United States
Environmental Protection
Agency
Environmental Monitoring
Systems Laboratory
PO Box 15027
Las Vegas NV 89114-5027
EPA 600'4-84-043
May 1984
Soil Sampling
Quality Assurance
User's Guide
Cooperative Agreement
CR 810550-01
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EPA-600/4-84-043
PROJECT SUMMARY
SOIL SAMPLING QUALITY ASSURANCE
USER'S GUIDE
by
Delbert S. Earth and Benjamin J. Mason
vironmental Research Center
versity of Nevada, Las Vegas
Las Vegas, Nevada 89154
Cooperative Agreement
CR 810550-01
Kenneth W. Brown, Project Officer
Exposure Assessment Research Division
Environmental Monitoring Systems Laboratory
Office of Research and Development
Las Vegas, Nevada
March 1984
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SOIL SAMPLING QUALITY ASSURANCE USER'S GUIDE
PROJECT SUMMARY
An adequate quality assurance/quality control (QA/QC)
program requires the identification and quantification of all
sources of error associated with each step of a monitoring
program so that the resulting data will be of known quality. The
components of error, or variance, include those associated with
sampling, sample preparation, extraction, analysis, and residual
error. In the past, major emphasis has been placed on QA/QC
aspects of sample analysis and closely associated operations such
as sample preparation and extraction. For monitoring a
relatively inhomogeneous medium such as soil the sampling
component of variance will usually significantly exceed the
analysis component. Thus, in this case a minimum adequate QA/QC
plan must include a section dealing with soil sampling. The
purpose of this document is to provide guidance in QA/QC aspects
related to soil sampling.
Generally soil monitoring is undertaken to carry out the
provisions and intent of applicable environmental laws with high
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priority requirements associated with hazardous waste management.
The objectives of soil monitoring programs are often to obtain
data on the basis of which to answer one or more of the following
questions.
o Are the concentrations of specified soil pollutants in a
defined study region significantly different from the
concentrations in a control region?
o Do the concentrations of specified soil pollutants in a
defined study region exceed established threshold action
levels?
o At the measured concentrations of specified soil
pollutants in a defined study region what is the
associated risk of adverse effects to public health,
welfare, or the environment?
For each of these applications the QA/QC required to determine
precisions and confidence levels for the data cannot be specified
without giving careful consideration to the consequences of
making an error, for example, in a decision to require, or not to
require, cleanup of a contaminated region. It follows in general
that to be maximally cost-effective and defensible the QA/QC
objectives of a soil monitoring program cannot be separated from
the objectives of the soil monitoring program itself.
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Approximately 20 percent of the total monitoring program
sample load should be allocated to QA/QC with about 5 percent of
this being dedicated to the analytical effort and 15 percent to
the sampling effort. Soil sampling programs must incorporate
statistical designs and QA/QC plans to provide quantitative
measures of both precision and representativeness.
Control samples are normally as important to a soil
monitoring study as are samples taken from the study region. The
data from control samples aid in the interpretation of the
results from the study region and also help to identify sources
and important transport routes for the soil pollutants.
Accordingly, the same level of effort and degree of QA/QC checks
should go into selecting and sampling a control region as goes
into sampling the study region.
Experience has shown that requiring approximately 5 percent
of all analytical samples to be duplicate samples will provide
adequate QA/QC for determining variance between samples collected
at approximately the same site. A precision less than +20
percent is probably unrealistic for a field soil sampling effort.
Table 1 provides recommendations for confidence levels and
precisions for soil sampling related to hazardous waste
investigations.
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TABLE 1
ILLUSTRATIVE CONFIDENCE LEVELS AND PRECISIONS
Confidence Level Precision
(Percent) (Percent)
Emergency Cleanup Activities 90 20
Remedial Response Studies 95 20
Planned Removal Studies > 95 £ 20
All statistical sampling plans are based on frequency
distributions with the most common being normal or log normal.
Generally the concentrations of pollutants in soil and
transport-related properties of these pollutants are distributed
log normally. In addition to obtaining information on the areal
distribution of soil pollutants it is necessary to determine the
distribution with depth.
Both Type I (false positive) and Type II (false negative)
errors should be considered in hypothesis testing. Tables are
provided for use in determining the required number of samples to
achieve defined precision and confidence levels. The location of
sampling is important, and a random process should normally be
used for selecting specific sampling sites. Stratification of
the sampling region may reduce the variance in cases where the
variance is considered to be unacceptably large. Compositing of
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samples is generally not recommended since it allows no estimate
of the variance among the samples being composited.
Suggested QA/QC procedures for soil samples include
preparation of the following samples, generally on the basis of
one QA/QC sample for each 20 samples: field blank, sample bank
blank, reagent blank, calibration check standard, spiked extract,
spiked sample, total recoverable, laboratory control standard,
re-extraction, split extract, triplicate sample, and duplicate
sample.
The major technique used to detect bias in a soil sampling
effort is the adding of known amounts of standard solutions to
some of the samples and comparing the resulting data. It is
especially difficult to demonstrate the complete absence of bias.
The confidence interval for soil samples is bounded by the
confidence limits (bounds of uncertainty about the average caused
by the variability of the experiment). The confidence interval
is used in the development of control charts, in identifying
outliers, and in determining if a set of samples exceed some
established standard. Generally the analysis of variance of the
data provides the best method for obtaining the information
needed for calculating the confidence interval. An approximation
of the confidence interval can be obtained by use of the ranges
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of replicates in a series. The tolerance limits are similar to
the confidence limits but are used to identify the interval and
limits into which data from the individual samples should fall.
The simplest test of hypotheses is either comparison of
two mean values or comparison between the mean and some
established standard, or action, value. The Student's t test is
generally used for both cases.
Once objectives have been defined for a soil monitoring
study, a total study protocol, including an appropriate QA/QC
program must be prepared. Usually not enough is known about the
sources and transport properties of the soil pollutants to
accomplish this in a cost-effective manner without additional
study. The suggested approach is to conduct an exploratory study
including both a literature and information search followed by
selected field measurements based on an assumed dispersion model.
The data resulting from this exploratory study serve as the basis
for the more definitive total study protocol. If one is dealing
with a situation requiring possible emergency action to protect
public health, it is necessary to compress the planning and study
design into a short time period and proceed to the definitive
study without delay. In either case, the objectives of the
monitoring study constitute the driving force for all elements of
the study design including the QA/QC aspects.
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To develop the exploratory study protocol with its
associated QA/QC plan one needs to combine into an assumed
dispersion model the information obtained prior to any field
measurements. On the basis of this model the standard deviation
of the mean for soil samples is estimated. Value judgments are
used to define required precision and confidence levels (related
to acceptable levels of Type I or Type II errors). A control
region is selected. The numbers of required samples may then be
calculated. Additional samples should be required to provide for
the validation of the assumed model. The locations of the
sampling sites should be selected by an appropriate combination
of judgmental (use of the assumed model), systematic (to allow
for the fact that the model may be wrong), and random (to
minimize bias) sampling. Sampling and sample handling must be
accomplished according to standardized procedures based on
principles designed to achieve both data of adequate quality and
maximal cost-effectiveness. Particular attention should be given
to factors surrounding the disposition of non-soil materials
collected with the soil samples.
The requirements for QA/QC for the exploratory study need
not be as stringent as for the more definitive study in the sense
that acceptable precisions and confidence levels may be relaxed
somewhat. Allowance should be made, however, for the collection
of a modest additional number of QA/QC samples over that
specified in the QA/QC plan to verify that the QA/QC study design
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is adequately achieving its assigned objectives. Also, all
normal analytical QA/QC checks should be used.
If the exploratory study is conducted well, it will provide
some data for achieving the overall objectives of the total
monitoring study; it will provide a check of the feasibility and
efficacy of all aspects of the monitoring design including the
QA/QC plan; it will serve as a training vehicle for all
participants; it will pinpoint where additional measurements need
to be made; and it will provide a body of information and data
which can be incorporated into the final report for the total
monitoring study.
For the more definitive study the selection of numbers of
samples and sampling sites, sample collection procedures, and
sample handling methods and procedures follow and build on the
principles discussed and results obtained in the exploratory
study.
Frequency of sampling is an important aspect of the more
definitive study which usually cannot be addressed in the
exploratory study because of the relatively short time span over
which the exploratory study is conducted. The required frequency
of sampling depends on the objectives of the study, the sources
of pollution, the pollutants of interest, transport rates, and
disappearance rates (physical, chemical, or biological
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transformations as well as dilution or dispersion). Sampling
frequency may be related to changes over time, season, or
precipitation. An approach that has been used successfully has
been to provide intensive sampling early in the life of the study
(e.g., monthly for the first year) and then to decrease the
frequency as the levels begin to drop. The important principle
is that the sampling should be conducted often enough that
changes in the concentrations of soil pollutants important to the
achievement of the monitoring objectives are not missed.
The important questions to be answered in the analyses and
interpretation of QA/QC data are, "What is the quality of the
data?" and "Could the same objective have been achieved through
an improved QA/QC design which may have required fewer
resources?" It is desirable to provide summarized tables of
validated QA/QC data in the final report. This approach allows
users to verify the reported results as well as begin to build a
body of QA/QC experimental data in the literature which allow
comparisons to be made among studies. Special emphasis should be
placed on how overall levels of precision and confidence were
derived from the data. If portions of the study results are
ambiguous and supportable conclusions cannot be drawn with regard
to the reliability of the data, that situation must be clearly
stated.
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The adequacy of all aspects of the QA/QC plan should be
examined in detail with emphasis on defining for future studies
an appropriate minimum adequate plan. Some aspects of the QA/QC
plan may have been too restrictive, some may not have been
restrictive enough. Soil monitoring studies should have checks
and balances built into the QA/QC plan which will identify early
in the study whether the plan is adequate and; if required, allow
for corrective action to be taken before the study continues.
This is one of the major advantages of conducting an exploratory
study.
There is insufficient knowledge dealing with soil monitoring
studies to state with confidence which portions of the QA/QC plan
will be generally applicable to all soil monitoring studies and
which portions must be varied depending on site-specific factors.
As experience is gained it may be possible to provide more
adequate guidance on this subject. In the meantime it is
recommended that many important factors of QA/QC plans be
considered as site-specific until proven otherwise.
Another important aspect of QA/QC is auditing. The purpose
of an audit is to insure that all aspects of the QA/QC system
planned for the project are in place and functioning well. This
includes all aspects of field, sample bank and laboratory
operations. Whenever a problem is identified corrective action
should be initiated and pursued until corrected. Sample
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chai n-of-cus tody procedures and raw data are checked as
appropriate and results of blind QA/QC samples routinely inserted
into the sample load are reviewed. Spot-checks of sampling
methods and techniques, sampling and analysis calculations, and
data transcription are performed. Checks are made to ascertain
that required documentation has been maintained and in an orderly
fashion, that each of the recorded items is properly categorized,
and cross-checking can be easily accomplished. Checks are made
to insure that data recording conforms to strict document control
protocols and the program's QA/QC plan.
It is recommended that an audit of the overall QA/QC plan
for sample documentation, collection, preparation, storage, and
transfer procedures be performed just before sampling starts.
This is to review critically the entire sampling operation to
determine the need for any corrective action early in the
program.
The project leader of a soil monitoring project is
responsible for ascertaining that all members of his project team
have adequate training and experience to carry out satisfactorily
their assigned missions and functions. This is normally
accomplished through a combination of required classroom
training, briefings on the specific monitoring project about to
be implemented, and field training exercises. Special training
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programs should be completed by all personnel prior to their
involvement in conducting audits.
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EPA-600/4-84-043
SOIL SAMPLING QUALITY ASSURANCE
USER'S GUIDE
by
Delbert S. Barth and Benjamin J. Mason
Environmental Research Center
University of Nevada, Las Vegas
Las Vegas, Nevada 89154
Cooperative Agreement
CR 810550-01
Kenneth W. Brown, Project Officer
Exposure Assessment Research Division
Environmental Monitoring Systems Laboratory
Office of Research and Development
Las Vegas, Nevada
March 1984
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NOTICE
The information in this document has been funded wholly or in
part by the United States Environmental Protection Agency under
Cooperative Agreement CR 810550-01 to the Environmental Research
Center. It has been subject to the Agency's peer and
administrative review, and it has been approved for publication
as an EPA document.
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ABSTRACT
The inherent inseparability of a cost-effective Soil
Sampling Quality Assurance/Quality Control (QA/QC) Plan from the
objectives of a soil monitoring program is emphasized. Required
precisions and confidence levels for the data cannot be defined
until the decisions which will be made on the basis of the data
are clearly stated and the consequences of making Type I (false
positive) or Type II (false negative) errors are weighed.
