
To perform the calculations involved in ANOVA the following
definitions are required (Freund, 1973, p. 341-343):
total sum of squares = SST =
(equal sample sizes)
k n
L: L:
i=l j =1
(x, ,-x. . ) 2
(8.52 )
= SS(Tr) + SSE
(for unequal sample sizes)
k ni
L: L:x2"
, . lJ
l=l J=l
- L8 T2.. (8.53)
treatment sum of squares = SS(Tr)
(equal sample sizes)

= n. E
(x.. - x..) 2
k T2..
E l
i=l n.
(for unequal sample sizes)
. T2..
error sum of squares SSE
(equal or unequal sample sizes)
k n
i=l j =1
lJ l
(8.56 )
SS (Tr)
treatment mean square = MS(Tr) =
k - 1
error mean square = MSE =
k(n - 1)
F statistic = F =
(8.59 )
sample size for each of k means = n
number of means = k
grand total of all the data = T..
T. .
grand mean
x.. =
(8.63 )
total of observations for ith treatment = Ti
(8.64 )
mean of the ith sample = -x..
. According to Snedecor and Cochran (1980, p. 218), in the above
notation subscript i denotes the class, and takes on values from 1
to k, where k is the number of classes. Similarly, subscript j
denotes the member of the class, from 1 to n.
The observations (x..) within each class (i) are assumed
normally distributed aboueJthe mean ~. with variance ~2 (Snedecor
and Cochran, 1980, p. 218). As statedlearlier, the variance is the
same for all classes, but the mean can vary among classes. The
mean of the k values of ~. is denoted as ~, and the linear model is
expressed as (Snedecor and Cochran, 1980, p. 219):
x.. = ~ + a..
lJ l
+ E. .
[i=l,...k; j=l,...n; E,,=N(0,~2)]

This. "fixed effects model" (or model I) shows that each observed
value is the sum of an overall mean (J1), a treatment or class
deviation (a.), and a random element (E..) from a normally
distributed population with mean 0 and g~andard deviation ~
(Snedecor and Cochran, 1980, p. 219). The model is referred to as
"fixed" because the a. are considered to be fixed, but unknown
quantities to. be me~sured. The random element represents
variations due to such things as unit-to-unit variation in
treatment effect, measurement errors, or individual characteristics
of the unit (Snedecor and Cochran, 1980, p. 219).
According to Snedecor and Cochran (1980, p. 221) the F value
is a "good criterion for testing the null hypothesis that the
population means are the same in all classes." An F value of 1
represents the condition where Ho is true, and large F values
indicate differences among the J1.. Snedecor and Cochran (1980,
p.228) note that the F test is m6re affected by nonnormality and
heterogeneity of variances with unequal sample sizes (n.) than with
equal sample sizes. 1
As .an example of one-way ANOVA consider the situation where
the trout populations (Platts et al., 1983, p.28) of three streams
are measured by the multiple-step Zippin approach for
electrofishing at five randomly selected sites in each of three
geographic regions. The data from this monitoring effort are shown
in Table VIII-18.
Using the SAS ANOVA procedure (SAS Institute, Inc., 1985b) we
modeled trout population as a function of stream (i. e., MODEL
TROUT=RIVER) to test the null hypothesis that stream has no effect
on trout population (i.e., treatment effect is zero). The results
of this test are shown in Table VIII-19. Note that the F VALUE
(2.60) is equal to MS(Tr) (109.9) divided by MSE (42.3). (NOTE:
SAS uses MODEL instead of "Treatment".) The probability of
obtaining a greater F value if the null hypothesis is true (PR > F)
is 0.0865. We can therefore reject with 90% confidence the null
hypotheis' and accept the alternative hypothesis that stream does
affect trout population (i. e., trout population varies across
streams). However, we would have to accept the null hypothesis at
the 95% level of confidence.
The SAS ANOVA procedure also allows the analyst to perform
several post-ANOVA hypothesis tests, including tests of differences
between means (SAS Institute, Inc., 1985b, p. 117). For this
example we used the Bonferroni t tests, Duncan's multiple range
test, Gabriel's multiple-comparison procedure, the Ryan-Einot-
Gabriel-Welsch multiple F test, the Ryan-Einot-Gabriel-Welsch
multiple range test, Scheffe's multiple-comparison procedure,
Tukey's studentized range test, and the Waller-Duncan k-ratio test.
The reader should consult statistics texts (e. g., Snedecor and
Cochran, 1980, p. 232-236) to learn more about these procedures.
The Waller-Duncan k-ratio test and Duncan's multiple range test
showed that (at 95 percent confidence) the mean trout population
for Black Stream (67.1) is statistically different from that of Red
Stream (61.8), but that the mean trout population for Blue Stream

Table VIII-18. Stream Trout Population      
Stream Region  1  2 3  4 5 
   - - Trout Population - - 
   (Pounds/Acre/Year - Year Class 2)
Black Mountain  75  70 65  72 68 
 Piedmont  68  72 70  70 67 
 Coastal Plain 60  65 64  63 58 
Blue Mountain  70  76 69  67 74 
 Piedmont  64  66 60  69 62 
 Coastal Plain 49  60 54  58 57 
Red Mountain  68  70 63  65 70 
 Piedmont  62  66 58  69 67 
 Coastal Plain 50  56 51  60 52 
Table VIII-19.
One-way ANOVA
1-Way ANOVA With River As Treatment
Analysis of Variance Procedure
Dependent Variable: TROUT
219.733 109.9 2.60
1777.467 42.3 
219.733 2.60 0.0865
0.0865 0.110021

is not statistically different from that of either Black Stream or
Red Stream. All other tests showed (at 95 percent confidence) no
statistical differences between the mean trout populations of the
three streams. Table VIII-20 shows results from both the Waller-
Duncan k-ratio test and the Bonferroni t test, which are
representative of all tests performed on differences between means.
Note that the two tests determined different minimum significant
differences, which caused the different test results.
Random Effects - Model II
Model II ANOVA conforms to the following equation for one-way
classification (Snedecor and Cochran, 1980, p. 238):
x.. =
J1 + A.
+ E. .
[i=l,...a; j=l,...n)
(8.67 )
Ai = N(0,aA2), Eij = N(O, a2)

A clear difference between the model II and model I equations is
the term A. which represents the difference between the value of
the ith cl~ss and the average value over the population (N=n8a)
(Snedecor and Cochran, 1980, p. 238). The value A. varies from
class to class, whereas a. (model I) is a fixed cla~s deviation.
Snedecor and Cochran (198~, p. 238) notes that for the simplest
version of model II the A. are assumed normally distributed with.
variance aA2 and mean 0. 1.Further assumptions are the E.. and A.
are indepenaent, and that E. . is normally distributed with1.~arianc~
a2 and mean 0. The varianc~Jof an observation is aA2+a2, with the
two terms called the 11 components of variance 11 (Snedecor and
Cochran, 1980, p. 238).
Snedecor and Cochran (1980, p. 239-254) discuss the random
effects model (model I I) in considerable detail, including a
comparison between model I and model II, use of model II in
measurement problems, intraclass correlation coefficients,
confidence limits related to the components of variance, samples of
unequal sizes, and tests of homogeneity of variance. The reader is
referred to this and other statistics texts for more on the random
effects model.
In a simple sense, the model I and model II ANOVA can be
applied in the following general situations.
Model I
class means differ
class deviation fixed
Model II
class means differ
class deviations differ
As an example, a study to investigate the phosphorus content of
runoff from corn fields, city streets, and mining areas may require
application of model II ANOVA since both the mean phosphorus
content and variability are likely to vary from class to class.
However, a split-plot study to explore the phosphorus content of
three corn plots receiving different levels of phosphorus

Table VIII-20.
Waller-Duncan k-ratio and Bonferroni t test results
-l-Way ANOVA With River As Treatment
Analysis of Variance Procedure
Waller-Duncan K-ratio t test for variable: TROUT
NOTE: This test minimizes the Bayes Risk under additive loss and
certain other assumptions.
K-Ratio = 100, DF = 42
Critical Value of t = 2.21
Minimum Significant Difference = 5.2403
MSE = 42.3206
F = 2.59605
Means with the same letter are not significantly different.
Bonferroni (Dunn) t test for variable: TROUT
NOTE: This test controls the Type I experimentwise error rate,
but generally has a higher Type II error rate than REGWQ.
ALPHA = 0.05 DF = 42 MSE = 42.3206
Critical Value of t = 2.49367
Minimum Significant Difference = 5.9236
Means with the same letter are not significantly different.

fertilizer may support application of model I ANOVA since the class
means should differ but the class deviations may be comparable.
D. Two-way analysis of variance
In two-way ANOVA we quantify the variation due to one variable
(treatments), the variation due to a second variable (blocks), ~nd
the variation due to chance (experimental error) (Freund, 1973, p.
348). We then calculate F statistics for both the treatments and
the blocks. The two null hypotheses are that the treatment effect
and block effect are zero. Snedecor and Cochran (1980, p. 258)
note that the post-ANOVA hypothesis tests discussed for one-way
ANOVA are also applicable to two-way ANOVA.
The terminology used in two-way ANOVA varies with the
application, "blocks" being used in agriculture and "replicates" or
"groups" used in other applications. As such, in a "randomized
block" experimental design sample units are randomly selected from
blocks under each treatment (Snedecor and Cochran, 1980, p. 255).
The following additional definitions are required for two-way
analysis of variance with no interaction (Freund, 1973, p. 350):
T 2-
. j
. T.. 2
block sum of squares = SSB =
- .
block mean square = MSB =
(8.69 )
MS (Tr)
F statistic for treatments =
F statistic for blocks =
number of treatments = k
number of blocks = n
Also, the error sum of squares and error mean square are redefined
as (Freund, 1973, p. 350):
SSE = SST - SS(Tr) - SSB
(8.74 )
(n-1) (k-1)
The linear model for two-way classification with
observation per cell is (Snedecor and Cochran, 1980, p. 259):

x.. = J.L + a. + (3. + E. .
lJ l J lJ
[i=l,...k; j=l,...n)
x.. = measurement for the ith treatment
J.LlJ = the overall mean
a. = treatment effects (La. = 0)
{3~ = block ef~ects (L{3. = ~)
E~. = random element ofJerror

The .two as'sumptions made in using this model are that (1) the
treatment and block effects are additive, and (2) the residuals
E.. are independent, random variables normally distributed with
m~an 0 and variance a2 (Snedecor and Cochran, 1980, p. 259-260).
and jth block
Snedecor and Cochran (1980, p. 264-272) discuss two-way ANOVA
in further detail, covering suc~ topics as least squares
estimation, blocking efficiency, more than one observation per
. cell, balancing the order in which treatments are given, and Latin
squares. .
Two-way ANOVA can be performed for two cases, one in which
there is no interaction between the two variables and one in which
there is an interaction between the two variables. For the case of
no interaction the above definitions are used. The ANOVA table for
a two-way analysis with no interaction is shown as Table VIII-21'
(Freund, 1973, p. 350).
In the above example, the researcher has anticipated some
regional effect on the trout populations for each of the streams.
The data in Table VIII-18 point out this fact since samples were
collected in the mountains, piedmont, and coastal plains region of
each stream. A two-way ANOVA with stream as the treatments and
region as the blocks was performed to test the hypotheses that both
treatment and block effects are zero. The results of this SAS
ANOVA procedure (SAS Institute, Inc., 1985b) are shown in Table
VIII-22. . Comparing Table VIII-22 with Table VIII-19 it is clear
that the addition of region to. the ANOVA has increased the F VALUE,
the R-SQUARE, and the significance of the F statistic. Note that
the F VALUE for river is higher in the two-way (7.80) than in the
one-way (2.60) ANOVA. This is due to the fact that the MSE (the
measure of variability due to chance) is lower in the two-way
The results of this two-way ANOVA cause us to reject with 95%
confidence both null hypotheses in favor of the alternative
hypotheses that stream and region each have an effect on trout
population. Remembering that this analysis assumes no interactions
between the two variables, we performed both the Waller-Duncan K-
ratio test and the Bonferroni t test on differences between means
for both stream and region. The results of this test for stream
and region are shown in Tables VIII-23 and VIII-24, respectively.
The results in Table VIII-23 differ from those in Table VIII-20
since the MSE is different. Table VIII-24 shows that mean trout
population is different for each region.

Table VIII-21.
Two-way ANOVA table
Source of Degrees of Sum of Mean    F
variation freedom squares square  
       SS (Tr) MS (Tr)
Treatments k - 1 SS (Tr) MS (Tr) =    
       k - 1 MSE
       SSB  MSB
Blocks n - 1 SSB MSB = - -
       n - 1 MSE
Error (n-l) (k-l) SSE MSE =    
     (n-l) (k-l) 
Total nk - 1 SST      
Table VIII-22.
Two-way ANOVA
2-Way ANOVA With River and Region As Treatments
Analysis of Variance Procedure
Dependent Variable: TROUT
0.0001 0.717738

Table VIII-23.
Waller-'Duncan k-ratio and Bonferroni t test results
2-Way ANOVA With River and Region As Treatments
Analysis of Variance Procedure
Waller-Duncan K-ratio t test for variable: TROUT
NOTE: This test minimizes the Bayes Risk under additive loss and
certain other assumptions.
K-Ratio = 100 DF = 40
Critical Value of t = 1.94
Minimum Significant Difference = 2.6586
MSE = 14.0933
F = 7.79565
Means with the same letter are not significantly different.
Bonferroni (Dunn) t test for variable: TROUT
NOTE: This test controls the Type I experimentwise error rate,
but generally has a higher Type II error rate than REGWQ.
ALPHA = 0.05 DF = 40' MSE = 14.0933
Critical Value of t = 2.49886
Minimum Significant Difference = 3.4254
Means with the same letter are not significantly different.

Table VIII-24.
Waller-Duncan k-ratio and Bonferroni t test results
2-Way ANOVA With River and Region As Treatments
Analysis of Variance Procedure
Waller-Duncan K-ratio t test for variable: TROUT
NOTE: This test minimizes the Bayes Risk under additive loss and
certain other assumptions.
K-Ratio = 100 DF = 40
Critical Value of t = 1.81
Minimum Significant Difference = 2.4835
MSE = 14.0933
F= 43.0605
Means with the same letter are not significantly different.
 A 69.467 15 Mountain
 B 66.000 15 Piedmont
 C 57.133 15 Coastal
Bonferroni (Dunn) t test for variable: TROUT
NOTE: This test controls the Type I experimentwise error rate,
but generaly has a higher Type II error rate than REGWQ.
ALPHA = 0.05 DF = 40 MSE = 14.0933
Critical Value of t = 2.49886
Minimum Significant Difference = 3.4254
Means with the same letter are not significantly different.
69.467 15 Mountain
66.000 15 piedmont
57.133 15 Coastal

For the case in which there are interactions between the two
variables the ANOVA table shown as Table VIII-25 is used (Freund,
1973, p. 353).
The following definitions apply to Table VIII-25 (Freund, 1973, p.
353) :
total sum of squares = SST =
k n r 1
E E E X2ijh - ---8T2
i=l j=l h=l knr
1 k
treatment sum of squares =SS(Tr)=---8 E
nr i=l
T2,.. -_8T2
l knr
E 8 T2... -
j =1 J
block sum of squares = SSB =
8 T2
interaction sum of squares =SSI=
k n
i=l j =1
8 T2". -
8 T2... - SS(Tr) - SSB (8.80)
error sum of squares = SSE = SST - SS(Tr) - SSB - SSI
(8.82 )
number of treatments = k
number of blocks = n
(8.83 )
number of observations for each k & n combination = r
(8.84 )
As an example of two-way ANOVA with interactions we ran the
SAS ANOVA procedure (SAS Institute, Inc., 1985b) on the data in
Table VIII-18 checking for interactions between stream and region.
This test could reflect, for example, the hun,ch that regional
effects on trout population differ across streams (e.g., perhaps
the streams are impacted differently by point and nonpoint
sources). The results of this test are shown in Table VIII-26.
Note that although R-SQUARE is greater than in Table VIII-22, the
F VALUE is smaller (yet still significant). The interaction of
stream and region has not improved the model noticeably since the
interaction F statistic (F=1.82) is not significant at the 95%
confidence level (PR>F is 0.1458).
D. More on analysis of variance
The above discussion of ANOVA is simple in many respects. For
example, in all cases there were no holes in the data set. That is,
there was a data value for each combination of variables, a
complete block design. In situations where multiple variables are
examined the complete block design is not likely to be either

Table VIII-25.
Two-way ANOVA with interaction
Source of Degrees of Sum of   Mean   F
variation freedom squares   square   
           SS (Tr) MS (Tr)
Treatments k - 1  SS(Tr) MS (Tr) =    
           k - 1 MSE
           SSB  MSB
Blocks  n - 1  SSB   MSB = - 
           n - 1 MSE
           SSI   MSI
Interaction (n-1) (k-1) SSI MSI =      -
         (n-1) (k-1) MSE
Error  kn ( r - 1) SSE MSE =     
          kn(r - 1) 
Total  rkn - 1 SST        
Table VIII-26.
Two-way ANOVA with interaction
2-Yay ANOVA Yith River and Region As Treatments
Interaction Between River and Region
Dependent Variable: TROUT
Analysis of Variance Procedure
1528.40 191.05 14.67
468.80 13.02 
219.733 8.44 0.0010
1213.733 46.60 0.0001
94.933 1.82 0.1458
0.0001 0.765271

feasible or economical. Gaugush; (1986, p. 99-102) discusses both
completely randomized and randomized block designs as "the two
designs upon which all designs are based." This text and other
statistical texts such as those by Win~r (1971) and Cochran (1963)
should be reviewed to gain a greater understanding of the
relationships between ANOVA and sampling design.
. Snedecor and Cochran (1980, p. 274-297) discuss the
consequences of and remedies for failures in meeting the
assumptions of ANOVA. This chapter addresses missing data points,
extreme values, correlations between errors, transformations, and
Tukey's test for nonadditivity of the effects of different factors.
In the discussion of transformations the authors describe variance-
stabilizing transformations, square-root transformations for
counts, arc sine transformations for proportions, and logarithmic
More than two variables can be used in ANOVA, but it is
advisable that computer resources be made available to facilitate
these analyses. The SAS ANOVA procedure (SAS Institute, Inc.,
1985b, p. 113) used in the above examples is recommended only for
balanced data sets (with some exceptions), but the SAS GLM (general
linear models) procedure is capable of handling both balanced and
unbalanced data (SAS Institute, Inc., 1985b, p. 114).
Gaugush (1986, p. 114) includes in his clear chapter on ANOVA.
a discussion of fixed and random treatment-population effects,
where treatment-populations are the "populations under
consideration in sampling designs or the controlled manipulations
employed' by the researcher in experimental designs." The following
statements taken from Gaugush (1986, p. 114 -118) summarize the
major points made in distinguishing between fixed and random
treatment-population effects.
Fixed effects refer to a set of treatment-populations which is
finite either by nature or by an "a priori" selection process;
more importantly, inferences are limited to only those
treatment-populations that are sampled.
Due to the nature of fixed effects, the inferential process
conventionally involves either or both estimation of
treatment-population means or mean differences and tests of
hypotheses about significant differences among means.
The ANOVA for fixed effects models is called Model I ANOVA.
Random effects refer to a
populations; inferences can
treatment-populations sampled.
random sample of
be made about
the entire
The inferential process involves tests of hypotheses in terms
of the variance component being estimated.
The ANOVA for random effects models is called Model II ANOVA.

Gaugush also notes that liliOVA models can be "mixed" when the
structure or nature of the treatment-population is partially random
(1986,p. 117).
As a final note on liliOVA, Gaugush discusses in some detail
factorial and hierarchical arrangements for fixed effects models
(1986, p. 118-133). In this section he discusses main effects as .
effects for which questions addressing differences among means at
each level of a single factor can be asked. For example, a main
effect question might ask whether significant differences exist
among the mean chlorophyll a concentrations at three stations on a
lake. In this case station is the factor and each station is a
level. Interaction effects involve relationships among levels of
different factors. Using the above example, an interaction effects
question might ask whether similar differences exist among the mean
chlorophyll a concentrations at three stations at three different
depths. The two factors involved are station and depth, with the
levels being each station and each depth. Again, the reader is
referred to Gaugush (1986) and statistics texts for further
discussion of these concepts.
Analysis of Covariance
Analysis of covariance is a procedure which combines the
features of analysis of variance (liliOVA) and regression (Snedecor
and Cochran, 1980, p. 365). A typical analysis of covariance model.
(corresponding to one-way liliOVA) can be represented as (Snedecor
and Cochran, 1980, p. 365):
Y., = a, + {3 (X.. - X..) + E. ,
1J 1 1J 1J
where Y.. = value of jth observation in the ith class
= population mean of the ith class
= the regression coefficient of Y on X
X.. = value of jth observation in the ith class of another
1J measured variable
X.. = mean of all X. . values

E.. = residual of jth observation in the ith class

The analysis of covariance model which corresponds to two-way
liliOVA is (Snedecor and Cochran, 1980, p. 365):
Y.. = Jl + a. + p. + {3 (X., - X..)
1J 1 J 1J .

Jl = the mean of the Y.. observations
p. = intraclass correl~tion

In one-way ANOVA where there are two additional, or auxiliary,
variables related linearly to Y.., the model is (Snedecor and
Cochran, 1980, p. 365): 1J
+ E. .
(8.86 )

Y. , = a. + {3l (Xl" - Xl".) + {32 (X2" - X2 )
1J 1 1J 1J" .
{3l = the regression coefficient of Y on Xl

Xl" = the value of the jth observation in the ith class of
1J Xl
+ E, .
(8" 87)
Xl". = the overall mean of X1ij'S
(32 = the regression coefficient of Y on Xl
X2" = the value of the jth observation in the ith class of
1J X2
X = the overall mean of X2' . 's
2. . 1J

. Analysis of covariance can be used
1980, p. 365-366):
to (Snedecor and Cochran,
increase the precision of randomized experiments
adjust for sources of bias in observational studies
examine the nature of treatment effects in randomized
study regressions in multiple classifications
The following discussion of analysis of covariance is adapted,
from a pair of articles written for a technical nonpoint source
newsletter (Spooner, 1986a and Spooner, 1986b).
Analysis of covariance can be used to test for differences in
the average value for a meteorologic or hydrologic parameter Y
(e.g", sediment concentration) between levels of a group variable
(e.g", seasons or years) after adjusting for the parameter X (e.g.,
flow or upstream concentration)" In this case X serves as a
regression covariate. For this discussion, periods of time in
years will be used as the group variable. Hence, the annual
average value of Y will be compared for different time periods
after adjusting for the effects of X on Y. This type of analysis
has merit when the Y and X parameters are correlated (i.e", exhibit
a significant linear relationship) .
There are several steps in this analysis. First, linear
regression of a parameter (Y) versus another parameter (X) should
be performed and tested for significance. Paired observations
(i.e., collected on the same date, from the same storm, or matched
samples representing the same parcel of water as it passes above
and below the area of interest) are required.
There are several uses for analysis of covariance i those
listed above, as well as to determine if the same relationship of
Y and X exists from year to year. In both cases, the added
information fr'om pairing X with Y should decrease the residual
error as compared to an analysis of variance that did not include
X. Therefore, a calculation of an adjusted yearly mean in Y would

allow a more precise comparison between yearly means of parameter
One statistical model for
expressed (Snedecor, 1967) as:
Y.. =Jl. + (3(x.. -X..) + E..
lJ 1 lJ lJ
where: ,th b .
Y., = J. 0 servatlon for Y in year i
(8.88 )
= mean for year i
= regression coefficient of Y on X
.th b . f .
X.. = J 0 servatlon or X ln year i
X. .
= mean value for all X. . IS

E .. = residuals or experimental
lJ observation for Y in
error for the jth
year i
Computation of an estimate for {3 was performed by least squares
(Snedecor, 1967). Note that this version of the covariance model
forces the slope of the reqression of Y on X to be the same for
each year.
Figure VIII-28 shows a general case in which each time period
is represented by separate lines which have a commmon (equal)
Adjusted means which correct for the bias in X between years
can be calculated by (Snedecor, 1967):
Ad j Y. = Y.. - b (X.. - X..)
(8.89 )
Y.. = sample mean of paramete Y for year i
= estimate of the regression coefficient of Y on X
X.. = sample mean of parameter X for year i
X.. = sample mean value for all X. . IS,
which each Y.. is adjusted. lJ

The result of this calculation is that each yearly mean for Y is
adjusted to an overall common value of X. For this model, the
common value of X is arbitrary.
the value to
The F-test of the adjusted means can be performed to determine
if there is sufficient evidence that at least one of the yearly
adjusted means is different from the other yearly adjusted means.
Simply, the F-test determines if there is still a difference

Figure VIII-28.

D. D.
~vear 1
L 0
L 6. 3.vear 2
L ~,.. g... 6'
""""0 0 0'. V ear 3
c~ ~O
o ...-e) .
~ 0
Parameter X
Parameter Y VS. X for three time periods.

between years afteroadjusting for the covariance.
be calculated by:
The F-ratio can
F-ratio =
(SSER - SSEF)/(k-1)
(8.90 )
SSER = residual sum of squares for the reduced model
with a common yearly mean (i.e., ~. = ~)
SSEF = residual sum of squares for the full ,model which
allows for separate means for each year (i.e.,
equation 1)
= number of years
= mean square error from the full model with
(N-K-1) d.f. (i.e., equation 1)
This F-statistic is compared to an F distribution with (k-1) and
(N-K-1) degrees of freedom (d. f.), where K is the number of years
and N is the total sample size. Given a significant F-ratio for
differences between adjusted yearly means, one may want to compare
which adjusted means are significantly different. The confidence
interval of a difference between two adjusted means (CID) can be.
obtained by:
C I D = (Ad j Y i' - Ad j Y j .) :!: t I ( SD 2 )
(8.91 )
(Adj Yi' - Adj Yj') = the difference between the adjusted
means for the ith and jth year
t = Student's t statistic with (2n-2) d.f.
= sample size per year
S 2
= variance of the difference between the adjusted mean
of the ith and jth year given by:
S 2 = MSE . 2/n +
(X, - X.) 2
l J
k n
E E (X.. - X,.) 2
hI j=l lJ l
MSE is the mean square error from the full covariance model and k is the
number of years.
If this interval contains the value zero, there is no evidence of
a significant difference between the means of the ith year and the
jth year.

The above covariance model fits a single pooled or equal slope
for all years. An extension to this model which allows separate
regression lines for each year is (Snedecor, 1967):
Y.. = J-i. + {3. (X, ,) + E. .
1J 1 1 1J 1J
(8.93 )
Y.. = the j th observation for Y in year i
= the mean for year i
= the regression coefficient of Y on X for year i
X.. = the j th observation for X in year i

E ., = the residuals or experimental error

The F-test for the homogeneity of slopes involves testing if
there is a significant reduction in the residual sum of squares
(SSE) by allowing separate slopes for each year as compared to the
model with pooled slopes. The F statistic for testing the
homogeneity of slopes is
F-ratio =
(SSER - SSEF)/(k-1)
SSER = residual sum of squares for the reduced model
with a common slope
SSEF= residual sum of squares for the full model which
allows for separate slopes for each year
= number of years
MSEF = mean square error from the full model

This F statistic is compared to an F distribution with (k-1) and
(N-2k) d.f. Figure VI~I-29 shows a general case in which each time
period is represented by its individual regression line.
If there is no evidence for separate slopes then the model
with common slopes (Eauation 93) should be used.
In summary, the homogeneity of slopes, midpoints, and adj usted
means between time periods can be tested separately, but
simultaneously for the individual time periods (e.g., years). The
homogeneity test then indicates if one or more signficant
differences exist among the slopes or adjusted means.
If there are not significant differences between the slopes,
then ~ll of the periods of time can be represented by a common
slope and the relationship between parameters Y and X is constant
over the tested period. If a slope is significantly different from

..iOll: .,.

Q -~..- -
,.d c
~ Qjo' =
C " 0
t:J. C" fill'
d;.'~ CO~" 0

~,' . 0..," 0
,,0 0". 0
o =".
,,0 0
,.,88t8r I
Figure VIII-29. General representation of regression between
paired observations of parameters, Y and X. Each unit of time has
its own slope.

the common slope, then it is represented by its own slope when
testing the homogeneity of the adjusted means. The appropriate
model, i.e., either a common slope or unique,. individual slopes,
should be used for this test.
A significant difference among the adjusted means indicates
that at least - one mean of the adj usted parameter Y values is
different from the other means of adj usted parameter Y values.
Examination of which time periods are different indicates if a
trend is occurring over the entire time period and what is the
direction and magnitude of such a trend. Further trend analyses in
which time is a continuous variable may be useful.
Caution must be used when interpretinq the results for the
comparisons of ad-;usted means when individual slopes are used.
When the slopes are not parallel, the comparisons of adjusted means
may not be the most meaningful analysis to perform. One may be
more interested in the behavior over the entire range of X. In
this case a picture may be worth a thousand words.
Spooner (1986b) goes on to offer tips on how to use the
Statistical Analysis System (SAS) computer program (SAS Institute)
for analysis of covariance. SAS is a handy program for water
quality professionals to use since it handles very large data bases
with many variables, and is directly available to all users of
EPA's STORET system. The following is adapted from Spooner's SAS'
The SAS program statements that generate
with unique slopes for each year are given by:
a covariance
A summary of the useful information generated by the Type I SS
from the above SAS program is given by Freund and Littell (1980, p.
202) :
X: SS due to a single regression of Y on X,
ignoring the grouping.
Year: SS due to adjusted yearly differences, assuming
a single regression relationship.
3 .
Year*X: An additional SS due to different regression
coefficients for the groups specified by the
factor YEAR.
If there is no evidence for separate slopes (i.e., the YEAR*X
interaction term in the previous SAS program is not significant)
then the model with common slopes (Equation 93) should be used.
The SAS model should be rerun without the interaction term.

The adjusted means and the test for the significance of the
difference between all possible pairs can be obtaine'd from the
PDIFF operations in the L8MEAN8 statement.
Kruskal-Wallis Test
The Kruskal-Wallis test is an extension of the Mann-Whitney
test described earlier. The procedure presented below is adapted
from Conover (1980).
Let k equal the number of random samples of possibly different
sizes. N is the total number of observations and is computed
N = l:
(8.95 )
Rank all of the data from lowest to highest.
Compute the sum of ranks, R., as the sum of the ranks for the
ith random sample. ComputelR. for all k random samples.
Compute the test statistic, T
T = -
k R.2
[ l: ~
i=l n.
N(N+1) 2
(8.96 )
[ i~l Rij' - N
(N:l) ,  ]
(8.97 )
82 =
Reject Ho at the level a, if T exceeds the quantile found in
Appendix D with k-1 degr~es of freedom.
Monotonic Trends
In NP8 data analysis, we often want to know whether there is
a tendency that a pollutant concentration increases or decreases
over time. If such a tendency exists, we say there is a trend.
Trend analysis is often used to determine whether the
implementation of a BMP actually reduces the pollutants in a
stream, or whether the development of an urban area is causing the
deterioration of the downstream water quality. To identify a
trend, we need to analyze the data on a long-term basis because
observed data often fluctuate randomly ov~r the short term. A
trend can be visually detected by plotting the observed data versus
time, although a statistical test might be required to analyze the
trend more accurately. Gilbert (1987) provided a list of time
series types (Figure VIII-30). Figure VIII-30(a) represents random
data. We can see that the data fluctuate randomly along their
average value. The data do not tend to increase or decrease over

Figure VIII-3D.
Types of time series (after Gilbert, 1987).

a long term. Figure VIII-30(b) represents a cyclical time series.
As with Figure VIII-30 (a), the data do not tend to increase or
decrease over the long term but follow a cyclical pattern. Many
time series have a cyclical nature, such as the mean monthly
temperature, or mean monthly flow rate in a stream, observed over
many years.
Figure VIII-30(c) represents an increasing-trend time series.
The data tend to increase over time in the long term although there
is a short-term fluctuation. Figure VIII-30 (d). represents an
increasing trend with a cyclical pattern. The data cycle during a
short period but tend to increase over the long term. The monthly
mean temperature over many years under a global warming environment
(if it exists) might follow this pattern. Figure VIII-30(e)
represents an increasing trend with data dependency. We can see
that large data tend to be followed by large data and small data by
small data and the overall trend is increasing. Figure VIII-30(f)
represents a random time series with an impulse. There is a spike
in the data, but it does not affect the long-term tendency of the
data, which is fluctuating along the average without a tendency of
increase or decrease. This may happen to a time series of
pollutant concentration in a stream affected by a spill. The spill
causes a spike in the concentration but does not affect the long-
term patten.
Figure VIII-30(g) represents a step change of the time series.'
There is no trend before or after the step change; that is, before
or after the sudden decrease, the time series tends to fluctuate
along its average. The only difference is that the average value
after the step change is less than that before the change. This
type of time series might reflect stream pollutant measurements
over time, when an upgrade of a wastewater treatment plant is
implemented. Figure VIII-30 (h) represents a random time series
followed by an increasing trend. The first part of the time series
has no trend while the second part tends to increase over time. In
NPS data, the first part might represent a measurement of stream
pollutants before industries were established in the upstream area.
The industries might release pollutants during their operation,
causing a gradual increase of stream pollutants, which is indicated
by the second part of. the time series.
The Mann-Kendall Test (Mann, 1945; Kendall, 1975) can be used
to - detect trends when the data available contain such value as
"below detection limit." For trends with a cyclical nature or
those interrupted by a sudden change (step trend), the seasonal
Kendall test (Hirsch et al., 1982) can be used. When a trend is
detected, the slope of the trend (change of data per time unit) can
be estimated by the Sen Slope Estimator (Sen, 1968). The slope can
then be used to predict future data. In the following, we discuss
some tests commonly used in NPS trend analysis and provide
examples. Berryman et al. (1988) provided a comprehensive review
of nonparametric trend analysis. After discussing these
nonparametric procedures, regression analysis is reviewed.

Cox and Stuart Test
The Cox and Stuart test can be used to detect whether there is
a trend for a time series. For a series of observed data, X" X"
. . X;, .. Xm, where m is the total number of data, the data are
arranged in_the order of time they are obtained. We need to know
whether there is an upward or downward trend for these data. In
other words, we need to know whether the data tend to increase or
decrease with time, or just fluctuate randomly along their average
value. The assumptions and test procedure are as follows:
1. The random variables Xl, Xl,
The measurement scale the data is at least ordinal (true for
most NPS data)
Either the data are identically distributed or there is a
.. .X;,
. . ,Xm
3 .
Example for Cox and Stuart Test
The annual total rainfall for 21 years is given in Table VIII-
27. Determine whether there is a tendency that the rainfall tends.
to decrease or increase over time.
Construct hypothesis.
Ho: There was no trend for the annual rainfall
Ha: There was either an upward or downward trend
annual rainfall. (This is a two-sided test.)
Use alpha=0.05 as confidence level.
for the
Calculate number of signs.
Group the data as in columns 1 and 2 in Table VIII-28. As the
total number of data is odd, the value at the middle point
(XI~36.4) is omitted. Assign the sign for each pair of data,
as in column 3 of Table VIII-28. From the table we get B=6,
Draw Conclusion
As the hypothesis is a two sided test, use alpha = 0.05 and n
= 10 to get the 1 and n values. From appendix P, we find 1 =
2, u = 9. - Because B is less than u and is greater than 1 -1,
Ho is rejected. We conclude that there is no trend for the
annual rainfall data at the confidence level of 0.05.

Procedure for the Cox and Stuart Test
I. Construct hypotheses:
Two-sided test:
Ho: No .!rend exists
Ha: There is a trend, either upward or downward
One-sided test I:
Ho: No upward trend exists
Ha: There is an upward trend
One-sided test 2:
Ho: There is no downward trend
Ha: There is a downward trend
2. Calculate number of signs.
Group the data into pairs (XI, XI +c), (X2, X2+c)...(Xi, Xi+c)... (Xm-c, Xm), where c=ml2 if m is
a even number, and c=(m+ 1)/2 if m is an odd number. If m is odd, the data at the middle of the time
series is excluded. Assign a sign for each pair. If Xi < Xi +c, a "+" sign is assigned. If Xi> Xi +c, a
"-" sign is assigned. A "tie" is assigned when Xi =Xi +c. Let n=total number of pairs with either a
"+" sign or "-" sign (ties are excluded), and B = total number of pairs with a "+" sign.
3. Draw conclusion.
Two-sided test:
From Appendix P, obtain the I and u values for the corresponding significant level (alpha) and n.
Reject Ho and accept Ha if B ~ u or B < I-I.
One-sided test I:
Multiply the alpha by 2 and use the new alpha and n to find out u in Appendix P. If B:::;u, reject
Ho and accept Ha.
One-sided test 2:
Multiply the alpha by 2 and use the new alpha and n to find out I in Appendix P. Reject Ho and
accept Ha if B > I-I.
Table VIII-27.
Annual total rainfall for 21 years
Year Rainfall (in.) Year Rainfaill (in.)
1 40.2  12 51. 2 
2 53.4  13 54..3 
3 43.5  14 41.5 
4 37.7  15 44.8 
5 50.2  16 46.7 
6 38.7  17 51. 8 
7 47.8  18 49.5 
8 39.5  19 34.1 
9 44.9  20 33.2 
10 41. 7  21 53.7 
11 36.4    

Table VIII-_28.
Sign calculation for Cox and Stuart test
X Xi+c Sign
40.2 51.2 +
53.4 54.3 +
43.5 41.5 -
37.7 44.8 +
50.2 46.7 -
38.7 51. 8 +
47.8 49.5 +
39.5 34.1 -
44.9 33.2 -
41. 7 53.7 +
Mann-Kendall Test
Like the Cox and Stuart test, the Mann-Kendall test also
analyzes the sign of the difference between later-measured data and
the earlier-measured data. As discussed above, the Cox and Stuart
test breaks the time series into two groups of data from the middle
point, then pairs the data in each group based on the order of time-
and takes the sign of difference for the pair. The Mann-Kendall-
test, however, pairs a later-measured datum to all data measured
earlier. This resu.lts in a total of n (n-l) /2 possible pairs of
data, where n is the total number of data in the time series. In
the Cox and Stuart test, there are only n/2 pairs of data for a
time series of Xl, Xz, ... X;, ... Xn, where n is the total number of
measurements and the data are arranged in the order of time they
are measured. The assumptions and test procedure for the time
series are as follows:
1. The random
. . .Xi,
.. .Xn
2 .
The measurement scale of the data is at least ordinal
for most NPS data) .
( true
Either the data are identically distributed or there
is a

Procedure for the Mann-Kendall Test
1. Construct hypotheses.
Two-sided test:
Ho: No -a'end exists
Ha: There is a trend, either upward or downward
One-sided test 1:
Ho: No upward trend exist
Ha: There is an upward trend
One-sided test 2:
Ho: There is no downward trend
Ha: There is a downward trend
2. Calculate signs.
Take the difference between the later-measured values to all earlier-measured values, (X; - X,),
wherej > k. Thats(X,-X,), (X,-X,), (X,-X,).. ..(X-XI)" (X,-X,), (X-X,),... (X-X,).... (X.-X.,), (X.-X,),
as listed in Table VIII-26. There are a total of n(n-1)12 possible differences. Assign a sign integer, sgn,
to each difference according to the following criteria:
Xk-Xj sgn
>0 1
o 0
<0 -1
See Table VIII-29 for calculation scheme.
Table VIII-29.
Data difference calculation for Mann-Kendall test.
X, X, X,  """ X, X
 X, - X, X, - XI ...... XI-X, X.-X,
  X, - X, ...... XI-X, X-X,
    ...,.. .... ....
     XI-X, X.-X.,
Sum all the integers.
n-l n

S= L L sgn (Xj-Xk)
k=l j =k+l
(8.98 )
The S value is basically the sum of all positive and negative
signs. It is easily seen that when s is a large positive number,
it indicates that later-measured values tend to be larger than
earlier-measured values and there might be an upward trend. When
S is a large negative number, the later-measured values tend to be
smaller than earlier-measured values, and there might be a downward
trend. When the absolute value of s is small, there might be no

trend. The statistical hypothesis test for the trend is done in
the followiTIg step.
Draw conclusion.
From Appendix R, use the nand S value to obtain the
probability value p, which is the probability that the calculated
S is greater than the specified S value in the table when no
trend is present. Compare the probability value p to the
confidence level (alpha) as follows.
Two-sided test:
Multiply the p value from appendix R by 2. If the multiplied
value is less than alpha, reject Ho and accept H1.
One-sided test 1:
Reject Ho if the probability value from appendix R is less
than alpha.
One-sided test 2:
Use the absolute value of the calculated S value to get the
probability value in appendix R. Reject Ho when the
probability value in appendix R is less than alpha.
The calculation for the Mann-Kendall test becomes tedious when~
n is large. Gilbert (1987) provided a FORTRAN program to alleviate.
the computation effort. When n is greater than 40, Gilbert
recommends using the normal approximation method, which
approximates the test to a normal distribution problem. For data
with seasonal cycles, the modified Mann-Kendall, also referred to
as the Seasonal Kendall test, should be used (Hirsch et al., 1982).
Basically, the test computes the S and variance of S as in the
Mann-Kendall test for each season, then sums them and computes Z
statistics, and then uses the standard normal distribution table to
test statistically significant trends. An example for the test was
provided by Gilbert (1987).
Trend Test with Seasonal and Autocorrelated Data
Both the Mann-Kendall and seasonal Kendall tests assume no
correlations among the data being analyzed. In NPS area, many data
follow seasonal patterns (F~gures VIII-30(b) and VIII-30(d)) and
might be autocorrelated (Figure VIII-30(e)). While the seasonal
Kendall test works with seasonal data, both tests require
independence o~ data. Autocorrelation data can cause errors in
both results. Therefore, in general trend analysis, we should test
for seasonality and autocorrelation first. In particular, we need
to ensure that the data are not correlated, or, if they are, to
make some corrections before applying the Mann-Kendal test or the
seasonal Kendall test. Reckhow et al. (1988) provide a test
procedure for this purpose as follows.
Remove all the known deterministic effects.