General and specific objectives for Soil Sampling QA/QC Plans are
presented and discussed with special emphasis on cases associated
with the management of hazardous wastes. Selected statistical
considerations are presented with special attention to analyses
of variance of soil monitoring data, methods of calculating
required numbers of soil samples to achieve desired precisions
and confidence levels, possible applications of Kriging, and
assignment of control limits to QA/QC data. The value of an
exploratory or preliminary study to the cost-effective
achievement of both the soil monitoring objectives and the
objectives of the Soil Sampling QA/QC Plan is strongly emphasized.
The value of developing a hypothetical model to estimate the
distribution in space and time of soil pollutants and thus to
assist in the design of the monitoring network is discussed.
Methods for determination of the number and locations of soil
sampling sites; sample collection methods and procedures to
include frequency of sampling; sample handling to include
labeling, preservation, preparation for analysis, and transport;
together with QA/QC aspects of all of the above are presented and
discussed. The ultimate goal in the analysis and intepretation
of data is to build a body of representative and comparable data
on the basis of which both general guidelines (factors applicable
to all sites) and specific guidelines (factors which are
site-specific) may be developed for Soil Sampling QA/QC Plans.
Finally, the importance of systems audits and training to the
achievement of soil sampling QA/QC objectives is presented and
discussed.
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SOIL SAMPLING QUALITY ASSURANCE USER'S GUIDE
CONTENTS
Notice ii
Abstract iii
Figures vi
Tables vi
1. Introduction 1
Background 1
Objectives 4
Audience 4
Approach 4
2. Objectives of Quality Assurance-Quality Control
Plans 6
Introduction 6
General identification of the objectives .... 8
Objectives for background monitoring 14
Specific objectives for monitoring in support
of CERCLA 15
3. Statistical Considerations 30
Introduction 30
Distribution of soil sampling data 31
Statistical designs 32
Data analysis 40
4. Exploratory Study 50
Introduction 50
Number and location of sites for sampling ... 51
Sampling and sample handling 53
Analysis and interpretation of data 55
5. Selection of Numbers of Samples and Sampling Sites 57
Introduction 57
Number of sampling sites required 58
Location of sampling sites 62
Quality assurance aspects 63
6. Sample Collection 65
Introduction 65
Size of samples and method of collection .... 65
Boring Log 66
Frequency of sampling 66
Quality assurance aspects 67
7. Sample Handling and Documentation 69
Introduction 69
Container preparation, labeling, preservation
and sample preparation 69
Quality assurance aspects 75
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8. Analysis and Interpretation of QA/QC Data .... 76
Introduction 76
Presentation of data Summaries 76
Presentation of results and conclusions .... 81
Quality assurance aspects 81
9. Systems Audits and Training 83
Introduction 83
Sample bank audit 84
Daily log 86
Bank logs 86
Sample collection audits 86
Field audits 87
Data management audits 88
Training 88
References 89
Appendices
A. Tools for estimating number of samples to achieve
specified levels of precision and confidence . . 93
B. Tables for use in calculating confidence and
tolerance limits and judging the validity of
measurements 99
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FIGURES
Number Page
2-1 Data acquisition flow for hazardous materials 16
2-2 Monitoring data flow 21
2-3 Technology and transfer data flow 23
3-1 Acceptance region for H:yo=30.0 35
3-2 Type II or 3 error 35
A-l Number of degrees of freedom required to
estimate the Standard Deviation within P% of
its True Value with confidence level Y . . 94
TABLES
2-1 Effect of increases in analyses and sample size 8
3-1 Analysis of variance of a nested soil
sampling design 34
3-2 QA/QC Procedures for soil samples 41
3-3 PCB study to determine contamination of
an area (hypothetical data) 48
5-1 Number of samples required to achieve a
sampling precision (P) at a confidence
level of (1-a) 60
5-2 Number of samples required to achieve a
sampling precision (P) at a confidence
level of (1-a) and a power of (1-6) 61
7-1 Sampling containers, preservation requirements,
and holding times for soil samples 71
7-2 Accountable document control requirements . . 74
A-l Estimated number of samples to achieve
specified levels of precision and confidence
when coefficient of variation (CV) is known 95
B-l Percentiles of the t distribution 100
B-2 Confidence interval for averages 101
B-3 Single classification factor (c^) to estimate
standard deviation from range, and equivalent
degrees of freedom (/)a 102
B-4 Tolerance interval for individuals 103
B-5 Critical values for discarding invalid
measurements 104
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CHAPTER 1
INTRODUCTION
BACKGROUND
Data resulting from any monitoring or sampling program
cannot be evaluated and interpreted with confidence unless
adequate quality assurance methods and procedures have been
incorporated into the program design. An adequate quality
assurance program requires that all sources of error associated
with each step of the monitoring or sampling effort be identified
and quantified.
Sources of error are then analyzed with an appropriate
statistical design to yield estimates of the various components
of variance. The component of variance analysis is based upon
the premise that the total variance for a particular population
of samples is composed of the sum of the variances from each of
the identified sources of error plus an error term which is the
sample to sample variance (a2). The population variance (a2) is
usually unknown: therefore, it must be estimated from a set of
samples collected from the population. The total sample variance
(s2) is estimated from the summation of the sum of squares (SS)
from each of the identified components of variance plus the error
SS. For example:
SSt = SSs+SSp+SSex+SSa+SSer
where SSt = Total SS
SSS = Sampling SS
SSp = Sample Preparation SS
SSex= Extraction SS
SSa = Analysis SS
SSer= Error SS
The result of this analysis provides a measure of the precision
of the analysis plus confidence limits.
To date the most highly developed aspect of quality
assurance undertaken i-n support of monitoring programs has
been for the analytical procedures. Such an approach is not
adequate in cases where the medium being sampled is not
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homogeneous, which is particularly true for soil and may also be
true in some instances for air, water, sediments or foods. For
example, two soil samples taken a few feet apart may differ in
important characteristics or chemical pollutant concentrations by
an order of magnitude or more. Therefore, quality assurance on
the analytical results is a necessary but not sufficient
condition for assessing total sample variability within the soil
population being sampled. The analytical errors may account for
a negligibly small portion of the total variance. In view of the
above it is clear that for soil monitoring programs a more
comprehensive quality assurance program is mandatory. This
document will address the quality assurance aspects associated
with soil sampling.
Prior to proceeding with the quality assurance aspects it
is necessary to discuss soil monitoring in general, monitoring
objectives, and possible actions which may be taken on the basis
of the resulting monitoring data. Clearly it is not possible to
separate the required quality assurance procedures for soil
monitoring from the objectives or purposes for which the soil is
being monitored.
Soil monitoring may be:
o carried out to meet the provisions and intent of
environmental laws such as the Resource Conservation and
Recovery Act (RCRA), the Comprehensive Environmental
Response, Compensation, and Liability Act (CERCLA), the
Federal Insecticide, Fungicide, and Rodenticide Act
(FIFRA), the Toxic Substances Control Act (TSCA), etc.
o source, transport or receptor oriented
o conducted to determine the presence of specified
contaminants in comparison to an appropriate background
level
o conducted to determine the levels of contaminant and
their spatial and temporal distribution
o conducted to provide input into an exposure and risk
assessment study
o part of a compliance monitoring scheme to measure the
efficacy of control actions
o part of a research, technology transfer, or
environmental model validation study.
Presumably, in each case where soil monitoring is deemed
necessary, administrative or legal actions are likely to be taken
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on the basis of an evaluation and interpretation of the resulting
data. The consequences of taking or not talcing action must be
clearly understood before it is possible to establish an
allowable confidence band for quality assurance of the data.
After weighing and evaluating the consequences, a value judgment
must be made by a responsible official concerning the acceptable
probability of making a Type I (false positive) or a Type II
(false negative) error (see Chapter 3 for discussion of Type I
and Type II errors). It is not possible to design a meaningful
quality assurance program until this step has been taken.
The acceptable probability for each type of error must be
established in relation to the consequences of making such errors
and depends upon the specific objectives of the soil monitoring
program. The Type I error is the error most often used in the
literature. In environmental monitoring, however, the Type II
error may be more important than the Type I error. The cleanup
of a highly toxic spill would be an example where a false
negative could create major problems for the environmental
manager. The Type II error would lead the manager to conclude
that a cleanup of some areas is not necessary when in fact the
action levels are being exceeded and cleanup is necessary. The
Type I and Type II error for the QA/QC effort should be equal to
the error levels chosen for the sampling effort itself. This
acceptable probability in different cases may, for example, range
from 20 percent to 1 percent or less. In some circumstances the
value judgment may simply be a statement of an allowable error
not to be exceeded in the final data.
There may be a temptation in many cases to avoid making the
necessary value judgments concerning acceptable probabilities of
making different kinds of error. The course of action often
substituted for the difficult value judgment is to adopt as a
guiding principle the concept that one should always strive to
achieve the highest precision and level of confidence (or lowest
error) possible with exisiting available resources. The
resulting data are then used as the basis for making decisions
with the assumption that this guiding principle gives the best
possible result. Obviously such an approach will rarely, if
ever, be cost-effective. Two types of errors are possible. The
data may be much better than required which indicates resources
have been wasted, or the data may not be of adequate quality
thereby resulting in costly decisions of doubtful validity. This
point may be summarized by stating that resource availability is
an important factor for consideration in the establishment of
quality assurance programs, but resource availability should not
be accepted as the sole determinant of required quality assurance
methods and procedures. Maximal cost-effectiveness should be the
overall goal. This generally means that a minimum adequate
quality assurance plan must be defined and then implemented.
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OBJECTIVES
This document is intended to serve as a user's guide
presenting and explaining selected principles and applications of
methods and procedures for establishing adequate quality
assurance on soil sampling aspects of environmental monitoring
programs. The soil sampling aspects treated include sample site
select ion, sample collection, sample handling, and analysis and
interpretation of resulting data. No detailed treatment of
analytical quality assurance procedures is given since that
important aspect of the overall problem has been adequately
treated elsewhere (USEPA-600/4 - 82 - 030 a -df 1982;
USEPA-600/4-84-012,1984). It should be noted, however, that
sampling quality assurance procedures are not fully separable
from analytical quality assurance procedures. This is
particularly true for sample collection and handling procedures.
If an intact, timely, and representative sample of proper size
and constituency is not adequately delivered to the analytical
laboratory, the analytical quality assurance procedures cannot be
expected to yield meaningful results. Thus the soil sampling
quality assurance procedures presented here should be viewed as
an important integral part of the overall quality assurance plan.
AUDIENCE
This document has been developed to serve as a user's guide
for anyone designing, implementing or overseeing soil monitoring
programs. It is especially applicable for personnel responsible
for regulatory programs where soil monitoring is an important
integral element. Special attention is given to soil sampling
examples related to CERCLA since such applications are deemed to
constitute high priority for soil sampling programs. Many of the
principles and procedures discussed, however, are applicable to
other situations as well.
APPROACH
Following the presentation in Chapter 2 of general and
specific objectives of quality assurance plans a brief survey of
selected applicable statistical methodology is presented.
Discussion of the value of an exploratory study to the
subsequent design of a soil sampling quality assurance program
leads logically into more detailed discussions of sample site
selection, sample collection, and sample handling. These
detailed discussions will include minimal coverage of soil
monitoring protocols, per se, since they were recently treated in
a comprehensive document (Mason, 1983). The focus of the
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discussions here will be quality assurance. The goal of each
discussion will be the development of design features for sample
site selection, sample collection, and sample handling to meet
quality assurance objectives of defined precision and levels of
confidence for each subject area.
Similarly, the goal of the discussion concerning analysis
and interpretation of data will be focused on quality assurance
aspects. Special attention will be focused on a technique known
as the components of variance analysis. This analysis results
from the use of a statistical sampling plan designed to measure
as many of the sources of variation as can be identified and
sampled in a cost effective manner. The analysis further
identifies the amount of total sample error (or variance) that
results from each component in the sampling - analysis chain.
The last two subjects treated are program audits and personnel
training.
To the maximum extent feasible throughout this report we
will present concepts and principles first and then present
selected examples of how these concepts and principles may be
applied in realistic situations.
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CHAPTER 2
OBJECTIVES OP QUALITY ASSURANCE-QUALITY CONTROL PLANS
INTRODUCTION
The main objective of any soil sampling quality
assurance-quality control (QA/QC) plan is to determine the
quality of the reported data and insure that it is adequate to
the degree required for the intended end use of the data. How
this objective is met depends upon the purpose of the particular
sampling program.
Soil is by its very nature extremely variable. Superimposed
on this variability are other sources of variation or error that
can be introduced into the final result by the sampling and
analytical efforts. The concept of total QA/QC has been used to
develop a system for assuring the quality of the results by
attempting either to provide control of the various steps in the
analytical process leading from sample collection to data
interpretation or to provide adequate replication for
statistically determining and quantifying the sources of
variation or error in the chain.
QA/QC requires that each step in this chain be shown to be
valid. USEPA (1976) has indicated that the quality of the data
considered to be acceptable must be defined as quantitatively as
possible. The variability of the soil and the requirement for a
quantitative standard for acceptability requires that a
statistical sampling plan be developed that assures the
precision, bias, completeness, comparability, and
representativeness of the sampling effort and of the resulting
data.
Statistical sampling is the mechanism by which the QA/QC
program can determine the sampling precision and can provide a
measure of the reliability of the entire sampling effort.
Buffington (1978) quotes Congressman George E. Brown Jr. as
saying "no number is significant, and subsequently worthy of
being recorded, without an estimate of its uncertainty." This
statement should be considered when designing the QA/QC plan for
a soil sampling effort.
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It is not uncommon to spend considerable money on a sampling
and analysis program only to find that the samples were not
collected in a manner that allows valid conclusions to be drawn
from the resulting data. Ku (1978) states "...the design of a
proper statistical sampling scheme depends almost entirely on the
purpose for which the results are going to be used. Hence,
without an explicit and defined purpose for an undertaking, the
design of the sampling scheme cannot be formatted for efficient
data collection and for the correct interpretation of results."
Skogerboe and Koirtyohann (1976) note "...cost considerations
most frequently serve as the excuse for failing to carry out even
the most rudimentary quality assurance checks." This failure to
accept the fact that quality assurance is cost effective
continues to plague the scientific community in spite of the
considerable body of literature to the contrary.
QA/QC programs for analytical laboratories are widely used
and accepted. These programs are strongly oriented toward the
analytical process, not toward the sampling effort. This
orientation was indicated by Plumb (1981) who suggested that 15
to 20 percent of the total analytical work load be dedicated to
the quality control program. Of this, five percent was allocated
to the sample collection effort and 15 percent to factors that
were considered to be a portion of the laboratory effort.
However, studies that have been done to determine the components
of variance (Snedecor and Cochran, 1982; and Bauer, 1971) in
final monitoring data indicate that reversing the quality control
sample allocation load would not only be more cost effective but
also provide a better estimate of the quality of the sampling or
monitoring effort.
The component of variance analysis identifies various
components of the environmental sampling scheme that influence
the total variance of the samples collected. The design of the
statistical study depends upon the purpose of the sampling and
the method of collection. A first approximation of the total
variance can be defined by the following equation (Bauer, 1971).
Vt=(Vs/k) + (Va/kn),
where k is the number of samples, n the number of analyses per
sample, kn the total number of analyses, Vt the total variance,
Va the analytical variance and Vs the sample variance.
One of the general purposes of a sampling effort should be
to obtain samples with the smallest feasible Vt and thus the best
available precision. Intuitively one can identify the portion of
a sampling effort where the greatest gain would be made in
reducing the variation in the data. Analytical programs
frequently attempt to attain a precision of less than + 1 percent.
-------
On the other hand, sample to sample variation for soils is often
on the order of 30 to 40 percent. Increasing n by one reduces
the contribution from the small analytical variance but has
little
or no effect on the total variance,
one reduces both the larger sampling variance
variance; thus, increasing k produces more gain
of the sampling effort.
Increasing k by
and the analytical
in the precision
The actual data presented in Table
approximately equal (Bauer, 1971) show
increasing the number of analyses while
samples constant and vice versa. These data
was previously described.
1 where Vs and Va are
both the impact of
holding the number of
show the gain that
Table 2-1. EFFECT OF INCREASES IN ANALYSES AND SAMPLE SIZE
n
kn
t*
1
1
1
2
4
1
2
4
1
1
1
2
4
2
4
0.0993
0.0793
0.0693
0.0396
0.0248
0.32
0.28
0.26
0.20
0.16
* total standard deviation
This information should be considered in determining the
objectives according to the steps outlined below.
GENERAL IDENTIFICATION OF THE OBJECTIVES
General
The objectives of any quality assurance effort focus
primarily upon verification of the required reliability of the
sampling data to support actions which will be taken on the basis
of interpretation of the data. An important consideration is the
percent of Type I or Type II error which will be deemed
acceptable. A decision on this matter leads to the definition of
required confidence levels. Reliability might be defined as the
probability that a particular measure of the soil system reflects
the true average value for all of the soil in a defined
geographical area in which the sample was taken. This requires
that the accuracy of the method, the representativeness of the
sampling, and the comparability of the data be determined.
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Accuracy and Comparability
The accuracy and comparability of the data are determined by
the analytical laboratory working with the agency's quality
assurance laboratories. Reference samples, spikes and duplicate
analyses are used as part of the routine, daily QC program. The
laboratories also are involved in an interlaboratory
collaborative program designed to aid in evaluating the
quality of the data produced by a particular laboratory using a
particular method. Environmental scientists must work
cooperatively with the analytical laboratory to insure that the
required field samples are taken for use by the laboratory for
conducting its own QC effort. The investigator is not likely to
be directly involved in the determination of the accuracy of the
method used by the laboratory unless he has a specific reason to
further verify the laboratories' performance.
Precision and Representativeness
The precision and the representativeness of the final
results are of primary concern to the investigator. Precision
measures the repeatability of the results obtained from analyzing
the collected soil samples. The statistical plan used to design
the sampling effort should take into consideration all of the
sources of variation likely to be encountered.
Representativeness of sampling has two components. First
the sample taken must reflect what is present in the soil. For
example if one must measure the macro structure of the soil an
undisturbed block sample must be taken and carefully prepared for
transport to the lab. A sample taken for analysis of metals on
the other hand can be disturbed. Another example of this aspect
of representativeness would be a landfill where scrap wood had
been used to absorb liquids placed in the landfill. The wood is
not soil and therefore should not be included in the analyses;
yet, it is a major component of the pollutant source term and
therefore should be measured. Thus, the objectives of the
sampling will determine how the sample should be taken and
handled during shipment, etc. This first aspect of
representativeness is difficult to quantify because it is often
quite subjective.
The second aspect of representativeness can be quantified
because it is closely tied to sampling precision. This aspect
addresses the reliability of the mean and the standard deviation
as measures of the amount of a chemical present in a particular
area. Increased sampling intensity, (spatially and/or
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temporally) independent sampling, sampling audits and the use of
confidence maps developed by Kriging are all examples of
techniques that can help insure that the sample is representative
of the conditions in the area under investigation.
The sampling plan should be designed in such a way that it
provides quantitative measures of both precision and
representativeness. The QA/QC required levels of reliability
vary with the purpose of the study. Six situations where soils
are likely to be sampled as a part of the USEPA's mandated
responsibilities are illustrated below. Each situation has its
own QA/QC requirements. The situations are:
o preliminary site investigations
o emergency cleanup operations
o remedial response operations
o sampling for litigation purposes
o monitoring
o research or technology transfer
Preliminary Site Investigation;
The purpose of a preliminary site investigation is to
provide information about a specific site that can be used in
making initial management decisions, and, should further work be
necessary, for designing a detailed and comprehensive monitoring
program. The data collected during the preliminary study are
often used to determine if a site will require further
investigation. Three basic conclusions from preliminary data
might be:
o No further study is needed.
o A detailed study is needed.
o A conclusion cannot be drawn without further study.
For such conclusions to be drawn there is a definite need
to measure the reliability of preliminary data. However, methods
that are often used could be classified as "look and see" or
"quick and dirty." Many times little attention is given to
statistics in sampling design, and the efforts are sometimes
biased by the interests of the particular investigator. Any
approach for collecting preliminary data without adequate QA/QC
should be strongly discouraged as counterproductive.
Judgmental sampling is often used in the preliminary site
investigation. This approach is based upon the investigator's
judgment as to where the samples should be taken. Judgmental
sampling may be the best approach to use if there is a limited
number of samples allowed by the study plan. The major
disadvantages of using judgmental sampling centers on the fact
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that the samples are biased and that very often little useful
information on spatial variation is obtained. This approach
prevents the investigator from making certain statements about
the reliability of data derived from the samples collected.
On the other hand, judgmental sampling can be combined with
other sampling plans in order to insure that particular aspects
of the site can be addressed. For example, examination of
historical data and a site visit may indicate areas where
pollutants were believed to be placed and how a plume from this
location may have moved in a particular direction. A sampling
plan can then be designed to focus the sampling at the original
disposal area and along the suspected plume axis. The exact
sampling locations can then be randomly or sequentially located;
the exact choice depending upon the purpose of the study.
Emergency Cleanup Operations
The emergency cleanup operation (immediate removal) has a
single focus remove the pollutant as quickly as possible to
achieve either a background level or a level that is not an
unacceptable threat to human health, welfare or the environment.
The principal role of QA/QC relates to a reliable determination
that cleanup operations have been adequate.
The contamination may be limited in scope; e.g., a group of
leaking barrels lying on the surface or a spilled tank truck. A
leaking landfill, on the other hand, could present an entirely
different demand on the investigator. Resources are limited for
site investigations no matter what the level in the chain leading
from discovery to abatement. The emergency cleanup operation
often leads to one of the higher steps in the chain. Criteria
for determining if the emergency cleanup operations should be
elevated to either a planned removal or a remedial response
operation are based to some extent on cost and the length of time
required to implement the action (USEPA, 1982).
The fact that the emergency cleanup operation can lead to
one of the more definitive types of monitoring operations places
a demand on the investigator to collect as much information on
the area as is possible within the time and resource constraints.
This demand suggests that an adequate statistical design
incorporating appropriate QA/QC measures should be used to
provide the quality of data needed for the decisons that must be
made by the On-Scene Coordinator. A decision made on the basis
of data collected following a statistical design is more likely
to be defensible as there is an identified measure of reliability
that can be placed on the decision process.
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Remedial Response Operations
As has been previously identified, the remedial response
operation is one of the possible steps in an environmental
cleanup process. Studies conducted under a remedial response are
normally quite detailed and have the latitude to provide for a
thorough soil investigation. The designs used in these
situations are likely to be directed to provide not only a
quantitative evaluation of the pollutant data but also a spatial
evaluation as well. The remedial response operation which is
designed as a permanent remedy, at times allows the investigator
to develop a data base on time trends.
Many of the actions used to control the impacts of a
pollutant depend upon the nature and properties of the soil at
the site. The studies conducted for remedial response usually
attempt to develop soil physical and chemical characterization
data along with the pollutant data.
Similar to remedial response, planned removal operations
may also involve extensive monitoring and sampling programs.
The detail and extent of a planned removal monitoring and
sampling program may be quite extensive. However, the planned
removal operation is limited by time (six months), thus limiting
the investigator from collecting data for time trend analysis.
Sampling for Litigation Purposes
All of the previously mentioned sampling situations have a
potential for litigation. There are, however, a group of studies
that are designed for specific litigation goals. Potential
questions may arise in court that must be addressed by studies
designed to provide specific data. Negotiations may require
studies that are designed to aid in drawing conclusions and
making decisions prior to taking a negotiating stance. These
studies require that a good experimental design be used.
Statistical designs incorporating appropriate QA/QC measures and
including "chain-of-custody" procedures are one of the best ways
to provide the kinds of information needed in these situations.
The litigation study is often similar to a research study in
that there is a specific hypothesis that is being tested or
evaluated by the investigator. Details will vary as the purpose
changes. The confidence levels desired and thus the cost of the
studies are usually higher than those encountered in other types
of field sampling efforts.
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Monitoring Studies
The purpose of a monitoring study may be routine or it may
be the outcome of a negotiation process. The study is often
designed to measure pollution levels and changes in spatial and
temporal distributions. Evaluation of these changes may require
the use of techniques such as intervention analysis or Kriging to
aid in identifying patterns which may not be directly obvious
from the monitoring data itself. These studies can occur over
long periods of time and have a routine aspect to them.
The design of a monitoring study and the associated QA/QC
procedures frequently is dictated by a negotiated settlement or
by some administrative review process. Designs that are costly
often have little chance of being implemented. The more
efficient the design, the better the likelihood that it will be
implemented. The reliability of the data combined with a measure
of cost effectiveness should be the primary consideration for
selecting the monitoring design. This implies that the QA/QC
program design should also be minimally adequate. Too often,
cost is the excuse for failing to apply even limited statistical
and QA/QC criteria in the monitoring design selection process
(Skogerboe and Koirtyohann, 1974).
Properly designed, quality assured, monitoring plans allow
the investigator to make comparisons within a particular
monitoring data base and also to make comparisons with other
monitoring studies. Thus, each properly designed monitoring
study can add to our overall knowledge of the environment rather
than just provide data of limited reliability for a limited use.
Research or Technology Transfer Studies
These studies are by nature designed to answer specific
questions. The purpose is to increase knowledge or to make a
decision about some characteristics of the soil system. The
experimental design should be statistically and quality
controlled. Failure to provide a measure of the reliability of
the data will ultimately lead to the results of the study being
questioned or invalidated by peer review.