If we-find a deterministic pattern in the data, we try to
remove the deterministic portion. For example, when analyzing
a time series of total phosphorus concentration in the river, if
we know the concentration is a function of the flow rate, we
should try to deterministically model the relationship between
the floW-. and concentration, then subtract the modeled
concentration data from the original data. We can then use the
residual for the following step.
2. Remove seasonal and trend effects.
To see whether there is a seasonal pattern in the data, make
a correlogram using equations provided by Pankratz (1983). A
correlogram is a plot of autocorrelation values versus the time
lag, and seasonality can be found in the correlogram. For
example, a significant correlation value for the time lag of 12
for a monthly time series indicates that an annual cyclical
pattern exists in the data. When a seasonal pattern is found in
the data, we can deseasonalize and detrend the data using the
seasonal Sen slope estimator with the seasonal median. We can
then use the deseasonalized and detrended data for the following
Test for autocorrlation and select appropriate trend analysjs
Create a correlogram again with the deseaonalized and
detrended data from step 2. If the autocorrelation is
significant, we must correct the autocorrelation. This can be
done with the method provided by Hirsch and Slack (1984), in
conjunction with the Mann-Kendall Test or seasonal Kendall test.
If correlation is not significant, a standard Mann-Kendall test
or standard seasonal Kendall test can be applied.
The following overview of regression is adapted from an article
by Spooner and Maas (1984).
Regression analyses are used to test mathematical expressions
that relate one or more dependent variables (response variables,
Y's) to one or more independent variables (X's, usually considered
to be measured. without error) (Spooner and Maas, 1984). There are
two primary purposes for utilizing regression techniques: 1) to
model the behavior of a dependent variable, and 2) to predict the
future behavior of the dependent variable. In the first approach,
one may wish to examine cause and effect relationships or establish
past trends. In prediction applications, one may use the
information collected to date to predict the future behavior of one
variable based on the expected behavior of another variable. Trend
analyses such as time series, slope and intercept estimations, and
confidence intervals become the key ingredients in the latter
applications. In all cases, regression techniques attempt to

explain as ~uch of the variation in the Y variable(s) as possible.
As such, the goal in regression analysis is to minimize the sum of
the squared distances of the Y values from the regression curve
(i.e., the unexplained variation): Hence, the techniques used are
often referred to as "least squares." .
Linear univariate regression, or linear regression, relates the
behavior of a single dependent variable (Y) to one or more
independent variables by a linear function. This is in contrast to
multivariate analysis which incorporates simultaneous consideration
of several dependent variables. The" linear" term reflects the
fact that the coefficients ({3i I s) of the X I S in the regression
equation are linear. The X's may be linear or non-linear (e.g., X
can represent X2, X3, X-1, etc.). The general form of a linear
univariate regression model, where E is an error term, is shown as
Equation 52, whereas Equation 53 is a linear regression model
containing just one independent variable.
Y = {3
+ {31.X1 +. . + {3..X. + E
Y = {3o + {31.X1 + E
If the coefficients of the Xis are not linear, then the model is.
a "non-linear" model. Non-linear models are commonly applied _to
physical systems, but are more difficult to analyze because~
iterative least squares techniques are involved. Thus, many non-
linear equations are linearized before analyses.
Multiple linear regression (also referred to as multiple
univariate linear regression, and multiple regression) analyses are
used when a single independent variable does not explain
sufficiently the behavior of the dependent variable (Y). Two or
more independent variables (Xis) are utilized in a linear function
to describe the behavior of Y. Equation 52 (general linear
univariate model) depicts a multiple regression model, while
Equation 53, with one independent variable, is just a simplified
form of the general linear univariate model.
In NPS research multiple (univariate) linear regression analyses
are most often used to determine the extent to which the value of
a water quality parameter (Y) is influenced by land use or
hydrologic factors (Xis) such as crop type, soil type, percentage
of land treatment, amount of rainfall, etc. Practical applications
of these regression results include the ability to predict the
water quality ~mpacts of changes in the independent variables.
The most common multiple regression equations are those that
involve a list of independent variables that may affect the
behavior of Y (i.e., time, treatments, rainfall, etc.). These Xis
can be continuous or discrete variables. Polynomial equations are
common models for empirical descriptions of the behavior of the
In both modeling and predictive uses' of multiple regression, the
user may wish to select the best" subset" of the independent

variables. _There is a point where useful information is no longer
gained by -adding new variables. Also, correlations among X 's
(multicollinearity) can mask the relationship of one X to the Y
variable due to the correlation of this independent variable with
another in the model.
In contrast to the univariate models discussed above, where only
one dependent response variable (Y) is involved, multivariate
models can have several dependent variables. Multivariate analyses
(which include ANOVA and principal component analysis, among
others) are designed to take into account the correlation structure
of the X' sand Y' s to reduce the overall variance. An NPS
applications might be to examine the effect of different BMP
implementation programs on several water quality parameters.
In summary,
guidance are:
the types of regression models discussed in this
One dependent variable (Y)
More than one Y and X
Linear regression
are linear
({3, ' s)
on the X-, s~
Non-linear regression
Coefficients ({3, 's) on the Xis
1, l
are non- lnear
One Y as a function of several
Researchers are strongly encouraged to read the detailed
discussion of regression in statistics texts such as Snedecor and
Cochran (1980), Cochran (1979), and Srivastava and Khatri (1979)
for a more complete discussion of this important statistical
Linear regression
Regression is a statistical method often used in water quality
analyses. Referring back to our list of water quality monitoring
objectives, we find that regression analysis can be used in
developing baseline information (relationships between variables of
interest), trend analysis (parameter versus time), and model
development and/or verification.
D. The model
In this guidance we will not delve into the origins and
derivations of regression techniques, but will instead just discuss
the uses of, assumptions made in, and equations used for regression
analyses. Regression analysis, in general, is "a means of studying
the variation of one quantity (dependent variable) at selected

levels of another quantity (independent variable)" (Remington and
Schork, 197D). A key to regression is that we express and quantify
this relationship with a mathematical model. The model to be
discussed in this section is the linear model of the general form
(Freund, 1973):
y = a + bx
(8.101 )
where y is the dependent variable, x is the independent variable,
and a and b are numerical constants representing the y-intercept
and slope, respectively. For a general theoretical approach to
regression the reader is referred to winer (1971) and other
statistics texts.
The first step in applying linear regression is to examine the
data to see if linear regression "makes sense." That is, use a
bivariate scatter plot (section III.D.1) to see if the points
approximate a straight line. If they do, then linear regression
"makes sense," but if they don't fall in a straight line it may be
that data transformation is needed or that a non-linear
relationship should be used.
To illustrate the use of linear regression we use the data in.
Table VIII-30 which are a selected (biased) subset of calibratipn
data for a plot-size runoff sampler (Dressing et al., 1987). In.-
this data set the sampling percentage (split) was measured for a
range of flow rates. The scatter plot in Figure VIII-31 shows that
linear regression can be applied to the data.
Table. VIII-30.
Runoff Sampler Calibration Data
 x  y  X  Y
Flow Rate Split  Flow Rate Split
(gpm)  (%)  (gpm)  (%)
52.1  2.65  25.8  2.83
19.2  3.12  17.6  2.84
 4.8  3.05  37.6  2.60
 4.9  2.86  41.4  2.54
35.2  2.72  40.1  2.58
44.4  2.70  47.4  2.49
13.2  3.04  35.7  2.60
13.9  3.19     
n = 15 x = 28.89 LX2 = 15,940.33 
   LX = 433.3 x2 = 834.44 
   LY = 41.81 y2 = 117.25 
   LXY = 1,166.93 L (x-x) 2 = 3,423.74 

  . .
I-  . 
...... 2.8  
(fJ 2.7  
. . .
17.&0 :35.70
Figure VIII-31.
Split versus flowrate.
D. Least squares method
To develop the regression line we use the method of least squares
which "demands that the line which we fit to our data be such that
the sum of the squares of the vertical deviations (distances) from
the points to the line is a minimum" (Freund, 1973). To determine
the values of a and b in the above general linear model, the
following normal equations can be used (Freund, 1973, p. 394):
( Ey) (Ex 2) - ( Ex) (Exy)
a =
n (Ex 2), - ( Ex) 2
n(Exy) - (Ex) (Ey)
b =
n (Lx 2) - ( LX) 2
For the above data we used the SAS REG procedure (SAS Institute,
Inc., 1985b) to determine the regression line parameters. Table
VIII-31 shows that the intercept (INTERCEP) is 3.132 and the slope
(FLOWRATE) is -0.012. Thus, the linear model for predicting split
versus flow rate is:
Split = 3.132 - 0.0128Flowrate

nIT .
~RATOA: 58.5125 Df.
D~IHATOR. .0171284 Df.
  SUI1 OF "fAN 
nooEl I 0.48662350 0.48662350 28.410
ERROR IS 0.22266984 0.01712845 
C TOTAL 14 0.70929]33  
ROOT ttSE 0.1308757 R-SQUARE 0.6861
DEP ~AN 2.787333 ADJ R-Sq 0.6619
C.V.  ".695175  
7154 N!DNUDAY. 0C'T18D I. I M6
INTERCfP 1 3.13171795 0.0729141' U.9'1
flONRATI! 1 -0.01192192 0.002236705 -5.330

2 . 5800
2. 37588E-I"

2 .6)82
2 . 9660
PR08 > IT I

f VALUE. 3"16.1012
PR08 >f. 0.0001
0.0619 2.3768 2.6""" 2 . 1978 1.823" I.IJ'"
0.0401 1.8161 1.9895 1.6071 3.1986 0.2171
O. 0656 2.9171 5.2119 2.7601 J.J888 -O.Of"5
0.0654 2.9565 3.2105 2.7591 3.5875 -0.2133
0.0566 2.6529 2 . 7912 2."185 5.0057 .0079337
0.0484 2.4971 2.7070 2.3009 2.9059 0.1916
0.0487 2.8691 3.0196 2.6127 5.2160 0.0657
0.0345 2.7496 2.8986 2.5511 3.1165 .0058677
O. 0422 2.8308 3.0130 2.62"8 5.2190 -0.0819
0.0590 2.5992 . 2.1617 2. J884 2.9785 -0.0835
0.01\59 2.545" 2.7329 2.U99 2.936" -0.0982
0.0421 2.'621 2 . 7446 2.3561 2 . 9506 -0.015ft
0.0554 2.4'12 2.6821 2.2612 2.8720 -1.0766
0.0371 2.6260 2.7862 2."122 5.0000 -0.1061
0.0416 2.8652 3.0688 2.6651 5.2669 0 . 2240
I, \

Now that- we have a simple linear regression line the obvious
questions to ask are:
(1) How well does the line fit the data?
(2) How c~n the line be used?
Before we address these questions we should review the assumptions
made in performing linear regression. These assumptions are
(Gaugush, 1986):
The x values are constants measured without error.
The units in the sample with anyone value of x are
randomly chosen from all units in th~ target
population with that value of x.
The values of y at any particular value of x are
normally distributed about the regression line.
The variance of y is the same at each value of x, i.e.,
the variance is homogenous.
5 .
The deviations of the observed points from the line are
independent. Multiple observations in a single unlt~
will not, in general, be independent. .
The first assumption is made because no consideration is given
to variation in x. The third assumption is necessary only if
hypothesis tests are performed or confidence intervals are
determined. The fourth and fifth assumptions are needed for the
parameter estimates to be the most precise possible (Gaugush,
1986) .
Tests for some of the above assumptions are described by Ponce
(1980a) . To test the fourth assumption we plot the residuals
against the predicted y values. As shown in Figure VIII-32 this
plot should be a band around a residual of 0 (Ponce, 1980a. Figure
VIII-33 shows this plot for the above data set. (Table VIII-30).
This plot, although not having a well-defined band around zero,
# does indicate that the variance is fairly homogenous.

To test the independence of the deviations of the observed points
from the regression line, Ponce (1980a recommends that we plot the
residuals in time-sequence (Figure VIII-34). Assuming that the
data in Table VIII-30 are in time-sequence we plotted the ordered
residuals as shown in Figure VIII-35. This plot illustrates that
the residuals are independent.
Gaugush (1986) notes that regression analysis is generally robust
against violation of several assumptions.. In other words, the
estimates of a and b may be useful even if assumptions are violated
somewhat. However hypothesis tests and confidence intervals will
not be correct if the normality assumption is violated.

. .10 J
Predicted Y
.~ ",.rr.".~\
..., '..,' ~~~.t~.;.~:~~~~.~~:~? ~.~ ~l~~~'~'" .~31A ~~,
'\".",-.<11: '..; ,,a....,:,...:. ~. ,:",~I' ...:':......r.f;J..~~~~~..f'.a:'
Case B
; ~ . ," .
.' '.-
",' ~. . : .
. ~ '.or' .
'.~ .~ ':'.:..~ .~.~
',' ..
Predicted Y


I .


, .
t .

I .
I .
. .
! ~
: :
+ I!_' e
-, ...
, ...
I a
! I
I .

I .
I .
I ...
I .
. ...

, .
, ...
--.----.----+----.----.--- . ~:
- ----. ---- . ---- . ----. I .
: . 0 . . . .. ...

.; : ~ ~. ~ ; ; ; ~ ;


Figure VIII-33.
Plpt of residuals versus predicted values.

Case A
" '

.. ... .........'.I1.".;......-r.,.:.,
,"j. ',.;
,'1.. n" '.
'. ....,..

. ~'~'. : .~;'..'~'; ~.~.
Case B ,~ f!!'f~.r!"!.I.lj
"".".'~,'~.~J~:'~~17:~~~A;,..~~~~~~ ,,'.~~:
,\......'~ '" ...'..,"j '- '...~!,,'. ..,..".....r:.~~...,~,,~~. .~


. . . . . " .'~' ., . . ,..,."::.,~"'.'.:,~ :'"."', :: :,'~'":,',,:,';'~.'.,;,,.' , , ,. . ... .
.;'. '" '.:'.:'.'~' ':; '.' ,":~.:X.:/h;',r~.;.:\!~'~/-{'
. ...':~~. ..., . ..~.: ,f . ,'. .
, ,
. . ~. ::
:.':., .
" ";..'.."
:..; ,::," "'~. :,'. :::: ~: " ;
" .
.~ .
, ,
. ," ,.,...

, ...
.. .
I c
I c
Figure VIII-35.
sequence plot of

D. T~sts of fit
To determine how well the regression line fits the data we can
test several things: .
Test whether the slope is zero.
Test whether the intercept is zero.
3 .
The confidence interval for a.
The confidence interval for b.
The proportion of variation in y explained by the model.
Before discussing tests for the above hypotheses and estimates
we need to define several mathematical terms used in the
calculations to follow. The following terms and definitions are
taken from Ponce (1980a) and Gaugush (1986):
The corrected total sum of squares is the total amount of
variation in y and is calculated by computing the sum of the
squared deviations (Y.-Y):
SS t t 1 = ~(Y.-Y) 2 = ~y2
corr. 0 a l
The model (regression) sum of squares is the amount of
variation in y that is associated with the regression on
x, and is calculated as:
SS d 1 = ~(Y.-Y) 2 = (~xy) 2j~x2
mo e l
where the Y. (reads as "Y hat") values are the Y values
generateJ from the regression equation
Y. = a + b.X
l 1
The error (residual) sum of squares is the amount of
variation in y not associated with the regression on x, and
is calculated as:
SS(error) = SS(total) - SS(model)
The model mean square (MS) is the model sum of squares
divided by the number of degrees of freedom (d.f.) for the
model. For linear regression, d.f. (model) is always 1.
MS(model) = SS(model)jd.f. (model)
The error mean square is the error sum of squares divided
by the error degrees of freedom (n-2).
MS(error) = SS(error)jd.f. (error)

To test whether the slope is different from zero (Ho: b=O) we can
use either -an F-test or at-test (Gaugush, 1986). For the F-test
we first calculate the model and error mean squares. The test
statistic is .
F = MS(model)/MS(error)
and is compared versus the critical F value with d.f. (numerator)
equal to d.f. (model) and d.f. (denominator) equal to d.f. (error).
In our example we let SAS calculate the F value (Table VIII-31) .
The calculated F value of 28.410 was compared by SAS against F
table values with the result that there is a probability of only
0.0001 that a greater F value could be obtained if Ho is true. In
other words, we reject Ho with a significance of 99.99 percent (1-
0.0001). The slope is not zero. (Perform this same test using the
above equations to check the results from SAS.)
Gaugush (1986) notes that a t-test can also be used to test the
null hypothesis of zero slope. The test statistic is
t = (b-O)/sb = b/sb
where b is the calculated slope and sh is the standard error of b.
The standard error of b is calculatea as (Gaugush, 1986, p. 64) ~
Sb = I (MS /r. (x. - -x) 2)
error 1
Again using the data from Table VIII-30, we calculate the sum of
the deviations of x from the mean x (flow rate) to be 3,423.7373,
so sb is equal to 0.0022367. The t value is -0.01192/0.0022367, or
- 5. T3 . Using a two- sided test at 0'=0.05 with 14 degrees of
freedom, the t value for comparison is (Appendix C) -2.1448.
Clearly, the t-test results agree with the F-test results; the
slope is not zero.
The same information calculated above was calculated by SAS and
appears in Table VIII-31. The standard error of b is the standard
error of FLOWRATE, the t value is the T FOR HO: PARAMETER=O for
FLOWRATE, and the PROB > IT! is the probability that a higher t
value could be obtained if Ho is true. Hence, we reject Ho at
99.99 percent significance.
The null hypothesis of a zero intercept can also be tested with
at-test (Gaugush, 1986, p. 64). For this case the equation is
t = (a-O) /s
= a/s
where a is the calculated intercept and s is the standard error of
a, calculated as a
s = [MS . ( 1/ n + x 2 / r. (x . - x) 2 ) ] ~
a error 1

From Table YIII-30 the mean of x (flow rate) is 28.8867. Using the
above equa~ion, s is calculated to be 0.0729142. Therefore, the
calculated t valug is 3.13172/0.0729142, or 42.951. We reject the
null hypothesis of zero intercept.
The SAS output in Table VIII-31 shows s as the standard error
for INTERCEP, the t value as T FOR HO: PAftAMETER=O for INTERCEP,
and the significance as PROB > I T I for INTERCEP. Thus, SAS
determined that we can reject Ho at 99.99 percent significance (1-
0.0001) .
SAS also has as an option under PROC REG a simultaneous test that
(1) the intercept is equal to a specified value and (2) the slope
is equal to another specified value (SAS Institute, Inc., 1985b).
A good reason for using this test is that the level of significance
determined above (using the same data) for a and b are incorrect
due to the fact that the estimates for a and bare not independent
(Freund, 1973). The following SAS steps are recommended for
performing a test for a zero intercept and slope of one (Spooner et
We performed this test on the data in Table VIII-3D, and the-
results are shown in Table VIII-31 in the area designated as TEST: .-:
Clearly, from theF value (400605) and associated probability of a
greater F if Ho is true (0.0001), we must reject the Ho that the
intercept is zero and the slope is 1. To illustrate a case in
which we cannot reject Ho, we ran the same test with intercept =
3.1 and slope = -0.01 (close to PARAMETER ESTIMATE values in Table
VIII-4). The results of this test are an F value of 0.6172 and an
associated probability of 0.5545 for a greater F value. Hence,
there is a 55.45 percent chance that a greater F value could result
if Ho is true. This joint Ho can not be rejected.
To determine the confidence intervals for a and b the following
formulas are used (Freund, 1973, p. 415):

a t ta/28se8[1/n + n8x2/(n(Ex2) -(Ex) 2)]~
b t ta/28se/[(n(Ex2)-(EX) 2)/n]~
where s is the standard error of the estimate, equal to Freund,
1973, p. 414):
= [(Ey2 - a (Ey) - b(Exy)) /n-2] ~
As noted above, the confidence intervals for a and b are not
independent, and it is best to not use the same data set for tests
concerning both.
Using the data in Table VIII-30, we will calculate the confidence
limits for the slope. The standard error of the estimate is 0.1309

and the resulting 95 percent confidence interval is -0.017 to -
0.007 (vertfy this).
The coefficient of correlation, r, measures the strength of
linear relationships (Freund, 1973). It ranges from -1 to 1, with
the extreme~values representing the strongest association and 0
representing no correlation. The statistic r is calculated as
(Freund, 1973, p. 422):
n(LXY) - (LX)-(LY)
r =
[n (LX2) - (LX) 2] 5'2- [n (Ly2) - (LY) 2] 5'2
The sign of r should be the same as the sign of the slope.
To explain the proportion of the variation in Y explained by the
model we calculate the coefficient of determination (the square of
the coefficient of correlation) which is defined as (Anderson and
McLean, 1974):
SS (model)
r2 =
SS (total)
Values for the coefficient of determination range between 0 and 1,~
with 1 representing the case where all observed y values are on the
regression line.
For the data in Table VIII-30, the coefficient of determination
r2 =
= 0.686
We had SAS calculate this value also, and it can be seen in Table
VIII-31 that the two results agree. Thus, the linear regression
model, which has flow rate as the independent variable, explains
68.6 percent of the variability in y (split).
The correlation coefficient calculated from sample data is an
estimate of the corresponding population parameter, p (rho),
referred to as the population correlation coefficient (Freund,
1973). To establish a confidence interval for p we will perform
normal correlation analysis which requires the assumption of x as
a normally distributed random variable in addition to the
assumptions of normal regression analysis (remember that we
considered x to be a constant in linear regression) .
Using Appendix K (Remington and Schork, 1970) we can determine
graphically the 95 percent and 99 percent confidence limits for p
knowing only nand r. For the data in Table VIII-30, n is 15 and
r is -0.8283 (negative slope, square root of r-square). So, the 99
percent confidence limits from Appendix K are approximately -0.95
to -0.50.

A t-test~can be used to test the null hypothesis that p 1S zero.
The t statistic (n-2 degrees of freedom) for this test is (Freund,
1973, p. 427):
t =
For the above data t would be -5.33. From Appendix C the two-sided
t value for 95 percent significance (d.f.=13) is -2.1604.
Therefore, we reject the null hypothesis (p= 0) and accept the Ha
that p is not zero. This test will most likely seem trivial in
many applications. .
The Fisher 2 transformation can be used to test null hypotheses
of rho equal to values other than zero (Freund, 1973). For this
test r is changed into a 2 value using (Freund, 1973, p. 428):
2 = - 81 og e [ ( 1 + r) / ( 1- r) ]
The test statistic is (Freund, 1973, p. 428):
z = z = (2-J1 )In-3
1//n-3 z.
where J1 is the 2 value for r equal to p. For illustration we test
the Eo Ehat p is -0.8 for the regression performed using the data
from Table VIII-30. The z statistic becomes:
z = (-1.1827 + 1.0986)/12 = -0.2913
The two-sided z statistic at 95 percent significance (Appendix B)
is -1.960; therefore we cannot reject Ho.
A confidence interval for p can be determined by calculating such
an interval for J1 , and then converting that interval to rand p
(Freund, 1973). 1he formula for the confidence interval for J1Z is
(Freund, 1973, p. 429):
za/2 za/2
2 - < J1 < 2 +
In-3 z ~-3
Since J1 equals 2 when r equals p, the interval for J1 gives an
intervaT for 2 in which p can be determined by substitu~ing p for
r in the above equation for 2. Again using our sample data, the 95
percent confidence interval for J1 becomes:
-1.1827 -
< J1 < -1.1827 +

-1.7485 < ~ < -0.6169
z .
Solving for p:
Lewer Limit of p:
    (1 + p)
-1.7485 = 1/2 ln  
    (1 - p)
    (1 + p)
-0.6169 = 1/2 In.  
    (1 - p)
Upper Limit of p:
-0.94 < P < -0.55
Freund (1973) provides a table of Z values to simplify this
procedure. Note that the 95 percent confidence interval for p
calculated using the Fisher Z transformation (- 0.94 to - 0.55)
compares favorably with the 99 percent confidence interval (-0.95
to -0.50) determined graphically using Appendix K.
D. Using the regression line
The most obvious use of the regression line is for prediction of-
y values for selected values of x. For example, using the
regression established above we can estimate the split for any flow~
rate (it is not good practice, however, to predict values beyond
the range of test conditions). For a flowrate of 10 gpm the split
is 3.01 percent, while for a flow rate of 50 gpm the split is 2.53
Since, in most cases, the regression line will not fit the data
perfectly, we should quantify the uncertainty associated with our
predicted values. We can use the regression line either to
establish the confidence interval for the population mean of y or
to determine the prediction interval for a single value of y. The
limits for the single value of yare wider than the corresponding
limits on the mean of y (Remington and Schork, 1970). This is due
to the fact that single observations vary more than means.
The equation for the confidence interval for the population mean
y at x = x is (Remington and Schork, 1970, p. 268):
b(x -x) ~ t1 /2S 8 8[1/n + (x -x) 2/((n-1)8s 2)]~ < ~y8x
o -cx Y x 0 x 0
(x -x)2/((n-1)8s 2)]~llJ (8.124)
< a + b(xo-x) + t1-CX/2Sy8x8[1/n + 0 x
This interval is most narrow at x and widens as x moves farther
from the mean. By calculating the interval at each point along the

regression_line a curve such as the one in Figure VIII-36 can be
plot ted. .
The equation for the prediction interval for individual values
,of y at x = Xo is (Remington and Schork, 1970, p. 269):

a+b(x -x) +t1 /2s e e[l+l/n+ (x -x)2/(n-1)es 2]~ (8.125)
o - -ex y x 0 x

Figure VIII-37 shows how this interval would appear as an overlay
on the population mean confidence interval shown in Figure VIII-28.
Table VIII-31 contains both the mean confidence interval values
and the individual prediction interval values calculated by SAS
(SAS Institute, Inc., 1985b). A plot of these values is shown in
Figure VIII-38. For the above predictions of split at 10 gpm and 50
gpm calculate the population mean confidence limits and prediction
interval limits and check them against the plot in Figure VIII-38.
They should fall on the appropriate curves.
One of the simplest (in theory) nonpoint source (NPS) control
applications of linear regression is the regression of a water
quality indicator against an implementation indicator. For
example, flow-adjusted total suspended solids (TSS) concentration
could be regressed against a sediment control variable such as the-
total combined erosion rate of all cropland for which delivery to-
the stream is likely to be 50 percent or greater. A significant:
negative slope would suggest (but not prove) that water quality has
improved because of implementation of sediment control practices.
Another possible use of simple linear regression is to model a
water quality parameter versus time. In this application a
significant slope would indicate change over time. The sign of the
slope would indicate either improvement or degradation depending
upon the parameter used. For NPS studies a simple regression
versus time will most likely be confounded by the variability in
precipitation and flows. Thus, considerable data manipulation
(transformations, stratification, etc.) may be required before
regression analysis can be successfully applied.
In many cases water quality parameters are regressed against
flow. This is particularly relevant in NPS studies. In analysis
of covariance regressions against flow are often performed prior to
the analysis of variance (ANOVA) (Spooner et al., 1985). One of
the implicit goals of NPS control is to change the relationship
between flow and pollutant concentration or load. This will be
discussed in greater detail under analysis of covariance.
In paired watershed studies, measured parameters from paired
samples are often regressed against each other to compare the
watersheds. These regression lines can be compared over time to
test for the impact of NPS control efforts (Spooner et al., 1985).
Again, this will be discussed in greater detail under analysis of

 0 2 .3 4 5 6 7 8 9 10 " '2
     Value of X     
Figure VIII-36.
Figure VIII-37.
Regression line with confidence intervals.
Liait for Mean
Upper Limit for
Limit for Individual
Value of I
Regression line with conficence intervals.

, 3.40
>- 3.00
C 2.80
:S 2.60
La 95l Mean
Lower 951. Predict
'0 ' '5
25 30
Value of X
Figure VIII-38.
Plot of mean and individual value confidence

Non-linear regresslon
The discussion of non-linear, or curvilinear, regression is
limited to cases where the non-linear relationship can be
transformed into a linear relationship for which simple linear
regression ~an be performed. Data inspection should indicate to
the analyst the nature of the relationship between the dependent
and independent variables. Possible curvilinear relationships
include exponential curves (semi-log), power functions (log-log),
and parabolas among others (Freund, 1973).
Non-linear regression for curvilinear functions involves
transformation to linear equations, followed by use of the methods
described above for simple linear regression. Transformations for
many functions are shown in Appendix L (Ponce, 1980a). Crawford et
al. (1983) list numerous regression models most often applied by
the USGS for flow adjusting concentrations.
Freund (1973, p. 400-402)
linear regression techniques
exponential curve of the form

y = a . b
illustrates application of non-
with an example for which an
best describes the relationship between y and x. The equation is~
converted to a linear form by taking the logarithms of both sides
so that
log Y = log a + x(log b) .
By susbstituting log y for y,
normal equations become
log a for a, and log b for b, the
Llog y = n(log a) + (log b) (Lx)
LX (logy) = (log a) (Lx) + (log b) (Lx2) .
The equations can be solved for log a and log b.
Multiple regression
Multiple regression is applied to quantify a relationship
between a dependent variable (Y) and more than one independent
variables (Xis) (Gaugush, 1986, p. 77). The assumptions made for
linear regression also apply to multiple regression (Ponce, 1980a,
p. 127). As for linear regression, the method of least squares is
also used to determine the best multiple regression line. The
general linear model to consider is (Ponce, 1980a, p. 128):
Y = a + b1X1 + b2X2 + .
. + b X
n n
(8.130 )

The corresponding normal equations are (Ponce, 1980a, p. 128):
(~x 2)b + (~x x )b
1 1 1 2 2) + (~x1x3)b3 +...+ (~x1xn)bn = ~xnY
(~x1x2)b1 + _(~x22)b2 + (~x2x3)b3 +...+ (~x2xn)bn = ~x2Y
(~x1x3)b1 + (~x2x3)b2 + (~x32)b3 +...+ (~x3xn)bn = ~x3Y
(8.132 )
(8.133 )
(~X1xn)b1 + (~x2xn)b2 + (~x3xn)b3 +...+ (~xn2)bn = ~xnY
After solving for the bls, a can be calculated from (Ponce, 1980a,
p. 128):
a =Y - b1X1 ~ b2X2 - b3X3 - ... - bnXn
Ponce (1980a, p. 128-133) presents an example of multiple
regression using three independent variables (Appendix M). The
reader is encouraged to follow through this example to develop an
understanding of multiple regression before using computerized-
procedures. . Gaugush (1986) states that multiple regression with-
two independent variables can be performed using text book:
formulae, but that matrix algebra is required for broader
applications. Winer (1971) provides a matrix algebra approach to
multiple regression, but the discussion is complicated and probably
not critical to appropriate use of multiple regression techniques
(especially when the researcher consults a statistician) .
Gaugush (1986, p. 77-81) provides an example of multiple
regression in which the SAS procedure GLM (SAS, Institute, Inc.,
1985b) is used (Appendix N). This example relates pollutant level
to three independent variables (distance from source, temperature,
and discharge). An interpretation of the SAS output is also
Key points made in the examples above include:
1. An F test indicates the significance of the regression.
2. The coefficient of multiple determination (r-square),
which is calculated as in simple linear regression, shows
the proportion of variation in Y explained by the model.
3. Computerized output such as that from SAS can be used to
refine the model for subsequent runs.
As a further note regarding use of SAS, the RSQUARE procedure
(SAS Institute, Inc., 1985b, p. 711) can be used in an exploratory
fashion to perform all possible multiple regressions for subsets of
independent variables, listing the models in decreasing order of R2
magnitude. Thus, the model with the largest R2 value will be

listed. . The STEPWISE procedure allows five approaches to stepwise
regression -for users who wish to determine which variables should
be included in a regression model (SAS Institute, Inc., 1985b, p.
763)". However, this procedure is not guaranteed to identify the
model with the largest R2. Other computer software packages such as
SPSS (Stati9tic~1 Package for the Social Sciences) can also be used
for multiple regression (Ingwersen, 1980).
The following discussion of R2, taken largely from a technical
nonpoint source newsletter (Spooner, 1984), emphasizes proper
interpretation of R2 values.
The purpose of regressing a response variable (Y) on one or
more independent (X) variables is to II explain II some of the
variation observed in the measured values in Y. The F tests
for each individual X variable can be used to determine if
they are individually important to the regression on Y. The
multiple correlation coefficient (R-square) is a measure of
the fraction of variation in Y explained by the linear
regression on Xl, X2, ..., Xn variables in the model.
Sp~cifically, R2 is the fraction of the sum of squares (SS) of
the deviations of Y from its mean that is attributed to the
regression. R2 values range from 0 (model useless) to 1-
(model perfect) .
L: (Y.-F)2
. 1 1
R2 =
SS Regression
SS Error
= 1 -
L: (Y.-F)2
. 1 .
SS Total
SS Total
The null hypothesis that R2=0 (i.e., b1= b2= b3= ...= bk= 0)
can be tested using the F-statistic to deEerm1ne whether or
not the regression model explains any of the variation in Y.
The F-statistic is (n-k-1) R2 / (k-1) (1-R2) with (k-1) and (n-k-
1) degrees of freedom. It should be noted that (k-1) is the
degrees of freedom (df) for the regression model SS and (n-k-
1) is the df for the error SS.
A small R2 may be significantly different
sample size (n) is large. Conversely, a
insignificant if n is small compared to the
in the model.
from zero if the
large R 2 may be
number of XIs (k)
If R2 is small, then most of the variation in Y is unexplained
by the linear regression model. This remaining IInoisell may be
random variation, or may be due to other independent variables
not considered in the regression. If these other variables
are added to the regression, the relationships among the XIs
already included may change.
When new
variables are added to the model, R2 always
This explains why a large R2 may not be meaningful

when the sample size is small. Also, it is not legitimate to
compare two models with different numbers of X's solely by
their R2 values.. However, R2 adjusted for the degrees of
freedom may be.used to compare models, where adjusted R2 is:
R-2 = (1 - R2) (n - 1) / (n-k-1)
a -
How does one test if a new variable added to a model adds
significant information to explain further the variation in Y
(i.e., is the increase in R2 significant)? In SAS, for
example, the" type I I I SS or IV SS" (also known as the partial
sum of squares) and their associated p tests can be used.
These statistics measure the amount of variation in Y
explained by the addition of an individual X after all other
Xis are in the model. An equivalent method is to compare the
SSE (sum of squares due to error) from "full" and "reduced"
models (i.e., SSE from models with and without, respectively,
the extra term in question). If the SSE is reduced
significantly by the addition of a new variable to the model,
then the variable is important. The P-statistic is:
P =
dfR - dfp dfp -

df .
where df. and F are the degrees of freedom for the reduced
and full model SS, respectively. Appendix 0 is an example of
using R2 for analysis of agricultural nonpoint source project
data (Spooner, 1984).
5 .
Multivariate regression
Multivariate regression can be a very useful technique in NPS
M&E efforts. It involves the development of a linear model to
relate two or more dependent variables to two or more independent
variables. A detailed discussion of the theory behind multivariate
regression is well beyond the scope of this document as it involves
considerable knowledge of multivariate normal theory and matrix
theory. Readers are referred to statistics texts (e.g., Srivastava
and Khatri, 1979) for more on multivariate regression.
Users of SAS (SAS Institute, Inc., 1985b, p. 655-710) can use
the REG procedure for multivariate regression. An example of the
MODEL statement used in this procedure is the following (SAS
Institute, Inc-., 1985b, p. 666):
MODEL Y1 Y2 = Xl X2 X3
Y1 and Y2 are the dependent variables
Xl, X2 and X3 are the independent variables
Within this procedure the MTEST statement can be used to test
hypotheses regarding the multivariate regression model. P values

are calculated for the following procedures (SAS Institute, Inc.,
198 5b, p. 1-2):
Wilks' lambda
Pillai's trace
Hotelling-Lawley trace
Roy's maximum root
Extreme Events
The majority of NPS pollution entering streams occurs during
runoff from precipitation events. This section presents an
approach for estimating annual precipitation and storm events,
describes the approach used by EPA's DESCON model for estimating
design flows, and concludes with statistical methods appropriate
for evaluating water quality extreme events. One of the key
characteristics that separate environmental, and in particularly
NPS-influenced data is the presence of extreme events. In Section
VIII.C, summary statistics were used to characterize the average
conditions. Section VIII.D described procedures for determining
whether conditions are changing. This section is appropriate for
evaluating extreme conditions. This is important for evaluating
standard violations or evaluating peak concentrations to determine.
if a BMP was effective.
Rainfall Analyses
Annual Precipitation
Chow (1951) presents
precipitation for a variety
outlined below assuming that
n years.
a method for computing annual
of return periods. This method is
the annual rainfall is available for
Compute the mean and standard deviation for the n years of
data. Also compute the coefficient of variation.
Use Table VIII-32 using
different return periods.
Compute the annual precipitation
periods using Equation 8.140.
(X )
for different return
Xc = x (1+ C K)
- v
The adequacy of the length of record n can be evaluated using
Equation 8.141 (Mockus, 1960)
Y = (4.30t loglOR) 2 + 6
where Y is the minimum record length in years, t is the student t
quantile at the 90% level with Y-6 degrees of freedom, and R is the
ratio of the 100 year event to the 2 year event. Application of
Equation 8.141 is iterative.

Table VIII--"32.
( Chow, 1954).
Return Period (years)
1.01 2 5 20
 Probability in percentage equal to 
 or greater than given variate 
C 99 50  20 5 1  C
.s        v
o -2.33 0 0.84 1. 64 2.33 0
0.5 -1.98 -0.09 0.80 1. 77 2.70 0.166
1.0 -1.68 -0.15 0.75 1. 85 3.03 0.324
1.139 -1.61 -0.16 0.73 1. 86 3.11 0.363
1.4 -1.49 -0.19 0.69 1. 88 3.26 0.436
1.5 -1.45 -0.20 0.68 1. 89 3.31 0.462
2.0 -1.28 -0.24 0.61 1. 89 3.52 0.596
3.0 -1.04 -0.28 0.51 1. 85 3.78 0.818
4.0 -0.90 -0.29 0.42 1. 78 3.91 1.000
E.1. 2
Storm Return Period
The method developed by Hershfield (1961) is the most usual
applied method in the field today and is commonly referred to as
"TP40." The method is based on interpolating the design storm from
four figures (Figures VIII-39 through VIII-42) and applying
Equation 8.142 developed by Weiss (1962).
I = 0.0256(C-A)x + 0.000256[(D-C) - (B-A)]xy +
O.Ol(B-A)y + A
where I is the rainfall amount and A, B, C, and D are interpolated
values from Figures VIII-39 through VIII-42, respectively. The
return period, x, and duration, y, are taken from Table VIII-33 and
VIII-34, respectively.
Table VIII-33. Linearized Rainfall Frequency Variate for Equation
8.142 (Weiss, 1962).
Return Period 1 2 5 10 25 50 100
in Years        
Linearize  -6.93 0 9.2 16.1 25.3 32.1 39.1
Variate, x       

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~ Ii "-U,Ij>f' ~ Y /0] I y~~,..".- ~ . ~-(
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'"d '-.
Ii ..

l1,-..,-=:::r. --.- '_- -1-ci-"YEAR Zl-HOUR Rk.NFALL (1INOtES) --~ n ~~ 4~'
.. ""~:I~" 1 S;JJt 'i ~ ~ I jv)~1
. ]f1ii/;-~~ ~;~ ~0,,2!.1, " , H 1;- Ck ~"'~b ,I ~A~,~/'
~ ~"~ h} 'i.. \..' """'- 1.11' I - "rt ':r:t1 R.. ~ "'"'-
" F( ). rv. :n ~ ~ ~ ~ ~ r- ~ ...1- a- ~...: ~ :\j1I"" ~ ;):
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. rr-f--~ 'I - tt :-4
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" ~, I -,q )~1. ~ ~JJ \ L~:f MI" ,- ~ ~ . "
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Table VIII-34. Linearized Rainfall Duration Variate for Equation
8.142 (Weiis, 1962).
Duration  0.17 0.33 0.5 0.67 1
in hours      
Linearize  -37 -24 -15.6 -9.4 0
Variate, y     
Duration  2 3 6 12 24
in hours      
Linearize  17.6 28.8 49.9 73.4 100.0
Variate, y     
Design Flows
This section describes the computational steps employed by
DFLOW and DESON for each of the three types of design flows
considered and has been extracted and adapted from Rossman (1990).
It begins with the extreme value design flow, since this type of
design flow also serves as a starting point in computing the
biologically-based design flow.
Extreme Value Design Flow
The extreme value design flow is computed from the sample of
lowest m-day average flows for each year of record, where "m" is
the user-supplied flow averaging period. Established practice uses
arithmetic averaging to calculate these m-day average flows. A log
Pearson Type III probability distribution is fitted to the sample
of annual minimum m-day flows. The design flow is the value from
the distribution whose probability of not being exceeded is l/R,
where R is the user- supplied return period. The procedure is
modified slightly to accommodate situations where some annual low
flows are zero.
Initialize each element of a vector X of daily flow
va~Bes to UNKNOWN (i.e., a very large number such as 1x
10 ).
Read in daily flow values from the retrieved STORET flow
file into X, where X(l) corresponds to the first day of
record. (Note: February 29th of leap years is ignored.)
Create m-day running arithmetic averages from the daily
flows in X, and replace the daily flows of X with these
values. The running average of X(i), X(i+1), ..., X(i+m-
1) is placed in X(i) .
Find the lowest m-day running average value for each
water year recorded in X (where a water year begins on
April 1) and store the resulting values in vector Y. Let
NY denote the number of entries in Y.

STEP 5a.
STEP 5b.
STEP 5c.
STEP 5d.
STEP 5e.
4et N be the number of non-zero entries in Y. Assume
~hat these Y-values are a sample drawn from a log Pearson
Type III probability distribution. The design flow, is
the value from this distribution whose probability of not
being exceeded is l/R, where R is the user-supplied
return period. Use the following procedure to find the
design flow:
Find the mean (U), standard deviation (S), and skewness
coefficient (G) of the natural logarithms of the non-zero
entries in Y.
Let FO be the fraction of entries in Y that are zero:
FO = (NY - N)/NY
Let P be the cumulative probability corresponding to the
user-supplied return period of R years, adjusted for the
presence of zero-flow years:
P = (l/R - FO)/(l - FO)
In other words, if FO is the probability of having a year
with zero stream flow, and l/R is the allowed probability'
of a year with an excursion below the design flow, then-
P is the corresponding excursion probability in years:
with non- zero flows.
Let Z be the standard normal deviate corresponding to
cumulative probability P. Z can be computed using the
following formula (Joiner and Rosenblatt, 1971):
Z = 4.91( p.14 -
(1- P) .14 )
or using Appendix B.
Compute the gamma deviate, K, corresponding to the
standard normal deviate Z and skewness G using the
Wilson-Hilferty transformation (Loucks. et al., 1981):
K = (2/g) ((1 + G*Z/6 - G2 /36) 3 - 1)
Compute the design flow as
exp(1! + K*S)
Biologically-Based Design Flow
It is computed by starting with a trial design flow, then
counting how often this flow is not exceeded by m-day average flows
in the historical record. (In contrast with the traditional method
of computing extreme value design flows, the m-day flow averages
are harmonic means, not arithmetic ones. This count is compared to
the allowed number of such occurrences, and the trial design flow

is adj usted-accordingly.
are as foll"ows:
The specific computational steps involved
STEP 7a.
Initialize each element. of a vector X of daily flow
va~Bes to UNKNOWN (i.e., a very large number such as Ix
1~ ).
Read in daily flow values from the retrieved STORET flow
file into X, where X(l) corresponds to the first day of
record. (Note: February 29th of leap yectrs is ignored.)
Create m-day running harmonic averages from the daily
flows in X, and replace the daily flows of X with these
values. The running average of X (i), X (i+l), ..., X (i+m-
1) is placed in X(i) and is computed as follows:
Define B(j) as l/X(i+j-l) if X(i+j-l > 0, and 0
otherwise, for j = 1 to m. Let DSUM be the sum of B(j)
for j = 1 to m and mO be the number of B(j) values that
equal o. Then replace X(i) with X(i) = (m-mO)/DSUM*(m-
mO) /m.
Note that
this procedure
of zero flows
into account the.
forming a harmonic
Compute an extreme value m-day average trial design flow
(DFLOW) using the biologically-based average number of
years between flow excursions (R) as the return period.
Compute the allowed number of flow excursions, A, (i.e.,
the number of distinct m-day average flows allowed to be
below the design flow) over the NDAYS of stream flow
record: A = NDAYS/365/R.
.Use the procedure described below to compute the number
of biologically-based flow excursions resulting under the
trial design flow DFLOW. Because the trial flow was
computed as an extreme value flow, the resulting number
of biologically-based excursions will most likely be
larger than the allowed number, A. If it is not, then
keep increasing the trial design flow by some fixed
increment until the resulting number of excursions
exceeds A.
Use the Method of False Position (Carnahan et al., 1969)
to successively refine the estimate of the biologically-
based design flow as follows:
Set lower and upper bounds on the design flow with their
corresponding excursion counts:
FL = 0;
XL = o.
FU = DFLOW; XU = number of excursions under DFLOW.