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OBJECTIVES FOR BACKGROUND MONITORING
General
Generally the design of soil monitoring programs requires
that the levels of defined hazardous or potentially hazardous
substances and their spatial and temporal trends be measured for
some specific purpose. Often it is critical not only to
quantitate levels and trends but also to link the existing levels
to sources. This is necessary to enable adequate control actions
to be taken whenever a situation that is hazardous to human
health, welfare, or the environment is identified. often the
situation is complicated by the fact that multiple sources
contribute to the measured levels.
The situation is further complicated by the presence of
pollutants of recent origin mixed with pollutants of past origin.
This mixing becomes especially important when the investigator
attempts to trace the migration from source to receptor and also
in predicting what future levels are likely to be after various
proposed control measures are implemented.
Identification of spatial and temporal trends along with
linkage of observed measurements to sources requires that
adequate background, reference or control samples be taken.
In the absence of such background samples, interpretation of
the resulting data may become extremely difficult, if not
impossible. The burden of proof that background samples are not
necessary, for a particular soil monitoring study, rests with the
principal investigator. In the absence of such proof a prudent
investigator will insure that the collection of adequate
background samples is included in the monitoring study design.
Furthermore, some EPA regulations concerning regulatory
monitoring (U. S. Code of Federal Regulations, 1983) specifically
require background sampling.
Since measured levels in presumably higher concentration
areas will be compared to background levels, QA/QC procedures are
just as critical for the background measurements as they are for
the study area measurements. Thus, for background sampling, a
QA/QC procedural umbrella must cover the selection of appropriate
geographical areas, the selection of sampling sites within the
geographical areas, sampling, sample storage and/or preparation,
sample analysis, and interpretation of the resulting data.
Under most circumstances background data will not be
available for a given monitoring location. These data must be
14
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acquired either before or during the exploratory or preliminary
investigation phase. The intensity of the background sampling
that is undertaken depends upon the pollutants being measured,
the soil characteristics and variability, the levels of pollutant
likely to be found in the study area and the purpose of the study.
Further discussion of the role of background studies is presented
in Chapter 4.
SPECIFIC OBJECTIVES FOR MONITORING IN SUPPORT OF CERCLA
The specific QA/QC precision and confidence level objectives
for any sampling study are controlled in part by the goals of the
particular study. Three example situations where soil sampling
will likely be undertaken are:
o hazardous materials investigations for areas such as
abandoned landfills or chemical spills
o monitoring studies
o technology transfer
The data flow that can occur in each of these situations is
outlined in Figures 1, 2 and 3. The data generated in each
category can provide input into the development of plans and
specifications for the other situations. Data that have been
subjected to a good QA/QC plan can be relied upon as a resource
for the development of new data.
The main area where the magnitude of the soil sampling can
be controlled is in the precision required by the sampling
designs. The accuracy of the sampling is unknown because the
true average is not available. Repeated sampling for a high
precision nevertheless must rely on the analytical accuracy
obtained in the laboratory to insure that the methods used
measure what is present in the soil sample. Thus the accuracy
for analysis applies only to the samples while the accuracy for
the study depends on the degree to which the samples are
representative of the area.
The steps outlined below are designed to provide a
monitoring effort with the needed sample precision and
representativeness (USEPA, FR 44:233, 1979 and Bauer, 1971).
1. Identify the objectives of the study. These should
reflect the specific items of information that are required to
make the decisions that will follow achievement of the study
objectives.
15
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I
End
End
I
Preliminary Site
Investigation
Ijuigoncy
Clean-tp
Figure 2-1. Data acquisition flow for hazardous materials.
16
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Remedial
Response
Litigation
Sampling
Monitoring
Effort
Figure 2-1. (Continued)
17
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Corrective
Action
Design Corrective
Measures
Figure 2-1. (Continued)
18
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Remedial
Response
Clean-up
Complete
is
Litigation
Planned
Planned
Renoval
Planned
Renoval
Figure 2-1. (Continued)
19
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Is
Research
Needed
Research
Studies
Figure 2-1. (Continued)
20
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Design
Monitoring Study
Acquire
Monitoring Data
Exceed
Standards
Initiate
Corrective Action
Figure 2-2. Monitoring data flow,
21
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Litigation
Anticipated
Litigation
Studies
Figure 2-2. (Continued)
22
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Technology
Transfer
Studies
ere
Objectives
Met
Figure 2-3. Technology transfer data flow,
23
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2. Determine the components of variance that are built into
the statistical design. Proper stratification of the study area
will lead to several sources of variation. The sources of
variation that can be controlled by the sampling are determined
by the particular sampling design used and by the pattern of
sample collection superimposed over the area. An analysis of
variance of the data provides information which can be used in
calculating components of variance. Table 3-1 gives an example
of a component of variance study on a set of hypothetical soils
data.
3. Choose the desired confidence level. A confidence level
of 95 percent or better is desirable; however, this is often not
possible because of either fundamental constraints or the
economics of the situation. The investigator may have to select
a level, determine the number of samples and replications
required and then compare this with the resources that are
available and recalculate the confidence level that can be
reasonably attained with the resources available. Of course, if
the revised level is not adequate to allow achievement of the
study objectives, then more resources must be found, the study
objectives must be revised, or the study must be abandoned. The
major point to be made here is that the confidence level should
be chosen before the study is conducted and not after the data
are collected.
4. Obtain sampling data from other studies that have
similar characteristics to the one being designed. Particularly
desired data are those where the results were derived from
replicated samples. These data will be used to calculate average
parameters such as the coefficient of variation, variance and
confidence intervals for early stages of the sampling process.
5. Calculate the mean and range of each set of replicates.
6. Group the sets of replicates according to concentration
ranges and by the types of samples that are believed to be
similar. An example of the groupings might be samples in the
range from 0 to less than 10, and 10 to less than 25 mg/1, etc.,
or by soil type such as those that were in sand, silt or clay.
7. Calculate the critical difference Rc (number not to be
exceeded to maintain adequate QA/QC) by noting that for any group
of n duplicate analyses that are considered similar to each
other, their ranges [R^] and means [X^] can be used to
24
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estimate the critical difference [Rc] between similar future
duplicate analysis for any specific concentration level [C].
Specifically,
Rc = 3.27 (C)
n
n
z
where X^ = Xf + Xj+j and Rj_ = Xj_ -
2
8. Develop a table of Rc values for various concentrations
that span the range of concentrations of interest. (A similar
approach makes use of confidence limits based on the standard
deviation rather than the range. ) These data are used to accept
or reject a set of replicated samples. The replicates are
usually duplicate samples, and therefore the difference between
the two values should lie within the critical range. If the
sample is rejected, the analyses should be rerun if possible.
The indication is that one or both of the samples or the analyses
were variant. Discarding of the results should only be done
after careful review of the data. There are situations in soil
sampling where the coefficient of variation can reach hundreds of
percent due to the variability in the soil system; therefore, the
suspected outlier may in fact be a part of a wide distribution.
This tends to be the case in situations where very high levels of
chemicals have been spilled over small areas or where chemicals
have flowed through desiccation cracks, animal burrows or old
root channels. Observations made by the field party can aid in
making a decision to discard a sample if appropriate comments
have been noted in the log books at the time of sample
collection.
9. The constructed preliminary Rc table is used until data
are acquired during the sampling. As the analyses proceed the
results are combined with those from previous studies. At the
point where approximately fifteen pairs (USEPA, FR 44:233, 1979)
of results are acquired from the particular study area a new
table should be calculated based upon the average range of the
data that has been accepted to date.
10. The data collected during the preliminary or
exploratory site investigation and during an emergency response
activity become the data base upon which later studies are
evaluated and/or designed.
The specific goals of each type of study will control the
required precision and confidence levels and the differences that
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are detectable between the samples and background. General
guidelines are given below for each of the situations covered.
Preliminary Site Investigation
The preliminary or exploratory investigation is the
foundation upon which many of the other studies in hazardous
waste work is based. Following preliminary data evaluation a
decision is made to either pursue a more definitive study or else
to terminate the investigation. The reliability of data obtained
from these investigations should be as high as feasible. The
initial plan should attempt to set the confidence level above 95
percent. If resources limit the number of samples that can be
taken, then the investigator should calculate the precision that
can be attained based upon the number of samples that can be
collected. If this new level of precision is deemed adequate,
the study should proceed.
Using five percent duplicate samples would provide adequate
QA/QC sampling under most situations (Plumb, 1981); however,
there should be a minimum of two sets of duplicates in each
strata sampled. Improved precision can be gained by increasing
the number of replicates at each QA/QC site sampled. Analyses of
splits of each of these samples provide data for within sample
variation. The latter information can be delayed until later
studies unless the within sample variation is expected to provide
information that can be used in making decisions about the site.
When resources are limiting, a two staged sampling design
may prove to be advantageous. The first stage would have a
limited scope and provide only limited data. Once a decision was
made that there was a possible source of pollution present,
additional sampling using a higher confidence level would be
initiated. The first stage could drop to a confidence level of
around 80 to 90 percent. The second stage should rely on
confidence levels of 95 percent or higher.
As previously stated coefficients of variation of different
soil parameters can range from a low of a few percent to a high
of several hundred percent. For example, a study of soil
variability done by Beckett and Webster (1971) indicated that it
was not uncommon for coefficients ranging from 23 to 84 percent
to occur within the same soil series. The use of a precision of
less than +20 percent for parameters related to transport is
probably unrealistic for any field soil sampling effort. On the
other hand, parameters related to static soil properties such as
percent clay, bulk density, etc., can have coefficents of
variation less than + 20 percent.
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Emergency Cleanup
The emergency site sampling is designed to identify those
areas where soil is contaminated and requires containment or
removal. A numerical sampling criterion is usually developed for
determining which areas are clean. Frequently the techniques
used for making these determinations are rough field tests that
lack the refinement of the laboratory analyses. Grids are often
used as a basis for surveying the site. These situations offer
an opportunity for more definitive information to be obtained if
adequate QA/QC procedures are built into the sampling efforts.
The use of grid sampling increases the likelihood of finding
the presence or absence of a chemical deposited in the soil. By
adding randomly placed duplicate or triplicate sampling locations
at 5 to 10 percent of the locations, the precision of the data
can be determined. Sampling replication coupled with appropriate
quality assurance checks in the laboratory, insures that the data
meet some predetermined level of precision and accuracy.
Analyses of splits of the samples will provide data to
measure the within sample variation. Replicate extractions from
a subset of the samples provides a means of measuring the
variation introduced by the extraction procedures. Replicate
analyses of a subset of the extractions provides a measure of the
analytical component of the total variance. These measures of
the components of variance provide information that can be
extremely valuable in designing any subsequent studies.
The need for increased precision occurs as the levels
approach an assigned threshold of significance or a predetermined
reference level such as a cleanup action level. A sample that is
highly contaminated needs little QA/QC to determine if it exceeds
background; but, a sample level close to background must have a
high precision in order to detect a difference. An attempt
should be made to provide a field measurement that meets a
reliability that has at least a 90 percent confidence level and a
precision of at least 20 percent.
Remedial Response Studies
These studies by their nature may end up in litigation;
therefore, a confidence level of 95 percent or better should be
used to provide the quality of data that is needed. The areas to
be surveyed should be stratified and sampled according to a
design that can be used to determine spatial variability as well
as concentration ranges. The experimental design should provide
27
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for an identification and evaluation of the components of
variance for the study situation. This requires that a suitable
statistical design be formulated and that appropriate QA/QC
procedures be implemented.
Studies conducted for remedial response purposes often
attempt to determine pollutant behavior and pollutant
distribution in order to provide a permanent remedy preventing
the migration or release of hazardous substances into the
environment. The experimental designs used in these cases should
be reviewed by a statistician and should be focused on those
areas that are required to meet the specific objectives of the
study. The objectives should be distinctly defined. If several
studies are being addressed with one set of samples, priorities
should be set to insure that the main purpose of the study is not
lost because of interference or statistical confounding.
If the sampling during exploratory or emergency response
investigations has been done properly, there will be a sound
basis for determining the sample size and sampling site
distributions. Where pollution migration is suspected, the
design will have to incorporate information on the vertical
distribution as well as the horizontal distributions. It is not
enough to sample the surface soil when the pollutant is expected
to be moving down with the permeating water. Nested designs are
required to provide the vertical components of the variation.
Planned Removal Studies
These studies are usually continuations of those initiated
during emergency cleanup studies. They are conducted in more
detail and should be designed to provide specific information
needed to resolve control option issues. The number of
replications may have to be increased if there is a need for a
higher level of precision. Greater care may be required in
determining the location and distribution of sampling sites in
order to provide the detail that is needed to test a specific
hypothesis.
An attempt at cost recovery is a likely successor to these
studies. The QA/QC must be adequate in order to insure that the
analytical and sampling methods and the statistical designs will
withstand detailed examination that results when litigation is
involved. The confidence level should be 95 percent or better
and the precision should be reduced to 10 to 20 percent if
possible. Preliminary data can be used to determine if this
precision reduction can be accomplished within reason. A more
sophisticated statistical design may have to be implemented that
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will provide increased precision without increasing costs
(Hammond, et al., 1958).
Monitoring
Soil monitoring is often associated with measuring the
changes that occur with space and time. Monitoring studies may
be undertaken as part of a litigation effort or they may be
undertaken in order to determine the trends in a pollutant's
concentration. Precision and confidence levels will have to be
adjusted to match levels required to achieve the objectives of
the studies. Some form of staged or split plot design may be
needed in order to be able to determine the components of
variance. Techniques such as intervention analysis (Hipel, et.
al., 1978) and trend line analysis will aid in determining if
there have been changes in the concentration patterns over time.
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CHAPTER 3
STATISTICAL CONSIDERATIONS
INTRODUCTION
This chapter reviews the role of statistics in the QA/QC
process. Statistics deals with the mathematics of collection,
analysis and interpretation of data. Without statistics there
would be little basis for determining if a particular sample was
reliable. There are numerous texts and references dealing with
statistics. A number of these references have direct bearing on
the collection of soil samples. The techniques presented in these
references will not be discussed in detail. The user is
encouraged to utilize the referenced materials if additional
and/or more detailed information is required. This chapter will
emphasize those techniques that have direct bearing on
determining the precision of the soil sampling and the resulting
analysis.
Box (1974) stated, "Environmental data are usually highly
variable and it is by facing this fact, rather than running away
from it, that we solve some of our problems." He gives credit
to Sir Ronald Fisher for the concept that "...we can exploit the
patterns of natural variation in data to design enquiries and
experiments so that errors are minimized." Techniques for
exploiting natural variability in soil sampling quality assurance
are presented below. The basic techniques that have a bearing on
soil sampling involve the use of statistical designs that are
capable of providing the information needed to perform a
component of variance analysis.
The component of variance analysis enables the environmental
scientist to determine the amount of variation that is associated
with the soil itself, and the variations associated with the
collection process, handling processes such as sample shipping,
storage, and preparation, and the analyses. Box (1974) sums up
the role of the component of variance analyses by stating, "An
appropriate study of components of variance how much variation
is associated with chemical analysis, how much with the sampling
method, how much with change of location..., together with the
knowledge of how much it will cost to take a sample and perform a
chemical analysis enables us to devise a testing scheme which
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can be dramatically more accurate and economical than one naively
chosen." Most soil sampling efforts fail to provide for the
needed statistical control and thus fall into a category of being
one of the studies that Box would classify as a testing scheme
that is "naively chosen."
DISTRIBUTION OF SOIL SAMPLING DATA
All statistical sampling plans are based upon the frequency
distribution of the data collected by the environmental scientist
and/or they are based upon the pattern that is anticipated after
reviewing data collected under similar conditions. One sample
collected from a location tells us little about the reliability
that we can place upon the number that results from the analysis
of that sample. A number of samples taken from that location
provides information on the variation of the values that can be
expected if all possible samples of soil were collected from the
same location. The variation in the data is as much a property
of the soil as is the amount of material upon which the analysis
is done.
The environmental scientist can obtain information on the
distribution of the values likely to be found in an area by
conducting an exploratory or pilot study. The exploratory
studies conducted during the initial phases of an investigation
can provide an indication of the site specific frequency
distribution pattern. The environmental scientist is interested
in finding the location of pollutants; therefore, the pilot study
should provide information on both contaminated areas and areas
of background soils. EPA's Regional Laboratories and EPA's
National Enforcement Investigation Center in Denver, Colorado can
provide information concerning the frequency distribution of
background samples and also information on the distribution of
analyses performed on contaminated soils. Another source of
information concerning distribution of soil pollutant
concentrations is the report, Environmental Monitoring at Love
Canal (USEPA, 1982).
The two most common frequency distributions encountered in
the soils literature are the normal and the log-normal
distributions. Where discrete events such as decay of
radioactive particles occur, the Poisson distribution is the more
common fequency distribution (Kempt home and Allmaras, 1965).
Rao, et al. (1979) have reviewed the frequency distribution of
spatial variability for soil physical properties. They indicate
that "soil properties such as bulk density, organic matter
content, clay content, and soil-water content at a given tension
are generally characterized by normal distributions.... However,
flow related soil properties such as air permeability, saturated
hydraulic conductivity, soil-water flux, pore-water velocity, and
31
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solute dispersion coefficients have been reported to be
log-normally distributed." These two distributions are "the most
frequently observed statistical distributions for describing the
spatial variability of soil physical properties."
The distribution pattern of chemical constituents of soil
including pollutants is truncated at zero. This characteristic
often gives rise to a frequency curve that is skewed to the low
end of the concentration scale. When this situation is
encountered the data can usually be transformed to a normal
distribution by taking the log of the data.
STATISTICAL DESIGNS
The design of the sampling study must be determined before
the sampling is undertaken. Frequently, improper designs contain
factors that are correlated with each other in such a fashion
that the sampling itself determines the outcome of the
investigation. This is in part avoided by proper use of
randomization during the collection process. Designs such as
those outlined by Mason (1983) or Peterson and Calvin (1965) can
greatly aid in determining the components of variation likely to
be encountered in the soil sampling effort.
The soil scientist often wants to provide information on the
spatial distribution of the concentration of a particular
constituent of the soil. Techniques such as those outlined by
Davis (1973) for Kriging, trendline analysis, discriminant
function analysis, cluster analysis and Fourier analysis
provide the needed information for evaluating the spatial
patterns in an area. Kriging provides one benefit that is useful
from the quality assurance point of view. Kriging has the
capability of providing a reliability map of the area under
investigation. This map is generated from the fact that
pollution samples located close to each other are often related
because of their position within a pollutant plume or within
their original geological deposition sequence. A series of
articles by Burgess and Webster (1980a), Burgess and Webster
(1980b), Webster and Burgess (1980), and Flatman (1984) give a
good presentation of the use of Kriging in soil sampling and
discuss the use of the error map. Mason (1982) also reviewed and
described the use of Kriging and its application to soil sampling.
Campbell (1978, 1979) discusses the use of discriminant function
analysis and autocorrelation in evaluating the spatial
distribution of soil properties.
Soil sampling faces a spatial distribution problem of
another sort in the fact that sampling with depth is required of
the data collection effort. Purely random samples cannot be
taken once the investigator penetrates the surface of the soil as
32
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each sample is now composed of subsamples. Some form of nested
design is required in order for the investigator to handle this
problem. Table 3-1 shows the analysis of variance that would be
undertaken for this type of soil data (Snedecor and Cochran ,
1982, p. 248 with modifications).
Type I and Type II Errors
Statistical sampling plans are designed not only to measure
the components of variance but also to aid the environmental
manager in making informed decisions about contaminants found
during an investigation of a site. The most common decision
would answer the question, "Is the area contaminated or not?"
The environmental scientist should design an experiment that will
provide data for testing the hypothesis that the study area mean
value is equal to the background mean value. Mathematically this
hypothesis is expressed as
Ho : (yS * ^B I°S = °B >
where y = mean and o^ = variance, the subscripts S = study area
and B = background. If this hypothesis is true then there is no
difference between the two areas. If the hypothesis is false
then the alternate hypothesis given below is used.
Ha : (ys * PB }
The alternate hypothesis means that the two mean values
are different. A similar test can be used to determine if the
pollutant in the study area soils equals some action level such
as a clean up level or an environmental standard.
The tests of the hypothesis are made on the basis of either
the normal distribution or a normalized distribution. The
hypothesis is accepted or rejected on the basis of a comparison
of a sample mean with the values delineating the acceptance
region (See Figure 3-1). Definition of the acceptance region
includes the acceptance of a probability that the sample mean
lies outside of the acceptance region (in the shaded portion of
the distribution shown in Figure 3-1). This probability is
defined by the significance level, the confidence level or the
Type I error (all three terms are synonymous).
33
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TABLE 3-1. ANALYSIS OF VARIANCE OF A NESTED SOIL SAMPLING DESIGN.
Location
i-l,...,a
1
2
3
4
Depth
j-1, ..
1
2
3
1
2
3
1
2
3
1
2
3
Ana 1-1
. ,b X
3.28
3.52
2.88
2.46
1.87
2.19
2.77
3.74
2.55
3.78
4.07
3.31
Ana 1-2
ijk
3.09
3.48
2.80
2.44
1.92
2.19
2.66
3.44
2.55
3.87
4.12
3.31
Sum- Anal
Xij
6.37
7.00
5.68
4.90
3.79
4.38
5.43
7.18
5.10
7.65
8.19
6.62
Sum-Loca Total
X£.. X..
19.05
13.07
17.71
22.46 72.29
I. C - (X...)2/(abn) - 72.292/24 - 217.7435
II. Analysis: £X£jk2- C - (3.282+..+3.3l2) - C - 10.2704
III. Depths: ZXij2/n - C - (6.372+...+6.622)/2 - C - 10.1905
IV. Locations: IXi..2/bn - C - (19.052+...+22.4&2)/6 - C - 7.5603
V. Depths in Locations - III-IV-10.1905-7.5603-2.6302
VI. Analysis of Sample - II - III =10.2704 - 10.1905 - 0.0799
ANOVA TABLE
Source of Degrees of Sum of
Variation Freedom Squares
Location
Depths /Location
Analysis/Depths/
Location
Total
3
8
12
23
7.5603
2.6302
0.0799
10.2704
Mean
Square
2.5201
.3288
.067
Components of
Variation
VA +
VA +
VA
nVD + bnVL
nVD
n « 2,b » 3,a « 4,s2 « 0.0067 estimates V^ or variance due to analysis
SD2 . (o. 3288-0.0067)/2 - 0.1610 estimates VD or variance due to depths
,L2 . (2.5201-.3288)/6 - 0.3652 estimates VL or variance due to location
34
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ACCEPTANCE REGION
202 /. 30.0
Fig. 3-1 Acceptance region for H. po = 30.0.
39.8
ti = 10.0
HE 3-2 - T)T>e H or P error.
20.2
30.0
39.8
35
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The Type I error whose probability is denoted by a, is the
case where we reject a hypothesis when in fact it is true. A
second error called the Type II error, whose probability is
denoted by 0 , is the case where we accept a hypothesis when in
fact it is false. The values of ot and 8 interact with each other.
When ot goes up 8 goes down. The two types of error are defined
in terms of their probabilities and can be controlled to desired
levels by appropriate sampling.
The Type I error is most frequently encountered in
statistical tests used in the literature. The significance or
confidence levels most often used are the 90, 95 and 99 percent
levels. The Type II error (false negative) is also used to
identify the power of the test which is equal to (1-B).
Figure 3-1 presents the acceptance region for testing the
hypothesis H:(ys = 30.0). The shaded portion represents the
probability of a Type I error (Juran et al., 1979). Figure 3-2
shows a situation where a sample with a mean of 10 is compared
with the distribution presented in Figure 3-1. Figure 3-2 is a
graphic presentation of the hypothesis that the mean of our
sample is equal to 30. The shaded portion of this figure
represents the portion of the distribution that would give a Type
II error (Juran et al., 1979).
Number and Location of Samples
One of the most useful tools for increasing the reliability
of the data collection process is the replication of samples.
Appendix A provides a set of tables and a graph for use in
determining the number of samples needed to detect a difference
between samples or to estimate the standard deviation with a
precision (p) at a particular confidence level. A computer code
developed by Heimbuch (1982) is also available for calculating
the sample size. The location of these samples should be
determined by use of some form of random selection process.
However, samples are collected from a systematic grid pattern
when Kriging will be employed in the analysis of the resulting
data.
Further gain is made in increasing the precision of the
analytical results from the sampling effort if the sample design
can incorporate stratification of sampling locations. This
technique makes use of the observation that certain locations
tend to be similar in their properties and they in turn are
different from samples taken in other locations. A typical
stratification used in soil science is the soil type. Soil types
are chosen because they represent an assemblage of soil units
that are closely related in their physical and chemical
properties.
36
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Role of Quality Assurance in Experimental Design
The Quality Assurance Officer should be intimately
involved in the review of the experimental or sampling design
proposed by the investigator. He should insure that the
information obtained provides measures of the components of
variance that are identified in the field. An additional quality
check that should be undertaken as part of the QA program is the
review of "the design by qualified soil scientists and other peers
that are in a position to provide the necessary oversight of the
sampling effort.
Broms (1980) makes the following statement; "There should
be a balance between the soil investigation method, the quality
of the soil samples, and the care and skill spent on the
preparation and the testing of the samples. There is no point in
spending time and money on careful sample preparation and on
testing if the quality of the samples is poor." The QA program
must address the total flow of information from the design to the
reporting of the results. The sampling design is the foundation
of the whole study, therefore, it should be given maximum support
if the purposes of the sampling effort are to be met.