STEP 7b.
Check on convergence of the bounds. If FU - FL is within
0.5% of FL, then end with DFLOW = FU. If XL is within
0.005 of A, then end with DFLOW = FL. If XU is within
0.005 of A, then end with DFLOW = FU. Otherwise proceed
tQ the next step.
STEP 7c.
Interpolate between the bounds to find a new trial design
flow, FT:
FT = FL + (FU - FL)*(A - XL)/(XU - XL)
and compute the number of excursions (XT) occurring for
this flow (see procedure described below) .
STEP 7d.
Update the bounds based on the value of XT: If XT <= A,
then set FL = FT and XL = XT. Otherwise set FU = FT and
XU = XT. Then return to the convergence check of step
The process used to count the number of flow excursions for a
given design flow proceeds in two phases. The first phase
identifies all excursion periods in the period of record. An.
excursion period is a sequence of consecutive days where each day
belongs to an m-day running average flow that is below the given~
design flow. Recall that "m" is the flow averaging period set by
the user. Phase two groups these excursion periods into excursion
clusters and counts up the total number of excursions occurring
within all clusters. An excursion cluster consists of all
excursion periods falling within a prescribed length of time from
the start of the first period in the cluster (120 days is the
default cluster length). The number of excursions counted per
cluster is subject to an upper limit whose default value is 5.
Before describing the detailed procedures for each of these
phases a simple numerical example will be used to illustrate the
method. Suppose that the design flow under consideration is 100
cfs and that the period of record yields a sequence of 4-day
running average flows as follows:
 4-Day Avg.  4-Day Avg.
DAY Flow, cfs DAY Flow, cfs
1  34  513   
2  65  to < 100
3  25  545   
4-12 > 100  546   
13  57  to > 100
14  34  end   
15  26     
16-512 > 100     

The first flow excursion period for this record consists of
the 4-day averages occurring on days 1, 2 and 3. Thus the period
extends from day 1 to day 6 (days 4, 5 and 6 belong to the
averaging period that begins on day 3). There are two other
excursion periods consisting of days 13 to 18 and 513 to 548.
Under the default clustering parameters, there are 2 excursion
clusters i cluster 1 contains periods 1 and 2, and cluster 2
contains period 3. The number of excursions in each cluster is as
1 1 4 6 6/4 = 1.5 3.0
 2 13 6 6/4 = 1.5 
2 3 513 36 36/4 =.9.0 5.0
Note that the number of excursions in each period equals the.
period length divided by the averaging period. The nominal numb~r
of excursions in cluster 2 is 9, and since this exceeds the limit~
of 5, only 5 are counted. The total number of excursions for the
design flow of 100 cfs in this example is 3 + 5 = 8.
The detailed procedure for counting biologically-based flow
excursions under a specified design flow is as follows:
P1(i) = day which begins excursion period i,
P2(i) = day which ends excursion period i,
XP(i) = number of excursions in period i,
XKLmax = maximum cluster length (e.g., 120
t = current day of record.
days) .
Set i = 0, P2(0) = 0, and t = 1.
If the m-day running
greater or equal to
proceed to Step 5.
average beginning on
the specified design
t is
If the current day t is more than a day beyond the end of
the current excursion period (t > P2(i) + 1), or if the
length of the current excursion period equals XKLmax then
begin a new excursion period by setting:
i = i + 1
P1(i) = t
P2(i) = m - 1
XP ( i ) = O.

Update the ending day of the current excursion period and
the excursion count for this period:
P2(i) = P2(i) + 1
XP(i) = (P2(i) - P1(i)) / m.
the end
to the next day of record (t = t + 1). If not at
of the record then return to Step 2. Otherwise
to phase 2.
i = current excursion period,
k = current excursion cluster,
K1 = day of record which begins cluster k,
XK(k) = number of excursions in cluster k,
XKmax = maximum number of excursions counted
(e.g., 5),
per cluster
Set i = 1, k = 0, and K1 = a large negative number.
If the length of the current cluster is greater than the
maximum length (i.e., P2(i) - K1 > XKLmax ) then begin a.
new cluster with. excursion period i, i.e.,
k = k + 1
K1 = P1(k)
XK(k) = O.
Update the excursion count for the current cluster,
XK(k) = minimum(XK(k) + XP(i), XKmax ) .
Proceed to the next excursion period (i = i + 1) and
return to Step 2. If no more excursion periods remain,
then total up the number of excursions in each cluster
(XK(l) +XK(2) + + XK(k)) to determine the total
number of excursions.
Human Health Design Flow
The overall harmonic mean daily flow can serve as a design
flow for human health water criteria that are based on lifetime
exposures. (See Rossman (1990) for justifying the use of the
harmonic mean.) Computation of the harmonic mean flow begins by
reading daily flow values into a vector X. Then the following steps
are followed:
Set NDAYS = 0, NZEROS = 0, DSUM = 0 and t = 1.
If X(t) equals UNKNOWN, then go to Step 5.
Otherwise set
If X(t) equals 0, then set NZEROS = NZEROS + 1 and go to
Step 5.

get DSUM = DSUM + l/X(t) .
Set t = t +. 1 . I f the end of the record has not been
reached then return to Step 2.
Compute the design flow HMEAN as
where DR = (NDAYS - NZEROS) / NDAYS.
Note that this procedure takes into account the possibility of
days with zero flow. The final estimate of the harmonic mean is a
weighted average of the harmonic mean of the non-zero flows and
zero. The weight attached to the harmonic mean of the non- zero
flows is simply the fraction of the total days of record that have
non-zero flows.
Frequency of Extreme Events
Gilbert (1987) presents an approach for evaluating
proportions. The method is based on computing the number of
observations exceeding a threshold value X. The proportion of
observations, p, exceeding X can be compuEed as
p = u / n
where u is the number of observations exceeding X and n is the
number of observations. trf'0r n 1:h30, Appendix U 8an be used to
develop"nonparametric 90 or 95 percentile confidence limits.
For n greater than 30, Equations 8.150 and 8.151 may be used. The
lower limit is equal to 0 if u is 0 and the upper limit is 1 if the
u is equal to n.
Lower 1
limit = 2
{ z; rtfl [ {U-On.5)2 + Z;4-Ufl ]'10\
x (u-O.5) + T -Zl-rtfl (u-O.5)
~~r = 12 x { (u+0.5) + Z;;rtfl +ZI-C1fl!{U+O.5) - (u+~.5i + Z;Zfl ]'h\
. n+ZI-C1fl
If np and n(l-p) are greater than 5 (some authors suggest a
value of 10), then Gilbert (1987) suggests that the normal
approximation can be used to compute the upper and lower limits
with the following equation:

[P(l-P) ]'12
P :t Zl-ex/2
The confidence intervals can be used to evaluate one-sample
hypotheses such as
Ho: p = 0.10
Ha: . p ~ O. 10
Very simply if the 95 percent confidence intervals include 0.10, we
accept the null hypothesis. Otherwise the null hypothesis is
An evaluation of proportions can also be used to determine the
necessary sample size to ensure that q percent of the population is
less than the largest randomly sampled observation. This approach
provided by Conover (1980) is demonstrated with the next example.
Example: :
Determine the number of random samples that would be
required to ensure with a 95 percent probability (0:'=0.05)
that 90 percent of the population is less than the.
largest observation.
Enter Appendix V with q equal to 0.9 and 1-0:' equal to
0.95 and directly read a sample size of 29. Therefore,
it would require 29 samples to ensure that the largest
observation is greater than 90 percent of the population.
Application of this example is similar to quality control
processes. In this case, once 29 samples have been collected, the
upper bound set by the largest observation. From then on, we would
expect that only 10 percent of the future samples would exceed the
upper bound with 95 percent confidence. If more than 10 percent of
future obqervations exceeded the upper bound, we would infer that
some change has occurred (Ward et al., 1990).
It is also possible to compare the proportions P1 and P2
between two samples with sample sizes 'equal to n1 and n. For
example, it may be appropriate to compare the percent of s~andard
violations from before and after. In this case, the null and two-
sided alternative hypothesis are
Ho: P1 = P2
Ha: P1 ~ P2

Moore and McCabe (1989) provide the test statistics as
P1 - P2
Z =

where sand p are given by
s =
P (l-p) (1.. +1..)
nl n2
p =
Ul + U2
nl + n2
They suggest that nLP, n1(1-p), n2P, and n2(1-p) all be greater
than or equal to 5 Lor application. If the absolute value of z
computed from Equation 8.153 is greater than the associated normal
deviate (e.g., 1.96 for a two-sided test with a equal to 0.05),
then the null hypothesis is rejected.
Multivariate analyses
There are several mulivariate procedures in addition to
multivariate regression discussed above. Mathematical descriptions
of these procedures are beyond the scope of this guidance, but
researchers should consult a statistician to assess the
opportunities for using these procedures. In general, the
multivariate procedures described in this section have not found
wide usage in day-to-day applications.
With the current availability of computerized statistical
procedures (e.g., SAS, SPSS) , it is possible to perform
multivariate analyses with ease, requiring of the researcher only
that he or she understands and meets the assumptions of the
particular test, and knows how to interpret correctly the results
of the test. It is extremely important that a qualified
statistician be consulted regarding the assumptions involved and
the appropriate interpretation of test results. Without such
precautions our current computer technology will only facilitate
the proliferation of misguided analyses and misinterpreted results.
The multivariate analyses to be described briefly in this
guidance include canoncial correlation, cluster analysis, principal
components and factor analysis, and discriminant analysis. These
procedures were selected for discussion based upon the work of
Gaugush (1986, p. 147-188), which should be reviewed in addition to
the detailed discussions provided in statistics texts for a better
understanding of these multivariate analyses.

Canonical correlation
Canonical correlation is a technique for analyzing the
relationship between two sets of variables, with each set able to
contain several variables (SAS Institute, Inc., 1985b, p. 139). It
follows tha~ simple and multiple correlation are special cases of
canonical correlation in which one or both sets of variables
contain only one variable (SAS Institute, Inc., 1985b, p. 139).
Gaugush (1986, p. 152) states that" [c] anonical correlation is
used to identify and estimate a linear function (called a canonical
variate) of one set of variables that is maximally correlated with
a linear function of a second set of variables." The SAS CANCORR
procedure (SAS Institue, Inc., 1985b, p. 140) finds as many
canonical variates as there are variables in the smaller set of
variables. The first and subsequent canonical variates are
uncorrelated, with the first having the highest correlation
coefficient, followed by the second highest correlation coefficient
for the second canonical variate, etc. It should be noted that
"the first canonical correlation is at least as large as the
multiple correlation between any variable and the opposite set of
variables" (SAS Institute, Inc., 1985b, p. 140).
Gaugush (1986, p. 152) notes that the information resulting
from canonical correlation is largely descriptive, and therefore~
the procedure has not been used as much as other multivariate
procedures which support hypothesis testing and/or prediction.
Gaugush (1986, p. 148) promotes the use of canonical
correlation to, for example, "describe the strength of a
relationship between a linear combination of nutrient variables and
a linear combination of biomass-related variables. 'I The strength
of such a relationship is estimated by the canonical correlation
Another use of canonical correlation is in determining how
many "common elements" are contained within two sets of variables
(Gaugush, 1986, p. 152). The percent overlapping variance (i.e.,
the squared canonical correlation coefficient) can be used to
indicate the relative importance of each canonical variate
(Gaugush, 1986, p. 153).
To utilize canonical correlation in hypothesis testing it is
important that the assumption of multivariate normality is
satisfied (Gaugush, 1986, p. 153). Snedecor and Cochran (1980, p.
361) discuss the multivariate normal distribution briefly and state
its property that "any variable has a linear regression on the
other variables (or on any subset of the other variables), with
deviations that are normally distributed." Gaugush (1986, p. 153)
notes that the assumption of multivariate normality is often
satisfied by "creating data distributions that are approximately
univariate normal."
To satisfy the assumptions of canonical correlation Gaugush
(1986, p. 153-154) recommends:

use transformations if needed to create roughly
symmetric univariate data distributions
carefully examine the validity of outliers and run
analyses with and without outliers to document their
impact on the correlations
transform data if necessary to create linear
relationships among the variables in each set of
Finally, Gaugush (1986, p. 154-161) gives an example application of
canonical correlation using the SAS CANCORR procedure described
Cluster analysis
Cluster analysis is a classification method for placing
"objects into groups or clusters suggested by the data, not defined
a priori, such that objects in a given cluster tend to be similar
to each other in some sense, and objects in different clusters tend
to be dissimilar" (SAS Institute, Inc., 1985b, p. 45). The types
of cluster analysis include (SAS Institute, Inc., 1985b, p. 45): .
disjoint clusters' which place each object in one and
only one cluster
hierarchical clusters in which one cluster may be
contained entirely within another cluster, but for which
no other kind of overlap is allowed
overlapping clusters with or without constraints. placed
on the number of objects that belong to two clusters
fuzzy clusters which are defined by a probability of
membership of each object in each cluster (these can be
disjoint, hierarchical or overlapping)
SAS offers several clustering options under the CLUSTER procedure
(SAS Institute, Inc., 1985b, p. 255-315).

Both Gaugush (1986, p. 163) and the SAS Institute (1985b, p.
48) acknowledge that Ward's minimum variance method and the average
linkage method are two of the best approaches to hierarchical
clustering. HQwever, SAS also notes that evaluations of clustering
methods have resulted in inconsistency and confusion (SAS
Institute, Inc., 1985b, p. 48). As a result of this variability in
assessments of clustering methods, it is recommended that the
researcher become familiar with a particular method (Gaugush, 1986,
p. 164) and/or use several methods on the same data base. By using
several methods on the same data base it should be possible to
interpret the result based upon agreement among the different
methods. SAS recommends inclusion of at least one less biased
method (e.g., density linkage) when trying several methods. Less
biased methods are based on nonparametric density estimation (e.g.,

single linkage and density linkage), whereas more biased methods
look for clusters based on size (e.g., k-means and Ward's minimum
variance method), shape, or dispersion (e.g, average linkage) (SAS
Institute, Inc., 1985b, p. 48).
Gaugus~ (1986, p. 165) recommends against performing formal
statistical tests with the results of cluster analysis. With no
such tests, no formal assumptions are imposed. However, Gaugush
(1986, p. 165) advises that the data should be symmetrically
distributed with no outliers. This could require data
transformation prior to cluster analysis. As a further point,
Gaugush (1986, p. 164-165) suggests that the data should be
standardized (i.e., value replaced by its deviation from the mean
divided by the standard deviation) if the variances of different
variables are of different magnitudes. Otherwise, the raw (o'r
tranformed) data are to be used.
Gaugush (1986, p. 165-169) illustrates the use of Ward's
method of cluster analysis by grouping reservoirs on the basis of
similarity in log total phosphorus concentration, log total
nitrogen concentration, log Secchi disk depth, and log chlorophyll
a concentration.
Kimball (1986) used cluster analysis to group wells on tpe
basis of similar variances. variables utilized in these cluster~
analyses were mean nitrate, well depth, maximum nitrate,-
coefficient of variation of nitrate and variance of nitrate. Mean
nitrate and coefficient of variation of nitrate yielded the most
information. A major conclusion made from this investigation of
wells in South Dakota was that "classification of ground water
sample locations by geologic environment and depth is crucial to
understanding the system."
Principal components and factor analysis
Principal component analysis (PCA) is a multivariate procedure
for examining relationships among several quantitative variables
(SAS Institute, Inc., 1985b, p. 621). PCA is used with factor
analysis to "create a relatively small number 'of new variables
(called "factors") from a larger number of original variables"
(Gaugush, 1986, p. 169). The primary use of these procedures is
exploratory analysis, i. e., hypothesis testing is not normally
performed (SAS Institute, Inc., 1985b, p. 621).
Gaugush (1986, p. 172) notes that PCA is usually performed
first. As an example, the author describes how PCA can be used to
develop a trophic state index from biological, nutrient, and
physical data. He goes on to illustrate how factor analysis can be
used to enhance the scientific interpretation of the principal
components thus developed.
In lay terms, PCA creates linear relationships (or factors)
that account for a maximum of the variance contained in the
original data set (Gaugush, 1986, p. 170). Factor analysis can
then be used to redefine the factors (i.e., the linear functions of

one or mOJ;e of the original variables) so that they can be
interpreted in more scientific terms. That is, factor analysis can
be used to reshape a principal component such that the factors
match more closely a researcher I s intuitive (or research-based)
model of the relationships among the variables.
Although hypothesis testing is not normally performed on the
results of PCA and factor analysis, Gaugush (1986, p. 171)
recommends that data distributions be approximately symmetric with
no outliers. As in other cases, data transformations may be needed
to meet these recommendations.
Due to problems of scale, Gaugush (1986, p. 171-172)
recommends that PCA and factor analysis be based on the correlation
matrix unless the variables are all of approximately the same
magnitude. In cases where the variables are of the same magnitude,
then the covariance matrix can be used.
This discussion of PCA and factor analysis is intended only to
familiarize the water quality researcher with the general use of
these te~hniques. Gaugush (1986, p. 169-178) goes several steps
further in describing these procedures, including an illustrative
example. SAS gives a fairly detailed mathematical description of.
PCA and factor analysis (SAS Institute, Inc., 1985b, p. 621-622 apd
p. 335-338, respectively), and offers procedures for performing~
both (PRINCOMP and FACTOR procedures) . .'
Discriminant analysis
Discriminant analysis resembles regression analysis, but with
a major difference in that the dependent variable in discriminant
analysis is categorical, whereas the dependent variable in
regression analysis is often continuous (Gaugush, 1986, p. 178).
Some of the uses for discriminant analysis are (SAS Institute,
Inc., 1985b, p. 41):
to find a mathematical rule (or "discriminant function")
for predicting which class an observation belongs to
given data for the independent quantitative variables
to find linear combinations of the independent
quantitative variables that best reveal the differences
among the classes
to fiVd a subset of the independent quantitative
, variables that best shows the differences among the
It should be understood that discriminant analysis requires
prior knowledge of all classes (e.g., a sample), whereas cluster
analysis has no such requirement (SAS Institute, Inc., 1985b, p.
42). In fact, cluster analysis is used to define the classes.
Gaugush (1986, p. 180) cautions that outliers can adversely
affect the results of discriminant analysis, and that the predictor

variables &hould follow a multivariate normal distribution within
each group; with variance-covariance matrices that are constant
across groups. There is, however, at least one procedure (NEIGHBOR
procedure) which can be used for nonnormal data (SAS Institute,
Inc., 1985b, p. 559-567).
Researchers are encouraged to follow the descriptions of
discriminant analysis offered by SAS (SAS Institute, Inc., 1985b,
p. 41-44) and Gaugush (1986, p. 178-181) before using the
procedure. Gaugush (1986, p. 181-188) provides an example
application of discriminant analysis in which pH and aluminum
concentration are used to predict the presence or absence of brook
Special Treatment of Environmental Data
Environmental data provide an interesting challenge to
statisticians because of the natural variability and inherent
difficulty in collecting environmental data that meet the typical
assumptions. As a result, significant research over the last 20
years has been placed on developing new or modifying existing
statistical procedures to handle these difficulties.
The previous sections of this document largely focused on tpe
normality assumption in order to select a parametric or a~
nonparametric test. This section describes methods for addressing
missing values, outliers, and censored data.
Missing data
Snedecor and Cochran (1980, pp. 274-279) present a few
standard approaches to dealing with missing data. These standard
approaches work from the assumption that the missing data fit the
same mathematical model as the data one has. Often, this
assumption might not be satisified in NPS monitoring efforts. For
example, samplers frequently malfunction under icy conditions in
northern climates. The data missing from these sampling periods
might not at all resemble the data collected during other periods.
Snedecor and Cochran (1980, p. 274) point out that
computerized versions of general analysis of variance, analysis of
variance and covariance, and multiple linear regression usually
handle missing data correctly. They caution, however, that one
should check that such programs provide standard errors or
instructions ~or computing them when comparisons on or among
treatment means are made.
Snedecor and Cochran (1980, pp. 275-276) present equations for
estimating a single missing observation in both a one-way and two-
way classification, and for determining the standard error of the
mean of the treatment with the missing value in comparisons of
treatment means. They also provide a way to correct for bias in
the calculation of the treatment's mean square in ANOVA.

Two itrative processes are described for estimating more than
one missing value. Both procedures use initial guesses of the
missing values. A third, noniterative method is also discussed by
Snedecor and Cochran (1980, pp. 277-279).
GilberL (1987) provides and illustrates methods for handling
missing data iri estimating the mean and variance (p. 177-185), in
detecting and estimating trends (pp. 208-237), and in nonparametric
tests (p. 241-244).
The detection of outliers is often the most interesting
component of the data analysis to the environmental manager. In
environmental analyses, it is often very difficult to distinguish
between erroneous observations (i.e., bad data) and extreme events.
. Although several authors have suggested methods for detecting
outliers, the time to detect erroneous data is as soon after data
collection as possible. Correcting old data is time consuming and
the usual solution is to throw the questionable data out of the
Snedecor and Cochran (1980, p. 279) state that outliers should.
be examined initially to determine the cause of the extreme valu~.
In some cases, the outlier can be traced to a mistake, and the~
correct value restored. In other cases, the extreme value is due
to a mistake for which a correction cannot be made. For these
situations the erroneous value should be dropped, and analyses
should be performed with allowance made for the missing value. In
still other cases the outlier cannot be traced to any known errors
and must be presumed to be a "real" data point.
Snedecor and Cochran (1980, pp. 279-282) discuss methods for
assessing single extreme values for samples from a normal
distribution, two extreme values from a normal distribution, and
suspected outliers in ANOVA in one-way and two-way classifications.
Gilbert (1987, pp. 186-203) presents several methods for detecting
and treating outliers.
Censored Data
Observations reported as less-than or non-detect are often
quite troublesome for many statistical procedures (as well as
databases). Quite simply, it is difficult to compute the mean (or
any of a numbe~ of statistics) when one or more of the values is
<0.5. Comparisons between censored data is also difficult. Is a
<0.5 more or less than <0. 9? Section VIII. C provides several
options for estimating summary statistics when some of the data are
censored. Helsel and Cohn (1988) provide definitive approaches for
estimating summary statistics for when there are multiple censoring
levels in the same data set although these methods are typically
computationally intensive.


Quality Assurance and Quality Control
Quality assurance (QA) and quality control (QC) are commonly
thought of as procedures used in the laboratory to ensure that
all analytical measurements made are accurate. Yet QA and QC
extend beyond the laboratory and should be thought of as
essential components of all phases and all activities within each
phase of a nonpoint source (NPS) monitoring project. This
section defines QA and QC, discusses their value in NPS
monitoring programs, and explains the U.S. Environmental
Protection Agency's (EPA's) policy on these topics. The
following sections provide detailed information and recent
references for planning and ensuring quality data and
deliverables that can be used to support specific decisions
involving nonpoint source pollution.
Definitions of Quality Assurance and Quality Control
Quality assurance:
An integrated system of management procedures and activities
used to verify that the quality control system is operating
within acceptable limits and to evaluate the quality of data
(Taylor, 1993; USEPA, 1994b).
Quality Control:
A system of technical procedures and activities developed
and implemented to produce measurements of requisite quality
(Taylor, 1993; USEPA, 1994b).
QC procedures include the collection and analysis of blank,
duplicate, and spiked samples and standard reference materials to
ensure the integrity of analyses and regular inspection of
equipment to ensure it is operating properly. QA activities are
more managerial in nature and include assignment of roles and
responsibilities to project staff, staff training, development of
data quality objectives, data validation, and laboratory audits.
Table IX-1 lists some common activities that fall under the
headings of QA and QC. Such procedures and activities are
planned and executed by diverse organizations through carefully
designed quality management programs that reflect the importance
of the work and the degree of confidence needed in the quality of
the results.
2 .
Importance of QA/QC Programs
While the value of a QA/QC program might seem questionable
while a project is under way, its value should be quite clear
after a project is completed. If the objectives of the project

Table IX-I. Common QA and QC activities (adapted from Drouse et al., 1986, and Erickson et al., 1991).
OA Activities
OC Activities
. Organization of project into component pans
. Assignment of roles and responsibilities to
project staff
. Use of statistics to determine the number of
samples and sampling sites needed to obtain
data of a required confidence level
. Tracking of sample custody from field
collection through final analysis
. Development and use of data quality
objectives to guide data collection efforts
. Audits of field and laboratory operations
. Maintenance of accurate and complete
records of all project activities
. Personnel training to ensure consistency of
sample collection techniques and equipment
. Collection of duplicate samples for analysis
. Analysis of bl3nk and spike samples
. Replicate sample analysis
. Regular inspection and calibration of
analytical equipment
. Regular inspection of reagents and water for
. Regular inspection of refrigerators, ovens,
etc. for proper operation
were used to design an appropriate data collection and analysis
plan, all QA/QC procedures were followed for all project
activities, and accurate and complete records were kept
throughout the project, then the data and information collected
from the project will be adequate to support a choice from among
alternative courses of action. In addition, the course of action
chosen will be defensible based on the data and information
collected. Development and implementation of a QA/QC program can
require 10 to 20 percent of project resources (Cross-Smiecinski
and Stetzenback, 1994), but this cost is recaptured in lower
overall costs due to the project being well planned and executed.
Likely problems are anticipated and accounted for before they
arise, eliminating the need to spend countless hours and dollars
res amp ling, reanalyzing data, or mentally reconstructing portions
of the project to determine where an error was introduced. QA/QC
procedures and activities are cost-effective measures that are
used to determine how to allocate project energies and resources
toward improving the quality of research and the usefulness of
project results (Erickson et al., 1991).
This chapter discusses many elements and aspects of QA/QC
programs that do not differ significantly from one type of
program to another, for instance from a point source permit
compliance sampling program to a NPS best management practice
effectiveness monitoring program. Therefore, much of the
following discussion is not specific to NPS projects. This does
not, however, mean that a well-designed and well-implemented
QA/QC program is not necessary for a NPS project. It is hoped
that the following discussion will convey to the reader the

importance of QA and QC to the success of every project involving
the collection and analysis of environmental data.
EPA Quality Policy
EPA has established a QA/QC program to ensure that data used
in research and monitoring projects are of known and documented
quality to satisfy project objectives. The use of different
methodologies, lack of data comparability, unknown data quality,
and poor coordination of sampling and analysis efforts can delay
the progress of a project or render the data and information
collected from it insufficient for decision making. QA/QC
practices should be used as an integral part of the development,
'design, and implementation of a NPS monitoring project to
minimize or eliminate these problems (Erikson et al., 1991;
USEPA, 1994a; USGS, 1992).
EPA's mandatory agency-wide Quality System policy requires
each office or laboratory generating data to implement minimum
procedures to assure that precision, accuracy, completeness,
comparability, and representativeness of data are known and
documented (USEPA, 1984; Erickson et al., 1991). This policy is
now based on the quality system standard developed by the
American Society of Quality Control (ASQC, 1994). Each office or
laboratory is required to specify the quality levels that data
must meet to be acceptable and satisfy project objectives. This
requirement applies to all environmental monitoring and
measurement efforts mandated or supported by EPA through
regulations, grants, contracts, or other formal agreements. To
ensure that this responsibility is met uniformly across EPA, each
organization performing work for EPA must document in a Quality
Management Plan (QMP) that is approved by its senior management
how it will plan, implement, and assess the effectiveness of QA
and QC operations applied to environmental programs (USEPA,
1994a). In addition, each non-EPA organization must have a well-
documented Quality Assurance Project Plan (QAPP) covering each
monitoring or measurement activity associated with a project
(USEPA, 1983, 1994b; Erickson et al., 1991).
The purpose of writing a QAPP prior to undertaking a NPS
monitoring project is to establish clear objectives for the
program, including the types of data needed and the quality of
the data generated (accuracy, precision, completeness,
representativeness, and comparability). This information is used
to design the program to meet these objectives. Developing a
QAPP prior to undertaking the NPS monitoring project also
establishes the boundaries of the project, in terms of the time
allotted to it and the decisions that can realistically be made
from the expected data and information that will be collected.
The QAPP should specify the policies, organization,
objectives, functional activities, QA procedures, and QC
activities designed to achieve the data quality goals of the
project. It should be distributed to all project personnel, and
they should be familiar with the policies and objectives outlined

in the QAPP to ensure proper interaction of the sampling and
laboratory operations and data management. All persons involved
in a NPS monitoring project who either perform or supervise the
work done under the project are responsible for ensuring that the
QA/QC procedures and activities established in the QAPP are.
adhered to.
The QMP and each QAPP must be submitted for review to the
EPA organization responsible for the work to be performed, and
they must be approved by EPA or its designee (e.g., federal or
state agency) as part of the contracting or assistance agreement
process before the work can begin. In addition, it is important
to note that these are "live" documents and programs in the sense
that once they have been developed they cannot be placed on a
shelf for the remainder of the project. All QA/QC procedures
should be evaluated and plans updated as often as necessary
during the course of a project to ensure that they are in
accordance with the present project direction and efforts
(Knapton and Nimick, 1991; USEPA, 1994b).
Data Quality Objectives (DQOs)
Prior to collecting environmental data in support of a NPS
project, it is important to determine the type, quantity, and
quality of data needed to meet the project objectives and support
a specific decision based on the results of the project. Not
doing so creates the risk of expending too much effort on data
collection (i.e., more data are collected than necessary), not
expending enough effort on data collection (i.e., more data are
necessary than were collected), or expending the wrong effort
(i.e., the wrong data were collected). . Proper planning and
execution of a data collection effort can prevent these problems.
EPA has developed the Data Quality Objectives Process as a
flexible planning tool that should be used to prepare for a data
collection activity. The information compiled in this effort is
then used to develop the QAPP (USEPA, 1994c).
The Data Quality Objectives Process
The Data Quality Objectives (DQO) Process process takes into
consideration the factors that will depend on the data (most
importantly, the decision(s) to be made) or that will influence
the type and amount of data to be collected (e.g., the problem
being addressed, existing information, information needed before
a decision can be made, and available resources). From these
factors the qualitative and quantitative data needs are
determined. The purpose of the DQO process is to improve the
effectiveness, efficiency, and defensibility of decisions made
based on the data collected, and to do so in a resource-effective
manner (USEPA, 1994c).
DQOs are qualitative and quantitative statements that
clarify the study objective, define the most appropriate type of
data to collect, and determine the most appropriate conditions

under which to collect them. DQOs also specify the minimum
quantity and quality of data needed by a decision maker' to make
any decisions that will be based on the results of the project.
By using the DQO process, investigators can ensure that the type,
quantity, and quality of data collected and used in decision
making will be appropriate for the intended use. Similarly,
efforts will not be expended to collect information that does not
support defensible decisions. The products of the DQO process
are criteria for data quality and a data collection design that
ensures that data will meet the criteria.
The DQO process consists of seven steps, described below.
The process is iterative. As one step of the process is
completed, its outputs might lead to reconsideration of previous
steps. The previous steps should then be repeated. Optimization
of the design (the last step) should begin only when all previous
steps have been completed. . When the optimization step is
reached, as at any time during the DQO process, it might be
necessary to reconsider earlier steps (i.e., to reiterate part or
all of the process) to determine the optimum design.
A brief description of each step of the DQO process and a
list of activities that are part of each step follow. For a
detailed discussion of the DQO development process, refer to
EPA's Guidance for the Data Quality Objectives Process (USEPA,
1994c), from which the following information was taken. This
reference contains a case study example of the DQO process. A
computer program, Data Quality Objectives Decision Error
Feasibility Trials (EPA QA/G-4D), is also available to help the
planning process by generating cost information about several
simple sampling designs based on the DQO constraints before the
sampling and analysis design team begins developing a final
sampling design in the last step of the DQO process. (Contact
John Warren, Quality Assurance Management Staff, 202-260-9464).
Step 1: State the problem. In this first step the problem
to be studied is described concisely. A review of prior studies
and existing information is important during this step to gain a
sufficient understanding of the problem in order to define it.
The specific activities to be 'completed during this step
(outputs) are:
Identify members of the planning team.
Identify the primary decision maker of the planning
team and define each member's role and responsibilities
during the DQO process.
Develop a concise description of the problem.
Specify the available resources and relevant deadlines
for the study.

Step 2: Identify the decision. Identify what questions the
study will attempt to resolve and what actions might be taken
based on the study. This information is used to prepare a
"decision statement" that will link the principal study question
to one or more possible actions that should solve the problem.
Possible options include take no action, take action, or modify
an action. A decision statement might be phrased as follows:
Determine whether [or which] NPS impacts require taking [one of
the alternative actions]. For example, if the question to be
addressed is "Are nutrients from agricultural runoff contributing
to the growth of algal mats in the river?" and the alternative
actions are "require vegetation buffers along streams" or "take
no action," then the decision statement is "Determine whether
nutrients from agricultural runoff are contributing to algal
growth and require regulation." The specific activities to be
completed during this step are:
Identify the principal study question.
Define the alternative actions that could result from
resolution of the principal study question.
Combine the principal study question and the
alternative actions into a decision statement.
If applicable, organize multiple decisions to be made
by priority.
Step 3: Identify the inputs to the decision. Identify the
information that needs to be obtained and the measurements that
need to be taken to resolve the decision statement. The specific
activities to be completed during this step are:
Identify the information that will be required to
resolve the decision statement.
Determine the sources for each item of information
identified above.
Identify the information that is needed to establish
the threshold value that will be the basis of choosing
among alternative actions.
Confirm that appropriate measurement methods exist to
provide the necessary data.
Step 4: Define the study boundaries. Specify the time
periods and spatial area to which decisions will apply and
determine when and where data should be ~ollected. This
information is used to define the population(s) of interest. The
term population refers to the total collection or universe of
objects from which samples will be drawn. The population could

be the concentration of a pollutant in sediment, a water quality
parameter, algae in the river, or bass in the lake. It is
important to define the study boundaries to ensure that data
collected are representative of the population being studied
(since every member of a population cannot be sampled) and will
be collected during the time period and from the place that will
be targeted in the decision to be made. The specific activities
to be completed during this step are:
Specify the characteristics that define the population
of interest.
Identify the geographic area to which the decision
statement applies (such as a county) and any strata
within that area that have homogeneous characteristics
(e.g., recreational waters, dairy farms).
Define the time frame to which the decision applies.
Determine when to collect data.
Define the scale of decision making, or the actual
areas that will be affected by the decision (e.g.,
first-order streams, dairy farms with streams running
through them, a county) .
Identify any practical constraints on data collection.
Step 5: Develop a decision rule. Define the statistical
parameter of interest, specify the threshold at which action will
be taken, and integrate the previous DQO outputs into a single
statement that describes the logical basis for choosing among
alternative actions. This statement is known as a decision rule.
It is often phrased as an "If.. .then. .." statement. For example,
"If the mean concentration of contaminant X in the water
downstream from farm Y exceeds 0.5 ~g/L, then vegetation will be
planted; otherwise, no action will be taken" The specific
activities to be completed during this step are:
Specify the statistical parameter that characterizes
the population (the parameter of interest), such as the
mean, median, or percentile.
Specify the numerical value of the parameter of
interest that would cause a decision maker to take
action, i.e., the threshold value.
Develop a decision rule in the form of an
"if.. .then..." statement that incorporates the.
parameter of'interest, the scale of decision making,
the threshold level, and the actions that would be

Step 6: Specify limits on decision errors. Define the
decision maker's tolerable limits of making an incorrect decision
(or decision error) due to incorrect information (i.e.,
measurement and sampling error) introduced during the study.
These limits are used to establish performance goals for the data
collection design. Base the limits on a consideration of the
consequences of making an incorrect decision. The decision maker
cannot know the true value of a population parameter because the
population of interest almost always varies over time and space
and it is usually impractical or impossible to measure every
point (sampling design error). In addition, analytical methods
and instruments are never absolutely perfect (measurement error).
Thus, although it is impossible to eliminate these two errors,
the combined total study error can be controlled to reduce the
probability of making a decision error. The specific activities
to be completed during this step are:
Determine the possible range (likely upper and lower
bounds) of the parameter of interest.
Identify the decision errors and choose the null
hypothesis. Decision errors for NPS pollution problems
might take the general form of deciding there is no
impact when there is [a false positive, or type I
error], or deciding there is an impact when there isn't
[a false negative, or type II error] .
Specify the likely consequences of each decision error.
Evaluate their potential severity in terms of
ecological effects, human health, economic and social
costs, political and legal ramifications, and other
Specify a range of possible parameter values where the
consequences of decision errors are relatively minor
(gray region). The boundaries of the gray region are
the threshold level and the value of the parameter of
interest where the consequences of making a false
negative decision begin to be significant.
Assign probability limits to point above and below the
gray region that reflect the tolerable probability for
the occurrence of decision errors.
Step 7: Optimize the desiqn. Evaluate information from the
previous steps and generate alternative data collection designs.
The design should specify in detail the monitoring that is
required to meet the DQOs, including the types and quantity of
samples to be collected; where, when, and under what conditions
they should be collected; what variables will be measured; and
the QA/QC procedures that will ensure that the DQOs are met. The
QA/QC procedures are fully developed when the QAPP is written

(see below). Choose the most resource-effective design that
meets all of the DQOs. The specific activities to be completed
during this step are: .
Review the DQO outputs and existing environmental data.
Develop general data collection design alternatives.
Formulate the mathematical expressions needed to solve
the design problem for each data collection design
alternative. This involves selecting a statistical
test method (e.g., Student's t-test), developing a
statistical model that relates the measured value to
the "true" value, and developing a cost function that
relates the number of samples to the total cost of
sampling and analysis.
Select the optimal sample size that satisfies the DQOs
for each data collection design alternative.
Select the most resource-effective data collection
design that satisfies all of the DQOs.
Document the selected design's key features and the
statistical assumptions of the selected design. It is
particularly important that the statistical assumptions
be documented to ensure that, if any changes in
analytical methods or sampling procedures are
introduced during the project, these assumptions are
not violated.
The DQO process should be used during the planning stage of
any study that requires data collection, and before the data are
collected. EPA's policy is to use the DQO process to plan all
data collection efforts that will require or result in a
substantial commitment bf resources. The DQO process is
applicable to all studies, regardless of size; however, the depth
and detail of the DQO development effort depends on the
complexi ty of the study. In general,. more complex studies
benefit more from more detailed DQO development.
Data Quality Objectives and the QA/QC Program
The DQOs and the quality objectives for measurement data
that will be specified in the QAPP are interdependent. The DQOs
identify project objectives; evaluate the underlying hypotheses,
experiments, and tests to be performed; and then establish
guidelines for the data collection effort needed to obtain data
of the quality necessary to achieve these objectives (Erickson et
al., 1991; USEPA, 1994c). The QAPP presents the policies,
organization, and objectives of the data collection effort and
explains how particular QA and QC activities will be implemented

to achieve the DQOs of the project, as well as to determine what
future research directions might be taken (Erickson et al.,1991;
USEPA, 1994c). At the completion of data collection and
analysis, the data are validated according to the provisions of
the QAPP and a Data Quality Assessment (DQA), using statistical
tools, is conducted to determine:
Whether the data meet the assumptions under which the
DQOs and the data collection design were developed.
Whether the total error in the data is small enough to
allow the decision maker to use the data to support the
decision within the tolerable decision error rates
expressed by the decision maker (USEPA, 1994c).
Thus, the entire process is designed to assist the decision
maker by planning and obtaining environmental data of sufficient
quantity and quality to satisfy the project objectives and allow
decisions to be made (USEPA, 1994b, 1994c). The DQO process is
the part of the quality system that provides the basis for
linking'the intended use of the data to the QA/QC requirements
for data collection and analysis (USEPA, 1994c).
Elements of a Quality Assurance Project Plan
QAPPs must be prepared according to guidance provided in EPA
Requirements for Quality Assurance Project Plans for
Environmental Data Objectives (USEPA, 1994b). EPA requires that
four types of elements be discussed in a Quality Assurance
Project Plan (QAPP). These elements are listed in Table IX-2 and
discussed briefly below. (For complete descriptions and
requirements, be sure to see USEPA (1994b). Additional
information on the contents of a QAPP is contained in Drouse et
al. (1986), Erickson et al. (1991), and Cross-Smiecinski and
Stetzenback (1994). Drouse et al. (1986) and Erickson et al.
(1991) are examples of EPA QAPPs prepared under previous
guidance. '
The elements described below should always be addressed in
the QAPP, unless otherwise directed by the overseeing or
sponsoring EPA organization{s). The types, quantity, and quality
of environmental data collected for each project could be quite
different. As noted in USEPA (1994b), "the content and level of
detail in each QAPP will vary according to the nature of the work
being performed and the intended use of the data." If an element
is not applicable or required, then this should be stated in the
QAPP. For some complex projects, it might be necessary to add
special requirements to the QAPP. Again, the QAPP must be
approved by the sponsoring EPA organization before work can
begin, and it should be reviewed annually (for multiyear
projects) and updated and reapproved as often as necessary during
the project. '

Table IX-2. Elements required in an EPA Quality Assurance Project Plan (USEPA, 1994b).
QAPP Element
Title and Approval Sheet
Table of Contents
Distribution List
Project/Task Organization
Problem Definition/8ackground
Project/Task Description .
Quality Objectives and Criteria for Measurement Data
Project Narrative (ORD only)
Special Training Requirements/Certification
Sampling Process Design
Sampling Methods Requirements
Sampling Handling and Custody Requirements
Analytical Methods Requirements
Quality Control Requirements
Instrument/Equipment Testing, Inspection. Maintenance Requirements
Instrument Calibration and Frequency
Inspection/Acceptance Requirements for Supplies and Consumables
Data Acquisition Requirements (Nondirect Measurements)
Data Management
Assessments and Response Action
Reports to Management .
Data Review, Validation, and Verification Requirements
Validation and Verification Methods
Reconciliation and User Requirements
Group A:
Prolect Manaqement
These elements cover basic project management, including
project history and objectives, roles and responsibilities of
participants, and other factors to ensure that the project has a
defined goal understood by all the participants and that all
planning activities have been documented.
Title and Approval Sheet
Provide the title of the plan; name of organization(s)
implementing the project; and names, titles, and signatures
of the appropriate approving officials and their approval

Table of Contents
List sections, figures, tables, references, and appendices.
If document control format is required, see Cross-Smiecinski
and Stetzenback (1994) and USEPA (1994b).
Distribution List
List all individuals and organizations who will receive
copies of the approved QAPP and subsequent revisions.
Project/Task Organization
Discuss the specific roles and responsibilities of all
individuals or organizations participating in the project.
A flow chart or box diagram is useful for depicting project
organization and responsibilities (Figure IX-1). Using the
diagram, explain the rationale for the organization (e.g.,
to maximize the interaction of site and task leaders). This
section provides details on the division of the project into
teams, support teams, review committees, and other groups
and identifies the persons and entities that will be .
involved in the project. All members of each project team
should be listed along with their affiliations with
participating organizations. The program manager, managers
or coordinators of any specific tasks, directors of
technical tasks to be conducted, and any organizations or
agencies that will be involved in the project should be
identified. Also identify the specific roles and
responsibilities (such as field sampling, laboratory
analyses, and report preparation) that will be conducted by
each person and organization involved in the project.