Components of Variance
The component of variance analysis provides an estimate of
the sources of variation that contribute to the total variation
seen in the sampling. It therefore provides an estimate of the
variance of the analytical process, of the sampling and of any
other factors incorporated in the experimental design. Bauer
(1971) and Snedecor and Cochran (1982) discuss the use of the
components of variance analysis. An excellent example of the use
of this technique is provided in a report by the Electric Power
Research Institute (Eynon and Switzer, 1983) on the sources of
variation encountered in using the RCRA extraction procedure on
utility ash. The example presented in Table 3-1 gives the
components of variance for hypothetical sampling data. This
technique can only be used if the design of the experiments is
done in such a manner that the variation due to the parameters
can be evaluated. This is accomplished by appropriate
replication at each level in the design.
37
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Compositing of Samples
One of the main techniques used to reduce sampling and
analytical costs is the use of the composite sample. Combining
the samples from several sampling locations reduces not only the
costs but also the variation of the mean obtained by sampling.
The technique is used extensively by agricultural workers when
estimating the amount of fertilizer to be placed on a farmer's
fields. Since the primary purpose of QA/QC is to measure the
precision of the samples obtained, this technique should be
avoided if at all possible. Peterson and Calvin (1965) make the
following statement about this technique:
"It should be pointed out that the composite
samples provide only an estimate of the mean of
the population from which the samples forming
the composite are drawn. No estimate of the
variance of the mean, and hence, the precision
with which the mean is estimated can be obtained
from a composite of samples. It is not
sufficient to analyze two or more subsamples
from the same composite to obtain an estimate of
the variation within the population. Such a
procedure would permit the estimation of
variation among subsamples within the composite,
but not the variation among samples in the field.
Similarly, if composites are formed from samples
within different parts of a population, the
variability among the parts, but not the
variability within the parts, can be estimated.
If an estimate of the variability among sampling
units within the population is required, two or
more samples taken at random within the
population must be analyzed separately."
Youden and Steiner (1975) caution against the use of the
composite sample for much the same reasons as those outlined
above. There is no measure of the precision, and therefore the
reliability, of the data obtained.
Split Samples, Spiked Samples and Blanks
Split samples, spiked samples and blanks are used to provide
a measure of the internal consistency of the samples and to
provide an estimate of the components of variance and the bias in
the analytical process.
38
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Samples can be split to:
o Provide samples to both parties in a litigation or
potential litigation situation.
o Provide a measure of the within sample variability
(this is needed in order to determine the influence of
other factors that may be confounded with sample
splitting.)
o Provide materials for spiking in order to test
recovery.
o Provide a measure of the sample bank and extraction
error.
The location of the sample splitting determines the
component of variation that is measured by the split. A split
made in the sample bank measures error introduced at that level.
A split made in the field measures field handling along with the
within sample variation. A split or series of subsamples made in
the laboratory for extraction purposes measures the extraction
error.
Spike samples are prepared by adding a known amount of
reference chemical to one of a pair of split samples. The
results of the analysis of a split compared with the non-spike
member of the split measures the recovery of the analytical
process and also provides a measure of the analytical bias.
Spike samples are difficult to prepare with soil material
itself. Frequently the spike solution is added to the extract of
the soil. This avoids the problem of mixing, etc. but does not
provide a measure of the interaction of the chemicals in the soil
with the spike, nor does it provide an evaluation of the
extraction efficiency.
Blanks provide a measure of various cross-contamination
sources, background levels in the reagents, decontamination
efficiency and any other potential error that can be introduced
from sources other than the sample. For example, a trip blank
measures any contamination that may be introduced into the sample
during shipment of containers from the laboratory to the field
and back to the laboratory. A field blank measures input from
contaminated dust or air into the sample. A decontamination
blank measures any chemical that may have been in the sample
container or on the tools after decontamination is completed.
The number of QA/QC samples have been selected by a rule of
thumb that one out of every twenty samples is to be assigned to
each of the categories of samples. This ratio has been used
successfully in several major USEPA studies (USEPA, 1982, 1984).
39
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Table 3-2 presents the breakdown of QA/QC samples used in these
previously conducted monitoring studies.
DATA ANALYSIS
The topics that follow are designed to provide insight into
the use of statistical techniques for evaluating the data
obtained during an investigation. They are not by any means
exhaustive, but are designed to provide the basis for designing
the quality assurance portions of a sampling effort and to
provide the basis for obtaining the most benefit from the data
acquired.
Bias
The variation seen in analytical data can be composed of
variation within the sample itself, variation introduced in
sample collection or preparation and variation in the analysis of
the samples. The variation can further be divided into sample
variation and bias. Bias identifies the component of the
sampling error that causes the mean value of the sample data to
be either higher or lower than the true mean value of the samples.
An example of a bias would be the error in analytical results
introduced by an instrument being out of calibration during a
portion of the analysis. Laboratories usually introduce
reference samples into their sample load in order to detect these
changes. Bias in soil sampling is difficult to detect. The
presence of bias can be proven by use of one of the techiques
described below. On the other hand it is difficult to prove that
bias is not present because the absence of bias may be the result
of the inability to measure it rather than its actual absence.
Standard Additions It is necessary to conduct special
experiments in order to detect bias in the sampling effort. The
major technique used is that of adding known amounts of standard
solutions to the samples: it is recommended that this be done in
the field or in a field laboratory. The main problem encountered
is that mixing soils to obtain homogeneity is difficult in a
laboratory much less in the field. Several known quantities of
the standard are added to samples taken in the field. The
results should follow the equation for a straight line:
y « a + bix
Bias is indicated if the data do not follow the straight line
equation, or if a < 0, and if precision errors are small. If the
40
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TABLE 3-2. QA/QC PROCEDURES FOR SOIL SAfFLES
Procedure
1. Field Blanks
Comments
One for each sampling team
per day. A sample container
filled with distilled,
de-ionized water, exposed
during sampling then analyzed
to detect accidental or
incidental contamination.
2. Sample Bank Blanks
The field blank, about 40% of
them, passed through the
sample preparation apparatus,
after cleaning, to check for
residual contamination.
3. Reagent Blank
One for each 20 samples to
check reagent contamination
level.
4. Calibration Check Standard
One for each 20 samples to
check instrument calibration.
5. Spiked Extract
6. Spiked Sample
7. Total Recoverable
One for each 20 samples to
check for extract matrix
effects on recovery of known
added analyte.
One for each 20 samples. A
separate aliquot of the soil
sample spiked with NBS Lead
Nitrate to check for soil and
extract matrix effects on
recovery.
One for each 40 samples, a
second aliquot of the sample
is digested by a more
vigorous method to check the
efficacy of the protocol
method.
41
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TABLE 3-2
Procedure
8. Laboratory Control Standard
nts
9. Re-extraction
10. Split Extract
11. Triplicate Sample
12. Duplicate Sample
One for each 20 samples. A
sa«ple of NBS River Sediment
carried through the
analytical procedure to
determine overall method
bias.
One for each 20 samples. A
re-extraction of the residue
from the first extraction to
determine extraction
efficiency.
One for each 20 samples to
check injection and
instrument reproducibility.
One for each 20 samples. The
prepared sample is split into
three portions to provide
blind duplicates for the
analytical laboratory and a
third replicate for the
referee laboratory to
determine interlab precision.
One for each 20 samples to
determine total random error.
42
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units of x and y are the same, the value of b]_ should be unity;
and significant deviations from unity indicates a proportional
bias (Allmaras, 1965).
Occasionally a laboratory will prepare "spikes" using only
the standard solutions. This should be avoided if possible
because of interactions that may occur between components of the
soil matrix and the chemicals under investigation. Radioactive
isotopes can provide a useful indication of the recovery of the
analytical process.
Internal Consistency If several samples of soil of different
size are analyzed for a constituent, the results should fit a
linear equation of the form:
y = a + b2Z
where "Z" is the quantity of sample analyzed. The amount of
chemical detected should be directly related to the quantity of
the sample analyzed. The equation should be linear; if not, bias
is indicated. The "b" term depends upon the proportion of soil
used. The value of "a" should not be less than zero. A negative
value for "a" and a constant value for "b" indicate a negative
bias. Consistency measurements can be combined with the method
of standard additions in order to provide a more definitive
evaluation of bias.
Analytical Procedures-- Analytical methods that make use of
different basic theories can provide information on the presence
of bias. This is especially true if one of the methods is
considered to be the "standard" for the industry. An example
from wet chemistry would be to make use of a colorimetric and a
gravimetric method. Bias is present if the results of the two
methods do not agree.
The use of referee laboratories can also aid in determining
the reliability of the data and in detecting bias in the analysis.
Techniques such as charge balance, summation of parts (more
important in physical analyses), comparative values and simple
examination of the data can all provide information on the
analytical reliability of the sample results.
Confidence Intervals
One of the major calculations performed on the data is the
calculation of the confidence interval (CD. This value is used
in much of the work undertaken in QA/QC. It is used in the
development of the control charts, in identifying outliers and in
43
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determining if a set of samples exceed some pre-identif ied
standard. Two approaches can be used for calculating the
intervals. Where statistical designs have been used in the
sampling and analysis of the samples, the Analysis of Variance
(ANOVA) provides the best method for obtaining the needed
information for calculating the confidence interval. An
approximation of the interval can be made by use of the range
between or among two or more samples in a series. Bauer (1971)
presents both techiques. When the number of replicates is
limited, i.e., two or three, the range may offer a better
estimate of the confidence level.
The confidence interval is bounded by the confidence limits
(CD. The confidence limits are "the bounds of uncertainty about
the average caused by the variability of the experiment" (Bauer,
1971). The limit is defined by the following equation.
CL = x + ts/v/n~
where x * mean, s = standard deviation, n = number of samples and
t * Student's t value at the desired level of confidence and n-1
degrees of freedom (See Appendix B, Table B-l, for values of t).
The range can also be used to calculate the CL by using the
following equation:
CL » x + AIR
where I R = the sum of the k ranges and A = a factor derived from
the relationship between the range, the standard deviation and t.
The values of A are presented in Appendix B, Table B-2, but can
be calculated from the following relationship:
A =
where k = the number of groups of data and n the number of
samples in each group. The values of GI and the equivalent
degrees of freedom for t are obtained from Appendix B,, Table
B-3, which is based upon the relationship s = R/CI, the defining
equation for the relationship between standard deviation and
range.
The tolerance limits (TL) are similar to the CL but are used
to identify the interval and limits into which the individuals of
44
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the population should fall. The defining equation for this value
is:
TL = x + ts
or TL - x + IZR
where lisa factor relating the range and the standard
deviation. The value of I is obtained from Appendix B, Table
B-4, or can be calculated from the relationship:
Outliers
Dixon (1953, 1965) has provided techniques for identifying
data points that lie outside acceptable limits and thus can be
considered to be points from a different population. The
differences may be due to bias, cross contamination or other
factors that have altered the chemical content of the sample or
the results obtained by the analysis of the sample. One
technique that is identified by Bauer (1971) makes use of the
range for determining if a particular value is a true outlier or
merely a value on the edge of the particular distribution, the
statistic
ti = | x - x| /R
is used to make the decision (x = mean). Appendix Bf Table B-5,
lists the values of ti that are the critical values for various
sample sizes.
Propagation of Errors
Consider the case where several measures (each with some
associated error) are made on the same or matched samples and
then an estimate is calculated from the measured values. In this
case, when the measured values are statistically independent and
the errors normally distributed, the following equations may be
used to estimate the variances of the calculated values, where x
45
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and y represent the measured variables, s represents the standard
deviation of the measured variables, and f (x.) and f (x,y)
represent the calculated estimates:
For Single Valued Function of an Observation;
f (x) Estimated variance of f (x)
In x s2/x2
sin x (cos2x)s2
xP P2x2(p-l)s2
For More Than One Attribute on the Same Sample;
f (x,y) Variance of f (x/y)
x + y sx2+sy2+2sxy
xy y2sx2+x2sy2+2xysxy
x/y [sx2+(x/y)2sy2-2(x/y)sxy]/y2
In(x/y) (l/x2)sx2+(l/y2)sy2-(2/xy)sxy
ln(xy) is true.
The following equation is used to calculate the t value. This
value is compared with the value of t taken from the table in
Appendix B.
46
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X - X
1 2
S = s ( + .1) 3j
n i n2
n s 2 n s 2 ,
where s = t V n 2 * 1
1 + 2-2
and xi and X2 are the mean values of the two samples and ni and
n2 are the number of samples collected from the respective
populations. s is the pooled sample standard deviation and sj.2
and S2^ are the individual sample variances. In the example
given previously, the two samples were from the background and
the study area. If ts < t at an assigned confidence level for ni
+ n2~2 degrees of freedom, then the difference between the means
is not significant at that confidence level. If ts > t, then the
difference is significant at that confidence level.
A similar equation, given below, can be used to test the
comparison between the sample mean and some action level such as
a clean up level. An example of a clean up level would be the 50
ppm level used for PCB's in soil.
t = X - AL
c
where AL = the action level s is the standard deviation (s) and
n is the number of samples. A one-tailed test is used in this
case because interest is only in those cases where x exceeds the
action level. If the calculated tc value exceeds the t value
taken from the table in Appendix B for (n-1) degrees of freedom
at an assigned confidence level, then, the hypothesis is false
and the sample exceeds the action level.
Example:
A preliminary study is done in an area suspected of being
contaminated with polychlorinated biphenyls (PCB's). Sixteen
soil samples were collected from both the study area and from a
background area. Table 3-3 lists the data and the analyses done
on the data.
47
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TABLE 3-3. PCB STUDY TO DETERMINE CONTAMINATION OF AN AREA
(HYPOTHETICAL DATA)
Background Area (ppb) Study Area (ppm)
35.8 38.5 47.0 50.0
45.5 36.0 62.0 49.6
35.5 40.5 47.0 53.5
32.0 35.5 59.5 68.0
50.0 45.5 40.0 60.0
39.0 37.0 57.5 45.0
37.0 36.0 48.5 42.5
47.0 53.0 53.0 58.7
XB = .0402 ppm SB2 = .000037 nB = 16 CVB* = +15.1%
xs = 52.61 ppm SS2 = 60.2598 "s = 16 CVg = +14.8%
*CV - Coefficient of variation in %
This example does not need the use of statistics to
determine that there is a difference between the two population
means. The t value is calculated as follows:
r 16(.000037+60.2598) *h
s * l 16+16-2 J
s . /32.1386 « 5.6691
m 52.61 - .0402 , 26.2281
C 5.6691/-27IT
the t value for 99 percent confidence level and a one tailed test
is 2.131 for 15 degrees of freedom (dof). A value of 26.2281 is
so large as to be improbable in samples of this size so the null
hypothesis is rejected, i.e., the samples with mean of 52.6 come
from a different population than the background samples.
A more appropriate use of this test would be to decide if
the study.area exceeds the 50 ppm clean up action level. The tc
value is calculated as follows:
52.61 - 50.00 _ 1.344
*c 7.7626X
and from Appendix B, tgo%, 15 = 1.341;
48
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this indicates that the study area concentration may be different
from the value of 50 as this value of tc could occur in 10
percent of the samples. Since the study area mean may exceed the
50 ppm action level, we could make the decison to clean the
entire site. This is not economical because it is apparent that
some locations exceed the value and others do not. A statistic
can be calculated that is analogous to the tolerance limit (TL).
We can assume that the standard deviation of the true mean
(SOppm) equals the sample standard deviation. This yields the
following equation:
TL1 = y + Ks
where K = the normal deviate for the selected confidence level
which may be obtained from the t table at infinite dof. Assuming
a 95% confidence level the TL1 becomes 50+(1.96)(7.7627) or 34.7
to 65.2. In this case the TL = y + ts = 52.61 +
(7.7627) » 52.61 + (1 .753) (7.7627) = 39.0 to 66.2 so
there is little difference between TL and TL' . Only one value
exceeds the 50 ppm level if one uses either the modified
tolerance limit (TL1) or the tolerance limit (TL).
If one decides that the upper limit cannot exceed 50 ppm under
any circumstances, it would be necessary to calculate the range
of values that could be considered equal to or less than 50. On
the basis of the lower limit therefore all of the samples would
lie within the range and would have to be removed. This latter
case is the more conservative but also the more costly decision.
49
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CHAPTER 4
EXPLORATORY STUDY
INTRODUCTION
Once objectives have been defined which involve the need for
soil sampling the next step is to develop a total study protocol
including an appropriate QA/QC program. In order to develop this
protocol answers to the following questions must be available or
estimates must be made.
o What are the likely sources of the pollutants of
concern?
o How have these sources varied in the past compared to
their present emissions?
o What are the important transport routes which
contribute to soil contamination?
o What is the geographical extent of the contamination?
o What average concentrations of the pollutants exist at
different locations and how do these vary as a function
of location and time?
o Do localized areas of high concentrations exist and if
so, where are they and what are their concentrations?
o Is it possible to stratify the sampling region in such
a way as to reduce the spatial variations within
strata?
o What are the soil characteristics, hydrogeological
factors, meteorological or climatic factors, land use
patterns, and agricultural practices affecting the
transport and distribution of the pollutants of concern
in soil?
o What is an appropriate background, or control region
to use for the study.
o What are the acceptable levels of precision and both
Type I and Type II errors for this study?
If detailed and specific answers to all of these questions
were available in advance, there would be no need to conduct the
study. The recommended approach is to conduct an exploratory
study that includes both a literature and information search
along with selected field measurements made on the basis of some
assumed dispersion model. If one is dealing with an emergency
50
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E uation such as a hazardous chemical spill, there usually will
not be time to proceed in the deliberate fashion recommended here.
Thus for the emergency situation it is often necessary to
compress all of the planning and study design into a very short
time period and then proceed to the final definitive study
without delay in order to afford maximum protection to human
health, welfare, and the environment. The following will assume
that there is a reasonable amount of time available to conduct an
exploratory study prior to the conduction of the more definitive
study.
To be maximally cost effective a major element of the
exploratory study is a literature and information search and an
information-seeking series of interviews. Much information
pertinent to the questions asked above may already be available
in the published literature, in the files of governmental
agencies or industrial corporations, in ongoing or completed
research at local universities, or in the knowledge of local
citizens. A carefully planned and organized effort should be
mounted to accumulate what relevant information is available.
Only after this information has been collected, collated and
evaluated should any field measurements be taken. It is a good
policy to adhere to a reasonable fixed period of time for the
collection and analysis of available information,otherwise this
process could drag on interminably. Only at the end of the fixed
time period, and based on whatever information is available at
that time, should the design and implementation of the field
measurements portion of the exploratory study be undertaken.
Even though the principal subject of this document is QA/QC
for soil sampling it is not possible to separate the QA/QC from
the total soil monitoring study design. The objectives of the
monitoring study are the driving force for all elements of the
study design including the QA/QC aspects. The results of the
exploratory study will be a set of information and field data
that will serve as the basis for the design of a definitive
monitoring study that includes the total integrated QA/QC program
for all media. One element of this total QA/QC program will be
the soil sampling QA/QC plan.
NUMBER AND LOCATIONS OF SITES FOR SAMPLING
What is desired for the final definitive study is the
appropriate number of sampling sites at the appropriate locations
to obtain data on the basis of which mean concentrations and
standard deviations for the regions of interest may be determined.
A method has been described in Chapter 3 for calculating the
number of required sites in a given region if one knows the
required precision, the standard deviation of the mean, and the
required levels of confidence (related to acceptable levels of
51
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Type I and Type II errors). The precision and confidence levels
must be specified, usually on the basis of a value judgment by a
responsible official of the agency conducting the soil sampling
study. The standard deviation of the mean of the total
population of soil samples in the study region must be estimated
on the basis of the standard deviation of a suitable sample of
the total population obtained during the exploratory study.
In general, a suitable soil sample from a number of possible
soil samples may be selected on the basis of random, judgmental,
or systematic sampling. A major input into selecting the optimum
sampling design is the information accumulated prior to the field
sampling phase. Usually the optimum approach will be a
combination of judgmental and systematic random sampling.
Assuming that appropriate information has been obtained in the
preliminary or information-gathering phase of the exploratory
study, a model may be hypothesized describing a likely spatial
distributon of soil contamination as well as identifying a likely
control area. Selection of a desired number and location of
sampling sites on the basis of a model is a judgmental approach.
Subsequently the model must be verified by collecting a limited
number of samples in areas outside of the suspected contamination
zone.
For example, suppose it is suspected that an abandoned
hazardous waste site is leaking wastes into the groundwater.
Further suppose that the groundwater is being used to irrigate
crops in the vicinity. Preliminary information has identified
some of the pollutants that have been placed in the waste site
and has determined the hydraulic gradient extending from the site
location. The recommended sampling approach is to establish a
radial grid system with the center at the waste site and the zero
azimuth line along the direction of the hydraulic gradient. The
largest number of samples would then be taken along the zero
azimuth and along the + 45° azimuth from zero. This is
judgmental sampling. However to make sure that important data
are not missed some additional samples should be taken close to
the waste site along each 45° azimuth (5 additional directions).
This adds systematic sampling to take care of cases where, for
example, some immiscible waste constituents may be moving in a
direction different from the hydraulic gradient, the hydraulic
gradient has not been properly defined, or there are other
sources contributing to the soil contamination. The location of
the samples taken along each axis and in the pollutant plume
should be selected at random.
For the selection and sampling of a control area a
combination of judgmental and random sampling is recommended.
Based on the available information and the assumed transport
model, select a background or control region which is similar to
the study area in every important aspect except for the expected
absence of contamination by selected waste constituents. Select
52
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a minimum of 12-15 sampling locations at randoir from the
background area to obtain data for calculating the mean and
standard deviation of the background concentrations of selected
waste constituents. It is recommended that approximately the
same degree of effort go into the selection and sampling of a
control area as goes into the selection and sampling of the study
area.
The QA/QC program for the exploratory study need not be as
stringent as that for the more definitive study. Keep in mind,
however, that reasonable levels of precision and confidence must
be attained in order for the resulting data to serve as an
adequate foundation for further studies. As a minimum, it is
recommended that duplicate samples be collected from at least 5
percent of all sampling locations and that another 5 percent of
all samples be split into triplicate samples. Furthermore it is
recommended that a modest number of additional independent
QA/QC soil samples be taken on a random basis at approximate
mid-points between selected sampling points in regions where the
hypothetical model predicts the highest concentrations will be
found. Data from these additional QA/QC samples will give some
measure of how well the QA/QC plan is achieving its objectives.
Duplicate sample results will help to establish precision
among different samples collected from the same site. Triplicate
splits of samples provide a measure of precision within a single
sample, which tests the homogeneity of the sample. The
additional QA/QC samples will provide data to use in evaluating
possible changes in means and standard deviations when additional
sampling points are added. If the two groups of samples (study
design and additional QA/QC) are statistically equal, the samples
can be combined. If not, then there is an indication of either
some form of bias in the sampling design or one or more errors in
the assumptions inherent to the sampling design. This matter
must be carefully evaluated in order to determine if additional
sampling is needed. In addition to the above QA/QC checks on
sampling, all normal analytical QA/QC procedures such as field
and trip blanks, etc., should be operative for the exploratory
study.
SAMPLING AND SAMPLE HANDLING
It is assumed that an approved protocol will be followed for
handling, labeling, transporting and chain-of-custody procedures
for sample containers and samples.
Generally a number on the order of 6 to 15 should be adequate
with the exact number being determined by a value judgment based
on study objectives, site-specific factors, and available
resources.
53
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If appropriate approved operating procedures for these subjects
are not available, then they must be prepared prior to beginning
the study. Sample volumes will be specified by the analytical
laboratory depending on the analytical methods to be used and the
desired sensitivity. Accordingly, principal attention will be
focused here on sampling methods, preparation of the samples for
analysis, and QA/QC aspects of both.
Some major concerns in sampling design include identifying
the required depth of sampling, whether or not sequential samples
at different depths will be required, whether samples should be
composited, frequency of sampling, sample preparation for
analyses and QA/QC aspects of all of the above. In deciding how
to deal with these concerns one must constantly keep in mind the
objectives for which the soil monitoring study is being conducted.
The exploratory study provides a limited opportunity to
investigate some of the above subject areas experimentally to
determine what effect the sampling parameters may have on the
QA/QC aspects of the total study. The expenditure of modest
additional resources in the exploratory study may well lead to
more cost-effective designs for the final definitive study.
The sampling device used to acquire the exploratory samples
should be consistent with the objectives of the final study. The
simplest sampling tool should be used. Where the contaminant is
believed to be on the surface, a soil punch or trowel may be used.
If the contaminant is soluble or is expected to be located more
than a meter below the surface a truck mounted core sampler such
as a split spoon sampler should be used.
Surface sampling should be augmented with a modest
number (see footnote, page 53) of sequential samples taken down
to 1.5 meters in order to determine if the pollutants have moved
downward. These additional samples should be located in the area
of major contamination. Data from these samples will provide
information for deciding if more than the surface soil needs to
be sampled in the final definitive study.
With regard to compositing of soil samples, the major
concerns are that the samples be representative and that high
concentrations not be significantly reduced by being averaged
with lower level samples. It is recommended that to improve
representativeness at least four different samples taken in the
vicinity of each selected sampling site be composited into a
single sample. In addition a modest number (see footnote, page
53) of single non-composited QA/QC samples should be collected
from sampling sites in high concentration areas for comparison of
resulting data with that from composited samples.
The exploratory study is not designed to obtain information
on temporal patterns in soil concentrations since the study is
expected to be completed in a relatively short period of time.
54
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Thus, temporal trends will normally be addressed in the final
study. If it is possible to select a time for the exploratory
study, it is best conducted at a time when the soil
concentrations would be expected to be at a maximum. It may be
necessary to use the hypothesized dispersion model in order to
make this decision. For example, the sampling normally should
not be done immediately following a heavy rain, during winds
exceeding 20 knots, or during a time when the ground is frozen.