Problem Definition/Background
State the problem to be solved or the decision to be made
and describe its history for this particular project.
Project/Task Description
Describe the work to be performed (measurements to be made,
applicable quality standards, any special personnel or
equipment. requirements, assessment tools needed, records and
reports needed) and the schedule for its implementation.
Quality Objectives and Criteria for Measurement Data
The DQO process will provide this information, or state the
project quality objectives and measurement performance
criteria that are necessary to support the management
decision(s) to be made based on the result(s) of the
project. State quality objectives in terms of project

Man.gemonl QA/OC Dal. Manloemen'
Suppo,' Suppo,' SUppo,'
 nevfew      WAlefshed 
 Commill..     Ove'II,,"I . 
    I -     I
        MAillE sITe TI!J\M
 canon    Or08nlo  ~  
t Iyd,ology Resupply SuUu, 11II,00en Acid. Aluminum  Oea, B,ook 5118
Figure IX-I. Sample organization chart for a quality assurance project plan (from Erickson et aI., 1991).

requirements, preferably in quantitative terms, rather than
in terms of analytical or sampling method capabilities.
Then, with the quality objectives stated, select the
appropriate methods to achieve the requirements (Cross-
Smiecinski and Stetzenback, 1994). The quality of data
should be expressed in terms of precision, accuracy,
comparability, representativeness, and completeness (defined
below). A table of quality objectives, like that in Figure
IX-2, is helpful.
Definitions of data quality terms
Precision (reproducibility)
Precision is a measure or mutual agreement among individual
measurements of the same property.. The coefficient of
variation (CV), also known as the percent relative standard
deviation (RSD), is used to express precision (Erickson et
al., 1991).
0/= (-=) 10 a
s = sample standard deviation;
x = arithmetic mean.
Precision is an .expression of mutual agreement of multiple
measurement values of the same property conducted under
prescribed similar conditions. It is evaluated by recording
and comparing multiple measurements of the same parameter on
the same exact sample under the same conditions. Relative
percent difference (RPD) is a measure of precision and is
calculated with the following formula (Cross-Smiecinski and
Stetzenback, 1994):
RPD= 2 (Xl-X2) (100)
Xl + X2
xI = analyte concentration of first duplicate;
Xl = analyte concentration of second duplicate.
Accuracy (bias)
Accuracy is the degree of agreement of a measurement (or an
average of measurements), X, with an accepted reference or
true value, T. Accuracy is expressed as the percent
difference from the true value {lOa [(X-T)/T]} unless
spiking materials are used and percent recovery is
calculated (Erickson et al., 1991).

Parameter Units Range Aa;uracy Precision Completeness
Particulate NO ,/SO.     
SSI' lJg/m' 10-1000 10% 20% 70%
47 mm TFIPC' lJg/m' 10-1000 10% 20% 90%
47 mm TFIPC lJg/mJ 1 to 25 20% 20% 90%
47 mm TFIPC lJg/m' 1 to 75 20% 20% 90%
Wand speed m/s 0 to 75 2% 2% 90%
Wind direction deg 0 to 360 2% 2% 90%
Dew point O.C -30 to 70 2% 5% 90%
Solar radiation wat.ts/m'    
Ambient temperature .O .20 to 50 1.C 20C 90%
. PM.. Size Selective Inlet HgII Volume Sampler    
. TetIon/~8t8 FiIt8t     
Figure IX-2. Sample quality assurance objectives (from Erickson et al., 1991).

Accuracy is the correctness of the value obtained from
analysis of a sample. It is determined by analyzing a
sample and its corresponding matrix spike. Accuracy can be
expressed as percent recovery and calculated using the
following formula (Air National Guard, 1993):
%R= A-B (100)
A = spiked sample result;
B = sample result;
C = spike added.
Comparability is defined as the confidence with which one
data set can be compared to another (Erickson et al., 1991).
Comparability is the quality that makes data obtained from
one study comparable to data from other studies. Consistent
sampling methodology, handling, and analyses are necessary
to ensure comparability. Also, assurance that equipment has
been calibrated properly and analytical solutions prepared
identically is necessary to attain data comparability (Air
National Guard, 1993).
Representativeness can be defined both qualitatively and
quantitatively; it depends on the experimental design and
choice of sampling methods. The desired degree of
representativeness is important in planning for the
collection of samples and the subsequent uses of. the data.
A relevant sampling design issue, for example, is to
determine how a sample will be collected to ensure it is
representative of the desired characteristic (Erickson et
Representativeness is a measure of how representative the
data obtained for each parameter is compared with the value
the same parameter has within the population being measured.
Since the total population cannot be measured, sampling must
be designed to ensure that the samples are representative of
the population being sampled (Air National Guard, 1993).
Completeness is defined as the amount of valid data obtained
from a measurement system compared to the amount that was
expected to be obtained under anticipated
sampling/analytical conditions (Erickson et al., 1991).

Completeness is the amount of valid data obtained from the
measurement system (field and laboratory) versus the amount
of data expected from the system. An assessment of the
completeness of data is performed at the end of each
sampling event, and if any omissions are apparent an attempt
is made to res ample the parameter in question, if feasible.
Data completeness should also be assessed prior to the
preparation of data reports that check the correctness of
all data. An example or a formula used for this purpose is:

I vi
%C = percent complete;
V = number of measurements judged valid;
n = total number of measurements necessary to achieve
a specified level of confidence in decision making
(Cross-Smiecinski and Stetzenback, 1994).
Project Narrative
This is a narrative description of work to be performed that
will demonstrate to technical or QA reviewers that the
project or task will achieve its quality objectives. See
USEPA (1994b) for complete details of what should be
included in a project narrative.
Special Training Requirements/Certification
If personnel will require any specialized training or
certification to successfully complete the project, discuss
how this training will be obtained and documented. ..
Documentation and Records
Itemize all of the information and records (e.g., raw data,
field logs, instrument printouts, results of calibration and
QC checks, analytical laboratory case narratives) that must
be included in a data report package, and describe the
desired report format and final disposition of records and
Group B:
Measurements and Acauisition
The Project/Task Description element (A6) contains a summary
of this information, which should be provided in detail in this
section. Methods that have been well-documented and are
available to all participants can merely be cited; for those not
well-documented, detailed copies of the methods and/or Standard
Operating Procedures (SOPs) must be provided in the QAPP. .

Sampling Process Design (Experimental Design)
Explain the experimental design or data collection design,
including types and numbers of samples required, sampling
locations and frequencies, sampling screening criteria (if
applicable), sample matrices, measurement parameters of
interest, and the rationale for the design. As with all
information contained in a QAPP, recording information such
as the reasoning behind decisions will make the data more
defensible in the future. Statistics can play an important
part in determining the sampling strategy. Therefore,
record all statistical procedures that will be used to
determine the sampling strategy. Two basic sampling
decisions that must be made are the types and numbers of
quality control samples to be collected (Keith, 1988). See
USEPA (1994b) for additional details on what to include in
this element of the QAPP.
Sampling Methods Requirements
Identify and describe all procedures for collecting samples
for each sampling method, as well as what should be done
when a sampling or measuring failure occurs and who is
responsible for taking corrective action. Other aspects
pertinent to sampling, such as record keeping, sample
storage, and transport to laboratories, should also be
described in this section (Cross-Smiecinski and Stetzenback,
1994) .
Sample Handling and Custody Requirements
Describe all aspects of sample handling and custody. Sample
custody is a documentation of where and with whom samples
are at all times from the moment they are collected in the
field to when they are analyzed in the laboratory. A sample
is considered to be under custody if: (1) it is in your
actual possession; (2) it is in your view, after being in
your physical possession; (3) it was in your physical
possession and then you locked it up to prevent tampering;
or (4) it is in a designated and identified secure area (Air
National Guard, 1993). Special tracking procedures called
"chain-of-custody" procedures are used whenever samples are
collec~ed for use in an enforcement action or when
demonstrating compliance with a regulatory requirement
(e.g., NPDES). Chain-of-custody forms should be printed on
multipart carbonless paper for tracking custody and should
have, at a minimum, space for recording date, time, name of
person accepting samples, sample numbers, and remarks
(Figure IX-3). Copies of the form must be completed in the
field, and signed by the field team when they transfer
custody of the samples to the shipper. Upon receipt in the

OROJ NO I OROJECT N...e    NO "o.-'''~d "'~'"
S""'PLERS 15,<7'8"""     M
rurE I TWE  o~!'CnIPTlt...   r,u"f~
    I    I 
A--_I>y: (Si9Vtn, I 08', RK8tW8a by: (S,~IJtW' R.,......., I)y (S,gn.IV,.! 08'1- Rec...,.d by: (SIgN"'"
p"",,, Name:   PMI Name   p...,. Hatne"   p,,", N8me"
A--_I>y: rs.q,w,tn, I 08'1- ~~d for UOOtl'O'V ay' o.lelflln8 Remetll.1  
 I$;_tn,   I   
PftnI H8me:   PMt NAme      
Figure IX-3. Sample custody chart (from Cross-Smiecinski and Stetzenback. 1994).
laboratory, the laboratory signs the remaining copies,
indicating they have accepted custody of the samples.
time the form is signed, the person signing the form
retains the bottom copy and passes the remaining copies along
with the samples. The laboratory should return at least one
copy of the completed chain-of-custody record to the client,
or proceed as directed in the QAPP.
In addition, a custody seal should be applied to the lid of
each sample container in such a fashion that the container

cannot be opened without breaking the seal. Further, an
additional custody seal should be placed across the lid of
the shipping container in such a way that the container
- cannot be opened without breaking the seal (see Cross-
Smiecinski and Stetzenback, 1994).
Analytical Methods Requirements
Describe the analytical methods and equipment required for
both field and laboratory activities, waste disposal
requirements, and specific performance requirements, as well
as what should be done when a failure in the analytical
system occurs and who is responsible for taking the
corrective action. Also include information on any
supporting methods or documents used to collect field or
laboratory data. For instance, if identifications of
benthic invertebrates are made, include information on the
source(s) used to verify identifications; if the amount of
riparian vegetation cover is estimated, describe the method
used to arrive at the estimate.
Analytical methods: Describe the methods that will be used
for the project. If the methods to be used are published
(e.g., by the U.S. Geological Survey, EPA, or ASTM) then it
is sufficient to indicate what methods will be used and
where descriptions of them can be found. If the best
methods to be used cannot be completely ascertained until
some samples have been analyzed, indicate the order of
preference for use of the methods. Any modifications to
published or standard methods or variations of them must be
documented, and the variations must be verified as providing
data of acceptable quality. .
Method validation: Method validation accounts for and
documents, at a minimum, the following characteristics:
known and possible interferences; method precision; method
accuracy, bias, and recovery; method detection level, and
method comparability to superseded methods, if any (USGS,
1992). All methods chosen for use in the project must be
Generally, laboratories with their own QA/QC procedures will
be used for sample analyses. The methods to be used in the
laboratory must be acceptable to project managers. All
potential laboratory facilities to be used in the project
should be extensively evaluated before their selection and
throughout their participation in the project.
Quality Control Requirements
Identify the QC procedures (types, frequency, and control
limits of QC checks) needed for each sampling, analysis, or

measurement technique. (They might have to be modified to
suit each project.) Also state what corrective action is
required when control limits are exceeded. Data collected
as part of field sampling and laboratory measurements must
be verified as accurate. Thus, some samples are taken or
measurements made to check for accuracy rather than to
collect additional data. Specify what means will be used to
check the accuracy of samples and measurements. Field
blanks, duplicate samples, replicate samples, spiked
samples, and spiked blanks. are commonly used methods.
Describe precisely how these control samples will be
prepared for analysis.
Standard reference materials (SRMs) should be used
periodically in any measurement system to monitor for
changes to the system that might go unnoticed. SRMs should
be used when a measurement change is noted to verify that
the change is not due to a change in the measurement system.
The optimum frequency of use of SRMs and also of replicates
of actual test samples depends on the integrity of the
measurement system and the magnitude of the errors involved
when the system ceases to give predictable results. All
measurements from last-known-in-control sample to first-
known-out-of-control.sample are suspect, so the length of
the period between these two samples must be calibrated to
be appropriate to the measurements being made (Taylor,
1993) .
Instrument/Equipment Testing, Inspection, and Maintenance
This section should include descriptions of the types of
preventive maintenance for equipment that will be used to
ensure that research schedules are adhered to and project
objectives are completed on schedule. The section should
include the following: a schedule of preventive
maintenance, an inventory of critical spare parts and
supplies, maintenance contract information, location of
important manuals and instructions, record keeping
requirements, training of instrument and equipment operators
(Cross-Smiecinski and Stetzenback, 1994). Some aspects of
training can be considered a part of preventive maintenance.
Describe in this section general safety precautions that
will be part of project operations. Examples include
materials handling, transportation of chemicals, hazardous
waste disposal procedures, emergency procedures, standard
safety operations, chemical hygiene, hazard communication,
hazardous waste management, waste disposal, location of
safety equipment, tour of facilities, and annual classes in
cardiopulmonary resuscitation and standard first aid (USGS,
1992) .

Instrument Calibration and Frequency
, Describe the procedures used for equipment calibration, the
frequency of calibration of each piece of equipment, and the
results of calibration procedures. Record any problems
encountered and corrective actions taken. This section
should identify each tool, gauge, instrument, or other
sampling, measuring, and test equipment used for data
collection activities for which quality must be controlled
and which must be calibrated to maintain performance within
specified limits. .
Inspection/Acceptance Requirements for Supplies and
Supplies and consumables to be used in the project must be
inspected and accepted, according to specified criteria, for
use in the project. Identify who will perform the
inspections and how they will be conducted.
Data Acquisition Requirements (Nondirect Measurement)
Data obtained from noninstrument sources such as computer
data bases, spreadsheets, and programs and literature files
need to be identified and acceptance criteria established
for the use of the data. Also discuss any limitations
resulting from uncertainty in the quality of the data and
the impact of adding more error to the results.
Data Management
This section should describe all aspects of data management,
from their generation in the field or laboratory to final
use or storage. Discuss the control mechanisms (and provide
examples of ,forms or checklists) for detecting and
correcting errors and for preventing loss of data during
data reduction. This discussion should also include all
data handling equipment and procedures that will be used to
process, compile, and analyze the data (hardware and
software) .
Groue C:
The purpose of these elements
will be implemented as prescribed;
for assessing the effectiveness of
and its associated QA/QC program.
is to ensure that the QAPP
they describe the activities
the implementation of the QAPP
Assessments and Response Actions
Assessments can include a variety of activities, such as
surveillence, peer review, management systems review,

.echriical systems audit, or performance evaluation. Audits
are assessments of the extent to which QA procedures and QC
activities are being adhered to. They may be performed by
- an internal (i.e., within the project structure) but
independent audit team or by an external audit team. Audits
may be performed before, during, and/or after the project is
performed. Audit frequency, intensity, and type should be
determined, and the audit(s) should be scheduled as part of
the overall program QA effort. This section of the QAPP
should describe the audits to be performed and the process
and procedures for responding to problems raised during
audits (Cross-Smiecinski and Stetzenback, 1994).
This section should also describe actions to be taken if and
when unexpected problems arise during the course of the
study. Problems that can be foreseen, such as running low
on commonly used laboratory supplies, should be addressed as
SOPs. Many problems, however, are encountered so
infrequently or are unpredictable enough that SOPs will not
be prepared for them. Special or emergency procedures
address these types of problems. It is difficult to address
unanticipated problems before they arise, but th~ QAPP
should specify who is responsible for handling problems that
arise from different aspects of the project (e.g., field
sampling, laboratory analysis, audits). It is helpful to
categorize problems based on their impact on the project
(e.g., critical, important, noncritical, unimportant) and to
specify the type of corrective action necessary based on the
problem1s category. A critical problem, for instance, would
be one that would affect obtaining data of the necessary
quality or quantity. Ifa critical problem arises, a
critical-problem response by project staff would be
required. This should be specified in the QAPP.
Reports to Management
This section specifies the type and frequency of reports to
be prepared and submitted to project management, as well as
the chain of responsibility for ensuring that reports are
prepared and submitted. The preparer of the reports and
recipients of each report should be identified. Any
required report contents and format should also be
GrouD D:
Data Validation and Usability
After the data collection has been completed, the data must
be examined to determine whether they conform to the specified
criteria and will satisfy project objectives.

Data Review, Validation, and Verification Requirements
The requirements used to review and accept, reject, or
qualify data should be identified, including any project-
specific calculations or algorithms.
Validation and Verification Methods
This section should describe each of the elements defined
below in enough detail to support use of the data for their
intended purpose and for comparability to past, present, and
future studies (Cross-Smiecinski and Stetzenback, 1994). If
computer software is used in data manipulations, record
which software is to be used. Software that performs
complex manipulations may have to be verified before its use
to ensure that it functions properly (Cross-Smiecinski and
Stetzenback, 1994).
Data reduction: The transformation of raw data into a more
useful form, calculations.
Data verification: A routine activity conducted by
technical, laboratory, and clerical personnel on small sets
of the data to determine whether data have been accurately
quantified, recorded, and transcribed; whether data have
been collected and analyzed in accordance with prescribed,
approved procedures; whether the data appear suitably
complete; and whether the data appear to be reasonable and
consistent, based on prior knowledge of the research.
For example, it is a good practice to enter data into the
data base twice, and scan them for outlying values. This
helps to detect and eliminate transcription errors. Range
checks, internal consistency checks, and quality assurance
evaluations should also be included for data certification
(Drouse et al., 1986).
Data validation: The process by which a sample, measurement
method, or datum is deemed useful for a specified purpose;
an independent, timely review of a body of verified data
against a predetermined set of qualitative and quantitative
criteria to evaluate their adequacy for their intended use.
Data reDortinq: Specify any special forms or formats (e.g.,
tables and figures) that are to be used, as well as who is
responsible for data reporting, due dates, etc.
Reconciliation with User Requirements
The precision, accuracy, completeness, representativenesss,
and comparability of data must be assessed using appropriate

techniques. This section should give details of the
formulas, statistical techniques, and procedures that will
be used to assess the data. The methods used to assess the
data must be in agreement with the DQOs. The terms
precision, accuracy, completeness, representativeness, and
comparability are defined on page IX-14, and some sample
data assessment formulas are given.
The following sections provide more specific information for
preparing QAPPs with respect to field and laboratory operations,
and data and reporting requirements.
Field Operations Program
Field operations are an important activity in a NPS
monitoring program. Field operations involve organizing and
designing the field operation, .selection of sampling sites,
selection of sampling equipment, sample collection, sample
handling and transport, and safety and training issues. For the
purposes of QA and QC, the process of conducting field operations
should be broken down into as many separate steps as are
necessary to ensure complete consideration of all of the elements
and processes that are a part of field activities. Field
operations described in this section have been broken down into
the phases mentioned above, but individual monitoring programs
might require the use of more or fewer phases. For example, if
the sample collection phase is very complex or if it is
anticipated that sample collection will often be done under
inclement weather conditions when field personnel might
experience discomfort and feel rushed, it is advisable to break
sample collection into separate preparation, sampling, and
termination phases and discuss QA and QC for each of the phases
separately. This will ensure that no details are omitted. Table
IX-3 summarizes many important items that should be considered in
a field operations portion of a QA/QC program.
1 .
Field Design
Adherence to the procedures specified in the QAPP for field
operations and documentation of their use for all aspects of
field operations are extremely important if the data obtained
from the project are to be useful for decision making,
supportable if questioned, and comparable for use by future
researchers (Knapton and Nimick, 1991). Data sheets prepared
beforehand, with quality reminders included where appropriate,
will help ensure that all data are collected and QA/QC procedures
are followed during all field activities.
General information that should be included in the
documentation of the design for field operations includes the
scale of the operations (laboratory, plot, hillslope,watershed) i
size of plots/data collection sites; designation of control
sites; basin characteristics; soil and vegetation types; maps

Table IX-3. Checklist of items that should be considered in the field operations section of a QA/QC program
(from USEPA. 1990). . .
I    Field Operations      I
 Element   Specifics       Check-off Responsibility
 Organization Field organization chart created """"" "'" - 
  Staff duties and responsibilities defined . . . . . . . . . .. - 
  Communication lines within and with other units   
  established ............................  
  Project documents made available to all staff ....... - 
  Staff qualifications established ................  
 Field Sampling sites investigated and selected. . . . . . . . . ..  
 Logistics Means of access to sampling sites determined . . . . . .. - 
  Sample transport and shipping procedures specified ... - 
  Field sample handling areas selected. . . . . . . . . . . .. - 
  Chain-of-custody for samples established . . . . . . . . .. - 
  Field equipment selected and supplied. . . . . . . . . . .. - 
  Procedures for decontamination of sampling equipment  - 
  established ...........................,  
 Monitoring Equipment installation procedures specified ........ - 
 Equipment Equipment maintenance and control schedules established - 
  Equipment maintenance manual updated and distributed. - 
  Trouble shooting and corrective action manual updated  - 
  and distributed . . . . . . . . . . . . . . . . . . . . . . . . . .  
 Quality Type(s) of control samples (blanks, duplicates, spikes,   
 Control analytical standards, reference materials) to be used have - 
 Samples been determined . . . . . . . . . . . . . . . . . . . . . . . ..  
  Frequency of control sample use has been determined . .  
 Field Audits QA field auditor designated . . . . . . . . . . . . . . . . ..  
  Aspects of field operations that will undergo quality   
  assessments as part of field audits have been determined - 
  Acceptance criteria for compliance with SOPs and the  - 
  QAP set for field events and activities ........... - 
  Field audit forms, with investigations to be conducted  - 
  and data to be collected, prepared ..............  
  Person(s) to review field audit records designated ....  
 Health and Field personnel properly trained ...............  
 Safety Proper field gear and clothing issued to field personnel  - 

Table IX-3. (cominued)
I  Field Operations    I
Element Specifics      Check -off Responsibility
SOPs Sample management        
 Sample collection procedures       - 
 Reagent preparation    . .    
 Equipment calibration and maintenance   
 Corrective action    . . ..  - 
 Waste disposal . . .   . .    
 Health and safety  .. ..  . .   
 Field measurements        
 Reagent/standard preparation . . .. ..   
 Equipment calibration and maintenance   
 Data reduction and validation      
 Reponing.  . . .      
 Corrective action    . .    
 Waste disposal .  . .  . .   
 Health and safety . . . . . .    
 Records management . . . . .  . . . . . .  
 Project-specific records  . ..  ..   
 Field operations records . .. .. ...   
with the location of plots/data collection sites within the
basin/catchment; weather conditions under which sampling is
conducted; equipment and methods used; problems that might be
encountered during sampling; dates of commencement and suspension
of data collection; temporal gaps in data collection; frequency
of data collection; intensity of data collection; and sources of
any outside information (e.g., soil types, vegetation
identifications) (Erickson et al., 1991). Some of these aspects
are discussed in greater detail in the following sections.
Sampling Site Selection
The selection of sampling sites is important to the validity
of the results. Sites must be selected to provide data to meet
the goals/objectives of the project. The QAPP should provide
detailed information on sampling site locations (e.g., latitude
and longitude); characteristics that might be important to data
interpretation (e.g., percent riparian cover, stream order); and
the rationale for selecting the sites used (Knapton and Nimick,
1991). Sites from other studies can be convenient to use due to
their familiarity and the availability of historical data, but
such sites should be scrutinized carefully to be certain that
data obtained from them will serve the objectives of the project.
If during the course of the project it is found that one or more

sampling sites are not providing quality data, alternative sites
might be selected and the project schedule adjusted accordingly.
The adequacy of the sampling locations and the sampling program
should be reviewed periodically by project managers, as
determined by data needs (Knapton and Nimick, 1991).
Sampling sites should be visited before sampling begins.
is important to verify that the sites are accessible and are
suitable for collection of the data needed. Consideration should
be given to accessibility in wet or inclement weather if samples
will be taken during such conditions. The sites should be
visited, if possible, in the type(s) of weather during which
sampling will occur. Plastic- laminated pictures of each
sampling site with an arrow pointing to each monitoring location
can assist field personnel in finding"the sites during inclement
weather when the sites might appear different.
If permission to access a site is needed (for instance, if
one or more sites are on or require passage through private
property) such permission must be obtained prior to the
commencement of sampling. The person(s) granting the permission
should be fully informed about the number of persons who will be
visiting during each sampling event, frequency of sampling,
equipment that will have to be transported to the sampling
site(s), any hazardous or dangerous materials that will be used
during sampling, and any "other details that might affect the
decision of the person(s) to grant access permission. A lack of
full disclosure of information to gain access permission creates
a risk of permission being revoked at some point during the
3 .
Sampling Equipment
Equipment for field operations includes field-resident
equipment such as automatic samplers and stage-level recorders
and nonresident sampling equipment such as flow, pH, and
conductivity meters; equipment needed to gain access to sampling
sites such as boats; and equipment for field personnel health and
safety, such as waders, gloves, and life vests. The condition
and manner of use of the field equipment determines the
reliability of the collected data and the success of each
sampling event. Therefore, operation and maintenance of the
equipment are important elements of field QA and QC. All
measurement equipment must be routinely checked and calibrated to
verify that it is operating properly and generating reliable
results (Spooner, 1994), and all access and health and safety
equipment should be routinely checked to be certain that it will
function properly under all expected field conditions.
A manual with complete descriptions of all field equipment
to be used should be available to all field personnel. The
manual should include such information as model numbers for all
measurement equipment, operating instructions, routine repair and
adjustment instructions, decontamination techniques, sampling
preparation instructions (e.g., washing with deionized water),

and use limitations (e.g., operating temperature range). If any
samples are to be analyzed in the field, the techniques to be
used should be thoroughly described in the manual.
4 .
Sample Collection
The process of sample collection should be described with
the same amount of detail as the equipment descriptions. A
thorough description of the sample collection process includes
when the sampling is to be done (e.g., time of day, month, or
year; before and/or before storms); the frequency with which each
type of sample will be collected; the location at which samples
are to be taken (i.e., depth, distance from shore, etc.); the
time between samples (if sampling is done repetitively during a
single sampling site visit); and how samples are to be labeled.
Each field person must be thoroughly familiar with the sampling
techniques (and equipment) prior to the first sampling" event.
Holding practice sampling events prior to the commencement of
actual sampling is an excellent way to prepare all field
personnel and will help to identify potential problems with the
sampling sites (access, difficulty under different weather
conditions), sampling equipment, and sampling techniques.
Quality control activities for field operations must ensure
that all field operations are conducted so that sampling is done
in a consistent manner and that all generated information is
traceable and of .known and comparable quality. Each field
activity should be standardized. Standard operating procedures
(SOPs) for field sampling have been .developed and might be
required depending on the agency for which the sampling is being
conducted. Elements of the field operations section of a QAPP
should include clear statements of the regulatory requirements
applicable to the project (Spooner, 1994). Any SOPs that are
part of regulatory requirements should be followed precisely.
The pictures taken of each sampling site to aid in locating the
sampling sites also help ensure consistency of field monitoring
across time and personnel by ensuring that the same spot is used
at each sampling event (Spooner, 1994).
Depending on the DQOs and data requirements of the program
(type of data and frequency of collection), additional quality
control samples might be needed to monitor the performance of
various field (as well as laboratory) operations including
sampling, sample handling, transportation, and storage.
As the samples are collected, they must be labeled and
packaged for transport to a laboratory for analysis (or other
facility for nonchemical analyses). Computer-generated sample
bottle labels prepared before the sampling event and securely
attached to each bottle help minimize mistakes. Sampling
location and preservation, filtration, and laboratory procedures
to be used for each sample should be recorded on each label
(Spooner, 1994). Be sure these labels are printed with
waterproof ink on waterproof paper, and use a No.2 pencil or
waterproof/solvent-resistant marker to record information.

5.. Sample Handling and Transport
Once samples have been collected, they must be analyzed,
usually in a laboratory. Handling and transport of sampling
containers and custody of sample suites is also a part of field
operations. Sample transport, handling, and preservation must be
performed according to well-defined procedures. The various
persons involved in sample handling and transport should follow
SOPs for this phase of the project. This will help ensure that
samples are handled properly, comply with holding time and
preservation requirements, and are not subject to potential
spoilage, cross-contamination, or misidentification.
. The chain-of-custody and communication between the field
operations and other units such as the analytical laboratory also
need to be established so that the status of the samples is
always known and can be checked by project personnel at any time.
The chain-of-custody states who the person(s) responsible for the
samples are at all times. It is important that chain-of-custody
be established and adhered to so that if any problem with the
samples. occurs, such as loss, the occurrence can be traced and
possibly rectified, or it can be determined how serious the
problem is and what corrective action needs to be taken. Field
data custody sheets are essential for this effort (Cross-
Smiecinski and Stetzenback, 1994; Spooner, 1994). Chain-of-
custody seals must be applied to sample containers and shipping
6 .
Safety and Training
When dealing with NPS monitoring, sampling activities often
occur during difficult weather and field conditions. It is
necessary to assess these difficulties and establish a program to
ensure the safety of the sampling personnel. The following types
of safety issues, at a minimum, should be considered and included
in training and preparation activities for sampling: exposure,
flood waters, debris in rivers and streams, nighttime collecting,
criminal activity, and first aid for minor injuries. The trade-
off between the need for data quality and the safety of personnel
is a factor that project staff should consider collectively.
Finally, the QAPP for the field operations should include
provisions for dealing with any foreseeable problems such as
droughts, floods, frozen water, missing samples, replacement
personnel during sickness or vacation, lost samples, broken
sample containers, need for equipment spare parts, and other
concerns (Spooner, 1994).
Laboratory Operations
Laboratory operations should be conducted with the same
attention to detail as field operations. Often, an independent
laboratory conducts sample analyses, so QA and QC for the
laboratory are not under the direct control of project personnel.

However, it is important that project personnel are certain that
the laboratory chosen to do analyses follows acceptable QA/QC
procedures so that the data produced "meet the DQOs established
for the project. Laboratories should be selected based on
quality assurance criteria established early in the project. The
Quality Assurance Officer for the project should be certain that
these criteria are used for selecting a laboratory to perform any
necessary analyses for the project and that any laboratories
selected meet all criteria. Laboratories can be evaluated
through the following measures (Air National Guard, 1993):
Performing proficiency testing through analysis of
samples similar to those which will be collected during
the project.
Performing inspections and audits.
Reviewing laboratory QA/QC plans.
One or more of these measures should be used by the project
manager, and the laboratories should be visited before entering
into a contract for sample analyses.
General Laboratory QA and QC
Numerous references are available on laboratory QA/QC
procedures, and one or more should be consulted to gain an
understanding of laboratory QA and QC requirements if project
personnel are not familiar with them already. The details of a
laboratory's QA/QC procedures must be included in the QAPP for
the NPS monitoring project. Some elements to look for in a
laboratory QA/QC plan include (Cross-Smiecinski and Stetzenback,
1994) :
How samples are received.
Proper documentation of their receipt.
Sample handling.
Sample analysis.
QC requirements (procedures and frequencies of QC
checks, criteria for reference materials, types of QC
samples analyzed and frequencies). .
Waste disposal.
Cleanliness and contamination.
Staff training and safety.

Data entry and reporting.
This section provides some information on laboratory QA/QC
procedures to which managers of monitoring programs should pay
particular attention when deciding to use a particular laboratory
for sample analysis (Table IX-4). More detailed references on
laboratory QA and QC should be consulted for further information.
Instrumentation and Materials for Laboratory Operations
The laboratory chosen to do chemical analyses should have
all equipment necessary to perform the analyses required,
including organic analysis, inorganic analysis, and assessments
of precision and accuracy. If any specialized analyses are
required (e.g., microbiology, histopathology, toxicology), be
'certain that the laboratory has the appropriate equipment and
that laboratory staff are adequately trained to perform the
desired analyses. As noted in the elements of the QAPP, periodic
calibration checks that are conducted to ensure that measurement
systems (instruments, devices, techniques) are operating properly
should be described in the QAPP, including procedures and
frequency (Cross-Smiecinski and Stetzenback, 1994).
3 .
Analytical Methods
The laboratory chosen for sample analysis should use
analytical methods approved by the agency for which the sampling
is being conducted or by project personnel, as appropriate.
Standard methods include those published by the U.S. Geological
Survey, the U.S. Environmental Protection Agency, and the
American Society for Testing and Materials, or those published in
Standard Methods for the' Analysis of Water and Wastes (Clesceri
et al., 1989). If any methods to be used are not published, they
should first be validated and verified as acceptable for the
project. Each approved and published method should be
accompanied by an SOP that is followed rigorously by the
laboratory (USGS, 1992).
Method Validation
The laboratory chosen for sample analysis should have well-
developed procedures for method validation. Method validation
should account for and document the following (at a minimum) :
known and possible interferences; method precision; method
accuracy, bias, and recovery; method detection level; and method
comparability to superseded methods, if applicable (USGS, 1992).

Table IX-4. Checklist of items that should be considered in the laboratory operations section of a QA/QC
program (from USEPA, 1990).
I     Laboratory Operations   I
 Element    Specifics      Check-off Responsibility
 Sample Sample receipt    ..       - 
 Management Sample storage . . . . ..       - 
  Sample handling   ..        - 
  Sample scheduling. . .          
 Equipment Equipment calibration and maintenance      
 SOPS Sample management  ..    ..     
  Analytical methods  . . ..       - 
  Sample preparation and analysis procedures  - 
  Reagem/standard preparation     - 
  Raw data requiremems.      - 
  Data reduction and validation     - 
  Precision, accuracy, and method    - 
  detection/reponing limits    ..  - 
  Reponing. . . . . . . . ..      - 
  Corrective actions  . .       
 Records Project-specific records . . . .   . . .   ..  
 Management Laboratory operations records .. ..   . .  
 QC Control samples ... .... ..  . . .  .. - 
 Procedures Method blanks . . . . . . . . . .   . . .  . ..  
  Matrix spikes. . . . . . . . . . . . . . . .. .. ,. . .. - 
  Matrix duplication/matrix spike duplicates  . .   
 Audits Laboratory audits schedule  ... .. ...     
 Health and Fire and emergency equipment . . . . .   ..  
 Safety Fire and emergency equipment inspection    - 
  Health equipment (masks, gloves, ...) . . .  ..  - 
  Waste disposal . . . . . . . . . . . . . . . .  ., . .  
Training and Safety
An analytical laboratory should be able to ensure its
customers that its personnel are adequately trained to perform
the necessary analyses. Individual laboratory staff should be
independently certified for each of the analyses they will
beallowed to perform in the laboratory. Selection of a
laboratory for sample analysis should be based on queries about
how often training is conducted, whether employees are limited to
using equipment for which they have been adequately trained,
whether the training program is independently certified, who

conducts the training, how the staff's competence with individual
instruments is measured, and other factors (USGS, 1992).
Safety for staff is an important consideration when choosing
a laboratory because, aside from the paramount concern for human
well-being, accidents can seriously delay sample analyses or
create a need for resampling. Prospective labo.ratories should be
inspected for their attention to safety procedures, including the
availability of safety equipment such as fire extinguishers,
safety showers and eyewashes, fume hoods, and ventilation
systems; use and disposal practices for hazardous materials; and
compliance with environmental regulations. Testing of safety
equipment should be conducted on a regular basis (USGS, 1992).
Additionally, laboratory safety includes procedures for
ensuring that the laboratory is accessible only to authorized
personnel to ensure confidentiality of the data. The laboratory
should have a system for accounting for and limiting (or denying)
laboratory access to all visitors, including persons affiliated
with projects for which the laboratory is analyzing samples
(USGS, 1992).
Procedural Checks and Audits
A laboratory should have established procedures (SOPs) for
conducting internal checks on its analyses and taking corrective
action when necessary. If more than one laboratory is used for
sample analyses, it will be important to know that the data
obtained from the two are of the same quality and consistency. A
protocol for conducting interlaboratory comparisons should also
be an element of a laboratory's QA/QC plan. For many projects
occasional samples are analyzed by a second laboratory to .
determine whether there is any bias in the data associated with
the primary laboratory's analyses.
Laboratory audits by independent auditors are normally
conducted on a prescribed basis to ensure that laboratory
operations are conducted according to accepted and acceptable
procedures (Cross-Smiecinski and Stetzenback, 1994).
Determination that a laboratory undergoes such audits and reviews
audit results might be sufficient to determine that a laboratory
will be adequate for conducting analyses of samples generated by
the NPS monitoring project.
Data and Reports
It is essential during the conduct of a NPS monitoring
project to document all data collected and used, to document all
methods and procedures followed, and to produce clear, concise,
and readable reports that will provide decision makers with the
information they need to choose among alternative actions, as
described in the DQOs.

Generation of New Data
All data generated during the project, whether in the field,
laboratory, or some other facility, should be recorded. Include
with the data any reference materials or citations to materials
used for data analyses. These include computer programs, and all
computer programs used for data reduction should be validated
prior to use and verified on a regular basis. Calculations
should be detailed enough to allow for their reconstruction at a
later date if they need to be verified (Cross-Smiecinski and
Stetzenback, 1994). Data generated by a laboratory should be
accompanied by pertinent information about the laboratory, such
as its name, address, and phone number, and names of the staff
who worked directly with the project samples.
Use of Historical Data
Historical data are data collected for previous projects
that concerned the same resource in the same area as the project
to be implemented. Historical data sometimes contain valuable
information, and their use can save time and effort in the
implementation and/or data analysis phases of a new project.
Before new data are collected, all historical data available
should be obtained and their validity and usability should be
assessed. Data validity implies that individual data points are
considered accurate and precise because the field and laboratory
methods used to generate the data points are known. Data
usability implies that a database demonstrates an overall
temporal or spatial pattern, though no judgment of the accuracy
or precision of any individual data point is made (Spreizer et
al., 1992). The validity of historical data can be difficult to
ascertain, but data usability can be assessed through a
combination of graphical and statistical techniques (Spreizer et
Specifically, historical data that can be shown to be either
valid or usable can be applied to a new project in the following
ways (Coffey, 1993; Spreizer et al., 1992; USEPA, 1994c):
If the quality (i.e., accuracy and precision) of
historical 'data is sufficiently documented, the data
can be used alone or in combination with new data. The
quality of historical data must be determined
absolutely, generally with the help of a statistician.
Characteristics derived from the historical data, such
as the variability or mean of data, can be used in the
development or selection of a data collection design.
Knowledge of expected variability assists in
determining the number of samples needed to attain a
desired confidence level, the length of monitoring
program necessary to obtain the necessary data, and the
required sampling frequency.

Spatial analysis of historical data can indicate which
sampling locations are most likely to provide the
desired data.
Historical data can provide insights about past impacts
and water quality that can be useful in defining a NPS
pollution problem.
Past trends can be ascertained and the present tendency
of water quality characteristics (degrading, stable, or
improving) can be established for trend analysis.
3 .
Documentation and Record Keeping
All information and records related to the NPS monitoring
project should be kept on file and kept current. This
documentation should include:
A record of decisions made regarding the monitoring
project design.
Records of all personnel, with their qualifications,
who participated in the project.
Intended and actual implementation schedules, and
explanations for any differences.
A description of all sampling sites.
Field records of all sampling events, including any
problems that arose related to sampling and corrective
actions taken.
Copies of all field and laboratory SOPs.
Equipment manuals and maintenance schedules (intended
and actual, with explanations for any discrepancies) .
Printouts from any equipment.
Sample management and custody records.
Laboratory procedures.
Copy of the laboratory QA/QC plan.
Personnel training sessions and procedures,
any training manuals or other materials.
All data generated during the project in hard copy and
electronic forms.

All correspondence related to the project.
Project interim and final reports.
Report Preparation
The original project description should include a schedule
and required format for required reports, including the final
report. Adherence to this schedule is important to provide
information and documentation of project progress, problems
encountered, and corrective actions taken. Reports are also
valuable for supporting continuation of a project if at any point
during the project its continuation is scrutinized or if
additional funding must be secured to ensure its completion.
Reports can also become the primary sources of historical .
information on projects if there are changes in project personnel
during the project. Project managers should decide on the
necessary content and format of all reports prior to commencement
of the project, and these will differ depending on funding and
intended audience.


Appendix A.
Appendix B.
Appendix C.
Appendix D.
Appendix E.
Appendix F.
Appendix G.
Appendix H.
Appendix I.
Appendix J.
Appendix K.
Appendix L.
Appendix M.
Appendix N.
Appendix o.
Appendix P.
Appendix Q.
Appendix R.
Appendix S.
Appendix T.
Appendix U.
Chain of Custody Procedures
Normal Distribution
Chi-square Distribution
F Distribution
Skewness Test
Kurtosis Test
Coefficients for W Test for Normality
W Test Percentage Points
Noncentral t-Distribution
Population Correlation Coefficient
Transformation of Linearization
Multiple Regression Example - Hand
Multiple Regression Example -
Example Use of R-Square
Confidence Limits for the Median of
Any Continuous Distribution
Quantiles of the Spearman Test
Probabilities for the Mann-Kendall
Nonparametric Test for Trend
Quantiles of the Wilcoxon Signed-
Rank Test Statistic
Nonparametric 95 and 90 percentile
confidence intervals on a proportions
Sample sizes for one-sided non-
parametric tolerance limits

Chain of custody Procedures
Water quality data to be used for legal purposes must be
collected and processed through approved procedures, which are
called "chain of custody" procedures. These procedures are
described in existing documents (U.S.E.P.A., 1978b, 1982bi and
Scalf, et al., 1981), and will, therefore, not be addressed in
this M&E guidance.

The Normal Distribution
(SOURCE: Remington and Schork,
1970 )
    .. ..  
    "  W-
0.00 0.3919 0.0000 0.5000 0.0000 1.0000 0.5000
0.01 0.3919 O.OCWO 0.4960 0.0010 0.9920 0.S04Q
0.02 0.3919 0.0010 0.4920 0.0160 0.9-.0 O.SOIO
0.02j1 0.3911 0.01 0.49 0.02 0.91 0.'1 
0.03 0.3911 0.0120 G.4810 0.0139 0.9761 0..5120
0.0. 0.3916 0.0160 0.4-.0 0.0319 0.9611 0..5160
0.0' 0.3914 0.0199 0.4101 0.0399 0.9601 0..5199
0.0.502 0.3914 0.02 0.'" 0.0. 0.96 0;'2 
0.06 0.3912 0.0239 0.4761 0.0.71 0.9'22 0.'139
0.07 0.3910 0.0279 0.4721 O.OSSI 0.9442 0.'279
0.07.53 0.3971 0.03 0.47 0.06 0.94 0.'3 
0.01 0.3977 0.0319 0.4611 0.0631 0.9362 0..5319
0.09 0.3973 0.03'9 0.4641 0.0717 0.9213 0.'3'9
0.10 0.3970 0.0391 0.4602 0.0797 0.9203 0..5391
0.1004 0.3969 0.0. 0.46 0.01 0.92 0..54 
0.11 0.396' 0.0.31 0.4.562 0.0176 0.9124 0..5431
0.12 0.3961 . 0.0.71 0.4'22 O.09SS 0.90" 0..5471
0.1257 0.39.51 0.0' 0.4' 0.10 0.9 O.SS 
0.13 0.39.56 0.0.517 0.4413 0.1034 0.1966 O.SS17
0.14 0.39.51 0.OSS7 0.4.,4) 0.11 J3 0.8187 O.SS57
0.1.5 0.394' 0.0596 O.~ 0.JJ92 0.1801 0.5596
0.1.510 0.3"'" 0.06 0.'" 0.12 0.11 0..56 
0.16 0.3939 0.0636 0.4364 0.1271 0.1729 O. .5636
0.17 0.3932 0.067.5 0.432j 0.13.50 0.16.50 0..5675
0.1764 0.3921 0.07 0.43 0.14 0.16 0.57 
0.11 0.3925 0.0714 0.4216 0.1429 0.1.571 0.5714
0.19 0.3918 0.07.53 0.4247 0.1.507 0."93 0.57'3
0.20 0.3910 0.0793 0.4207 0.1.515 0.1415 0.5793
0.2019 0.3909 0.01 0.42 0.16 0." 0..51 
0.21 0.3902 0.0132 0.4161 0.1663 0.8337 0.~8!2
0.22 0.3894 0.0171 0.4129 0.1741 0.12S9 0 '''I
0.227.5 0.3111 0.09 0.41 0.11 0.12 C. 
0.23 0.3885 0.0910 0.4090 0.1119 0.1111 0.' J
0.24 0.3176 0.0941 0.40S2 0.1897 0.1103 0.2 ~
0.25 0.3167 0.0917 0.4013 0.1974 0.1026 O.h .
0.2533 0.3863 0.10 0.40 0.20 0.10 0.60 
0.26 0.3157 0.1026 0.39'" 0.20.51 0.7949 0.6026
0.27 0.3147 0.1064 0.3936 0.2121 0.7172 0.6064
0.2793 0.3837 0.11 0.39 0.22 0.71 0.61 
0.28 0.3836 0.11 03 0.3897 0.220S 0.7795 0.6103
0.29 0.3125 0.1141 0.3859 0.2212 0.7711 0.6141
0.30 0.3114 0.1179 0.3121 0.13.51 0.7642 0.6179
O.30S' 0.3101 0.12 0.31 0.24 0.76 0.62 
0.31 0.3802 0.1217 0.3783 0.2434 0.7566 0.6217
0.32 0.3790 0.12SS 0.374' 0.2j10 0.7490 O.W'
. AbItractecI (rom Noll_I B",.." i S,IIIfIionJ#-A,!'ii6fl M~/u smc-2J. U.s.
GeM. PMtiD. 0ftIc:e. Washiallon. D.C.. 1 '3.    
t, L.-8I A-E nfli' 10 OM 8b8Ged .... U8der the ~ ."..., --.  

  T'B! NOaMA1. DCI'1"U8lmON  
1 It A B C D 
0.33 0.3778 0.1293 0.3707 0.2586 0.7414 0.6293
0.33\9 0.3776 0.13 0.37 0.26 0.74 0.63
0.34 0.376~ 0.133\ 0.3669 0.2661 0.7339 0.633\
O.H 0.3752 0.1361 0.3632 0.2737 0.7263 0.6361
O.H83 0.3741 0.14 0.36 0.21 0.72 O.~
0.36 0.3739 0.1406 O.H94 0.21\2 0.7118 0.6406
0.37 0.372' 0.1"3 O.H" 0.2186 0.7114 0.6443
0.38 0.3712 0.1410 O.H20 0.2961 0.7039 0.6410
0.38" 0.3704 0." 0.35 0.30 0.70 0.65
0.39 0.3697 0..,17 0.3413 0.3035 0.6965 0.6517
0.40 0.3683 0.\554 0.3446 0.3108 0.6192 0.6554
0.41 0.366A 0..,91 0.J409 0.3182 0.6111 0.659\
0.41~ 0.3~ 0.16 0.34 0.32 0.61 0.66
0.42 0.3653 0.1628 0.3372 0.3255 0.6745 0.6621
0.43 0.3637 O.I~ 0.3336 0.3328 0.6672 0.6664
0.4399 0.3622 0.17 0.33 0.34 0.66 0.157
0." 0.3621 0.1700 0.3300 0.3401 0.6599 0.6700
0.45 0.3605 0.1736 0.326' 0.3473 0.6527 0.6736
0.46 0.3589 0.1772 0.3228 0.3545 0.~55 0.6m
0.4677 0.3'76 . 0.18 0.32 0.36 O.~ 0.60
0.47 0.3572 0.1108 0.3192 0.3616 0.6384 0.6IlOl
0." O.H" 0.1844 0.3.,6 0.3681 0.6312 0.68oM
0.49 0.3538 O. II 79 0.3121 0.3759 0.624\ 0.6079
0.4959 0.H28 0.19 0.3\ 0.31 0.62 0.69
0.50 0.H2\ 0.19\5 0.3085 0.3829 0.6171 0.69"
0.51 0.3503 0.1950 0.3050 0.3199 0.6101 0:6950
0.'2 0.3415 0.19" 0.30" 0.3969 0.6031 0.6985
0.~244 0.3477 0.2 0.3 0.40 0.6 0.70
0.53 0.3467 0.20\9 0.2981 0.4039 0.5961 0.7019
0.54 0.3441 0.2054 0.2946 0.4\01 0..5192 0.7054
0.55 0.3429 0.2018 0.2912 0.4177 0..5123 0.1081
0."34 0.3423 0.2\ 0.29 0.42 0..51 0.71
0.-'6 . 0.34\0 0.2\23 0.2177 0.4245 0."" 0.7123
0.-'7 0.3391 0.2157 0.2143 0.4313 0..7 ~71"
0.58 0.3372 0.2\90 0.2110 0.431\ 0."19 7190
0..5821 0.3366 0.22 0.21 0." 0." 0.72
0.59 0.3352 0.224 0.2776 0.""" 0.".52 O. '7224
0.60 0.3332 0.22-'7 0.2743 0.45., 0..541.5 0.72S7
0.61 0.33\2 0.229\ 0.2709 0.4581 0.5419 0.'7291
0.6128 0.3306 0.23 0.27 0.46 0.54 0.73
0.62 0.3292 0.2324 0.2676 0.*7 0..53.53 0.7324
0.63 0.3271 0.23-'7 0.26'3 0.4713 0..5217 0.73-'7
o.~ 0.32.51 0.2319 0.2611 0.4771 D.-'m 0.7389
0.~33 0.3244 0.24 0.26 0.48 0..52 0.14
0.65 0.3230 0.2422 0.~78 0.4843 0..5151 0.1422
0.66 0.3209 0.2454 0.2.546 0.4901 0.5093 0.7454
0.61 0.3181 0.2416 0.2.514 0.4971 0..5029 0.7486
0.674.5 0.3118 0.2.5 0.2.5 0..50 0..50 0.1.5
0.68 0.3166 0.2.511 0.2483 0..503.5 0.496.5 0.1.511
0.69 0.3144 0.2.549 0.2451 G.S098 G.4902 0.7549
0.70 0.3123 0.2.510 0.2420 0..5161 0.4839 0.1-
0.7063 0.3109 0.26 0.24 0..52 0.48 0.76
0.71 0.3101 0.2611 0.2389 0..5223 0.4177 0.1611
0.72 0.3079 0.2642 0.2358 0..521.5 G.411.5 0.1~2
0.73 0.30" 0.2673 0.2327 0..5346 0.4654 0.1613
0.1311 0.3031 0.21 0.23 0.54 G.46 0.11
0.74 0.3034 0.2104 0.2296 0..5401 0.4593 0.1104
0.7.5 0.3011 0.2134 0.2266 0..5467 0.4.533. 0. 77J4
0.16 0.2989 .0.21~ o.22J6 1""21 0...,3 0.1164
0.11 0.866 0.2194 0.22106 o.SSIT 0...13 0.17't4

  1111 NOIUCAL ~  
z . A B C D E
t.7712 0.2961 0.21 0.22 0.56 0..- 0.78
0.7. 0.2943 0.2123 0.2117 0.5646 0.43" 0.7'2.3
0.79 0.2920 0.2152 0.2148 0.5705 0.4295 0.7852
8.10 0.2197 0.2111 0.2119 0.J763 0.4237 0.71'1
8.1064. 0.21'2 0.29 0.21 0.58 0.42 0.79
...\ 0.2174 0.29\0 0.2090 0.512\ 0.4\79 0.79\0
...2 0.2150 0.2939 0.206\ 0.5878 0.4\22 0.7939
...3 0.2127 0.2967 0.2033 0.5935 0.4065 0.7967
..14 0.2103 0.2995 0.2005 0.599\ 0.4009 0.7995
0.1416 0.2100 0.30 0.20 O.tO 0.40 0.10
..85 0.2110 0.3023 0.\917 0.6017 0.3953 0.1023
1.86 0.2756 0.305\ 0.\949 0.6102 0.3898 0.105\
0.17 0.2732 0.3078 0.\922 0.6157 0.3143 0.107'
8.1179 0.27\4 0.3\ 0.\9 0.62 0.31 0.11
o.U 0.2109 0.3\06 0.1894 0.621\ 0.3789 0.1106
0.89 0.2615 0.3133 0.1867 0.6265 0.3735 0.'133
0.90 0.266\ 0.3\59 0.\14\ 0.6319 0. 368\ 0.1159
0.91 0.2637 0.3\86 0.\'14 0.6372 0.3628 0.'186
0.91" 0:2624 0.32 0.\8 0.64 0.36 0.'2
8.92 0.2613 0.32\2 0.\718 0.6424 0.3576 0.1212
0.93 0.1589 0.32.38 0.\762 0.6476 0.3524 0.123.
0.94 0.1565 0.3264 0.\736 0.6528 0.3472 0.1264
8.95 0.1541 0.3219 0.\7\\ 0.6579 0.342\ 0.1289
0.9,.2 0.153\ 0.33 0.\7 0.66 0.34 0.'3
0.96 0.15\6 0.3315 0.\685 0.6629 0.337\ 0..315
0.97 0.2492 0.3340 0.\660 0.6610 0.3320 0.'340
0.91 0.2461 0.3365 0.\635 0.6729 0.327\ 0.1365
0.99 0.2444 0.3389 0.\611 0.6178 0.3212 0.1389
0.9945 0.2433 0.34 0.\6 0.61 0:32 0.14
\.00 0.2420 0.3413 0.\587 0.6127 0.3\73 0.1413
1.0\ 0.2396 0.3438 0.1 S62 0.6175 0.3125 0.143'
\.02 0.237\ 0.346\ 0.\539 0.6923 0.3077 0.146\
\.03 0.2347 0.3415 0.1515 0.6970 0.3030 0.1415
1.036 0.2332 0.35 0.15 0.70 0.3 0.15
UN 0.2323 0.3508 0.\492 0.7017 G.291J 0.1501
\.05 0.2299 0.353\ 0.\469 0.7063 0.2937 0.853\
\.06 0.2275 0.35" 0.\446 0.7\09 0.219\ 0.85,.
1.07 0.215\ 0.3517 0.\423 0.7\" 0.2146 0.8517
1.08 0.2227 0.3599 0.140\ 0.7\99 0.210\ 0.8599
\.080 0.2226 0.36 0.14 0.72 0.28 0.86
1.09 0.2203 0.362\ 0.1379 0.7243 0.2757 0.162\
1.10 0.2\79 0.3643 0.1357 0.7287 0.27\3 0.1643
1.1\ 0.2\55 0.3665 0.1335 0.7330 0.2670 0.1665
\.12 0.2131 0.3616 0.13\4 0.7373 0.2627 0.1686
1.\264 0.2115 0.37 0.13 0.74 0.26 0.17
\.13 0.2\07 0.3708 0.\292 0.7415 0.1585 0.8708
\.14 0.2013 0.3729 0.\27\ 0.74" 0.1543 0.1729
1.\5 0.20$9 0.3749 0.\151 0.7499 0.150\ 0.'749
\.16 0.2036 0.3770 0.\230 0.7540 0.2460 0.1170
\.\7 0.20\2 0.3790 0.\2\0 0.7510 0.2420 0.'790
1.\75 G.2OOO' 0.3. 0.12 0.76 0.24 o.U
1.11 0.1919 0.31\0 0.\\90 0.7620 0.2310 O.U\O
1.\9 0.\965 0.3130 0.1170 0.7660 0.2340 O.U30
1.20 0.\942 0.3149 0.1151 0.7699 0.230\ 0.1149
1.21 0.1919 0.3169 0.113\ 0.7737 0.2263 0.1169
1.22 0.1895 0.3U8 0.1112 0.7175 0.2225 O.IUI
1.227 0.\110 0.39 0.11 0.78 0.22 0.19
1.23 0.\172 0.3907 0.\093 0.7113 0.2\17 0.1907
\.).1 0.\849 0.3915 0.\075 0.7850 0.2\50 0.1915
1.15 0.1126 0.3944 0.\056 0.7117 G.2\13 0.8944

I It A B C D 
1.26 0.1804 0.3962 0.1031 0.7923 0.2077 0.1962
1.27 0.1711 0.3910 0.1020 0.7959 0.201&1 0.8910
1.21 0.1"1 0.3997 0.1003 0.7995 0.2005 0.1997
1.282 0.1755 0.40 0.10 0.10 0.20 0.90
1.29 0.1736 0.4015 0.0985 0.1029 0.1971 0.9015
1.30 0.1714 0.4032 0.0961 O.IOM 0.1936 0.9032
1.31 0.1691 0.4CW9 0.0951 0.1091 0.1902 0.90019
1.32 0.1669 0.4066 0.0934 0.1132 0.1161 0.9066
1.33 0.1647 0.4012 0.0911 0.1165 0.1835 0.9012
1.34 0.1626 0.4099 0.0901 0.1191 0.1102 0.9099
1.341 0.1624 0.41 0.09 0.12 0.11 0.91
1.35 O.I~ 0.411 5 0.0885 0.1230 0.1770 0.9115
1.36 0.1512 0.4131 0.0869 0.1262 0.1731 0.9131
1.37 0.1561 0.4147 0.0853 0.1293 0.170'7 0.9147
1.31 0.1539 0.4162 0.0831 0.1324 0.1676 0.9162
1.39 0:1518 0.4177 0.0823 0.83" 0.1645 0.9177
1.40 0.1497 0.4192 0.0lOI 0.8385 0.1615 0.9192
1.405 0.1417 0.42 0.01 0.84 0.16 0.92
1.41 0.1476 0.4207 0.0793 0.1415 0.1585 0.9207
1.42 0.1456 0.42.22 0.0778 0.8444 0.1556 0.92.22
1.43 0.1435 0.4236 0.0764 0.8473 0.1527 0.9236
1.44 0.1415 0.4251 0.0749 0.1501 0.1499 0.92.51
1.45 0.1394 0.426.5 0.0735 0.1529 0.1471 0.926.5
1.46 0.1374 0.4279 0.0721 0.85.57 0.1443 0.9279
1.47 0.1354 0.4292 0.0701 0.1.584 0.1416 0.9292
1.476 0.1343 0.43 0.07 0.16 0.14 0.93
1.41 0.1334 0.4306 0.0694 0.1611 0.1389 0.9306
1.49 0.1315 0.4319 0.0611 0.1638 0.1362 0.9319
1.50 0.1295 0.4332 0.0661 0.1664 0.1336 0.9332
1..51 0.1276 0.4345 0.0655 0.1690 0.1310 0.9345
1..52 0.12.57 0.43.57 0.0643 0.1715 0.1215 0.93.57
1..53 0.1231 0.4370 0.06)0 0.1740 0.1260 0.937U
1..54 0.1219 0.4312 0.0611 0.1164 0.1236 0.9382
1..5.5 0.1200 0.4394 0.0606 0.1119 0.1211 0.9394
1.5" 0.1191 0.44 0.06 0.11 0.12 0.94
1.56 0.1112 0.4406 0.0594 0.1112 0.1111 0.9406
1..57 0.1163 0.4411 0.0582 0.1136 0.1164 0.9411
1..51 0.1145 0.4429 0.0571 0.1159 0.1141 0.,.29
1..59 0.1127 0.4441 0.0559 0.1112 o.a 111 0."'1
1.60 0.1109 0.4452 0.0.548 0.1904 0.1096 0.9452
1.61 0.1092 0.4463 0.OSJ7 0.1926 0.1074 0.9463
1.62 0.1074 0.4474 0.0526 O.IMI 0.1052 0.,.74
1.63 0.10.57 0.4484 0.0516 0.1969 0.1031 0.M84
1.64 0.1040 0.4495 0.0505 0.1990 0.1010 0.,.95
1.645 0.1031 0.45 0.05 0.90 0.10 G.95
1.65 0.1023 0.4505 0.0495 0.9011 0.0989 0.9505
1.66 0.1006 0.4515 0.0415 0.9031 0.0969 0.9515
1.67 0.0919 0.4525 0.0475 0.9051 0.0949 0.952.5
1.68 0.0973 . 0.4535 0.0465 0.9070 0.09)0 0.9535
1.69 0.09.57 0.4545 0.0455 0.9090 0.0910 0.9545
1.70 0.0940 0.4554 0.0446 0.9109 0.0191 0.9554
1.71 0.0925 0.4564 0.0436 0.9127 0.0873 G.9564
1.72 0.0909 0.4573 0.0427 0.9146 0.0854 G.9rn
1.73 0.0893 0.."82 0.0418 0.9164 0.0836 0.9582
1.74 0.0171 0.4591 0.0409 G.9111 0.0819 0.9591
1.75 0.0163 0.4599 0.0401 0.9199 0.0801 0.9599
1.751 0.0162 0.46 0.04 0.92 0.08 0.96
1.76 0.0141 0.4601 0.0392 0.9216 0.0716 o.NOI
1.77 0.0833 0.4616 0.0314 0.t233 0.0767 U616
1.71 0.0811 0.4625 0.0375 0.t249 0.0751 0.M15

   TBI ND8MAL I8I881I1ON  
, "  A B C D 
1.'79 0.0804  0.4633 0.0367 0.9266 0.0734 0.9633
1.10 0.0790  0.464\ 0.03'9 0.9211 0.0719 0.9641
1.11 0.077'  0.4649 0.03'2 0.9297 0.0'703 0.9649
1.12 0.0761  0.4656 0.0)44 0.9312 0.0611 0.9656
1.13 0.0748  0.4666 0.0336 0.9318 0.0672 0.""
I.'" 0.0734  0.4671 0.0329 0.9342 0.0658 0.9671
1.1, 0.072\  0.4671 0.0322 U3S7 0.0643 0.9671
1.16 0.0707  0.4686 0.0314 0.9371 0.0629 0.9616
1.17 0.06M  0.4693 0.0307 0.9385 0.0615 0.-3
1.11 0.0611  0.4699 0.0301 0.9399 0.0601 0.'"
1.111 0.0610  0.47 0.03 0.94 0.06 0.97
...9 0.0669  0.4706 0.0294 0.9412 O.OSII 0.9706
1.90 0.0656  0.4713 0.0217 0.9426 0.0574 0.9713
1.91 0.0644  0.4719 0.0211 0.9439 0.0561 0.9719
1.92 0.0632  0.4726 0.0274 0.94'1 0.0S49 0.9726
1.93 0.0620  0.4732 0.0261 0.9464 0.0536 0.m2
1.94 0.0601  0.4738 0.0262 0.9476 0.0'24 0.9738
1.9, 0.0596  0.4744 0.02S6 O.MII 0.0512 0.9744
1.960 0.0585  0.475 0.02.S 0.9, 0.0' 0.975
1.97 0.0573  0.4756 0.0244 0.9512 0.0411 0.9756
1.91 0.0562  0.4761 0.0239 0.9'23 0.0477 0.9761
1.99 0.0551  0.4767 0.0233 0.9534 0.0466 0.9767
2.00 0.0540  0.4772 0.0228 0.954' 0.0'" 0.9772
2.01 0.0529  0.4778 0.0222 0.9556 0.0444 0.97'71
2.02 0.0519  0.4783 0.0217 0.9'" 0.0434 0.9713
2.03 0.0501  0.4788 0.0212 0.9576 0.0424 0.9711
2.04 0.0491  0.4'793 0.0207 0.9'" 0.0414 0.9'793
2.05 0.0411  0.4'791 0.0202 0.9596 . 0.0404 0.9791
2.054 0.04M r 0.48 0.02 0.96 0.04 0.98
2.06 0.0471  0.4.03 0.0197 0.9606 0.0394 0.9103
2.07 0.0461  0.4101 0.0192 0."15 0.0385 0.9.
2.01 0.0459  0.4112 0.0111 0.962.5 0.0375 0.9812
2.09 0.0449  0.4117 0.0113 0.9634 0.0366 0.9817
2.10 O.OMO  0.4121 0.0179 0.9643 0.0357 0.9121
2.11 0.0431  .0.4126 0.0174 0.9651 0.0349 0.9826
2.12 0.0422  0.4IJO 0.0170 0.9660 O.u.o 0.9830
2.13 0.0413  0.4134 0.0166 0.9661 0.0332 0.9834
2.14 0.0404  0.4131 0.0162 0.9676 0.0324 0.9138
2.1' 0.0396  0.4142 0.0158 0.9614 0.0316 0.9"'2
2.16 0.0317  0.4146 0.0154 0.9692 0.0301 0.9846
2.17 0.0!79  0.4150 0.0150 0.9700 0.0300 0.9850
2.11 0.0371  0.4154 0.0146 0.9707 0.0293 0.9854
2.19 0.0363  0.4157 0.0143 0.9715 0.021' 0.9857
2.20 0.0355  0.4161 0.0139 0.9722 0.0278 0.9161
2.21 0.0347  0."'" 0.0136 0.9729 0.0271 0.9164
2.22 0.0339  0.4161 /G:'013~ 0.9736 0.0264 0.9161
2.23 0.0332  0.4171 --o..QUJ) 0.9743 0.02.S7 0.9871
2.24 0.0325  0.417' 0.012' 0.9749 0'02.S1 0.917'
U5 0.0317  0.4171 0.0122 0.9756 0.0244 . 0.9871
2.26 0.0310  0.4111 0.0119 0.9762 0.Q23I 0.9111
2.27 0.0303  0.'" 0.0116 0.9768 o.CW2 0.9884
2.21 0.0297  0.418'7 0.0113 0.m4. 0.0226 0.9117
2.29 0.0290  0.4190 0.0110 0.9710 0.0220 0.9190
2.30 0.0213  0.4193 0.0107 0.9716 0.0214 0.9893
2.31 0.0277  0.4196 0.0104 0.9'791 0.0209 0.9196
2.32 0.0270  0.4198 0.0102 0.979'7 0.0203 0.9191
2.326 0.0267  0.49 0.01 0.98 0.02 0.99
2.33 0.0264  0.4901 0.0099 0.9102 0.0198 0.9901
2.34 0.0258  0.4904 0.0096 0.9807 0.0193 0."
2.3, 0.0252  0.4906 0.84 0..12 0.0111 0. 9!106

  T1I! NOaMAl DISTIl!B1.1'nON  
 It A B C D 
2.36 0.0246 0.4909 0.0091 0.9817 0.0183 0.9909
2.37 0.0241 0.4911 0.0089 0.9822 0.0178 0.9911
2.38 0.023S 0.4913 0.0087 0.9827 0.0173 0.9913
2.39 0.0229 0.4916 0.0084 0.9832 0.0168 0.9916
1.40 0.0224 0.4918 0.0082 0.9836 0.0164 0.9911
HI 0.0219 0.4920 0.0080 0.9840 0.0160 0.9920
2.42 0.0213 0.4922 0.0078 0.9845 0.01S5 0.9922
2.43 0.0208 0.4925 0.0075 0.9849 0.01S1 0.9925
2.44 0.0203 0.4927 0.0073 0.9853 0.0147 0.9927
2.45 0.0198 0.4929 0.0071 0.9857 0.0143 0.992t
2.46 0.0194 0.4931 0.0069 0.9861 0.0139 0.9931
2.47 0.0189 0.4932 0.0068 0.9865 0.0135 0.9932
2.48 0.0184 0.4934 0.0066 0.9869 0.0131 0.9934
2.49 0.0180 0.4936 0.0064 0.9872 0.0128 0.9936
2.$0 0.017S 0.4931 0.0062 0.9876 0.01%4 0.99)1
2.51 0.0171 0.4940 0.0060 0.9879 0.0121 0.9940
2.S2 0.0167 0.4941 0.0059 0.9883 0.0117 0.9941
2.'3 0.0163 0.4943 0.0057 0.9816 0.0114 0.9943
2.54 0.01 S8 0.4945 0.0055 0.9889 0.0111 0.9945
2.55 0.0154 0.4946 0.0054 0.919% 0.0108 0.9946
2.56 0.0151 0.4948 0.0052 0.9895 0.0105 0.9948
2.57 0.0147 0.4949 0.0051 ' 0.9898 0.0102 0.9949
2.576 0.014S 0.495 0.005 0.99 0.01 0.995
2.58 0.0143 0.4951 0.0049 0.9901 0.0099 0.9951
2.59 0.0139 0.495% 0.0041 0.9904 0.0096 0.995%
2.60 0.0136 0.4"3 0.0047 0.9907 0.0093 0.9953
2.61 0.0132 0.4955 0.0045 0.9909 0.0091 0.9955
2.6% 0.0129 0.4956 O.oo.w 0.9912 0.0018 0.9956
2.63 0.0126 0.4957 0.0043 0.99 IS  0.0085 0.9957
2.64 0.0122 0.4959 0.0041 0.9917 0.0013 0.9959
2.65 0.0119 0.4960 O.OCWO 0.9920 0.0080 Q.996O
2.70 0.0104 0.4965 0.0035 0.9931 0.0069 0.9965
2.75 0.0091 0.4970 0.0030 0.9940 0.0060 0.9970
2.80 0.0079 0.4974 0.0026 0.9949 0.0051 0.9974
2.85 0.0069 0.4"8 0.0022 0.9956 O.oo.w 0.9978
2.90 0.0060 0.4981 0.0019 0.9963 0.0037 0.9911
2.95 0.0051 0.4984 0.0016 0.9961 0.0032 0.9984
3.00 0.0044 0.4987 0.0013 0.9973 0.0027 0.9917
3.05 0.0038 0.4919 0.0011 0.9977 0.0023 0.9919
3.090 0.0034 0.499 0.001 0.998 0.00% 0.999
3.10 0.0033 0.4990 0.0010 0.9911 0.0019 0.9990
3.15 0.0028 0.4992 0.0008 0.9984 0.0016 0.9992
3.20 0.0024 0.4993 0.0007 0.9916 0.0014 0.9993
3.25 0.0020 0.4994 0.0006 0.9911 0.0012 0.9994
3.291 0.0018 0.4995 0.0005 0.999 0.001 0.9995
3.30 0.0017 0.4995 0.0005 0.9990 0.0010 0.9995
3.35 0.001S 0.4996 O.OOCM 0.9992 0.0008 0.9996
3.40 0.0012 0.4997 0.0003 0.9993 0.0007 0.9997
3,45 0.0010 0.4997 0.0003 0.9994 0.0006 0.9997
3.$0 0.0009 0.4991 0.0002 0.9995 0.0005 0.9991
3.SS 0.0007 0.4991 0.0002 0.9996 0.0004 0.9991
3.60 0.0006 0.4991 0.0002 0.9997 0.0003 0.9991
3.65 0.0005 0.4999 0.0001 0.9997 0.0003 0.9999
3.70 0.0004 0.4999 0.0001 0.999' 0.0002 0.9999
3.75 0.0004 0.4999 0.0001 0.9991 0.0002 0.9999
3.10 0.0003 0.4999 0.0001 0.9999 0.0001 0.9999

The t-Distribution
(SOURCE: Remington and Schork, 1970)
   I'I8C8N'nUI ~ 1'81 I 118ft11U11DN8  
&f. '.... '.... '... '.... '... , ..... '.... '.- '.-
I 0.3150 0.7270 1.376 3.071 6.3131 11. '706 31.121 63.651 636.'1'
2 0.21" 0.6172 1.061 1.186 1.92Il1O 4.3027 6.96S 9.92AI J UN
3 0.2766 O.SI4O 0."1 1.638 1.34 3.IW 4.541 S.1409 11.t2A
4 0.2707 0.5692 0.941 1.S33 1.1311 1.7764 3.747 4.6041 UIO
S 0.%672 0.S591 0.920 1.476 1.01S0 1.$'706 U6' 4.0321 "'"
6 0.2648 O.S536 0.906 1.440 1.9432 1.4469 3.143 3.70'74 ,.t5
7 0.2632 0.5493 0.896 1.41S 1.1946 1.3646 1.998 3,4995 s..
I 0.%619 0.5461 0.119 J.]97 I.159S' 1.3060 1.896 US54 5.0"1
9 0.%610 0.5436 0.A3 1.313 1.1331 1.2622 1.121 3.2491 4.711
10 0.%602 0.5416 0.179 1.372 1.1125 1.1211 1.764 3.1693 4.587
II 0.2596 0.S400 0.176 1.363 1.7939 1.2010 1.711 3.1051 un
12 0.1S9O 0.5317 0.173 1.356 I. 7123 1.1718 1.611 3.054S 4.111
13 0.2516 0.5375 0.170 1.3SO 1.17'09 1.1604 1.6S0 3.0123 4.221
14 0.2512 0.5366 0.168 1.345 1.7613 2.1"" 1.624 1.9761 4.140
IS 0.25'79 0.53S1 0.166 1.341 I. 7530 1.131S 1.602 1.9467 4.m
16 0.2576 0.S358 O.I6S 1.337 1.7459 2.1 ::: 1."3 1.92D8 4.GIS
17 0.2574 O.S3044 0.163 J.]33 I. 7396 1.1 1.567 1.1982 3.11"
II 0.2571 0.5331 0.162 1.330 1.7341 1.1009 1..5.52 1.1'714 3.1122
19 0.2569 0.5333 0.161 1.321 I. 7291 1.0930 1.539 1.1609 3.183
20 0.2567 0.S329 0.160 1.325 1.7247 1.0160 U2I 1.14S3 3.1SO
21 G.2566 0..5325 0.1.59 1.323 1.7207 1.0796 1..511 2.1314 3.11'
Z2 0.2564 0..5321 0.1.51 1.321 1.7171 l.m9 1.- 1.1IA 3.792
23 0.2563 0.5311 0.1.51 1.319 1.7139 1.061'7 l..soo 1.t073 U67
24 0.2562 O.S3IS 0.1.57 1.311 I. 71 09 1.0639 1.492 1. 7969 3.74.5
2.5 0.2561 0..5311 0.156 1.316 I. 7011 1.059S l.4IS 1.7174 3.72.5
26 0.2560 O.S309 0.156 J.]IS 1.70S6 1.05"" 1.479 2.1717 3.70'7
27 0.2.559 0..5307 0.1"" J.]14 I. 7033 2.0518 1.473 2.1707 UIG
21 0.25.51 0..5304 O.I.5S 1.313 1.7011 2.0410$ 1.467 1. 7633 U74
29 0.2551 0.S302 0.154 J.]II 1.6991 1.06S2 2.462 2.7564 3.659
30 0.2.556 O. S300 0.154 1.310 1.6973 1.0623 1.4S? 1. 7.soo 3.616
3S 0.25.53 O.S2t2 0.1.521 1.3062 1.6196 1.030 1 1.431 1.7239 U9t9
. O.25SO O.S286 0.IS07 1.3031 1.6139 2.0211 1.423 2.104S 3..5SII
4S 0.2549 O.S2Il '18497 1.3007 1.6794 1.0141 1.412 1.6196 3.S2i07
so 0.2547 0.S271 UI9 1.2987 1.67.59 1.0016 2..3 2.6778 3,496.5
60 O.254S 0.S272 -477 1.2959 1.6707 2.0003 1.390 1.6603 3,4606
70 0.2543 O.S268 ...&461 1.2t38 1.6669 I.9MS 1.311 2.6410 3,43SS
80 0.2542 O.S26S 1.1.80662 1.2t22 1.6641 1.990 1 1.374 2.6311 3.4169
90 0.2541 0.S263 0."51 1.2t10 I. 6620 I. 9867 1.368 1.6316 3.4G22
100 0.2S40 0.5161 0.".52 1.2901 1.6602 I. 9140 1.364 2.6260 3.J909
120 0.2539 0.S2.5I 0."" 1.2117 urn I. 9799 1.3.51 2.611.5 3.3736
140 0.2531 0..5256 0.1442 1.2176 1.6.5,. I. 9771 1.3S3 1.6114 U61S
160 0.2538. O.S2.5S 0."39 1.2169 1.654S U749 1.3.50 1.6070 U.527
110 0.2537 0.S253 0."36 1.2163 1.6.534 1.9133 1.347 2.603S 3.34S6
200 0.2537 o..5m 0."34 1.2158 I.6S25 1.9719 l.34S 2.6006 3.3400
. G.2533 0.5244. 0."16 1.1116 1.6..9 1.9600 1.326 2.51S1 3.2905
. The aea of tIUI88biI an aV8Cl8d with kiDd ~ . . ra (rom 1>8- ~~
r...... 6tb Ed.. pp. 32-JS. Geit:J PIIInr ..0.-" DiiIioII of GeiIY CI8aica1 .
ArdMIy, N.Y. . .    

The Chi-square Distribution
(SOURCE: Remington and Schork, 1970)
  PDaHTU.S Of 111! CBI-QJAU~.   
d.f. x: ...., x:..., Z:.II z:.... x:...  x:. 18  x.... z:... z'
I 0.000000393 0.0000393 0.0001" 0.000982 0.00393  0.0158 0.0662 0.148 0.215
2 0.00100 0.0100 0.0201 0.0506 0.103  0.211 0.446 0.713 1.022
3 0.0153 0.0717 0.115 0.216 0.352  O.S14 I. 0CI5 1.424 1.169
4 0.0639 0.207 0.297 0.'" 0.711  I.OCM I.EA9 2.195 1.753
5 0.151 0.412 0.554 O.IJI 1.145  \.610 2.343 3.000 USS
6 0.299 0.676 0.872 1.237 1.635 ~ 3.070 3.828 4.570
7 O.48S 0.989 1.239 1.690 2.167 3.122 4.671 U93
8 0.710 1.344 1.646 2.110 2.733  3.490 4.594 5.527 60423
9 0.972 I. 735 2.088 2.700 3.32S I 4.161 5.310 6.393 US?
10 1.265 2.1S6 2.558 3.247 3.940  U6S 6.179 7.267 I.~S
11 US7 2.603 3.053 3.816 4.575  5.578 6.989 8.148 9.237
12 1.934 3.074 ),571 4.404 5.226  6.304 7.807 9.034 10.182
13 2.305 3.565 4.107 5.009 '-892  7.042 8.634 . 9.926 11.119
14 2.697 4.075 4.660 5.629 6.571  7.790 9.467 10.821 11.079
IS 3.101 4.601 5.229 6.262 7.261  8.547 10.307 11.721 13.030
16 J.S36 5.142 5.812 6.908 7.962  9.312 1 t.I 52 12.624 13.,.3
17 3.980 5.697 6,408 7.564 8.672  10.015 12.002 13. SJ1 14.937
18 4.439 6.265 7.015 8.231 9.390  10.165 12.157 14.440 15.193
19 4.912 6.144 7.633 8.907 10.117  11.651 13.716 '15.352 16.150
20 5.398 7.434 8.260 9.591 10.151  12.443 14.578 16.266 17..
21 5.896 8.034 8.897 10.283 11.591  13.240 15.445 17.182 11.761
22 6.405 8.643 9.542 10.912 12.338  14.041 16.314 '8.101 19.729
23 6.924 9.260 10.196 I I. 681 13.~1  14.'" 17.117 19.021 211.690
24 7.451 9.886 10.856 IUOI 13.'"  15.659 18.062 19.94] 2...S2
2S 7.991 10.S20 11.524 13.120 14.611  16.473 11.940 20.867 22.616
26 8.511 11.160 12.198 13."'" IS. 379   17.292 19.120 2\.792 23.5'79
27 9.09] 11.101 12.179 14.573 16.151  11.114 20.703 22.719 24. S44
21 9.656 12.461 13.565 1'-301 16.928  18.939 2\.588 23.647 25.S09
29 10.227 13.121 14.256 16.047 17.701  19.761 22.475 24.577 26,475
30 10.804 13.787 14.953 16.791 18.493  20.599 23.364 25.508 27."'2
35 1 3.788 17.192 18.509 20.569 22.465  24.797 27.836 30.17U 31.212
40 16.906 20.707 22.164 24.4]] I 26.509  29.051 32.345 3U72 37.134
45 20.136 24.311 25.901 28.366 30.612  J3.3SO 36."" 39.585 41.995
so 23.461 27.991 29.707 32.357 34.764  37.619 41.449 "".]13 46.164
60 30.340 35.53S 37.485 40.412 43.11'  46.459 SO. 64 1  53.109 SU20
70 37.467 43.275 45.""2 48."8 51. 739  55.329 59.898 63.346 66.396
80 "".791 SI.172 53. S40 ".1S3 60.391  64.271 69.207 72.915 76.111
90 52.276 59.196 61.754 65.647 69.126  73.291 78.558 82.511 1S.993
100 59.897 67.328 70.065 74.222 77.930  82.358 87.945 92.129 95.101
120 75.461 83.1S2 86.924 91.573 95.705 ' 100.624 106.106 111.4'9 11S.465
140 91.393 100.655 104.035 1~.137 1I3.659 ! 119.029 115."8 130.766 135.149
160 107.598 117.610 121.346 126.170 13\.756 1137.5046 144.783 ISO.158 154.156
110 124.033 134.115 131.121 144.741 149.969  156.153 163.161 169.511 "4.SIO
200 140.661 152.241 ISU32 162.721 161.279 \ 17U3S 113.003 119.049 194.319

  It" I:... I:... I:... Z:.M z:... Z:.1tI Z:... Z:.... Z:.-
 I 0.." 0.708 1.074 I. 6062 2.706 3.141 5.024 6.635 7.179 12.116
 2 1.316 1.133 2.<408 3.219 ..60' 5.991 7.371 9.210 10.597 15.202
 , 2.366 2.~ 3.665 ....2 6.251 7.11S 9..348 11.345 12.138 17.730
 4 3.357 4.eM5 4.178 5.919 7.7'79 9."1 11.\43 \3.277 IU60 19.991
 5 U'I '.\32 6.064 7.219 9.136 11.070 12.132 15.016 16.750 22.105
 , '..348 6.211 7.231 ""1 10."5 12.592 14.449 16.112 11.548 24.103
 7 6.346 7.283 8.383 9.103 12.017 14.067 16.0\3 11.475 20.278 26.011
 I 7.344 1.351 9.'24 II. 030 \3.362 IS. 507  17.535 20.090 21.95' 27.161
 , 1.343 9.414 10.656 12.242 14.614, 16.919 19.023 21.666 23.519 29.666
' 10 9.342 10.473 11.711 \3.442 1'.917 11.307 20."3 23.209 25. III 31.41'
~ II 10.341 I \.530 12.199 14.631 17.275 19.675 21.920 24.m 26.757 33.136
 12 11.340 12.,... 14.011 15.112 11.549 21.026 23.336 26.217 28.300 34.121
 J3 12.340 \3.636 1S.119 16.985 19.112 22.362 24.736 27.611 29.119 36.471
 14 \3.339 14.615 16.222 11.151 21. 064 23.615 26.119 29.141 31.319 31.109
 15 14.339 1'.733 17.322 \9.311 22.307 24.996 27."1 30.571 32.601 39.71'
 16 1'.331 16.710 lUll 20.46' 23.542 26.296 28.14' 32.000 34.267 41.301
 17 16.331 17.12. 19.'11 21.61S 24.769 27.517 30.191 33.409 35.711 .2.179
 II 17.338 18.168 20.601 22.760 2'.919 28.169 3 \.526 34.10' 37.156 44.434
 19 11.331 19.910 21.689 23.900 27.2CM 30.144 32.1'2 36.191 38.,.2 45.973
 20 19.337 20.951 22.775 2'.031 21.412 31.410 34.170 37.566 39.997 47.491
 21 20.337 21.991 23.851 26.171 29.61' 32.671 35.479 31.932 41.401 .9.010
 22 21.337 23.031 24.939 27.30. 30.1 \3 33.924 J6. 71 I 40.289 42. 796 5O.SIt
 23 22.337 24.069 26.011 21.429 32.007 35.172 38.076 41. 638 44.111 '2.000
 24 23.337 25.106 27.096' 29."3 33.196 36..1S 39.]64 42.910 45."1 53.479
 25 24.337 26.143 28.172 30.675 34.382 37.6'2 40.646 44.314 46.'21 54.947
 26 25.336 27.179 29.246 31.795 35.563 31.'" 41.923 45.642 ".290 56.40'7
 27 26.336 28.214 30.319 32.912 36.741 40.11 3 43.194 46.963 49."5 57.1"
 21 27.336 29.249 31.391 34.027 37.916 41.337 44.461 48.271 50.993 59.300
 29 28.336 30.283 32.461 35.139 39.017 42.537 4'.722 49.,.1 52.336 60.734
 30 29.336 31.316 33.'30 36.250 40.256 43.773 46.979 50.892 '3.672 62.161
 35 34.336 36.475 38.159 .1. 771 46.059 49.102 53.203 57.342 60.275 69.191
 40 39.335 .1.622 44.165 .7.269 RI05 ".758 59.342 63.691 66.766 76.095
 .5 44.335 46.761 49.452 52.729 57.505 61.656 65.<610 69.957 73.166 12. 116
 50 49.335 51.192 54.723 ".1" 63.167 67.50' 71.420 76.154 79.490 89.561
 60 59.335 62.135 65.226 68.972 74.397 79.012 13.291 11.379 91.952 102.695
 70 69.334 72.351 75.689 79.715 1'.527 90.531 95.023 100.425 leM.21S II'.'"
 10 79.334 12.566 16.120 90.405 96.571 101.179 106.629 112.329 116.321 121.261
 90 19.334 92.761 96.52. 101.054 107.565 1\3.14' 111.136 124.116 128.299 140.713
 100 99.334 102.~ 106.906 111.667 111.49' 124.342 129.561 13'.106 140.169 153.165
 120 119.334 123.219 127.616 132.106 140.233 146.567 1S2.211 151.950 163.648 177.602
 140 139.334 I<6UeM 148.269 15U54 161.127 168.6\3 174.648 111.140 186.146 201.612
 160 159.33<6 163.191 168.176 174.121 113.311 190.516 196.915 2
The F Distribution
(SOURCE: Remington and Schork,
   PDal'mUS 0' THE F DGnBtmON   
/.  2       
   4  6 1 I t
I 40'30 ~. 50404. S62'. $1640 "". "29" ".." 6013"
2 "I.' 999.0 999.2 999.2 999.3 999.3 999.4 999.4 999.4
3 161.0 141.' 141.1 1 31.1 134.6 132.1 131.6 130.6 13.'
4 14.14 61.2' 56.11 53." 61.11 $0.53 49.66 49.00 41.41
5 41.11 31.\2 )),20 31.09 29.15 21.12 21.\6 27.64 27.24
6 35." 21.00 23.10 21.92 20.11 20.03 19.66 19.03 11.69
1 29.25 21.69 18.17 11.19 16.21 ".52 ".02 14.63 14.33
I 2'-42 18.49 1$.13 14.39 13.49 12.16 12.40 12.04 11.17
9 22.16 16.39 13.90 12.S6 11.11 11.13 10.70 10.37 10.11
10 21.04 14.91 12.55 11.21 10.41 9.92 9.52 9.20 ..,6
II 19.69 13.11 11.$6 10.35 UI 9.05 1.66 1.35 1.12
12 18.64 12.97 10.10 9.63 1.19 1.31 1.00 1.11 1.41
13 11.81 12.31 10.21 9.01 1.35 7.16 1.49 1.2\ 6."
14 11.14 11.18 9.13 1.62 7.92 1.43 1.01 6.10 6.sa
IS 16.59 11.34 9.34 8.15 "" 1.09 6.14 6.47 '.36
16 16.12 10.97 9.00 1.94 1.27 6.1' 6.66 6.19 5."
11 15.12 10.66 1.13 1.61 1.02 6.S6 6.22 5.96 5.TS
II 15.38 10.39 1.49 1.46 6.11 6.35 6.02 5.76 5.56
19 15.01 10.16 1.21 1.26 6.62 6..1 5.85 5.59 5.39.
20 14.12 9.95 1.10 1.10 6.46 6.02 5.69 5." 5.14
21 14." 9.17 1.94 6.95 6.32 HI 5.56 5.3\ 5.11
22 14.31 9.61 1.10 6.11 6.19 5.16 5.44 5.'9 4.99
23 14.19 9.47 1.61 6.601 6.01 5.65 5.33 5.09 4.19
24 14.03 9.34 1.55 6.59 5.91 '.55 5.23 4.99 4.10
as IUI 9.22 1.45 6.49 HI 5.66 5.15 4.91 4.7\
26 13.14 9.12 1.36 6.4\ 5.10 5.31 5.07 4.13 4.64
27 13.61 9.02 1.27 6.33 5.13 5.3\ 5.00 4.76 4.57
21 13.$0 ..,3 1.19 6.15 '.66 5.24 4.93 4.69 4.50
29 13.39 US 1.\2 6.19 '.59 . '.'1 4.1'7 4.64 4.45
30 13.29 1.77 7.05 6.\2 5.53 5.\2 U2 4.58 4.39
40 12.61 U5 6.60 5.70 5.13 4.73 4." 4.2\ 4.02
60 11.97 1.76 6.17 '.3\ 4.76 4.37 4.09 3.17 ).6!)
120 11.31 1.3% 5.79 4.95 4.42 4.04 3.17 3.55 UII
iZ) 10.13 6.9\ 5.42 4.62 4.10 3.14 3.47 3.27 3.\0
" Muitillly tlla8 .ntria by 100..   The relation F 8/.(/' h) = F 1-'8/11 (/..,,)
~ i. Ihe number of .... of (N8dom '" tile _tor. C - - ,... of "". F cIIIIrI-.
. is &118 .""'- o( -- of (JWdoe 18 &118 .......-. - tIII8 _I fill ..... of ,,......,..

I. 10 12  20 24 JO 40  120  
 ., 60 GO 
I 6056" 6/07" 61,." 6209" 6135" 6161" 6287" 6313" 6)40" '*" 
2 999.4 999.' 999.' 999.' 999.5 999.5 999.5 999.5 "'.5 999.' 
3 129.2 121.3 127.' 126.' I~.' 1~.4 I~.O 124.' 124.0 113.5 
4 ".05 .7..1 46.76 46.10 45.17 45.43 '5.09 ".75 ".40 ".05 
5 26.92 26.'2 ~." 25.3' 25.14 24.17 24.60 24.33 ~.06 13.79 
6 18.'1 17.99 17.56 17.12 16.19 16.67 16... 16.21 IU' 15.15 .~.
7 1'.08 13.71 13132 12.93 12. 73 12.53 12.33 12.12 11.91 11.10 
. 11.54 II. It 10.84 10." 100JO 10.11 9.92 '.73 9.53 9.33 
, '.19 '.57 '.2' 1.90 '.72 U5 '.37 '.19 '.00 7.81 
10 '.75 '.'5 '.13 7.80 7.64 7.47 7.30 7.12 6.94 6.76 
II 7,'2 7.63 7.32 7,01 6.85 U. 6.52 1.35 6.17 6.00 
12 7.29 7.00 6.71 6.40 6.25 6.09 5.'3 5.76 5.59 5.'2 
13 6.80 6.52 6.13 '-93 5.78 5.63 5.47 5.30 5.14 4." 
I' 6.40 6.13 5." 5.56 5.'1 5.25 5.10 '.94 '.17 '.60 
., 6.08 5." 5.54 5.25 5.10 '.!IS 4.80 4.64 4.47 4.JI 
16' 5.'1 5.55 5.27 4.99 4." 4.70 4.54 4,39 4,23 4.06 
17 5.58 5.32 5.05 '.78 '.63 '.48 4.33 4.1' 4.02 US 
18 5.3' 5.13 4.87 '.59 '.'5 4.30 ..., '.00 3.84 U7 
It '.22 '.97 '.70 4.43 4.29 4.14 3.99 3.84 U. 3.51 
20 s.o. '.12 4.56 4.29 4." 4.00 3.16 3.70 3.54 U. 
21 4.!IS '.70 4." 4.17 4.03 3." 3.74 3.5. 3,42 3. 
22 U3 ..,. 4.33 4.06 3.92 3.78 3.63 U. 3.32 3.1, 
13 '.73 '.48 4.13 3.96 3.12 3.6. 3.53 3.3' 3.22 3.05 
2. '.64 '.39 '.14 3.87 3.74 3'.59 3.4' 3.29 3.14 2." 
25 '.56 '.31 4.06 3.79 3.66 3.52 3.37 3.22 3.06 2.8 
26 .... '.24 3.99 3.72 3.5' U. 3.30 3." 2.99 2.12 
27 '.'1 '.17 3.92 3.66 3.S2 3.3. 3.13 3.01 2.92 2.7, 
21 '.35 '.11 3.16 3.60 3.46 3.32 3.18 3.02 2.86 2.8 
29 '.29 '.0' 3.10 3.54 3.'1 3.27 3.12 2.97 2.., 2.64 
JO '.2' '.00 3.75 3." 3.36 3.22 3.07 2.92 2.76 2." 
40 3.17 3.64 3.40 3.\, 3.01 2.87 2.73 2.57 2.41 2.2J 
60 3.54 3.31 3.01 2.83 2.69 2.55 2..1 2.~ 2.01 Lit 
120 3.2' 3.02 2.78 2.53 2.40 2.26 2.11 1.95 1.76 1.54 
GO 2,96 2.7' 2.51 2.27 2.13 1.99 1.84 1.66 1.45 1.00 


I.   IS  20 24 30  60  
 10 12  40 120 ~
I 24224 2..26 24630 24816 24MO ~ 151" 15153 15359 2.S46S
2 199.4 199.4 199.4  199.4 199.' 199.' 199.' 199.' 199.' 199.'
3 43.69 43.39 43.01  42.78 41.62 41.47 41.31 41.15 41.99 41.83
4 20.91 20.'70 20."  20.17 20.03 19.89 19.75 19.61 19.47 19.31
, 13.62 13.3' 13.15  11.90 11.7' 11.66 11.53 11.40 11.27 11.14
6 10.2' 10.03 9.11  9.59 9.47 9.36 9.24 9.12 9.00 ....
7 1.3. '.1' 7.97  7.75 7.65 7.53 7.42 7.31 7.19' 7.01
. 7.21 7.01 6.11  6.61 6.50 6.40 6.29 6.1' 6.06 '.tS
9 6.42 6.13 6.03  '.13 '.73 5,62 ",2 '.41 '.30 '.19
10 "." '.66 5,47  '.%7 '.17 '.07 4.97 ...6 4.75 4.64
II '.42 '.24 '.0'  4.86 4.76 4.65 4." 4." 4.M 4.13
12 '.09 4.91 4.72  4.53 4.43 U3 4.13 4.12 4.01 3.90
13 4.82 4.64 4.46  4.%7 4.17 4.07 3.97 3.87 3.76 3.65
14 4.60 4.43 4.2S  4.06 3.96 3.86 3.76 3.66 3.5, 3."
15 4.42 4.15 4.07  3.11 3.79 3.69 3.58 3,4. 3.37 3.26
16 4.27 4.10 3.92  3.73 3.64 3.54 3,44 3.33 3.22 3.11
17 4.14 3.97 3.79  UI 3.'1 3.41 3.31 3.21 3.10 1."
I' 4.03 3.86 3.61  3.50 3.40 3.30 3.20 3.10 1.90 1..,
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29 2.89 2. SO  2.2.1 2.., 2.06 1.99 1.93 1.89 1.16
30 2." 2.49 2.2.1 2.14 2.0, 1.98 1.93 I." 1.1,
40 2." 2.44 2.23 2.09 2.00 1.93 1.81 1.13 1.19
60 2.19 2.39 2.11 2.04 1.9, 1.11 1.12 1.'7'7 1.14
120 2.15 2.3' 2.13 1.99 1.90 1.12 1.'7'7 1.12 1.68
CI) 2.11 2.30 2.08 1.94 1.1, 1.11 1.12 1.61 1.63
Ii it die ..... 01"- 01 ".... i8 ... _.    
? it........ 01-- 01........... 81111 "'I'.    

/, 10 12 " . M . . eo I. 
I 60.19 60.71 61.22 61.74 61.00 61.26 62.53 62.79 6U6 6U3
2 9.39 9.41 9.42 9.44 9.45 9.46 9.47 9.47 9.48 9.49
3 '.23 '.22 '.20 '.1' '.18 '.17 '.16 5.15 '.14 '.13
4 3.92 3.90 3.87 3.14 3.n 3.'2 3.80 3.79 3.11 3.16
, 3.30 3.27 3.204 3.21 3.19 3.17 3.16 3.14 3.12 3.10
6 2.94 2.90 2.81 2.14 2..2 2.80 2.11 2.76 2.74 2.72
7 2.70 2.67 2.63 2.59 2.58 2.56 2.54 2.51 U9 U7
. 2.54 2.50 2.46 2.42 2.40 2.38 2.36 2.34 2.J2 2.29
9 2.42 2.31 2.34 2.30 2.28 2.25 2.21 2.21 2.1. 2.16
10 2.32 2.11 2.i4 2.20 2.1. 2.16 2.13 2.11 2.01 2.06
II 2.25 2.21 2.17 2.12 2.10 2.01 2.05 2.03 2.00 ..,7
12 2.19 2.15 2.10 2.06 2.04 2.01 ..,9 I." 1.93 ..,0
\3 2.14 2.10 2.05 2.01 1.98 I." ..,3 1.90 1.88 1.85
14 2.10 2.05 2.01 I." 1.94 ..,1 1.89 1.86 1.83 1.10'
15 2.06 2.02 1.97 1.92 1.90 1.81 1.85 1.82 1.79 1.76
16 2.03 1.99 1.94 1.89 1.81 1.14 1.11 1.11 1.15 1.72
17 2.00 1.96 1.91 1.86 1.14 1.81 1.11 1.15 1.72 1.69
II 1.9. 1.93 1.89 1.14 1.81 1.11 1.15 1.72 1.69 1.66
19 1.96 1.91 1.86 I." 1.79 1.76 1.73 1.70 1.61 1.63
20 1.94 1.89 1.14 1.79 1.77 1.74 1.71 1.68 1.64 1.61
21 1.92 1.17 1.13 1.78 1.15 1.72 1.69 1.66 1.62 1.59
22 1.90 1.86 1.11 1.76 1.73 1.70 1.61 1.64 1.60 1.5'1
21 1.89 1.84 1.80 1.74 1.72 1.69 1.66 1.62 1.59 I."
24 1.8. 1.13 1.18 1.73 1.10 1.67 1.64 1.61 1.5'1 1.53
25 1.87 1.12 1.77 1.72 1.69 1.66 1.63 1.59 1.56 1.52
26 1.16 1.11 1.76 I. 71 1.68 1.6S 1.61 1.5. 1.54 1.50
27 1.85 1.80 1.75 1.70 1.61 1.64 I.tO 1.57 1.53 1.49
2. 1.14 1.79 1.74 1.69 1.66 1.6J 1.59 1.56 1.52 1.48
29 1.13 1.7' 1.73 1.61 1.6S 1.62 1.58 1.55 1.51 1.47
30 1.12 1.71 1.72 1.61 1.64 1.61 1.57 1.54 1.50 1.46
40 1.76 1.71 1.66 1.61 1.57 1.54 1.51 1.47 1.42 1.31
60 1.71 1.66 1.60 1.54 1.51 1.48 1.44 1.40 1.35 1.29
120 1.65 1.60 ..,5 1.48 U5 1.41 1.J7 1.)2 1.26 1.19
co 1.60 1.55 1.49 1.42 U. 1.34 1.30 1.24 1.17 1.00

   PDaHTD.IS O' 1'111 F ~   
I. .         
  2  4 S 6 1 I t
1 H) 1.50 1.20 1.51 8.82 I.n 9.10 9.19 9.16
2 U7 3.00 3.lS 3.23 3.2. Ul 1.34 US ),)7
3 2.CU UI 2.36 2.39 2041 2042 2.43 2.46 2."
4 1.11 2.00 2.0S 2.06 2.07 2.01 2.08 2.08 2.01
S 1.69 I.IS 1.11 I." 1.89 I." I." I." 1.89
, 1.62 1.76 1.71 1.19 1.19 1.78 1.78 1.78 1.17
7 U7 1.70 1.72 1.12 1.11 1.11 1.70 1.70 1.69
I 1.54 1.66 1.67 1.66 1.66 I. liS  1.64 1.64 1.63
9 UI 1.6% 1.63 1.63 1.62 1.61 1.60 1.60 I."
10 1.49 1.60 1.60 U9 I." 1.51 1.51 1.56 1.56
II 1.41 UI UI U7 1.56 I." 1.54 I.SJ I.SJ
12 1.46 1.56 U6 US 1.54 1.'3 I.S2 1.51 1.'1
JJ 1.4S US US 1.5) I.S2 I.SI I.SO 1.49 I..
14 1.46 U3 U3 1.51 1.51 I. SO  1.49 1.48 1.47
IS 1.43 U2 U2 UI 1.49 1.48 1.41 1.46 1.46
16 1.42 UI UI I. SO  1.48 1.47 1.46 1.46 US
J7 1.42 UI I. SO  1.49 1.47 1.46 US 1.66 1.43
II 1.41 1.30 1.49 1.48 1.46 US 1.66 1.4) 1.42
19 1.41 1.49 1.49 1.41 1.46 . I." 1.43 1.42 1.41
20 1.40 1.49 1.48 1.47 1.45 1.66 1.43 1.42 1.41
21 1.40 1.48 1.48 1.46 I." 1.43 1.42 1.41 I..
22 1.40 1.48 1.47 1.4S I." 1.42 1.41 1.40 I.J'
23 1.39 1.41 1.41 US 1.43 1.42 1.41 1.40 I.Jt
24 1.39 1.41 1.46 1.66 1.4) 1.41 1.40 1.39 1.31
2S 1.39 1.41 1.66 1.66 .1.42 1.41 1.40 1.39 1.3'
26 1.3. 1.46 US 1.66 1.42 1.41 1.J9 1.31 1.37
21 1.31 1.66 US 1.43 1.42 1.40 1.39 1.31 1.37
21 1.31 1.66 I.:S 1.43 1.41 UO 1.39 I.J. 1.37
29 1.31 1.4S I. S 1.43 1.41 1.40 1.31 1.37 1.16
SO 1.31 US I." 1.42 1.41 1.3' 1.3' 1.37 1.16
40 1.36 I." 1.42 1.40 1.39 1.J1 1.36 I.JS 1.34
60 I.3S 1.42 1.41 1.31 1.11 US 1.33 1.32 1.31
120 1.34 1.40 1.J9 1.11 US 1.33 1.11 1.30 1.211
CI) 1.32 1.39 1.37 US 1.33 1.11 1.29 1.21 1.21
r. iI tile num- 0("- o( (/'lldom in tile 11..-101'.    
. ~ .. 811_. fIII:-: fill (I8ioftI - .. ~ IU '--'-.    
 .... fill IIIiI .... ...... willi tiM V- . ~......... r...,., ,.. l .......,
Ird Ed.. Vol. I, TaIMe 11,1"'- LaMoa: .....,"-. 

I. 10 12 .  20 24 30   120 
 IS 40 60 .
I 9.32 9.41 9.49 9.51 9.63 9.61 9.11 9.16 9.10 9.1,
2 3.31 3.39 1.41 1.43 1.43 1.44 1.4, 1.46 1.41 3..
3 2.44 2.4' 2.46 2.46 2.46 2,41 2.47 2.47 2." 2.47
4 2.01 2.01 2.01 2.01 2.01 2.01 2.01 2.01 2.01 2.01
, 1.19 1.19 1.19 I." 1.11 1.11 1.11 1.17 1.17 1.17
6 1.77 1.77 I.,. 1.76 I." I." I." 1.74 1.74 1.14
7 1.69 1.61 1.61 1.67 1.61 1.66 1.66 1.6, 1.6, 1.6,
. 1.63 1.62 1.62 1.61 1.60 1.60 1.59 1.59 1.51 1.51
9 1.59 1.51 1.57 1.56 1.56 I." I." I." 1.53 1.53
10 1.5, I.,. 1.53 1.52 1.'2 1.'1 1.'1 1.50 1.49 1.41
.11 1.S2 1.'1 1.50 1.49 1.49 1.41 J.47 1.47 1.46 J.4,
12 1.50 1.49 1.41 1.47 1.46 1.4, J.4' 1.44 1.43 1.42
\3 1.41 1.47 1.46 1.4, 1.44 J.43 1.42 1.42 1.41 1.40
14 1.46 1.4' 1.44 J.43 1.42 1.41 1.41 1.40 1.39 1.31
IS 1.4' 1.44 1.43 J.41 1.41 1.40 1.J9 1.31 1.37 I.U
16 1.44 1.43 1.41 1.40 1.J9 1.31 1.37 I.U 1.3' 1.14
17 1.43 1.41 1.40 1.39 1.31 1.37 1.36 1.3' 1.14 1.33
II 1.42 1.40 1.39 1.31 1.31 1.36 1.3, 1.14 1.33 1.32
19 1.41 1.40 1.3. 1.37 1.36 1.3, 1.34 1.33 1.32 1.30
20 1.40 1.J9 1.37 1.36 1.3, 1.14 1.33 1.32 1.31 1.29
21 1.39 1.31 1.37 I.U 1.34 1.33 1.32 1.31 1.30 1.21
22 1.39 1.37 1.36 1.14 1.33 1.32 1.31 1.30 1.29 1.21
13. 1.31 1.37 1.3, 1.14 1.33 1.32 1.31 1.30 1.21 1.21
24 1.3' 1.36 1.3' 1.33 1.32 1.31 1.30 1.29 1.21 1.26
2.5 1.37 1.36 1.14 1.33 1.32 1.31 1.29 1.28 1.27 1.2.5
26 1.37 1.3, 1.34 1.32 1.31 1.30 1.29 1.21 1.26 1.2.5
27 1.36 1.3S 1.33 1.32 1.31 1.30 1.28 1.27 1.26 1.24
2. 1.36 1.14 1.33 1.31 1.30 1.29 1.21 1.27 1.2.5 1.24
29 1.3, 1.14 1.32 1.31 1.30 1.29 1.27 1.26 1.2, 1.13
30 1.3, 1.14 1.32 1.30 1.29 1.21 1.27 1.26 1.24 1.13
40 1.33 1.31 1.30 1.21 1.26 1.2' 1.24 1.22 1.21 1.19
60 1.30 1.29 1.27 1.2.5 1.24 1.22 1.21 1.19 1.17 I. IS 
120 1.21 1.26 1.24 1.22 1.21 1.19 1.1. 1.16 1.\3 1.10
QO 1.2.5 1.24 1.22 1.19 1.10 1.16 1.14 1.12 1.01 1.00

Skewness Test
(SOURCE: Remington and Schork,
PaCZHT1Ul or TBI ...w"" tIlT rrA11n1C ~.
Sizl %   SJu%  
_'I (a'>'.M (a,>.... -,.  
" " (II'>'.M (a.>....
25 0.711 1.061 200 0.210 0.403
30 0.662 0.986 2-'0 0.2-'1 0.360
35 0.621 0.923 JOe) 0.230 0.329
40 0.587 0.870 3-'0 0.213 0.305
45 0.558 0.82-' 400 0.200 0.215
-'0 0.534 0.787 4-'0 0.111 0.269
   500 0.179 0.2-'5
60 0.492 0.723 5-'0 0.171 0.2A3
70 0.459 0.673 600 0.163 0.233
80 0.432 0.631 6-'0 0.157 0.224
90 0.409 0.596 700 0.151 0.215
100 0.319 0.567 7-'0 0.146 0..
   100 0.142 0.202
12-' 0.3-'0 0.501 1-'0 0.131 0.196
1-'0 0.321 0.* 900 0.134 0.190
175 0.291 0.430 9-'0 0.130 0.11'
200 0.210 0.403 1000 0.127 0.110
For a full UplaDalioD - See. 8-SoI.  
. T1Ie data of &Ilia 1Ab1, are uU'laed 1ritb tiDd ~ from
su.-,riJuI Tell, {or Slalin~iIIIu. 3rd 4.. Vol. J. able 34. III" B,
1966. LoDdoD: BeDdcy HoUle.   

Kurtosis Test
(SOURCE: Remington and Schork,
 PDaHr1US Of OLUY'S EUaT08l Tal' rrA11n1C,. 
" 1..81 I.... I.... I.... I.... I.."
11 0.6675 0.7153 0.7400 0.1199 0.9073 0.9359
16 0.6829 0.7236 0.7452 0.1133 0.1114 0.9137
21 0.6950 0.7304 0.7495 0.1631 0.1168 0.9001
26 0.7040 0.7360 0.7530 0.8570 0.8616 0.89Q1
31 0.7110 0.7406 0.7559 0.8511 0.1625 0.88:7
36 0.7167 0.74080 0.7513 0.1461 0.1571 0.8769
41 0.7216 0.7470 0.7604 0.1436 0.1540 0.1122
46 0.7256 0.7496 0.7621 0.1409 0.1501 0.1612
51 0.7291 0.7511 0.7636 0.1315 0.1411 0.1641
61 0.7347 0.7554 0.7662 0.1349 0.1434 0.1592
71 0.7393 0.7513 0.7613 0.1321 0.1403 0.1549
II 0.7430 0.7607 0.7700 0.1291 0.1376 0.8515
91 0.7460 0.7626 0.7714 0.1279 0.1353 0.1414
101 0.7417 0.7644 0.7726 0.'264 0.1344 0.1460
201 0.7629 0.7731 0.7796 0.1 171 0.1220 0.1322
301 0.7693 0.7711 0.7821 0.1140 0.1113 0.1260
401 0.7731 0.7807 0.7147 0.1111 0.11S5 0.1213
501 0.7757 0.7825 0.7161 0.1103 0.1136 0.1191
601 0.7776 0.7131 0.7873 0.1092 0.1123 0.1179
701 0.7791 0.7141 0.7871 0.1014 0.1112 0.1164
101 0.7103 0.7157 0.7U5 0.1077 0.1103 0.11S2
901 0.7114 0.7864 0.7890 0.1071 0.1096 0.1142
locn 0.7822 0.7169 0.7194 0.1066 0.1090 0.1134
For. full UpianatiOD - Sec. "~2.    
. Tbe da&a of U1iJ t&ble are &IWK&8d with IWId p8ftIIiIaioG from BiQ_trilul TIIJIIu /0'
SlMWtcial. 3rei Ed.. Vol. I. Table 34. pan A. 1966. LGaOoa: "Ucy H-. 

Coefficients for W Test for Normality
(SOURCE: Anderson and Mclean, 1974)
   Coefficients lan-i-I) (or tne . talt for aOnlAh ty.  
     (or n . 2 (I ) 50    
~  ~ 4  6 7 8 9 10 
1  0.7071 0.7071 0.6872 0.6646 0 6411 0.623~ 0.6052 0.5111 0.5739 
2   .0000 .1677 .241~ .2106 .~031 .~164 .~2U .3291 
3     .0000 .0875 .1401 .1743 .1976 .2141 
4       .0000 .0561 .0~7 .1224 
5         .0000 .031111 
~ 11 12 13 14 15 16 17 II 19 20
1  0.5601 0.5475 0.5~59 0.5251 0.5150 0.5056 0.41168 0.4116 0.4801 O. 4734
2 .3315 . ~325 .~325 .3311 . ~~06 .3290 .~273 .3253 .3232 .3211
3 .2260 .2347 .2412 .2460 .2495 .2521 .2540 .2553 .2561 .2565
4 .1429 .1586 .1707 .1802 .1878 .1939 .1988 .2027 .2059 .2085
5 .0695 .0922 .1099 .1240 .1353 .1447 .1524 .1587 .1641 .1616
6 0.0000 0.0303 O. 05~9 0.0727 0.0880 0.1005 0.1109 0.1197 0.1271 0.1334
7   .0000 .0240 .0433 .0593 .072~ .0837 .0932 .1013
8     .0000 .0196 .0359 .0496 .0612 .0711
9       .0000 .0163 .0303 .0422
10         .0000 .0410
~ 21 22 23 24 25 26 27 21 29 30
 1 0.4643 0.4590 0.4542 0.4493 0.4450 O. 4407 0.4366 0.4328 0.4291 0.4254
 2 .3185 .3156 .3126 .3091 .3069 .3043 .~011 .2992 .2968 .2944
 3 .2578 .2571 .2563 .2554 .2543 .2533 .2522 .2510 .2499 .2487
 4 .21111 .2131 .2139 .2145 .2148 .2151 .2152 .2151 .2150 .2148
 5 .1736 .1764 .1787 .1807 .1822 .1836 .1841 .1857 .1864 .1870
 6 0.1399 0.1443 0.1480 0.1512 0.1539 0.1563 0.1584 0.1601 0.1616 0.1630
 7 .1092 .1l50 .1201 .1245 .1283 .1316 .1346 .1372 .1395 .1415
 8 .0104 .0871 .0941 .0997 .1046 .1089 .1l21 .1162 .1l92 .1219
 9 .0530 .0618 .0696 .0764 .0823 .0876 .01123 .0965 .1002 .1036
10 .0263 .0361 .0459 .0539 .0610 .0672 .0721 .0771 .0822 .0862
11 0.0000 0.0122 0.0228 0.0321 0.0403 0.0476 0.0540 0.0598 0.0650 0.0697
12   .0000 .0107 .0200 .0284 .0351 .0424 .0483 .0537
13     .0000 .0094 .0171 .0253 .0320 .0381
14       .0000 .0014 .0159 .0227
15         .0000 .0076

  Coefficienu {a,,-i-ll for the . teat for DGr8&lity,  
    for II . 2(l)SO ( CI:IIIt.)    
~ 31 32 33 34 35 36 37 38 39 40
1 0.4220 0.4188 0.4156 0.4127 0.4096 0.4068 0.4040 0.4015 0.3989 0.3964
2 .2921 .2898 .2876 .2854 .2834 .2813 .2794 .2774 .2755 .2737
3 .2475 .2463 .2451 .2439 .2427 .2415 .2403 .2391 .2380 .2368
4 .2145 .2141 .2137 .2132 .2127 .2121 .2116 .2110 .2104 .2098
5 .1874 .1878 .1880 .1882 .1883 .1883 .1883 .1881 .1880 .1878
6 0.1641 O. 1651 0.1660 0.1667 0.1673 0.1671 0.1683 0.1686 0.1689 0.1691
7 .1433 .1449 .1463 .1475 .1487 .1496 .1505 .1513 .1520 .1526
8 .1243 .1265 .1284 .1301 .1317 .1331 .1344 .1356 .1366 .1376
9 .1066 .1093 .1118 .1140 .1160 .1179 .1196 .1211 .1225 .1237
10 .0899 .0931 .0961 .0988 .1013 .1036 .1056 .1075 .1092 .1108
11 0.0739 0.0777 0.0812 O. 0844 0.0873 0.0900 0.0924 0.0947 0.0967 0.0986
12 .0585 .0629 .0669 .0706 .0739 .0770. .0798 .0824 .0848 .0870
13 .0435 .0485 .0530 .0572 .0610 .0645 .0677 .0706 .0733 .0759
14 .0289 .0344 .0395 .0441 .0484 .0523 .0559 .0592 .0622 .0651
15 .0144 .0206 .0262 .0314 .0361 .0404 .0444 .0481 .0515 .0546
16 0.0000 0 . 0068 0.0131 0.0187 0.0239 0.0287 0.0331 0.0372 0 . 0409 0.0444
17   .0000 .0062 .0119 .0172 .0220 .0264 .0305 .0343
18     .0000 .0057 .0110 .0158 .0203 .0244
19       .0000 .0053 .0101 .0146
20         .0000 .0049
~ 41 42 43 44 45 46 47 48 49 50
I 0.3~0 0.3917 0.3894 0.3872 O. 3850 0.3830 0 . 3808 0.3789 0.3770 0.3751
2 .2719 .2701 .2684 .2667 .2651 .2635 .2620 .2604 .2589 .2574
3 .2357 .2345 .2334 .2323 .2313 .2302 .2291 .2281 .2271 .2260
4 .2091 .2085 .2078 .2072 .2065 .2058 .2052 .2045 .2038 .2032
5 .1876 .1874 .1871 .1868 .1865 .1862 .1859 .1855 .1851 .1847
6 0.1693 O. 1694 O. 1695 O. 1695 0.1695 O. 1695 O. 1695 0.1693 0.1692 0.1691
7 .1531 .1535 .1539 .1542 .1545 .1548 .1550 .1551 .1553 .1554
8 .1384 .1392 .1398 .1405 .1410 .1415 .1420 .1423 .1427 .1430
9 .1249 .1259 .1269 .1278 .1286 .1293 .1300 .1306 .1312 .1317
10 .1123 .1136 .1149 .1160 .1170 .1180 .1189 .1197 .1205 .1212
11 O. 1004 O. 1020 O. 1035 0.1049 0.1062 0.1073 0.1085 0.1095 O. 1105 0.1113
12 .0891 .0909 .0927 .0943 .0959 .0972 .0986 .0998 .1010 .1020
13 .0782 .0804 .0824 .0842 .0860 .0876 .0892 .0906 .0919 .0932
14 .0677 .0701 .0724 .0745 .0765 .0783 .0801 .0817 .0832 .0146
15 .0575 .0602 .0628 .0651 .0673 .0694 .0713 .0731 .0748 .0764
16 0.0476 0.0506 0.0534 0.0560 0.0584 0.0607 0.0628 0.0648 0.0667 0.0685
17 .0379 .0411 .0442 .0471 .0491 .0522 .0546 .0568 .0588 .0608
18 .0283 .0318 .0352 .0383 .0412 .0439 .0465 .0489 .0511 .0532
19 .0188 .0221 .0263 .0296 .0328 .0357 .0385 .0411 .0436 .0459
20 .0094 .0136 .0115 .0211 .0245 .0277 .0307 .0335 .0361 .0386
21 O. 0000 0.0045 0.0087 0.0126 0.0163 0.0197 0.0229 0.0259 0.0288 0.0314
22   .0000 .0~2 .0081 .0118 .0153 .0185 .0215 .0244
23     .0000 .0039 .0076 .0111 .0143 .0174
24       .0000 .0037 .0011 .0104
25         .0000 .0035

W Test Percentage Points
(SOURCE: Anderson and Mclean, 1974)
  'ft'~_u,. poiDti of tlw . tut for II . $(1) SO  
n 0.01 0.02 0.05 0.10 0.50 0.90 0.95 0.98 0.99
 0.753 0.756 0.767 0.789 0.959 0.998 0.999 1.000 1. 000
 .687 .707 .748 .792 .935 .987 .912 .996 .997
 .686 .715 .762 .806 .927 .979 .986. .991 .993
6 0.713 0.743 0.788 0.826 0.927 0.974 0.981 0.986 0.989
7 .:30 .760 .803 .838 .928 .972 .971 .985 .988
8 .a9 .778 .818 .851 .932 .972 .978 .'.'/84 .987
9 .764 .791 .829 .859 .935 .972 .978 .984 .986
10 .781 .806 .842 .869 .938 .972 .978 .983 .986
11 0.792 0.817 0.850 0.876 0.940 0.973 0.171 0.984 0.986
12 .805 .828 .859 .883 .943 .973 .979 .984 .986
13 .814 .837 .866 .889 .945 .974 .971 .984 .986
14 .825 .146 .87C .895 .9C7 .975 .980 .984 .986
15 .835 .855 .881 .901 .950 .975 .980 .984 .987
16 0.844 0.863 0.887 0.906 0.952 0.976 0.981 0.985 0.987
17 .851 .869 .892 .910 .954 .977 .981 .985 .987
18 .858 .874 .897 .914 .956 .978 .982 .986 .988
19 .863 .879 .901 .917 .957 .978 .982 .986 .988
20 .868 .884 .905 .920 .9511 .11711 .983 .986 .988
21 0.873 0.888 0.908 0.923 0.1160 0.1180 0.1183 0.987 0.1181
22 .878 . &!I2 .911 .926 .961 .980 .984 .987 .989
23 .881 .895 .914 .928 .962 .1181 .984 .987 .989
24 . sac  .8118 .916 .930 .963 .981 .984 .987 .981
25 .888 .1101 .918 .931 .964 .981 .985 .1188 .981
26 0.891 0.1104 0.920 0.1133 0.1165 0.1182 0.985 0.188 0.989
27 .894 .906 .923 .935 .965 .982 .985 .988 .990
28 .896 .908 .924 .1136 .1166 .982 .985 .988 .990
29 .&!I8 .910 .926 .937 .966 .982 .1185 .988 .990
30 .900 .912 .927 .931 .967 .983 .985 .988 .900
31 0.902 0.914 0.11211 0.940 0.1167 0.1183 0.986 0.1188 0.11110
32 .1104 .915 .930 .941 .968 .983 .986 .1188 .990
33 .906 .917 .931 .1142 .968 .983 .986 .9811 .9110
34 .908 .9111 .lIn .943 .961 .983 .986 .1189 .990
35 .910 .920 .1134 .94' . .969 .984 .986 .989 .990
36 0.1112 0.922 0 . U5 0.945 0.170 0.184 0.986 0.989 0.990
37 .91C .112' .936 .946 .970 .984 .987 .11811 .990
38 .916 .925 .938 .947 .971 .984 .987 .9811 .990'
311 .917 .927 .931 .9ea .971 .984 .987 .989 .991
40 .919 . 928 .940 .949 .$72 .985 .987 .989 .991
cl 0.920 0.929 0.941 0.950 0.972 0.985 0.987 0.989 0.991
42 .922 .930 .942 .951 .972 .985 .987 .989 .991
43 .923 .932 .943 .951 .973 .985 .987 .9110 .991
C4 .924 .933 .94' .952 .973 .985 .187 .990 .991
C5 .926 .934 .945 .953 .973 .1185 .988 .9110 .9111
C6 0.927 0.935 0.1145 0.1153 0.974 0.185 0.988 0.910 0.991
47 .928 .936 .1146 .154 .974 .985 .1188 .910 .991
48 .921 .937 .947 .954 .97' .1185 .188 .990 .9111
C9 .929 .937 .947 .955 .974 .985 .988 .9110 .991
SO .930 .938 .9.7 .955 .974 .985 .988 .9110 .9111

Noncentral t-Distribution
(SOURCE: Winer, 1971)
M .J t DIiI6"""" t .
VaJues of the oo......dttaJity paruIIIICer for a oaeliMd teIt with II - .050
    p - type 2 error     
 .01 .0.5 .10 .20 .30 .40 ..50 .60 .70 .80 .90
1 16.47 12..53 10..51 8.19 6.63 .5.38 4.31 3.3.5 2.46 1.60 .64
2 6.88 .5..52 4.81 3.98 3.40 2.92 2.49 2.07 1.63 1.1.5 ..50
3 .5.47 4.46 3.93 3.30 2.8.5 2.48 2.13 1.79 U3 1.02 .46
4 4.9.5 4.07 3.60 3.04 2.64 2.30 1.99 1.67 1.34 .96 .43
.5 4.70 3.87 3.43 2.90 2..53 2.21 1.91 1.61 1.29 .92 .42
6 4.5.5 3.7.5 3.33 2.82 2.46 2.1.5 1.86 U7 1.26 .90 .41
7 4.4.5 3.67 3.26 2.77 2.41 2.11 1.82 1..54 1.24 .89 .40
8 4.38 3.62 3.21 2.73 2.38 2.08 1.80 U2 1.22 .88 .40
9 4.32 3..58 3.18 2.70 2.3.5 2.06 1.78 Ul 1.21 .87 .39
10 4.28 3..54 3.1.5 2.67 2.33 2.04 1.77 1.49 1.20 .86 .39
11 4.2.5 3.52 3.13 2.6.5 2.31 2.02 1.7.5 1.48 1.19 .86 .39
12 4.22 3.50 3.11 2.64 2.30 2.01 1.74 1.47 1.19 .8.5 .38
13 4.20 3.48 3.09 2.63 2.29 2.00 1.74 1.47 1.18 .8.5 .38
14 4.18 3.46 3.08 2.62 2.28 2.00 1.73 1.46 1.18 .84 .38
1.5 4.17 3.4.5 3.07 2.61 2.27 1.99 1.72 1.46 1.17 .84 .38
16 4.16 3.44 3.06 2.60 2.27 1.98 1.72 1.4.5 1.17 .84 .38
17 4.14 3.43 3.0.5 2..59 2.26 1.98 1.71 1.45 1.17 .84 .38
18 4.13 3.42 3.04 2..59 2.26 1.97 1.71 1.4.5 1.16 .83 .38
19 4.12 3.41 3.04 2..58 2.25 1.97 1.71 1.44 1.16 .83 .38
20 4.12 3.41 3.03 2..58 2.25 1.97 1.70 1.44 1.16 .83 .38
21 4.11 3.40 3.03 2..57 2.24 1.96 1.70 1.44 1.16 .83 .38
22 4.10 3.40 3.02 2..57 2.24 1.96 1.70 1.44 1.16 .83 .37
23 4.10 3.39 3.02 2..56 2.24 1.96 1.69 1.43 1.1.5 .83 .37
24' 4.09 3.39 3.01 2..56 2.23 1.9.5 1.69 1.43 1.1.5 .83 .37
2.5 4.09 3.38 3.01 2..56 2.23 1.9.5 1.69 1.43 1.1.5 .83 .37
26 4.08 3.38 3.01 2..5.5 2.23 1.9.5 1.69 1.43 1.1.5 .82 .37
27 4.08 3.38 3.00 2..5.5 2.23 1.9.5 1.69 1.43 1.1.5 .82 .37
28 4.07 3.37 3.00 2..5.5 2.22 1.9.5 1.69 1.43 1.1.5 .82 .37
29 4.07 3.37 3.00 2..5.5 2.22 1.94 1.68 1.42 1.1.5 .82 .37
30 4.07 3:37 3.00 2.54 2.22 1.94 1.68 1.42 1.1.5 .82 .37
40 4.04 3.3.5 2.98 2..53 2.21 1.93 1.67 1.42 1.14 .82 .37
60 4.02 3.33 2.96 2.,52 2.19 1.92 1.66 1.41 1.13 .81 .37
100 4.00 3.31 2.9.5 2..50 2.18 1.91 1.66 1.40 1.13 .81 .37
GO 3.97 3.29 2.93 2.49 2.17 1.90 1.64 1.39 1.12 .80 .36
Pr (DoDcanral t > tl_1 6 - (,ul - PtX Vft/CJ)] - 1 - p.

t Tbjs table is reproduced from: The power of StudeDt's t test. JOIITNII o{ tM
AnIII"iaIn StGtistical A#ociGtiDlI, 196.5, 60, 32~333, with the permission of the author,
D. B. OweD. aud the editon.

 VaJues of the aoocenU'lJjty parameter for a ODHided test with II - .025 
f    P - type 2 error     
 .01 .05 .10 .20 .30 .40 .50 .60 .70 .80 .90
1 32.83 24.98 20.96 16.33 13.21 10.73 8.60 6.68 4.91 3.22 ua
2 9.67 7.77 6.80 H5 4.86 4.21 3.63 3.07 2.50 1.88 1.09
3 6.88 5.65 5.01 4.26 3.72 3.28 2.87 2.47 2.05 U7 .94
4 5.94 4.93 4.40 3.76 3.31 2.93' 2.58 2.23 1.86 1.44 .87
5 5.49 4.57 4.09 3.51 3.10 2.75 2.43 2.11 1.76 1.37 .82
6 5.22 4.37 3.91 3.37 2.98 2.64 2.34 2.03 1.70 1.32 .80
7 5.06 4.23 3.80 3.27 2.89 2.57 2.27 1.98 1.66 1.29 .78
8 4.94 4.14 3.71 3.20 2.83 2.52 2.23 1.94 1.63 1.27 .77
9 4.85 4.07 3.65 3.15 2.79 2.48 2.20 1.91 1.60 1.25 .76
10 4.78 4.01 3.60 3.11 2.15 2.45 2.17 1.89 U9 1.23 .75
11 4.73 3.97 3.57 3.08 2.73 2.43 2.15 1.87 U7 1.22 .74
12 4.69 3.93 3,54 3.05 2.70 2.41 2.13 1.85 U6 1.21 .74
13 4.65 3.91 3.51 3.03 2.69 2.39 2.12 1.84 U5 1.21 .73
14 4.62 3.88 3.49 3.01 2.67 2.38 2.11 1.83 U4 1.20 .73
15 4.60 3.86 3.47 3.00 2.66 2.37 2.09 1.82 U3 1.19 .72
16 4.58 3.84 3.46 2.98 2.65 2.36 2.09 1.81 U3 1.19 .72
17 4.56 3.83 3.44 2.97 2.64 2.35 2.08 1.81 U2 1.18 .72
18 4.54 3.82 3.43 2.96 2.63 2.34 2.07 1.80 U2 1.18 .72
19 4.52 3.80 3.42 2.95 2.61 2.33 2.06 1.80 Ul 1.17 .71
20 4.51 3.79 3.41 2.95 2.61 2.33 2.06 1.79 Ul 1.17 .71
21 4.50 3.78 3.40 2.93 2.60 2.32 2.05 1.79 1.50 1.17 .71
22 4.49 3.77 3.39 2.93 2.60 2.32 2.05 1.78 1.50 1.17 .71
23 4.48 3.77 3.39 2.93 2.59 2.31 2.05 1.78 1.50 1.17 .71
24 4.47 3.76 3.38 2.92 2.59 2.31 2.04 1.78 1.50 1.16 .71
25 4.46 3.75 3.37 2.92 2.58 2.30 2.04 1.77 1.49 1.16 .71
26 4.46 3.75 3.37 2.92 2.58 2.30 2.04 1.77 1.49 1.16 .70
27 4.45 3.74 3.36 2.91 2..58 2.30 2.03 1.77 1.49 1.16 .70
28 4.44 3.73 3.36 2.90 2.57 2.29 '2.03 1.77 1.49 1.16 .70
29 4.44 3.73 3.35 2.90 2.57 2.29 2.03 1.77 1.48 1.16 .70
30 4.43 3.73 3.35 2.90 2.57 2.29 2.02 1.76 1.48 1.16 .70
40 4.39 3.69 3.32 2.87 2.5.5 2.27 2.01 1.75 1.47 1.15 .69
60 4.36 3.66 3.29 2.8.5 2..53 2.2.5 1.99 1.73 1.46 1.14 .69
100 4.33 3.64 3.27 2.83 2..51 2.23 1.98 1.73 1.45 1.12 .68
co 4.29 3.60 3.24 2.80 2.48 2.21 1.96 1.71 1.44 1.12 .68
  Pr [aoac:cntraJ , > '1_1 6 - (PI - J;)( vii/o)] - 1 - p.  

( COlllilulMf)
VaJues of the DODCeDuality paramcser fOf. 0I1ided tat with . - .010
f      p .. type 2 elTOf    
  .01 .05 .10 .20 .30 .40 .50 .60 .70 .80 .90
1  82.00 62.40 52.37 40.80 33.00 26.79 21.47 16.69 12.27 8.07 ".00
2  15.22 12.26 10.74 8.96 7.73 6.73 5.83 4.98 4.12 3.20 2.08
3  9.34 7.71 6.86 H7 .5.17 4.59 4.07 3..56 3.03 2.44 1.66
4  7..52 6.28 5.64 4.88 4.34 3.88 3.47 3.06 2.63 2.14 1.48
.5  6.68 5.62 5.07 4.40 3.93 3.54 3.17 2.81 2.42 1.98 1.38
6  6.21 .5.2.5 4.74 4.13 3.70 3.33 2.99 2.66 2.30 1.88 1.32
7  .5.91 5.01 4.53 3.96 3.SS 3.20 2.88 2..56 2.22 1.82 1.27
8  5.71 4.8.5 4.39 3.84 3.44 3.11 2.80 2.49 2.16 1.77 1.24
9  5.56 4.72 4.28 3.75 3.37 3.04 2.74 2.43 2.11 1.74 1.22
10  5.45 4.63 4.20 3.68 3.31 2.99 2.69 2.39 2.08 1.71 1.20
11  5.36 4.56 4.14 3.63 3.26 2.94 2.65 2.36 2.0.5 1.69 1.18
12  5.29 4.50 4.09 3.58 3.22 2.91 2.62 2.33 2.03 1.67 1.17
13  5.23 4.46 4.04 3.55 3.19 2.88 2.60 2.31 2.01 1.6.5 1.16
14  .5.18 4.42 4.01 3.51 3.16 2.86 2.51 2.29 1.99 1.64 I.U
15  5.14 4.38 3.98 3.49 3.14 2.84 2..56 2.28 1.98 1.63 1.14
16  5.11 4.35 3.95 3.47 3.12 2.82 2.54 2.26 1.97 1.62 1.14
17  5.08 4.33 3.93 3.45 3.10 2.80 2..53 2.15 1.96 1.61 1.13
18  5.05 4.31 3.91 3.43 3.09 2.79 2..52 2.24 1.9.5 1.60 1.13
19  .5.03 4.29 3.89 3.42 3.07 2.78 2..50 2.23 1.94 1.60 1.12
20  .5.01 4.27 3.88 3.40 3.06 2.77 2..50 2.22 1.93 1.S9 1.12
21  4.99 4.2.5 3.86 3.39 3.05 2.76 2.49 2.22 1.92 1.S9. 1.11
22  4.97 4.24 3.8.5 3.38 3.04 2.7.5 2.48 2.21 1.92 1.S8 1.11
23  4.96 4.23 3.84 3.37 3.03 2.74 2.47 2.20 1.91 1.S8 1.11
24  4.94 4.22 3.83 3.36 3.02 2.73 2.47 2.20 1.91 1.S7 1.11
25  4.93 4.20 3.82 3.3.5 3.02 2.73 2.46 2.19 1.90 1.S7 1.10
26  4.92 4.19 3.81 3.34 3.01 2.72 2.4.5 2.19 1.90 1.S7 1.10
27  4.91 4.19 3.80 3.34 3.00 2.72 2.4.5 2.18 1.90 1.S6 1.10
28 I 4.90 4.18 3.79 3.33 3.00 2.71 2.44 2.18 1.89 1.S6 1.10
29  4.89 4.17 3.79 3.32 2.99 2.71 2.44 2.17 1.89 1.S6 1.10
30  4.88 4.16 3.78 3.32 2.99 2.70 2.44 2.17 1.89 1.S.5 1.09
40  4.82 4.11 3.74 3.28 2.9.5 2.67 2.41 2.1.5 1.86 1.S4 1.08
60  4.76 4.06 3.69 3.24 2.92 2.64 2.38 2.12 1.84 1.S2 1.07
100  4.72 4.03 3.66 3.21 2.89 2.62 2.36 2.10 1.83 1.S1 1.06
ac  4.65 3.97 3.61 3.17 2.8.5 2..58 2.33 2.07 1.80 1.48 1.04
   Pr [DODCeDtra11 > '1_1 " - (P1 - JAiA v;;/a)] ... 1 - p.  

population Correlation Coefficient
(SOURCE: Remington and Schork, 1970)
c:a.un I'Oa CCMPV11NO c::cNnDCNa utGn JIOa 1111
POP\J1..A nON COU!L\ nON CD!P?IC!N1' p
CONJ'ID!NQ I.VU. 95%8 .
... -.. -4 -., -4 -1 -.
-.. -of -.
. ... ... ...
... .4
..                          - .. ... .... ....
.   ,  I I  ......,.-  . 1 1 i I  ,          
     '...-r   ;     I         ;;..   ~    
.   ..   I   l   ....-r       ..-1'         
   A     '..,.....   ...r     ..-1'          
...         '  .~, !..;               
   1 1   i I.A"; /                 
    ,   '/I   f'Y                 
         fi ,I  I         r/     AI, 
.   J     .II '/1 ' :/                " 
   I     1/1   /"    1/            M 
...   I  I   /1 iY',/    ; 1            
 ,     "   /."    1 ,/   ,    1/      
. !       1/1 ,/i '7      1 ,/    1/     'I ,'I 
 ;   I    II /i /i   A  !          
.  I      l/i /. V    ,   1/          
        ,(  l/i vi    :..             
.         II ,/1 l'                 
     I   I I II "  1               
       !/I   /,              ,     
        ,  /, ;                  
..       I    I 0/1                 
.          I         I           
 'III            I I              
...               ' ,              
             , J.        I.".       
  1/\           VV               
               I        V       
       ~        ....             
.                         '     
.  -.. -    -        - .  -  .         
.. ...
.. ... -
.. ... ... ..
... ... .. .. .. .,.-"
..... III r C88pI8 ......... ....-...,
. The data of this table are auaaed with killd pennissioa from 8It1-trUuI TGb/~1 {o,
St.,inicilllu. 3rd Ed.. Vol. I. Table 15. 1966. LoacIDa: Beauey Hollie.

CllAaTi I'OIt 00MI'VnNQ CXMIIDDO lAWn I'OIt 'nil
... -4 ...
.., -..
... ... .... .. .4 ... ... ...
-~ -
-. -
. ..
..     I           +
.                .
       1..0     ""[;.0    .
.0                .
.~1            [/    +
      1/1..   ''''  "rr ~  
       ,;   !V I.  .
   i/  "   I  
 I I "I -yo          
....         -.r       
-0    '" I./.          
      ~   ....    .....   
        I L.-i-    I I I 
-             I r  
         I   I  I  
-.. -4 .. -..
.., ..
... ... .of
... ... ...
.... ~ ..,
... fII. (...,.. ....... ......-.,
. Th. cWa O( this table an ntracud with ItiDd pmniuioa (rom BilI~iJc. Tull, for
SllIIiIticiMI. 3rd Ed., Vol. I. Tabl. .,. 1966. Lo~Gva; Beouey HOllie.

Transformation of Linearization
(SOURCE: Ponce, 1980a)
Table 39. Transformations of linearization of different functions (after
Chow, 1967),
T),.. ., t.........
:-.,,.....~.... C'aI8I'tII.....
A~ j ,,....
~.. 1_"'"
I' . . . ... '  .  1,1 - . .. 'I..
I'."" .  I." II", " . .... + c.... .".1
,..; lot.  18., ~.. .. . ..... + ..... ..
, . .. . It. . .....   ~ ['-to]
. -"  - -., + 11- .. .,1(. - l1li1
,   , - .. . - ...
I'.."'~/' II.  ,  WI . . + "./..
I' . "18 + ..' .  'I, 1./,, - . + 'I..
, , . .'., + ...., '  I', 111,1 - '''.1 + C.,.""
i ' . r + .... .  ....:! lee ~ 1 - ... let. + c.... .....
I , . r +... lei'  '''':! '''!!] - ... I.' + If - II~ II
,    ~. ~.
j'.f.-.!-   ' -.. '-"J .-.. ,
. - r.    - - --.-1.--
I . -.  I ' -.. ,-.. ,-to ,-to
I,... ~  . -.. ~ -1.+_+~1rI
' -
. ....  , -.. ,-to'.
 . I   -
II .... ~~ J - ........ .. c.... ..111
" - ...., - ~ '+ ....
[~l- ...[f1e8'I(\"'."l+I188.I1r1
u' fIe8 II .
II I,. ~ . t. . ....
II !,. """., .h..... . ..
lot ,::na. ,I
I'" , - .'''''1 . lee ~ + f1e8 .....

[~:,] - -... ..... + ,,we + ..~., [~:' ]
1..-'" - ~ + Wo'.-.,
;~] . -.... - c.-.a... II ~.. [It,:']

!!::: 1 . ~ + .....;. ..1
....... I. t)'... 14 .Rd 1~. ,I. ..... ~ ft.. ... --Uft ...- ,. .. .....-. ~
'f I,. .". .. 'W"'.

II I, - '''f~ "..., . , ..ft ...

Multiple Regression Example - Hand Calculated
(SOURCE: Ponce, 1980a)
The mechanics of the least squares determination of the multiple
regression line are outlined using an illustrated example.
presented here has been taken directly from Freese. 1967.
(The example
1 tis i nc 1 uded
with only minor modification because 1 feel it presents the concept in a
very clear and concise manner.) Consider the data presented in Table
37. With this data we would like to fit an equation of the form
Y = a + b1X1 + b2X2 + b3X3

Table 37. Data for the example illustrating the least squares
determination of the multiple regression line (after Freese, 1967).
 y Xl Xz X3
 65 41 79 75
 7~. 90 48 R3
 8~ ,1 67 74
 50 42 52 61
 55 57 52 59
 59 32 82 73
 82 71 80 72
 66 60 65 66
 113 98 96 99
 86 80 81 90
 104 101 78 86
 92 100 59 88
 96 84 84 93
 65 72 48 70
 81 55 93 85
 77 77 68. 71
 83 98 51 84
 97 95 82 81
 90 90 70 78
 87 93 61 89
 74 45 96 81
 70 ' 50 80 77
 75 60 76 70
 75 68 74 76
 93 75 96 85
 76 82 58 80
 71 72 58 68
 61 46 69 65
Sums 2,206 1,987 2,003 2,179
Means 78.7857 70.9643 71.5357 77.8214
(n . 28)    

According to the principle of least squares, the best estimates of the
lib" coefficients can be obtained by solving the set of least squares nonnal
equat ions.
b, equation: (txf)b, + (tx,XI)b, + (I:x,x,)b, = I:x, Y
b, equation: (I:x,x.)b, + (txl)b, + (I:x1x,)b, = I:XIY
b, equation: (I:x,x,)b, + (tx1x')b, +
(I:xl)b, = I:x,y
,.. -,.." y - (I:XtXI:X~
",x,x, - 8J\"'1 n
The corrected sums of s qllares and products are computed; n the
famil i ar manner:
I:yl = I:Y. - (I:Y)' = (652 + ... + 611) - (~)2 = 5,974.7143
n .
I:x' = tX, - (t~,)2 = (41. + ... + oW) - (1:7)2 = 11,436.9643
tx,y = I:X,Y - (tX,~(I:Y) = (41)(65). + .. . + (46)(61) - (1,98~2.206) = 6,428.7858
S imil arly,
tx,xz = -1,171.4642
I:x,x, = 3,458.8215
I:xl = 5,998.9643
tx.x, = 1,789.6786
tXIY = 2,632.2143
txl = 2.806.1072

tx,y = 3.327.9286

Putting these values in the nonmal
equations gives:
11,436.9643bl - 1,171.4642b2 + 3,458.8215b3 . 6,428.7858

- 1,171.4642bl + 5,998.9643b2 + 1,789.6786b3 = 2,632.2143

3,458.8215bl + 1,789.6786b2 + 2,606.1072b3 = 3,327.9286

These equations can be solved by any of the standard procedures for
simultaneous equations. One approach is as follows:

Divide through each equation by the numerical coefficient of
bi - 0.102.427.897b2 + O.302.424.788b3 = -0.562.105.960
b1 - 5.120.911.334b2 - 1.527.727,949b3 = -2.246,943.867
b1 + 0.517.424.389b2 + O.753,466,809b3 = 0.962,156,792
Su~tract the second equation from the first and the third from
the first so as to leave two equations in b2 and b3.
5..018.483.437b2 + 1.830,152,737b3 = 2.809,049.827
-O.~19,eS2.:~~~: . 0.4S1,042,021b3 = -0.40~.OSO,832
Divide through each equation by the numerical coefficient of
b2 + 0.364.682,430b3 = 0.559,740,779
b2 + 0.727,660,494b3 = 0.645,397,042
Subtract the second of these equations from the first, leaving
one equation in b3.
-O.362.978,064b3 = -0.085,656,263
So lve for b3.

b3 = -0.085,656,263 = 0.235,981,927
Substitute this value of b3 in one of the equations (say the
first) of step 3 and solve for b2.
b2 + (0.364,682,430)(0.235,981,927) . 0.559,740,779
b = 0.473,682,316
Substitute the solutions for b2 and b3 in one of the
equations (say the first) of step 1, and solve for b1.
b1 - (0.102,427,897)(0.473,682,316) + (0.302,424,788)(0.235,981,927)
= 0.562,105,960

bl = 0.539,257,459
8. As a check. add up the original normal equations and substitute
the solutions for bl. b2 and b3'
13.724.3216b1 = 6,617.1787b2 + 7,854.6073b3 = 12,388.9287
12,388.92869 = 12,388.9287. check.
Given the values of bl. b2' and b3 we can now compute
a = Y-b,X,-b,X2-t),X, = -11.7320
Thus. after rounding of the coefficients, the regression equation is
y = -11.jJ~ ~ U.~39 Xl + 0.474 A2 + O.~3n X3
It should be noted that in solving the normal equations more digits have
been carried than would be justified by the rules for number of significant
digits. Unless this is done. the rounding errors may make it difficult to
check the computations.
11.3.3 Testing the Significance of the Multiple Regression Line
At this pOint in our regression analysis we should ask, "How well does
the regression line fit the data?" The analysis of variance procedure to
be used here is similar to that outlined for the significance test of the
simple linear regression line.
However, in this case the degrees of
freedom for the reduction are equal to the number of independent variables
fitted. The reduction sum of squares for any least squares regression can
be found using the general equation:

SSreg = (est. coefficients)(right side of their respective
normal equations)
Therefore, for Freese's example
SSIeQ = b,(tx,y) + bz(I:x2y) + b,(tx2Y)
The anova table for the test of significance is as follows in. Table 38:

Table 38. ANOVA results for the test of significance of the multiple
regression developed from the data given in Table 36 (after Freese. 1967).
Reduction due to Xl. X2~ and X3 . . . 3
Residuals. . . . . . . . . . . . . . 24
Total. .
. . . . . . . . .
. . . . . 27
To test the significance of
the regression we compute Fs where
F - ked~ttion MS
s -
Residual M5
For the case at hand Fs = 92.46. which is significant at the 0.01 level.
In some instances we would like to know the contribution each
independent variable makes in the prediction of the dependent variable. In
other words, what portion of the total 55 can be attributed to each
individual independent variable. The statistical method to use for this
type of analysis is stepwise regression. The procedures for stepwise
regression are not outlined here, but can be found in any good statistics
11.3.4 Coefficient of Multiple Determination
The coefficient of multiple determination is calculated in the same
manner as that for the simple linear regression.
(54 )
For our illustrative example, r2 = 0.92, which means 92 percent of
the variation in Y is associated with the regression.

Multiple Regression Example - Computerized
(SOURCE: Gaugush, 1986)
Multiple regrellion
173. The concepts applicable to simple linear regression extend
to multiple regression. The purpose is still to quantify a relation8b1p
between a dependent response variable and eome independent variable.
However. in multiple regreesion there is more than one independent
variable. Since there may exist interrelationships between the
eo-called independent variables. the regreseion coefficients for the
dependent variables from a multiple regression are not the same ae would
be obtained if the dependent variable wae regressed on each independent
variable eeparately.
174. The formulas for a multiple regression will not be derived
in this manual. For simple two-factor (i.e., two independent variable.)
multiple regrelsion, formulas are available in some textbooks, but broad
application of multiple regrelsions requirel matrix algebra. We will
presume that the calculations will be done on 8 computer and shall
therefore concentrate on the interpretation of computer output. Com-
puter table and graphic output presented in this chapter were obtained
from SAS procedure GLM (SAS (1981) GRAPH User's Guide; SAS (1982) User's
175. An example of multiple regression data i5 given in Table 10.
These data represent levels of a pollutant measured a~ various distances
downstream fro~ a Sw~rt:. ~~ poll~~~~: ~c:re3~t~ ~1th di~t~~~! fr~
the source of pollution, but additional factors are expected to
influence the reeults of measurements taken on different occalions.
Therefore, two other independent variables have been included in the
multiple regression--temperature and discharge. The model is then
Yi . a + 81X1i + 82X21 + 83X21 + &1

  Table 10   
 Hypothetical Data for Multiple Regression Example 
Observation Pollutant Distance, m Te1lq)erature, 0c 3
m /aec
1 15.5 1,000 24  0.8
2 12.9 1,000 20 .  1.0
3 14.8 1,000 19  1.3
4 10.3 1,000 25  1.8
5 10.7 1,000 15  2.0
6 14.9 2,000 17  0.5
7 6.6 2,000 20  1.0
8 9.5 3,000 21  1.0
9 5.1 3,OJU 15  2.0
10 7.(, 4,UOU 15  0.5
11 11.9 4,000 24  0.8
12 5.4 4,000 21  1.0
where Xl' X2' and X3
charge, respectively.
176. Examination of the computer output (Table 11) will illu-
.trate several concepts. The output first indicates that the analysis
vas performed on a dependent variable called POLLUTNT. The sources of
variation are listed as MODEL and ERROR, which will sum to the CORRECTED
TOTAL (. ty2) as before. Note that the model now has 3 d.f., one for
refer to distance, temperature, and dis-
each of the independent variables.
Since there vere 12 observations,
the CORRECTED TOTAL carries 11 d.!., one being lost when the variables
are adjusted about their means. Three degrees of freedom were required
for the three variables in the model, le~v~n! eight as a mea.ure of ran-
dom error. The computer provides calculations of the sum of squares for
aach source, and the corresponding mean square. AD P test is calculated
for the mean square of the model, using the m.an .quare error. Par the
Ixample in Table 11, the F test indicates that the regression dais
v .

Iccount for a significant portion of the total variation. This Ftl.t '
i. a joint test of all three of the independent variables and does not
indicate which one(s) contribute significantly to the dlscription of

   Table 11  
Computer Output for Multiple Regression Example 
 (General Linear Model Procedure) 
MODEL 3 97.73161461 32.57720487 4.84
ERROR 8 53.82505206 6.72813151 PR > P
CORRECTED TOTAL 11 151.55666667  0.0331
0.644852 24.9011 2.59386420  10.41666667
DISTANCE 1 54.19739726 8.06 0.0219
TEMP 1 7.19969359 1.07 0.3312
DISCHARG 1 36.33452376 5.40 0.0486
DISTANCE 1 77.32993941 H.9 0.0095
TEMP 1 1.69303058 0.25 0.6294
DISCHARG 1 36.33452376 5.40 0.0486
INTERCEPT 17.59409833 3.02 0.0166 5.82622109
DISTANCE -0.00225161 -3.39 0.0095 0.00066415
TEMP 0.11241376 0.50 0.6294 0.22409610
DISCHARG -3.78579922 -2.32 0.0486 1.62909000

177. That portion accounted for by the 80del 1. liven by the r2
value, which is the ratio of the MODEL sum of squares (- IjbjIi(Xj)2,
the bj being the estimate of the Bj) to the CORRECTED TOTAL sum of
squares (IYi)' Thus 65.49 percent of the variation va. accounte~ for by
the model. There are several important points to be made about the.e
calculations. Usual practice is to adjust about the mean (i.e., to fit
an intercept not necessarily equal to zero), but there are S088 excep-
tions. An option in the computer algorithm vill provide results not
adjusted about the means, but the r value then does not have the s...
178. Following the synopsis of t~. mo~el are the resuJtR of the
il'dividual i..dtsp_ndent variables rOt the regreuion. M before, tvo
types of sums of squares are 'provided, but in the case of multiple
regression they differ. They are the "sequential S\D18 of squares" or,
in the jargon of SAS GLK, Type I SS, and partial suma of squares or
Type III 55.
179. The sequential sums of squares are commonly, but not neces-
sarily, larger than the corresponding partial sums of squares; indeed,
Table 11 provides an example of a case where one partial sum of squares
is larger. The sequential suma of squares depend on the order in which
they were entered into the computer program. Here distance was entered
first. and on its own accounted for 54.1974 of the sum of squares car-
ried by the model. This is exactly the same as vould be obtained if a
simple linear regression vas done for POLLUTNT on DISTANCE, with no
other variables in the model. TEMP was the second variable entered into
the model, so the variable POLLUTNT was already adjusted for DISTANCE
when TEMP wa. entered. A model containing DISTANCE and TEMP carries a
sum of squares of 61.3971 (not given explicitly) so that contribution of
TEMP, given that DISTANCE is already in the model, is 61.3971 - 54.1974
- 7.1997. DISCHARG was laat to enter the model, so the effect of
DISTANCE and TEMP jointly vas already included. Accordingly, the sum of
squares carried by DISCHARG, given that DISTANCE and TEMP are already in
the model. 18 97.7316 - 61.3971 - 36.3345.

180. The partial 8U88 of squaree for eech variable are obtained
a8 if !!! other variablel were already included in the model; i.e., they
give the contribution to the total sum of Iquares carried by each vari-
able adjusted for the previous inclulion of all other variables jointly.
Thus, the partial sum of Iquares for DISCHARG is here equal to the
.equential sum of squares since this was the last variable entered.
Clearly, the sequential sums of squares will differ according to the
order that the variables are entered. The partial lums of squares are
independent of this ordering.
181. The appropriate sums of
depend on the circumStances. These
if one of the variables were to be
Iquares for telting hypothelis
tests are specific to the model 10
omitted, or another variable added,
the values would change.
182. For instance, in the example, the partial sums of squares
Ihow that there is virtually no merit in including TEMP in the model in
addition to DISTANCE and DISCHARG (i.e., the hypothesis 82. 0 can be
accepted). The sequential sums of squares allo show that there would be
little or no merit in including TEMP in addition to DISTANCE, but
neither sequential nor partial sums of squares provide a test of adding
DISCHARG to DISTANCE or vice versa. Nor do we see how a model that
includes TEMP and DISCHARG would perform. For these we would have to
fit two-variable models or enter the variables in a different order.
183. The final sectic:: of output from the computer contains the
parameter estimates, or regression coefficients. These values, as with
.imple linear regression, can be used to estimate the mean pollution,
given values 01 di6tAUca, tc~~CrQ'~4~, ~d di8ctarie. The e~~:ion f~r
this example would be
POLLUTNT. 17.5941 - 0.00225*DISTANCE + 0.1124*TEKP - 3.7858*DISCHARG
184. Note, however, that
able are always calculated with
the model. The parameter would
the regression coefficients for a vari-
adjustments for!!! other variables in
have to be raesttmated if TEMP were

Example Use of R-Square
(SOURCE: Spooner, 1984)
From the above discussion it may be apparent that we can de"cribe
Bean water quality concentration value" for each monitoring station a" a
function of a series of independent variables. 'Ibis regression .odel.
takes the form of:
Y = B 0+B\X1 + ~X2 + B.3X3 + E

X\ may be precipitation 01" stream flow
X2 may be 50il type.
X3 may be percentage of the drainage area
with agricultural BMPs applied.
From our experiences we know that Xt and Y are usually highly corre-
lated (large R2) at monitoring station" impacted primarily by NPS. X2
and X3 may 01" may not turn out to increB-'e significantly the value of
R2. Obviously, we can add more X's (crop type, se8-'on, streaa flow) to
explain an increasing amount of the variation in Y.
Will such a model, however,. be U-'eful to u,,? Probably not if our
purpose is to document in a limited tlae period whether the BMP" we are
i.plementing are having a positive effect on in-streaa water quality.

Thu", what we really want to know i" whether Y is correlated (sig-
nificant R2) with X3. Suppose we had a project area with 12 water
sampling site" each with a corresponding drainage area. We will 8-'suae
that precipUation patterns did not vary within the watershed and that
all sites were sampled simultaneously (within a few hours). Although we
i8plemented phosphorus-control BMPs throughout the project area, i.ple-
.entation had inevitably progres"ed further In soae sub-bulna of the
project area than in others. Assuming that the land use percentages in
each b8-'ln were approximately equal, this situation affords an excellent
opportunity to use the R2 from a siaple regression .odel (Y:BO+~X + E)
to determine whether there was a significant usociation between the
level of BMP application and the aean P concentration at the corre-

~ponding station.
Such a situation might have generated the following
Total P Conc(Y)

J of Drainage Area with
1 1
The R2 value for these data is only 0.36 which means that only a small
fraction of the variation in Y is explained by the presence or absence
of BMPs (Not a surprising result since we have neglected to account for
rainfall or stream flow, which we know have a major effect). However,
using the F test described above, we find that this R2 value is highly
significant (at the 95J confidence level). This means that the results
proba~ly did not occur by chance, and provide statistical evidence that
the BMP implementation caused a decrease in pollutant concentrations.
(Final Suggestion: Look at your project area sub-basins and see if such
paired watershed analysis might be appropriate I)

Confidence Limits for the Median of
Any continuous Distribution
  a    a
n 0.05 0.01 n 0.05 0.01
 1 u 1 .J!  1 .J! 1 .J!
5     41 14 28 12 30
6 1 6   42 15 28 13 30
7 1 7   43 15 29 13 31
8 1 8 1 8 44 16 29 14 31
9 2 8 1 9 45 16 30 14 32
10 2 9 1 10 46 16 31 14 33
11 2 10 1 11 47 17 31 15 33
12 3 10 2 11 48 17 32 15 34
13 3 11 2 12 49 18 32 16 34
14 3 12 2 13 50 18 33 16 35
15 4 12 3 13 51 19 33. 16 36
16 4 13 3 14 52 19 34 17 36
17 5 13 3 15 53 19 35 17 37
18 5 14 4 15 54 20 35 18 37
19 5 15 4 16 55 20 36 18 38
20 6 15 4 17 56 21 36 18 39
21 6 16 5 17 57 21 37 19 39
22 6 17 5 18 58 22 37 19 40
23 7 17 5 19 59 22. 38 20 40
24 7 18 6 19 60 22 39 20 41
25 8 18 6 20 61 23 39 21 41
26 8 19 7 20 62 23 40 21 42
27 8 20 7 21 63 24 40 21 43
28 9 20 7 22 64 24 41 22 43
29 9 21 8 22 65 25 41 22 44
30 10 21 8 23 66 25 42 23 44
31 10 22 8 24 67 26 42 23 45
32 10 23 9 24 68 26 43 23 46
33 11 23 9 25 69 26 44 24 46
34 11 24 10 25 70 27 44 24 47
35 12 24 10 26 71 27 45 25 47
36 12 25 10 27 72 28 45 25 48
37 13 25 11 27 73 28 46 26 48
38 13 26 11 28 74 29 46 26 49
39 13 27 12 28 75 29 47 26 50
40 14 27 12 29     
SolU'ce: After Geigy, 1982.        
Given are the values I and u such that for the order statistics xII] and xI")' Prob[x(11 < true median < xI"I] i!: 1 - a.

  Appendix Q   
  (Source: Conover, 1980) 
Quantiles of the Spearman tes.t statistic.
n p = .900 .950 .975 .990 .995 .999
4 .8000 .8000     
5 .7000 .8000 .9000 .9000  
6 .6000 .77]4 .8286 ..8857 .9429 
7 .5357 .6786 .7450 .857] .8929 .9643
8 .5000 .6190 .7]43 .8095 .8571 .9286
9 .4667 .5833 .6833 .7667 .8167 .9000
10 .4424 .5515 .6364 .7333 .78]8 .8667
11 .4]82 .5273 .6091 .7000 .7455 .8364
12 .3986 .4965 .5804 .6713 .7273 .8182
13 .379] .4780 .5549 .6429 .6978 .79]2
14 .3626 .4593 .5341 .6220 .6747 .7670
15 .3500 .4429 .5179 .6000 .6536 .7464
16 .3382 .4265 .5000 .5824 .6324 .7265
17 .3260 .4118 .4853 .5637 .6152 .7083
]8 .3148 .3994 .47]6 .5480 .5975 .6904
]9 .3070 .3895 .4579 .5333 .5825 .6737
20 .2977 .3789 .445] .5203 .5684 .6586
21 .2909 .3688 .435] .5078 .5545 .6455
22 .2829 .3597 .4241 .4963 .5426 .6318
23 .2767 .3518 .4150 .4852 .5306 .6]86
24 .2704 .3435 .406] .4748 .5200 .6070
25 .2646 .3362 .3977 .4654 .5100 .5962
26 .2588 .3299 .3894 .4564 .5002 .5856
27 .2540 .3236 .3822 .4481 .4915 .5757
28 .2490 .3175 .3749 .440] .4828 .5660
29 .2443 .3113 .3685 .4320 .4744 .5567
30 .2400 .3059 .3620 .4251 .4665 .5479
For n greater than 30 the approximate quantiles of p may be obtained from 
    p J;:'l   
where. x" is the p .quantile of a standard normal.random variable; obtained from Table 1.
SOURCE. Adapted from Glasser and Winter (1961). with corrections. with permission from the
Biometrika Trustees.

a The entries in this table are selected quantiles wp of the Spearman rank correlation coefficient
p when used as a test statistic. The lower quantiles may be obtained from the equation
Wp = -Wt-p
The critical region corresponds to values of p smaller than (or greater than) but not including the
appropriate quantile. Note that the median of p is O.

Probabilities for the Mann-Kendall
Nonparametric Test for Trend
  Values of n    Values of n 
S 4 5 8 9 S 6 7 10
o 0.625 0.592 0.548 0.540 1 0.500 0.500 0.500
2 0.375 0.408 0.452 0.460 3 0.360 0.386 0.431
4 0.167 0.242 0.360 0.381 5 0.235 0.281 0.364
6 0.042 0.117 0.274 0.306 7 0.136 0.191 0.300
8  0.042 0.199 0.238 9 0.068 0.119 0.242
10  0.0283 0.138 0.179 11 0.028 0.068 0.190
12   0.089 0.130 13 0.0283 0.035 0.146
14   0.054 0.090 15 0.0214 0.015 0.108
16   0.031 0.060 17  0.0254 0.078
18   0.016 0.038 19  0.0214 0.054
20   0.0271 0.022 21  0.0320 0.036
22   0.0228 0.012 23   0.023
24   0.0387 0.0263 25   0.014
26   0.0319 0.0229 27   0.0283
28   0.0425 0.0212 29   0.0246
30    0.0343 31   0.0223
32    0.0312 33   0.0211
34    0.0425 35   0.0347
36    0.0528 37   0.0318
     39   0.0458
     41   0.0415
     43   0.0528
     45   0.0628
Source: From Kendall, 1975. Used by pennission.
Repeated zeros are indicated by powers; for example, 0.0347 stands for 0.00047.
Each table entl)' is the probabilil)' that the Mann-Kendall statistic S equals or exceeds the specified
value of S when no trend is present.
This table is used in Section 16.4.1.

    Appendix S     
  (Source: Conover, 1980)   
Quantiles of the Wilcoxon . signed ranks test statistic.
           n(n + 1)
 WO.005 WO.OI WO.025 Wo.os WO.IO WO.20 WO.30 WO.40 WO.50 2
n=4 0 0 0 0 1 3 3 4 5 10
5 0 0 0 1 3 4 5 6 7.5 15
6 0 0 1 3 4 6 8 9 10.5 21
7 0 1 3 4 6 9 11 12 14 28
8 1 2 4 6 9 12 14 16 18 36
9 2 4 6 9 11 15 18 20 22.5 45
10 4 6 9 11 15 19 22 25 27.5 55
11 6 8 11 14 18 23 27 30 33 66
12 8 10 14 18 22 28 32 36 39 78
13 10 13 18 22 27 33 38 42 45.5 91
14 13 16 22 26 32 39 44 48 52.5 105
15 16 20 26 31 37 45 51 55 60 120
16 20 24 30 36 43 51 58 63 68 136
17 24 28 35 42 49 58 65 71 76.5 153
18 28 33 41 48 56 66 73 80 85.5 171
19 33 38 47 54 63 74 82 89 95 190
20 38 44 53 61 70 83 91 98 105 210
21 44 50 59 68 78 91 100 108 115.5 131
22 49 56 67 76 87 100 110 119 126.5 153
23 55 63 74 84 95 110 120 130 138 176
24 62 70 82 92 105 120 131 141 150 300
25 69 77 90 101 114 131 143 153 162.5 325
26 76 85 99 111 125 142 155 165 175.5 351
27 84 94 108 120 135 154 167 178 189 378
28 92 102 117 131 146 166 180 192 203 406
29 101 111 127 141 158 178 193 206 217.5 435
30 110 121 138 152 170 191 207 2"20 232.5 465
31 119 131 148 164 182 205 221 235 248 496
32 129 141 160 176 195 219 236 250 264 528
33 139 152 171 188 208 233 251 266 280.5 561
34 149 163 183 201 .222 248 266 282 297.5 595
35 160 175 196 214 236 263 283 299 315 630
36 172 187 209 228 251 279 299 317 333 666
37 184 199 222 242 266 295 316 335 351.5 703
38 196 212 236 257 282 312 334 353 370.5 741
39 208 225 250 272 298 329 352 372 390 780
40 221 239 265 287 314 347 371 391 410 820
. 41 235 253 280 303 331 365 390 411 430.5 861
42 248 267 295 320 349 384 409 431 451.5 903
43 263 282 311 337 366 403 429 452 473 946
44 277 297 328 354 385 422 450 473 495 990
45 292 313 344 372 403 442 471 495 517.5 1035
46 308 329 362 390 423 463 492 517 540.5 1081
47 324 346 379 408 442 484 514 540 564 1128

Appendix 8
(cant. )
          n(n + 1)
 Wo.oos WO.D. WO.02S Wo.os WO.IO WO.20 WO.30 WOAO Wo.SO 2
48 340 363 397 428 463 505 536 563 588 1176
49 357 381 416 447 483 527 559 587 612.5 1225
50 374 398 435 467 504 550 583 611 637.5 1275
For n larger than 50, the pth quantile W. of the Wilcoxon signed ranks test
statistic may. be approximated by w.=[n(n+l)I4]+x"./n(n+l)(2n+1)/24,
where x" is the pth quantile of a standard normal random variable. obtained from
Table AI.
SOURCE. Adapted from Harter and Owen (1970). with permission from the Institute of
Mathematical Statistics.

a The entries in this table are quantiles w. of the Wilcoxon signed ranks test statistic T.
given by Equation 5.7.6. for selected values of p s .50. Quantiles w. for p > .50 may be
computed from the equation
w. = n(n + 1)/2- wl-.

where n(n + \)/2 is given in the right hand column in the table. Note that peT < w.):S p and
peT> "'.):S 1- p if Ho is true. Critical regions correspond to values of T less than (or.
greater than) but not including the appropriate quantile.

           Appendix T          
        (Source: Gilbert, 1987)       
.Nonparametric 95% and 99% cOIif idence intervals on a proportion.
u  n . 1   n . 2    n . 3   n . -   n . 5   n . 6  
0 0 0 .95 .99 0 0 .78 .90 0 0 .63 .78 0 0 .53 .68 0 0 .50 .60 0 0 .41 .5- 0
1 .01 .05 1 1 .01 .03 .97 .99 .00 .02 .86 .~ .00 .01 .75 .86 .00 .01 .66 .7e .00 .01 .59 .71 1
2     .10 .22 1 1 .06 .1- .98 1 .0- .10 .90 .96 .03 .08 .81 .89 .03 .06 .73 .83 2
3         .22 .37 1 1 .1- .25 .99 1 .11 .19 .92 .97 .08 .15 .85 .92 3
u  n. 7   n . 8    n . 9   n . 10   n . 11   n a 12  U
o 0 0 .38 .50 0 0 .36 .-5 0 0 .32 .-3 0 0 .29 .38 0 0 .26 .36 0 0 .2- .25 0
1 .00 .01 .55 .6- .00 .01 .50 .59 .00 .01 .-- .57 .00 .01 .H .51 .00 .00 .40 .50 .00 .00 .37 .45 1
2 .02 .05 .66 .76 .02 .05 .64 .71 .02 .0It .56 .66 .02 .0- .56 .62 .01 .03 .50 .59 .01 .03 .46 .55 2
3 .07.13 .77 .86 .06 .11 .71 .80 .05 .10 .68 .75 .05 .09 .62 .70 .04 .08 .60 .66 .04 .07 .54 .65 3
- .1- .23 .87 .93 .12 .19 .81 .88 .11 .17 .75 .83 .09 .15 .70 .78 .08 .1- .67 .74 .08 .12 .63 .70 -
5 .24 .34 .95 .98 .20 .29 .89 .94 .17 .:5 .83 .89 .15 .22 .78 .85 .13 .20 .7- .81 .12 .18 .71 .77 5
6 .3& .45 .99 1 .29 .36 .95 .98 .25 .32 .90 .95 .22 .29 .85 .91 .19 .26 .80 .8i .17 .24 .76 .83 6
u  n a 13   n . ,-   n . 15   n . 16   n . 17   n = 18  u
o 0 0 .23 .32 0 0 .23 .30 0 0 .22 .28 0 0 .20 .26 0 0 .19 .26 0 0 .18 .25 0
1 .00 .00 .H .n .00 .00 .32 .-2 .00 .00 .30 .39 .00 .00 .30 .36 .00 .00 .28 .35 .00 .00 .27 .H 1
2 .01 .03 .n .52 .01 .03 .42 .50 .01 .02 .39 .-6 .01 .02 .37 .-5 .01 .02 .35 .-3 .01 .02 .33 ._1 2
3 .0- .07 .52 .59 .03 .06 .50 .58 .03 .06 .H .54 .03 .05 .H .52 .03 .05 .-2 .50 .03 .05 ._1 .H 3
- .07 .11 .59 .68 .06 .10 .58 .64 .06 .10 .53 .61 . .06 .09 .50 .58 .05 .08 .-9 .57 .05 .08 .H .53 -
5 .11 .17 .66.73 .10 .15 .63 .70 .09 .1- .61 .67 .09 .13 .56 .64 .08 .12 .54 .62 .08 .12 .53 .59 5
6 .16 .22 .74 .79 .15 .21 .68 .75 .13 .19 .67 .72 .13 .18 .63 .70 .12 .17 .59 .66 .11 .16 .59 .66 6
7 .21 .26 .78 .84 .19 .2- .76 .81 .18 .22 .71 .77 .17 .20 .70.H .16 .19 .65 .73 .15 .18 .63 .69 7
8 .27 .3- .83 .89 .25 .32 .79 .85 .23 .29 .78 .82 .21 .27 .73 .79 .20 .25 .72 .76 .18 .24 .67 .75 8
9 .32 ._1 .89 .93 .30 .37 .85 .90 .28 .33 .61 .87 .26 .30 .80 .83 .24 .28 .75 .80 .23 .27 .73 .77 9
u  n . 19   n . 20   n . 21   n a 22   n . 23   n . 24  u
o 0 0 .17 .2- 0 0 .16 .22 0 0 .15 .21 0 0 .15 .20 0 0 .1- .19 0 0 .13 .19 0
1 .00 .00 .:5 .32 .00 .00 .24 .31 .
Appendix U
(Source: Conover, 1980)
Sample sizes for one-sided nonparametric tolerance limitsG.
I - IX q = .500 .700 .750 .800 .850 .900 .950 .975 .980 .990
.500 I 2 3 4 5 7 14 28 35 69
.700 2 4 5 6 8 12 24 48 60 120
.750 2 4 5 7 9 14 28 55 69 138
.800 3 5 6 8 10 16 32 64 80 161
.850 3 6 7 9 12 19 37 75 94 189
.900 4 7 9 II 15 22 45 91 144 230
.950 5 9 II 14 19 29 59 119 149 299
.975 6 II 13 17 23 36 72 146 183 368
.980 6 II 14 18 25 38 77 155 194 390
.990 7 13 17 21 29 44 90 182 228 459
.995 8 15 19 24 33 51 104 210 263 528
.999 IO 20 25 31 43 66 135 273 342 688
G The quantity tabled is the sample size n such that qn :S a. for use in finding the tolerance limits
   P(Xw:s p of the population) 2: 1- a   
   P(q of the population sx(nl) 2: 1- a   


Air National Guard. 1993. Draft final Remedial
Investigation/Feasibility Study work plan. Wyoming Air National
Guard 153rd Tactical Airlift Group, Cheyenne Municipal Airport,
Cheyenne, Wyoming. Prepared by Aepco, Inc. and Tetra Tech, Inc.
Alberts, E.E., G.E. Schuman, and R.E. Burwell. 1978. Seasonal
runoff losses of nitrogen and phosphorus from Missouri Valley
loess watersheds. J. Environ. Qual. 7(2) :203-207.
Allen, D.M., S.K. Service and M.V. Ogburn-Matthews. 1992.
Factors influencing the collection efficiency of estuarine
fishes. Trans. Am. Fish. Soc. 121(2) :234-244.
Aller, L., T. Bennett, J.H. Lehr, and R.J. Petty. 1985.
DRASTIC: a standardized system for evaluating ground water
pollution potential using hydrogeologic settings. EPA/600/2-
85/018. U.S. Environmental Protection Agency, Washington, DC.
Anderson, R.L.
1941. Distribution of the serial correlation
Ann. Math. Stat. 8(1) :1-13.
Anderson, V.L., and R.A. McLean. 1974. Design of experiments, a
realistic approach. Marcel Dekker, Inc., New York, New York.
APHA-AWWA-WPCF. 1975. Standard methods for the examination of
water and wastewater. 14th ed. American Public Health
Association, Washington, DC.
ASIWPCA. 1986. America's clean water: the states' nonpqint
source assessment 1985. Appendix. Association of State and
Interstate Water Pollution Control Administrators, Washington,
ASQC. 1994. Specifications and guidelines for quality systems
for environmental data collection and environmental technology
programs. ANSI/ASQC E4-1994. American Society for Quality
Control, ASQC Quality Press, Wisconsin.
Bailey, G.W. and T.E. Waddell. 1979. Best management practices
for agriculture and silviculture: an integrated review. In Best
Management Practices for Agriculture and Silviculture. Ann Arbor
Science, Ann Arbor, Michigan.
Baker, D.B., K.A. Krieger, R.P. Richards, and J.W. Kramer. 1985.
Effects of intensive agricultural land use on regional water
quality in northwestern Ohio. In Perspectives on Nonpoint Source
Pollution. Proceedings of a National Conference, May 19-22,
1985, Kansas City, Missouri. EPA 440/5-85-001. U.S.
Environmental Protection Agency, Washington, DC.
Ball, J. 1982. Stream
Wisconsin Department of
Wisconsin Department of
classification guidelines for Wisconsin.
Natural Resources Technical Bulletin.
Natural Resources, Madison, Wisconsin.

Barbour, M.T., and J.B. Stribling. 1991. Use of habitat
assessment in evaluating the biological integrity of stream
communities. In Biological Criteria: Research and Regulation
Proceedings of a Symposium. EPA-440/5-91-005. U.S.
Environmental Protection Agency, Office of Water. July.
Barbour, M.T., J.B. Stribling and J.R. Karr. 1995. Multimetric
Approach for Establishing Biocriteria and Measuring Biological
Condition. In Biological Assessment and Criteria. Tools for
Water Resource Planning and Decision Making, ed. W.D. Davis and
T. Simon, pp. 63-76. Lewis Publishers, Boca Raton, Florida.
Barnett, V. and T. Lewis. 1979. Outliers in statistical data.
John Wiley & Sons, Inc., New York, New York.
Berryman, D., B. Bernard, D. Cluis and J. Haemmerli. 1988.
Nonparametric tests for trend detection in water quality time
series. Water Resour. Bull. 24:545-556.
Brakensiek, D.L., H.B. Osborn, and W.J. Rawls. 1979. Field
manual for research in agricultural hydrology. Agriculture
Handbook No. 224, U.S. Department of Agriculture, Science and
Education Administration, Washington, DC.
Brown, M.P. 1981. Quality assurance plan for research and
monitoring of the West Branch Delaware River model implementation
program. New York State Dept. of environmental Conservation,
Albany, New York.
Brown, M.P., P. Longabucco, and M.R. Rafferty. 1986. Nonpoint
source control of phosphorus - a watershed evaluation volume 5,
the eutrophication of the Cannonsville Reservoir. New York State
Department of Environmental Conservation, Bureau of Technical
Services and Research, Albany, New York.
Carsel, R.F., C.N. Smith, L.A. Mulkey, J.D. Dean, and P. Jowise.
1984: Users manual for the pesticide root zone model (przm),
release 1. EPA/600/3-84/109. U.S. Environmental Protection
Agency, Washington, DC.
Cassell, E.A.,and D.W. Meals. 1981. Comprehensive water
quality monitoring and evaluation program for the St. Albans Bay
rural clean water program watershed project. Vermont Water
Resources Research Center, Burlington, Vermont.
Chambers, J.M., W.S. Cleveland, B.o Kleiner, and P.A. Tukey.
1983. Graphical Methods for Data Analysis. Duxbury Press,
Chow, V.T. 1951. The log-probability law and its engineering
applications. Separate No. 536, 80. American Society of Civil
Engineering. November.

Clarkson, C.C., D.E. Lehnig, S.V. Plante, R.S. Taylor, and
Williams. 1984. Hydrologic basis for suspended sediment
criteria. Prepared by Camp, Dresser & McKee for U.s.
Environmental Protection Agency, Washington, DC.
Clausen, J.C. 1985. The St. Albans Bay watershed RCWP: a case
study of monitoring and assessment. In Perspectives on Nonpoint
Source Pollution. Proceedings of a national conference, May 19-
22, 1985, Kansas City, Missouri. EPA 440/5-85-001, U.S.
Environmental Protection Agency, Washington, DC.
Clausen, J.C., Wayland, K.G., K.A. Saldi, and K. Guillard.
Movement of nitrogen through an agricultural riparian zone:
Field studies. Water Sci. Tech. 28(3-5) :605-612.
Clean Water Partnership. 1989. Water quality monitoring for the
Clean Water Partnership. A guidance document. Minnesota
Pollution Control Agency, Division of Water Quality. March.
Clesceri, L.S., A.E. Greenberg, and R.R. Trussell, eds. 1989.
Standard methods for the examination of water and wastewater.
17th ed. American Public Health Association, American Water
Works Association, and Water Pollution Control Federation,
Washington, DC.
Cochran, W.G. 1977. Sampling techniques.
and Sons, New York, New York.
3rd ed.
John Wiley
Coffey, S. 1993. The nonpoint source manager's guide to water
quality and land treatment monitoring. North Carolina
Cooperative Extension Service, North Carolina State University.
Coffey, S.W., J. Spooner, and M.D. Smolen. 1993. The Nonpoint
Source Manager's Guide to Land Treatment and Water Quality
Monitoring. NCSU Water Quality Group, Department of Biological
and Agricultural Engineering, North Carolina State University,
Raleigh, North Carolina.
Cohen, A.N. 1990.
Francisco Estuary.
An introduction to the ecology of the San
San Francisco Estuary Project, San Francisco,
Colby, B.R. 1956. Relationship of sediment discharge to
streamflow. U.S.G.S. Open File Report. U.S. Geological Survey,
Reston, Virginia.
Conover, W.J. 1980.
Wiley, New York.
Practical Nonparametric Statistics, 2nd ed.
Conquest, L. L., S. C. Ralph, and R. J. Naiman. 1994.
Implementation of large-scale stream monitoring efforts:
sampling design and data analysis issues. In Biological
Monitoring of Aquatic Systems, ed. S.L. Loeb and A. Spacie.
Lewis Publishers, Boca Raton, Florida.

Cowie, G.M., J.L. Cooley and A. Dutt. 1991. Use of modified
benthic bioassessment protocols for evaluation of water quality
trends in Georgia. USDI/GS Project 14-08-0001-G1556 (03); ERC-
06-91; USGS/G-1~56-03. Technical Completion Report, Institute of
Community and Area Development, University of Georgia, Athens,
Georgia and Environmental Resources Center, Georgia Institute of
Technology, Atlanta, Georgia. July.
Cox, D.R., and Stuart, A.
location and dispersion.
1955. Some quick tests for trend in
Biometrika 42:80-95.
Crawford, C.G., J.R. Slack, and R.M. Hirsch, 1983.
Nonparametric tests for trends in water-quality data using the
statistical analysis system. U.S.G.S. Open File Report 83-550.
U.S. Geological Survey, Reston, Virginia.
Cross-Smiecinski, A., and L.D.. Stetzenback. 1994. Quality
planning for the life science researcher: Meeting quality
assurance requirements. CRC Press, Boca Raton, Florida.
Cummins, K.W. 1994. Bioassessment and Analysis of Functional
Organization of Running Water Ecosystems. In Biological
Monitoring of Aquatic Ecosystems, ed. S.L. Loeb and A. Spacie.
Lewis Publishers, Ann Arbor, Michigan.
Cupp, C. E. 1989. Stream Corridor Classification for Forested
Lands of Washington. Report for Washington Forest Protection
Association, Olympia, Washington.
Dauble, D.D., and R.H. Gray. 1980. Comparison of a small seine
and a backpack electroshocker to evaluate near shore fish
populations in rivers. Prog. Fish Cult. 42:93-95.
Davenport, T.E. and M.H. Kelly. 1984. Water resource data and
preliminary trend analysis for the Highland Silver Lake
monitoring and evaluation project, Madison County, Illinois.
IEPA/WPC/84-030, Illinois Environmental Protection Agency,
Springfield, Illinois.

Davenport, T.E., andM.H. Kelly. 1984. Soil erosion and
sediment transport dynamics in Blue Creek watershed, Pike County,
Illinois. IEPA/WPC/83-004. Planning Section, Water Pollution
Control, Illinois Environmental Protection Agency, Springfield,
Dean, J.D., P.P. Jowise, and A.S. Donigian, Jr. 1984. Leaching
evaluation of agricultural, chemicals (leach handbook). PB8-4-
236413, U.S. Environmental Protection Agency, Athens, Georgia.
Dewey, M.R., L.E. Holland-Bartel and S.T. Zigler. 1989.
Comparison of fish catches with buoyant pop nets and seines in
vegetated and nonvegetated habitats. North. Am. J. Fish. Manage.

Dressing, S., and F.J. Humenik. 1986a. Rural clean water
program statu~ report on the cm&e projects 1985. Biological and
Agricultural Engineering Dept., North Carolina State University,
Raleigh, North Carolina.
Dressing, S.A., J. Spooner, J.M. Kreglow, E.O. Beasley, and P.W.
Westerman. 1987. Water and sediment sampler for plot and field
studies. J. Environ. Qual. 16(1) :59-64.
Dressing, S.A., J.M. Kreglow, R.P..Maas, F.A. Koehler, W.K.
Snyder, and F.J. Humenik. 1982. Best management practices for
agricultural nonpoint source control: II. Commercial fertilizer.
Biological and Agricultural Engineering Dept., North Carolina
State University, Raleigh, North Carolina.
Dressing, S.A., R.P. Maas, ~.D. Smolen, and F.J. Humenik, eds.
1984. Proceedings of the rural clean water program. Biological
and Agricultural Engineering Dept., North Carolina State
University, Raleigh, North Carolina.
Drouse, S.K., D.C. Hillman, J.L. Engles, L.W. Creelman and S.J.
Simon. 1986. National surface water survey~ National stream
survey (Phase 1 - Pilot, Mid-Atlantic Phase 1 Southeast
screening, and episodes pilot) quality assurance plan.
EPA/600/4-86/044. NTIS No. PB87-145819. Prepared by Lockheed
Engineering and Management Services Co., Inc., Las Vegas, Nevada,
for U.S. Environmental Protection Agency, Office of Research and
Development, Environmental Monitoring Systems Laboratory, Las
Vegas, Nevada. December. .
El-Shaarawi, A.H., and E. Damsleth. 1988. Parametric and
nonparametric tests for dependent data. Water Resour. Bull.
Erickson, H.E., M. Morrison, J. Kern, L. Hughes, J. Malcolm and
K. Thornton. 1991. Watershed manipulation project: Quality
assurance implementation plan for 1986-1989. EPA/600/3-91/008.
NTIS No. PB91-148395. Prepared by NSI Technology Services
Corporation, Corvallis, Oregon for Corvallis Environmental
Research Laboratory, Oregon. January.
Erlebach, W.E., 1979. A systematic approach to monitoring trends
in the quality of surface waters. In Everett, L.G. and K.D.
Schmidt, Eds., Establishment of water quality monitoring
programs. Proceedings of a symposium held in San Francisco, CA
June 12-14, 1978, AWRA, Minneapolis, Minnesota.
Everett, L.G. 1980. Groundwater monitoring.
Company, Schenectady, New York.
General Electric
Field, R., A.N. Tafuri, and H.E. Masters. 1977. Urban runoff
pollutiqn control technology overview. EPA-600/2-77-047. U.S.
Environmental Protection Agency, Washington, DC.

Freund, R.J., and R.C. Littell. 1981.
guide to the anova and glm procedures.
Cary, North Carolina.
SAS for linear models:
SAS Institute, Inc.,
Freund, J.E. 1973. Modern elementary statistics.
Hall, Englewood Cliffs, New Jersey.
Gaugush, R.F., ed. 1986. Statistical methods for reservoir
water quality investigations. Instruction Report E-86-2, U.S.
Army Engineer Waterways Experiment Station, Vicksburg,
Gibson, G.R., M.T. Barbour, J.B. Stribling, J. Gerritsen and J.R.
Karr. 1994. Biological Criteria: Technical Guidance for
Streams and Small Rivers. EPA 822-B-94-001. U.S. Environmental
Protection Agency, Office of Water, Washington, DC. September.
Gilbert, R.O. 1987.
Pollution Monitoring.
Statistical Methods for Environmental
Van Nostrand Reinhold Company, New York.
Gray, J.S. 1989.
rich assemblages.
Effects of environmental stress on species-
Bioi. J. Linn. Soc. 37:19-32.
Grayman, W.M. 1984. Application of the routing and graphical
display system to the streams of the United States. U.S.
Environmental Protection Agency, Office of Water, Washington, DC.
Green, R.H. 1993. Application of repeated measures designs in
environmental impact and monitoring studies. Austr. J. Ecol.
Gulland, J.A. 1983. Fish stock assessment: A manual of basic
methods. FAO/Wiley Series, Vol. 1. Wiley & Sons, New York.
Guy, H.P., and V.W. Norman. 1970. Field methods for measurement
of fluvial sediment. U.S. Geological Survey, TWRI Book 3,
Chapter 2, Washington, D.C.
Hall, D. C., and W.R. Berkas. 1988. Comparison of instream and
laboratory methods of measuring sediment oxygen demand. Water
Resour. Bull. 24:533-544.
Hallberg, G.R., R.D. Libra, E. A. Bettis, and B~E. Hoyer. 1984.
Hydrogeologic and water quality investigations in the Big Spring
basin, Clayton county, Iowa. Iowa Geological Survey, Open File
Report 84-4. .
Hallberg, G.R., B.E. Hoyer, E.A. Bettis III, and R.D. Libra.
1983. Hydrogeology, water quality, and land management in the Big
Spring basin, Clayton County, Iowa. Iowa Geologic Survey Open-
File Report 83-3.

Harcum, J.B. 1990. Water-quality data analysis protocol
development. Ph.D. diss., Department of Agricultural and
Chemical Engineering, Colorado State University, Fort Collins,
Hawkins, C.P., J.L. Kershner, P.A. Bisson, M.D. Bryant, L.M.
Decker, S.V. Gregory, D.A. McCullough, C.K. Overton, G.H. Reeves,
R.J. Steedman and M.K. Young. 1993. A hierarchical approach to
classifying stream habitat features. Fisheries 18(6) :3-12.
Hawkins, R.H., R.G. Werner, and J.O. Crevelling. 1974.
report-runoff quality in a suburban stream. New England
Interstate Water Pollution Control Commission.
Hayes, M.L. 1983. Active fish capture methods. In Fisheries
Techniques, ed. L.A. Nielsen and D.L. Johnson, pp. 123-145.
American Fisheries Society, Bethesda, Maryland.
Helsel, D.R., and T.A. Cohn. 1988. Estimation of descriptive
statistics for multiply-censored water-quality data. Water
Resour. Res. 24(12) :1997-2004.
Hershfield, D.N. 1961; Rainfall Frequency Atlas of the United
States. U.S. Weather Bureau Technical Paper 40. May.
Hilsenhoff, W.L.
stream pollution.
1987. An improved biotic index of organic
Great Lakes Entomologist ?:31-39.
Hipel, K.W. 1988.
impact assessment.
Nonparametric approaches to environmental
Water Resour. Bull. 24(3).
Hipel, K.W., A.I. McLeod and R.R. Weiler.
of water quality time series in Lake Erie.
1988. Data analysis
Water Resour. Bull.
Hirsch, R.M., J.R. Slack and R.A. Smith. 1982.
trend analysis for monthly water quality data.
Res. 18:107-121.
Techniques of
Water Resour.
Hirsch, R.M., and J.R. Slack. 1984. A nonparametric trend test
for seasonal data with serial dependence. Water Resources
Research 20:727-732.
Hoaglin, D.C., F. Mosteller, and J.W. Tukey. 1983.
Understanding Robust and Exploratory Data Analysis.
wiley, New
Hodges, J.L., and E.L. Lehmann. 1963. Estimates of location
based on rank tests. Ann. Math. Stat. 34:598-611.
Hollander, M., and D.A. Wolfe.
methods. John Wiley and Sons,
1973. Nonparametric statistical
Inc., New York, New York.

Horn, C.R. and W.M. Grayman. 1985. National
of water quality using the EPA reach file and
Draft. u.s. Environmental Protection Agency,
Washington, DC.
and local modeling
related data.
Office of Water,
Horn, C.R. 1986. Draft Memorandum of Understanding. U.s.
Environmental Protection Agency, Office of Water, Washington, DC.
Hubert, W.A. 1983. Passive capture techniques. In Fisheries
Techniques, ed. L.A. Nielsen and D.L. Johnson, pp. 95-122.
American Fisheries Society, Bethesda, Maryland.
Hurlbert, S.H. 1984. Pseudoreplication and the design of
ecological field experiments. Ecol. Monogr. 54(2) :187-211.
I.E.P.A. 1979. Water quality management plan, Volume III.
Illinois Environmental Protection Agency, Springfield, Illinois.
IHD-WHO Working Group on Quality of Water. 1978. Water quality
surveys: a guide for the collection and interpretation of water
quality data. Unesco/WHO, Sydenhams Printers, Poole, Dorset,
United Kingdom.
Ingwersen, J.B. 1980. Statistical analysis using SPSS at the
USDA-Fort Collins computer center. WSDG-AD-00002. U.S.
Department of Agriculture, Forest Service.
ITFM. 1994. Water-quality monitoring in the United States.
Intergovernmental Task Force on Monitoring Water Quality,
Interagency Advisory Committee on Water Data, Water Information
Coordination Program. Washington, DC. January.
ITFM. 1994. Water-quality monitoring in the United States.
Technical appendixes. Intergovernmental Task Force on Monitoring
Water Quality, Interagency Advisory Committee on Water Data,
Water Information Coordination Program.. Washington, DC.
Jamieson, C.A., ed. 1986. Summary of the 1986 rcwp data
analysis workshop. U.S. Environmental Protection Agency, Office
of Water Regulations and Standards, Washington, DC.
Jerald, A., Jr. 1983. Age determination. In Fisheries
Techniques, ed. L.A. Nielsen and D.L. Johnson, pp. 301-324.
American Fisheries Society, Bethesda, Maryland.
Karr, J.R., and D.R. Dudley. 1981. Ecological perspective on
water quality goals. Environ. Manage. 5:55-68.
Karr, J.R., K.D. Fausch, P.L. Angermeier, P.R. Yant and I.J.
Schlosser. 1986. Assessing biological integrity in running
waters: A method and its rationale. Special Publication 5.
Illinois Natural History Survey, Urbana, Illinois.

Keith, L.H., ed. 1988. Principles of environmental sampling.
American Chemical Society, Washington, D.C.
Keith, L.H., W. Crummett, J. Deegan Jr., R.A. Libby, J.K. Taylor
and G. Wentler. 1983. Principles of environmental analysis.
Analytical Chemistry (55) :2210-2218.
Kendall, M.G. 1975. Rank correlation methods, 4th edition.
Charles Griffin, London.
Khaleel, R., K.R. Reddy, and M.R. Overcash. 1980. Transport of
potential pollutants in runoff water from land areas receiving
animal waste: a review. Water Research. 14:421-436.
Kimball, C.G. 1986. 1986 annual rcwp progress report - project
20. South Dakota Dept. of Water and Natural Resources, Pierre,
South Dakota.
Klemm, D.J., P.A. Lewis, F. Fulk, and J.M. Lazorchak. 1990.
Macroinvertebrate field and laboratory methods for 'evaluating the
biological integrity of surface waters. EPA-600-4-90-030. U.S.
Environmental Protection Agency, Environmental Monitoring and
Support Laboratory, Cincinnati, Ohio.
Klemm, D.J., Q.J. Stober and J.M. Lazorschak. 1992. Fish field
and laboratory methods for evaluating the biological integrity of
surface waters. EPA/600/R-92/111. U.S. Environmental Protection
Agency, Environmental Monitoring and Support Laboratory,
Cincinnati, Ohio. March.
Knapton, J.R., and D.A. Nimick. 1991. Quality assurance for
water-quality activities of the U.S. Geological Survey in
Montana. U.S. Geological Survey Open File Report 91-216. U.S.
Geological Survey, Helena, Montana. August.
Knisel, W.G., ed. 1980. CREAMS: a field-scale model for
chemicals, runoff, and erosion from agricultural management
systems. Conservation Research Report No. 26. U.S.Department of
Agriculture, Washington, DC.
Kreglow, J.M., S.A. Dressing, R.P. Maas, F.A. Koehler, L.
Christensen, W.K. Snyder, and F.J. Humenik. 1982. Best
management practices for agricultural nonpoint source control: I.
animal waste. Biological and Agricultural Engineering Dept.,
North Carolina State University, Raleigh, North Carolina.
Loftis, J.C., P.S. Porter, and G. Settembre. 1987.
analysis of industrial wastewater monitoring data.
Pollut. Control 59(3) :145-151.
J. Water
Lyons, J. 1992. Using the Index of Biotic Integrity (IBI) to
Measure Environmental Quality in Warmwater Streams of Wisconsin.
General Technical Report NC-149. U.S. Department of Agriculture,
Forest Service, North Central Forest Experiment Station.

Maas, R.P. 1989. Designing effective nonpoint source water
quality monitoring programs. Prepared for the Tennessee Valley
Authority. November.
Maas, R.P., J.M. Kreglow, S.A. Dressing, F.A. Koehler, L.
Christensen, W.K. Snyder, and F.J. Humenik. 1982. Best
management practices for agricultural nonpoint source control:
III. sediment. Biological and Agricultural Engineering Dept.,
North Carolina State University, Raleigh, North Carolina.
Maas, R.P., S.A. Dressing, J. Spooner, M.D. Smolen, and F.J.
Humenik. 1984. Best management practices for agricultural
nonpoint source control: IV. Pesticides. Biological and
Agricultural Engineering Dept., North Carolina State University,
Raleigh, North Carolina. .
MacDonald, L.H., A.W. Smart, and R.C. Wissmar. 1991. Monitoring
Guidelines to Evaluate Effects of Forestry Activities on Streams
in the Pacific Northwest and Alaska. EPA/910/9-91-001. U.S.
Environmental Protection Agency, Region 10, Seattle, Washington.
MACS. 1993. 'Standard operating procedures and technical basis.
Macroinvertebrate collection and habitat assessment for low
gradient non-tidal streams. Draft. Prepared by The Mid-Atlantic
Coastal'Streams Workgroup. August 24.
Mandel, J. 1964. The statistical analysis of experimental data.
Interscience Publishers division of John Wiley and Sons, New
York, New York.
Mann, H.B. 1945. Non-Parametric tests against trend.
Econometrica 13:245-259.
Martin, D.M.
water program
Department of
1984'. Annual report, Rock Creek rural clean
comprehensive monitoring and evaluation. Idaho
Health and Welfare, Division of Environment, Boise,
Maxted, J. R. and E. L. Dickey. 1993. Statistical analysis of
replicate data - Fall 1991 biological survey. Preliminary
technical report. Delaware Department of Natural Resources and
Environmental Control, Division of Water Resources. Dover,
Delaware. August. .
Meador, M.R., T.F. Cuffney and M.E. Gurtz. 1993. Methods for
sampling fish communities as part of the National Water-
assessment Program. Open File Report 93-104.' U.S. Geological
Survey, Raleigh, North Carolina.
Mendenhall, W. 1971. Introduction to Probability and
Statistics. Duxbury Press, Belmont, California. Cited in
MacDonald et al., 1991.
Metcalf and Eddy, Inc. 1979. Wastewater engineering: treatment,
disposal, reuse. Second Edition. McGraw~Hill, New York, New York.

Mitsch, ~.J., R.J. Stevenson, J.R. Taylor, and M.A. Cardamone.
1983. Water contamination in the Ohio River basin in Kentucky -
a summary report. Systems Science Institute, University of
Louisville, Kentucky.
Mockus, V. 1960. Selecting a flood-frequency method.
Soc. Engin. Trans. 3:48-51,54.
Moore, D.S., and G.P. McCabe. 1989. Introduction to the
Practice of Statistics. W.H. Freeman and Company, New York.
Mosteller, F., and R.E.K. Rourke. 1973.
Addison-Wesley, Reading, Massachusetts.
Sturdy Statistics.
National Research Council. 1986. Ecological Knowledge and
Environmental Problem-Solving. Concepts and Case Studies.
National Academy Press, Washington, DC.
Ohio EPA. 1987. Biological criteria for the protection of
aquatic life: Volumes I-III. Ohio Environmental Protection
Agency, Division of Water Quality Monitoring and Assessment,
Surface Water Section, Columbus, Ohio.
Ohio EPA. 1992. Executive Summary and Vol I: Summary, Status,
and Trends. In Ohio Water Resource Inventory. Ohio
Environmental Protection Agency, Division of Surface Water,
Ecological Assessment Section, Columbus, Ohio.
Omernik, J.M. 1987. Ecoregions of the coterminous United
States. Ann. Assoc. Am. Geogr. 77(1) :118-125.
Omernik, J.M. 1995. Ecoregions: A spatial framework for
environmental management. In Biological assessment and criteria:
Tools for water resource planning and decision making, ed. W.S.
Davis and T.P. Simon, pp. 49-62. Lewis Publishers, Boca Raton,
Pankratz, A. 1983. Forecasting with univariate box-Jenkins
models. Wiley and Sons, Inc., New York.
Pennsylvania RCWP Coordinating Committee. 1984. The Conestoga
headwaters rural clean water program, pn19, 1984 annual progress
report. U.S. Department of Agriculture, Soil Conservation
Service, Harrisburg, Pennsylvania.
Plafkin, J.L., M.T. Barbour, K.D. Porter, S.K. Gross and R.M.
Hughes. 1989. Rapid Bioassessment Protocols for Use in Streams
and Rivers: Benthic Macroinvertebrates and Fish. EPA/440/4-89-
001. U.S. Environmental Protection Agency, Office of Water,
Washington, DC.
Platts, W.S., W.F. Megahan, and G.W. Minshall. 1983. Methods
for evaluating stream, riparian, and biotic conditions. Gen.
Tech. Rept. INT-138. U.s. Department of Agriculture, Forest
Service, Ogden, Utah.

Ponce, S.L. 1980a. Statistical methods commonly used in
water quality data analysis. WSDG Technical Paper WSDG-TP-00001.
US Department of Agriculture, Forest Service.
Ponce, S.L. 1980b. Water quality monitoring programs. WSDG
Technical Paper WSDG-TP-00002. u.s. Department of Agriculture,
u.s. Forest Service.
puri, L.M., and P.K. Sen. 1971. Nonparametric methods in
multivariate analysis. Johri Wiley & Sons, Inc., New York, New
Reckhow, K.H. 1979. Sampling designs for lake phosphorus
budgets. In eds. Everett, L.G. and K.D. Schmidt, Establishment of
water quality monitoring programs. Proceedings of a symposium
held in San Francisco, California, June 12-14, 1978, AWRA,
Minneapolis, Minnesota. .
Reckhow, K.H., K. Kepford and W.W. Hicks. 1993. Methods for the
analysis of lake water quality trends. EPA 841-R-93-0003. u.S.
Environmental Protection Agency, Washington, DC.
Remington, R.D., and M.A. Schork. 1970. Statistics with
applications to the biological and health sciences. Prentice-
Hall, Englewood Cliffs, New Jersey.
Rossman, L.A. 1990. DFLOW User's Manual. EPA 600/8-90/051.
U.S. Environmental Protection Agency, Office of Research and
Development, Cincinnati, Ohio.
Richards, R.P. 1986. Monte carlo studies of sampling strategies
for estimating tributary loads, ii: effects on bias and precision
due to differences among watershed sizes and the transported
materials monitored. Water Quality Laboratory, Heidelberg
College, Tiffin, Ohio.
Richards, C., and G.W. Minshall. 1992. Spatial and temporal
trends in stream macroinvertebrate communities: the influence of
catchment disturbance. Hydrobiologia 241(3).:173-184.
Salas, J.D., J.W. Delleur, V. Yevjevich, and W.L. Lane. 1980.
Applied Modeling of Hydrologic Time Series. Water Resources
Publications, Ft. Collins, Colorado.
SAS Institute, Inc. 1985a. SAS user's guide: basics.
edition. SAS Institute, Inc., Cary, North Carolina.
Version 5
SAS Institute, Inc. 1985b. SAS user's guide: statistics.
Version 5 edition.SAS Institute, Inc., Cary, North Carolina.
Scalf, M.R., J.F. McNabb, W.J. Dunlap, R.L. Cosby, and J.
Fryberger. 1981. Manual of ground-water sampling procedures.
NWWA/EPA Series.

Schlosser, I.J., and J.R. Karr. 1980. Determinants of water
quality in agricultural watersheds. UILU-WRC-80-0147, University
of Illinois Water Resources Center, Urbana, Illinois.
Sen, P.K. 1968.
on Kendalls tau.
Estimates of the regression coefficient based
Journal of the American Statistical Association
Shelley, P.E. 1979. Monitoring requirments, methods, and costs
for the nationwide urban runoff program. U.S. Environmental
Protection Agency, Water Planning Division. .
Sherwani, J.K. and D.H. Moreau. 1975. Strategies for water
quality monitoring. Report No. 107, Water Resources Research
Institute of the University Raleigh, North Carolina.
Simons, D.B., R. Li, T.P. Ballestero, and K.G. Eggert. 1981.
Workshop in sampling requirements for monitoring and evaluaiton
of watershed management practices, May 20-21," 1981. U.S.EPA
Environmental Research Laboratory, Athens, Georgia.
Simonson, T., and J. Lyons. 1992a. Evaluation Monitoring of
Stream Habitat During Priority Watershed Projects. Wisconsin
Department of Natural Resources. May.

Simonson, T., and J. Lyons. 1992b. Evaluation Monitoring of
Stream Fish Communities During Priority Watershed Projects.
Wisconsin Department of Natural Resources. May.
Skalski, J.R., and D.H. McKenzie. 1982. A design for aquatic
monitoring programs. J. Environ. Manage. 14:237-251.
Smith, F., S. Kulkarni, L.E. Myers, and M.J. Messner. 1988.
Evaluating and presenting quality assurance data. In Principles
of environmental sampling, ed. L.H. Keith, pp. 157-168. American
Chemical Society, Washington, DC.
Smolen, M. 1984.
Evaluation Project
Engineering Dept.,
North Carolina.
Water quality models. National Water Quality
Notes, No.9, Biological and Agricultural
North Carolina State University, Raleigh,
Smolen, M.D., R.P. Maas, J. Spooner, C.A. Jamieson, S.A.
Dressing, L.C. Stanley, and F.J. Humenik. 1986b. NWQEP 1986
annual report, status of agricultural nps projects - Draft.
Biological and Agricultural Engineering Dept., North Carolina
State University, Raleigh, North Carolina.
Snedecor, G.W. and W.G. Cochran. 1980. Statistical methods.
7th ed. The Iowa State University Press, Ames, Iowa.
Snedecor, G.W. and W.G. Cochran. 1967. Statistical methods.
6th ed. The Iowa State University Press, Ames, Iowa.

Sokal, R.R., and F.J. Rohlf. 1981. Biometry. W.H. Fremman and
Co. San Francisco, California. Cited in MacDonald ~t al., 1991.
Southerland, M., and J.B. Stribling. 1995. Status of biological
criteria development and implementation. In Biological Criteria
Tools for Water Resources Planning and Decision Making, ed. W.D.
Davis and T. Simon, pp. 79-94. Lewis Publishers, Boca Raton,
Spooner, J. 1984. Use and misuse of r-square in regression
analysis. National Water Quality Evaluation Project Notes,
Technical Supplement to No. 12, Biological and Agricultural
Engineering Dept., North Carolina State University, Raleigh,
North Carolina.
Spooner, J. 1986a. Analysis of covariance, Part I. National
Water Quality Evaluation Project Notes, Technical Supplement to
No. 18, Biological and Agricultural Engineering Dept., North
Carolina State University, Raleigh, North Carolina.
Spooner, J. 1986b. Analysis of covariance, Part II. National
Water Quality Evaluatio~ Project Notes, Technical Supplement to
No. 19, Biological and Agricultural Engineering Dept., North
Carolina State University, Raleigh, North Carolina.
Spooner, J. 1994. Nonpoint source water quality monitoring
designs and data analysis techniques: A review. Review draft.
North Carolina Cooperative Extension Service, North Carolina
State University.
Spooner, J. and R.P. Maas. 1984. Regression-basic concepts and
definitions. National Water Quality Evaluation Project Notes,
Technical Supplement to No. II, Biological and Agricultural
Engineering Dept., North Carolina State University, Raleigh,
North Carolina.
Spooner, J., C.A. Jamieson, R.P. Maas, S.A. Dressing, M.D.
Smolen, and F.J. Humenik. 1986. Rural clean water program
status report on the cm&e projects 1985 - supplemental report:
analysis methods. Biological and Agricultural Engineering Dept.,
North Carolina State University, Raleigh, North Carolina.
Spooner, J., R.P. Maas, S.A. Dressing, M.D. Smolen, and F.J.
Humenik. 1985. Appropriate designs for documenting water quality
improvements from agricultural nps control programs. In
Perspectives on Nonpoint Source Pollution. Proceedings of a
national conference, May 19-22, Kansas City, Missouri. EPA
440/5-85-001. Washington, DC.
Spreizer, G.M., T.J. Calabrese and R.S. Weidner. 1992.
Assessing the usability of historical water-quality data for
current and future applications. In Current practices in ground
water and vadose zone investigations, ASTM STP 1118. D.M.
Nielsen and M.N. Sara, ed. Pp. 377-390. American Society for
Testing and Materials, Philadelphia, Pennsylvania.

Srivastava, M.S., and C.G. Khatri. 1979. An introduction to
multivariate statistics. North Holland, New York.
Stein, J., ed. 1980.
Random House, Inc.
The Random House college dictionary.
Storch, T.A. 1986. A comparison of water quality in Chautauqua
Lake, New York: 1937-1983. In Lake and Reservoir Management,
Volume II. Proceedings of the Fifth Annual Conference and
International SYmposium on Applied Lake & Watershed Management,
November 13-16, 1985, Lake Geneva, Wisconsin. North American
Lake Management Society, Merrifield, Virginia.
Strahler, A. N.
1957. Quantitative analysis of watershed
Amer. Geophys. Union Trans. 38:913-920.
Taylor, J.K. 1993. Standard reference materials handbook for
SRM users. NIST Special Publication 260-100. National Institute
of Standards and Technology, Standards and Reference Materials
Program, u.S. Department of Commerce, Technology Administration.
The Volunteer Monitor. Published by the Coastal Resources
Center, The University of Rhode Island, Rhode Island Sea Grant
Program, Narragansett, Rhode Island.
Thomas, B.J. 1970. Sedimentation activities in
Pacific division, In Proceedings of a Seminar on
Transport in Rivers and Reservoirs. April 7-9.
Hydrologic Engineering Center.
the north
Sedimen t
U. S. ACE,
USDA. 1981. Forest management for water quality. Forest
Service, Area Planning and Development.
USDA-FS. 1994. Evaluating the effectiveness of forestry best
management practices in meeting water quality goals or standards.
Miscellaneous publication 1520. G.E. Dissmeyer. USDA Forest
Service, Southern Region, Atlanta, Georgia. June.
USDA-SCS. 1993. Water Quality Monitoring. Draft. U.S.
Department of Agriculture, Soil Conservation Service, Washington,
DC. June.
USEPA. 1973. Biological field and laboratory methods for
measuring the quality of surface waters and effluents. EPA-
670/4-73-001. Program Element 1BA027. C.I. Weber, ed. U.S.
Environmental Protection Agency, National Environmental Research
Center, Office of Research and Development, Cincinnati, Ohio.
USEPA. 1975. Model state water monitoring program. National
Water Monitoring Panel. EPA-440/9-74-002. U.S. Environmental
Protection Agency, Washington, DC.

USEPA. 1978a. An assessment of major nonpoint pollution
sources: relative magnitudes, cost-effective controls,
institutional constraints. Booz, Allen, and Hamilton, Inc.,.
Bethesda, Maryland.
USEPA. 1978b. Microbiological methods for monitoring the
environment, water, and wastes. EPA-600/8-78-017. u.s.
Environmental Protection Agency, Washington, DC.
USEPA. 1979. Methods for chemical analysis of water and wastes.
EPA-600/4-79-020. u.s. Environmental Protection Agency,
Washington, DC.
USEPA. 1980a. An approach to water resources evaluation of
nonpoint silvicultural sources (a procedural handbook). EPA-
600/8-80-012. U.S. Environmental Protection Agency, Washington,
USEPA. 1980b. Water quality management needs assessment FY '80-
'84. Draft. u.s. Environmental Protection Agency, Water
Planning Division, Washington, DC.
USEPA. 1981. Guidelines.for evaluation of agricultural nonpoint
source water quality projects. u.s. Environmental Protection
Agency, Interagency Taskforce, Washington, DC. April.
USEPA. 1982a. Chesapeake bay: introduction to an ecosystem.
Chesapeake Bay Program, Annapolis, Maryland.
USEPA. 1982b. Data collection and quality assurance for the
nationwide urban runoff program. u.s. Environmental Protection
Agency, Water Planning Division, Washington, DC.
USEPA. 1982c. Results of the nationwide urban runoff program.
Volume II and Appendices. u.s. Environmental Protection Agency,
Water Planning Division, Washington, DC.
USEPA. 1983. Interim guidelines and specifications for
preparing quality assurance project plans. EPA-600/4-83-004.
QAMS-00S/80. u.s. Environmental Protection Agency, Office of
Monitoring Systems and Quality Assurance, Office of Research and
Development, Washington, DC. February.
USEPA. 1983. Technical support manual: Waterbody surveys and
assessments for conducting use attainability analyses. Volume I.
U.S. Environmental Protection Agency, Office of Water,
Washington, DC. November.
USEPA. 1983. Water Quality Standards Handbook. u.s.
Environmental Protection Agency, Office of Water Regulations and
Standards. Washington, DC. December.
USEPA. 1983a. Chesapeake Bay program: findings and
recommendations. U.S.Environmental Protection Agency, Region 3,
Philadelphia, Pennsylvania.

USEPA. 1983b. Results of the nationwide urban runoff program,
volume I - final report. u.s. Environmental Protection Agency,
Water Planning Division, Washington, DC.
USEPA. 1984. Policy and program requirements to implement the
mandatory quality assurance program. EPA Order 5360.1. U.S.
Environmental Protection Agency, Washington, D.C. April.
USEPA. 1984. Technical support manual: Waterbody surveys and
assessments for conducting use attainability analyses. Volume
II: Estuarine systems. u.s. Environmental Protection Agency,
Office of Water, Washington, DC.
USEPA. 1984. Technical support manual: Waterbody surveys and
assessments for conducting use attainability analyses. Volume
III: Lake systems. u.s. Environmental Protection Agency, Office
of Water, Washington, DC. November.
USEPA. 1984a. A probabilistic methodology for analyzing water
quality effects of urban runoff on rivers and streams first
draft. u.s. Environmental Protection Agency, Office of Water,
Washington, DC.
USEPA. 1984b. Directory of environmental data bases. PB86-
214434. U.S. Environmental Protection Agency, Water Division,
Region 5, Chicago, Illinois.
USEPA. 1984c. Draft ground-water monitoring issue paper.
Environmental Protection Agency, Office of Ground Water
Protection, Washington, DC.
USEPA. 1984d. Ocean monitoring strategy. u.s. Environmental
Protection Agency, Monitoring and Data Support Division,
Washington,. DC.
USEPA. 1984e. Report to congress: nonpoint source pollution in
the u.s. u.s. Environmental Protection Agency, Office of Water
Program Operations, Washington, DC.
USEPA. 1985. Guidance for State Water Monitoring and Wasteload
Allocation Programs. EPA 440/4-85-031. U.S. Environmental
Protection Agency, Office of Water Regulations and Standards,
Washington, DC. October.
USEPA. 1985. Summary of u.S. EPA-approved methods, standard
methods, and other guidance for 301 (h) monitoring variables. EPA
503/4-90-002. U.S. Environmental Protection Agency, Office of
Water, Washington, DC. September.
USEPA. 1985a. Fiscal year 1985 monitoring strategy update for
NPDES compliance. Draft. u.s. Environmental Protection Agency,
Office of Water Enforcement and Permits, Washington, DC.

USEPA. 1985b. Planning workshop to develop recommendations for
a ground-water monitoring strategy. u.s. Environmental.
Protection Agency, Office of Ground Water Protection, Washington,
DC. . . .
USEPA. 1985c. Resource document for the ground-water monitoring
strategy workshop. u.s. Environmental Protection Agency, Office
of Ground Water Protection, Washington, DC. .
USEPA. 1986. Handbook: Stream Sampling for Waste Load
Allocation Applications. EPA/625/6-86/013. u.s. Environmental,
Protection Agency, Office of Research and Development,
Washington, DC. September.
USEPA. 1986. RCRA Ground-Water Monitoring Technical
Guidance Document. OSWER-9950.1. U.S. Environmental
Agency, Office of Solid Waste and EmergencY,Response,
DC. September.
Enforcemen t
USEPA. 1987. Bi,oaccumulation Monitoring Guidance: Selection of
Target Species and Review of Available BioaccumulationData. EPA
430/9-86--005. Volume L 'u.S. Environmental Protection Agency,
Office of Marine and Estuarine Protection, Washington, DC~
March. . .
USEPA. 1987. An overview of sediment quality in the United
States. EPA-905/9-88-002. u.S. Environmental Protection Agency,
Region 5, Chicago, Illinois.
USEPA. 1987a. Handbook, ground water. EPA/625/6-87/016.
Environmental Protection Agency, Washington, DC.
USEPA. 1987b. Nonpoint source guidance. u.S. Environmental
Protection Agency, Office of Water, Washington, DC.
USEPA. 1989. Ecological assessments of hazardous waste sites:
A field and laboratory reference document. 'W. Warren-Hicks, B.R.
Parkhurst, andS.S. Baker, Jr., eds. EPA/600/3-89/013. U.S.
Environmental Protection Agency, Office of Research and
Development, Washington, DC. March. .
USEPA. 1989. Rapid Bioassessment Protocols for Use in Streams
and Rivers: Benthic Macroinvertebrates and Fish. EPA/440/4-
89/001. U.S. Environmental Protection Agency, Office of Water,
Washington, DC. May. '
USEPA. 1989. Statistical analysis of ground-water monitoring
data at RCRA facilities - Interim final guidance. EPA/530-SW-89-
026. NTIS PB89-151047. U.S. Environmental Protection Agency,
Office of Solid Waste, Waste Management Division, Washington, DC.'

USEPA. 1990. Environmental Monitoring and Assessment Program:
Ecological Indicators. EPA/600/3-90/060. U.S. Environmental
Protection Agency, Office of Research and Development,
Washington, DC. September.
USEPA. 1990. Monitoring Lake and Reservoir Restoration. EPA
440/4-90-007. U.S. Environmental Protection Agency, Office of
Water, Washington, DC. August. ..
USEPA. 1990. Surface water monitoring program guidance. Draft.
U.S. Environmental Protection Agency, Office of Water Regulations
and Standards, Assessment and Watershed Protection Division.
Washington, D.C. September.

USEPA. 1990. Volunteer Water Monitoring: A Guide for State
Managers. EPA 440/4-90-010. U.S. Environmental Protection
Agency, Office of Water, Washington, DC.
USEPA. 1991. A Review of Methods for
Contaminated Ground-Water Discharge to
91-010. U.S. Environmental Protection
Washingt?n, DC. April.

USEPA. 1991. Monitoring Guidance for the National Estuary
Program. EPA 503/8-91-002. U.S. Environmental Protection
Agency, Office of Water. August.
Assessing Nonpoint Source
Surface Water. EPA 570/9-
Agency, Office of ,Water,
USEPA. 1991. Volunteer Lake Monitoring: A Methods Manual. EPA
440/4-91-002. U.S. Environmental Protection Agency, Office of
Water, Washington, DC. December.
USEPA. 1991. Watershed Monitoring and Reporting for Section 319
National Monitoring Program Projects. U.S. Environmental
Protection Agency, Office of Water, Washington, DC. August.
USEPA. 1992. A Guide to Selected National Environmental
Statistics in the U.S. Government. EPA-230-R-92-003. U.S.
Environmental Protection Agency, Washington, DC. April~

USEPA. 1992. Inventory of Exposure-Related Data Systems
Sponsored by Federal Agencies. EPA-600-R-92-078. U.S.
Environmental Protection Agency, Washington, DC.
USEPA. 1992. NPDES Storm Water Sampling Guidance Document. EPA
833-B-92-001. U.S. Environmental Protection~Agency, Office of
Water. Washington, DC. July. .
USEPA. 1992. Office of Water Environmental.and Program
Information Systems Compendium,. . EPA-800-B-92-001. U.S.
Environmental Protection Agency, Washington, DC.