Sample preparation for analyses introduces some
possibilities for errors. The sample preparation may involve
drying, grinding, mixing, and sieving. Prior to any sample
preparation procedures vegetation, sod, or other non-soil
material must be removed from the soil fraction.
Grinding and mixing equipment as well as any sieves used
must be carefully cleaned between each sample in order to avoid
cross-contamination. The final rinse water used for cleaning
equipment should be sampled in order to provide a sample blank
for use in evaluating the decontamination efficiency. Collection
of one sample blank after processing a group of 20 samples has
been used successfully in a number of EPA studies (USEPA 1982,
1984). These samples should be submitted to the laboratory along
with the other QA/QC samples. After evaluation of the sample
blank data obtained from the exploratory study, a decision may be
made to increase or decrease the frequency of blank collections.
One of the most serious possibilities for error during the
sampling process is discarding vegetation, sod or other non-soil
material collected with the soil sample. It is recommended that
all discarded material be retained, including any materials
retained on the sieve. Ten percent of these samples should be
sent to the analytical laboratory for analysis with the remainder
being archived. The results of these analyses will give a
quantitative estimate of the possible errors introduced by
removal of non-soil materials. Care must be taken in evaluating
and interpreting these data as data quality will be a function of
analytical capability.
ANALYSIS AND INTERPRETION OF DATA
Analysis and interpretation of the total integrated
information and data resulting from the exploratory study will
provide the basis for designing the final definitive monitoring
study including all elements of the QA/QC plan. For example,
decisions must be made on whether or not the selected control
area is adequate and appropriate; whether the hypothesized model
is valid; whether the study area should be stratified and if so,
how; what number of samples should be collected at what
55
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locations; whether or not the QA/QC plan for sampling is adequate
and if not, how it should be changed; etc.
If the exploratory study is conducted well, it will provide
some data for achieving the overall objectives of the total
monitoring study? it will provide data concerning the feasibility
and efficacy of most aspects of the monitoring design including
the QA/QC plan; it will serve as a training vehicle for all
participants; it will pinpoint where additional measurements need
to be made; and it will provide a body of information and data
which may be incorporated into the final report for the total
monitoring study.
56
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CHAPTER 5
SELECTION OF NUMBERS OF SAMPLES AND SAMPLING SITES
INTRODUCTION
The QA/QC plan must be designed in such a way as to allow
for estimation of errors in the determination of, as a minimum,
mean concentrations and standard deviations of the means. In
some cases the primary interest may be in the determination of a
reasonable mean of extreme values (the stratum having the highest
mean concentration) which must be compared to an acceptable
threshold level. In the latter case protective actions will
generally be required if the acceptable threshold level is deemed
to be exceeded. For this case the QA/QC plan must provide data
on the basis of which one may state with what confidence level
the threshold action concentration is, or is not, exceeded. Both
Type I and Type II errors must be taken into consideration.
These errors can only be controlled by choosing an appropriate
number of samples.
On the basis of data from the exploratory study the
following information will be available.
o Mean concentrations and standard deviations of the
means for stratified regions (assuming it was deemed
necessary to stratify the study region)
o Mean concentrations and standard deviation of the mean
for the control region
o Results of tests, at specified confidence levels, to
determine whether or not the mean concentrations in all
strata are significantly different from the control
region mean concentration
o Results of tests, at specified confidence levels, to
determine whether or not peak or maximum measured
concentrations exceed any established threshold action
levels
o Some measure, through analysis of variance tests, of
the distribution of observed variances among various
elements of the sampling plan, sample handling, and
sample analysis
57
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The problem now is to determine which elements of the
exploratory study provide sufficient information to meet the
program objectives, and where additional measurements will be
necessary. Generally, since the exploratory study was designed
to provide only a limited sample of the desired study population
(and perhaps a biased sample) it will be necessary to obtain some
additional measurements to improve the levels of precision and
confidence, to confirm the results, and to expand the
measurements to cover regions not previously sampled.
NUMBER OF SAMPLING SITES REQUIRED
The minimum number of samples ,n, required to achieve a
specified precision and confidence level may be estimated by use
of the tables given in Appendix A. For values outside the range
of the tables the following equations may be used (Mason, 1983):
2 I \ 2 t2 (CV) 2
n _ t(a/2,n-l) *0) or its equivalent n = fo/2fn-l)
P2 P2
where a is the standard deviation of the mean for the total
population, p is the precision and must be in the same units as
Qt the confidence level is 1-a, and ^01/2,n-1) is tne value of
Student's t distribution for the two-tailed test at n-1 degrees
of freedom. In the second equation CV is the coefficient of
variation and if CV is in percent, p must be in percent. These
equations must be solved by iteration or graphically since t is a
function of n-1. Normally the two-tailed t test is used unless
the objective of the study is to determine whether or not a
defined value is exceeded. In the latter case a one-tailed t
test is used and t -.is substituted for
a, n-1
fca/2,n-1
The tables in Appendix A are labeled to make them applicable for
both one and two-tailed tests.
If one approximates the population mean y by a sample mean,
x, obtained from the exploratory study, it is possible to
calculate the required number of samples to achieve a specified
precision at a specified confidence level. The next problem is
to estimate what sources of error may be involved in proceeding
in this fashion.
First, this entire approach assumes that the measurements
are independent of one another and are distributed normally. If
one or the other, or both, of these assumptions is not valid,
58
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undetermined errors may be introduced. Furthermore the standard
deviation, s, of the sample obtained in the exploratory study may
not be a good approximation of the standard deviation, o, of the
entire population. This problem can be evaluated by comparing
the standard deviation obtained in the final definitive study to
the one obtained from the exploratory study and testing to see if
they are different at some prescribed level of confidence.
If the normal distribution assumption is not valid, then an
assumption of a log normal distribution may suffice. If the
measurements are dependent on one another, it may be possible to
replace classic statistical techniques with Kriging. Examination
of the data collected from the exploratory study should enable
one to make decisions on these matters.
If one of the objectives of the final definitive study is to
compare measured peak values to an acceptable threshold level,
another possible source of error must be dealt with. This source
of error is addressed by modifying the equation so that the
minimum sample size, n, is given by the following formula (USEPA,
Dallas Lead, 1984):
. (a*Btn-l)°a Qr its equivalent n . VB,n-VCV'd
P
Where a = probability of a Type I error, 6 = probability of a
Type II error, 03 = standard deviation of the differences between
all points in the strata having the highest mean concentration
and the acceptable threshold value, pa = minimum value of the
difference considered to be above the threshold value, and
tfct+Brn-l) is the value of Student's t distribution needed for
the one-tailed test at n-1 degrees of freedom. Note that if the
study region is stratified, this sample size would be applicable
only to the stratum having the highest mean concentration.
Table 5-1 gives some examples of determinations of required
minimum numbers of samples for hypothetical data of different
standard deviations to achieve different levels of precision and
confidence where the presented values come directly from the
appropriate tables in Appendix A. Table 5-2 gives similar
examples for hypothetical data to determine the required minimum
numbers of samples needed to decide if an acceptable threshold
value has been exceeded at different levels of precision and
confidence.
59
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Table 5-1. Number of Samples Required to Achieve an
Analytical Precision (p) at a Confidence Level of (1-a)
Standard Deviation
(%)
1
5
10
50
100
Confidence
Level
(%)
99
95
90
99
95
90
99
95
90
99
95
90
99
95
90
1
10
6
5
166
96
69
664
385
271
-
-
-
-
-
Number of Samples
Precision
(%)
5 10 50
322
221
211
10 5 2
631
521
31 10 3
18 6 2
13 5 2
664 166 10
385 99 6
271 70 5
664 31
385 18
271 3
100
1
1
1
2
1
1
2
2
1
5
3
2
10
6
3
60
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Table 5-2.
Precision
(1-6).*
Number of Samples Required to Achieve an Analytical
(p) at a Confidence Level of (1-a) and a Power of
Standard
Deviation
Confidence
Level
Power
1
Number of Samples
Precision (%)
5 10 50
100
5
10
50
99
95
90
99
95
90
99
95
90
99
95
90
99
95
90
99
95
90
99
95
90
99
95
90
99
95
90
90
80
70
90
80
70
90
80
70
326
215
165
251
155
114
203
120
83
1302
857
657
1004
619
452
813
619
452
-
-
-
16
10
8
13
8
6
11
6
5
55
36
28
43
27
20
36
21
15
1302
857
658
1004
619
452
813
471
327
16
4
3
5
3
3
5
3
2
16
10
8
13
8
6
11
6
5
326
215
165
251
155
114
203
120
83
1
1
1
1
1
1
1
1
1
2
1
1
2
1
1
2
1
1
16
10
8
13
8
6
11
6
5
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
6
4
3
b
3
3
5
3
2
* Since 6 is the probability of making a Type II error (false
negative), the power, or 1-g, is the probability of not making
a Type II error.
61
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An example of a sample calculation is presented below:
Suppose °d = 10 percent, confidence level(1-a) = 95 percent,
Power (1-3) = 90 percent, and p2
Then n - fto)2 = * o+B,n-l-
Solution must be by iteration. Try ni~l = °°.
Then ni = t2a+6/oo = (t^+t^J2 = (1.645+1.282) 2 = 9.
Recalculate n2 with ni~l » 8.
Then n2 = (t^g+t^g)2 = (1.B60+1.397) 2 . n.
Recalculate n3 with n2-l = 10; Then n3 = = (1-833 + 1-383)2 = 10 = n3 = n.
Thus the desired n = 10 as shown in Table 5-2.
It is usually necessary to calculate the probable total cost
of the program, including all QA/QC samples. By comparing total
cost to the available resources one can determine the feasibility
of continuing with the study. If inadequate resources are
available, either more resources must be obtained, the study
objectives must be changed, or the study should be abandoned.
Experience indicates that the second item, changing the study
objectives, is the most likely option.
LOCATION OF SAMPLING SITES
The location of the sampling sites will depend on whether
the sampling is random, judgmental, systematic, or some
combination. All information and data resulting from the
exploratory study should be used to assist in the location of
sampling sites. Assuming that a reasonable validation of the
model used for designing the exploratory study has been achieved,
the study region may be stratified as deemed appropriate. An
approach using a combination of judgmental and random sampling is
recommended where the stratified areas to be sampled are located
judgmentally, but the specific sampling sites within the
stratified areas are selected on a random basis.
In the event it is impossible to obtain a sample at a
randomly selected sampling location, a sample should be obtained
62
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from the closest available alternate site. For example, the
selected site may be beneath an asphalt or concrete parking lot,
a road, or a building. In these cases it is not recommended to
use drastic measures such as jackhammers or picks to collect soil
samples. Any errors introduced by moving to the closest
alternate site are not apt to influence unduly the overall
results.
The movement of pollutants over the surface of a site and
through the soil mass may be strongly influenced by the shape of
the terrain, by soil type, by geological formations, by
vegetation and by land use. If any of these factors are
important, the sampling design should be stratified in order to
include each important factor. For example, a liquid pollutant
deposited on a hill top will move down slope. Maximum
concentrations are likely to occur in low areas as opposed to
ridge tops. Stratification of such an area into three strata -
ridge top, hill side, valley floor - is recommended. This design
allows the analysis of variance to remove the variation due to
these three strata from the total error term; thus, the estimated
sample variance will be reduced.
Within each stratum the location of sample points should be
randomly located. The number of sampling points assigned to a
stratum should be assigned on the basis of the percentage of the
total area located in that stratum.
Two other techniques can help to identify the location of
sample sites. The use of Kriging to analyze the exploratory
study data can generate an error map for the site. If the error
map is generated on the basis of a desired confidence level, the
araas that do not meet this level of reliability can be
identified and sampled.
Geophysical measurement techniques can be used to locate
plumes of pollutants under some geological conditions. The
pollutant pattern identified under these conditions can be used
to stratify the sampling by "plume" and "non-plume" areas. There
may be the need to identify a third stratum covering an
intergrade along the edges of the plume.
QUALITY ASSURANCE ASPECTS
The best QA/QC plan that can be designed on the basis of
what is known about a study area and a control area may not be
adequate to achieve the desired levels of precision and
confidence. Accordingly, it is recommended that additional
samples be included in the definitive study design that may help
to determine whether or not desired levels for QA/QC have in fact
63
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been achieved. Conceptually there are at least two different
approaches available to achieve this goal. If an independent
(different) method is available for measuring the parameters of
importance, that method can be used and the results compared to
those achieved by the first method. Generally an independent
method is not available for monitoring of contaminated soils.
Another approach is to deliberately overdesign the study by
taking and analyzing many more samples than the recommended
numbers for a minimum adequate design. This is usually deemed to
be undesirable because of the additional cost which it entails.
The recommended approach is a modification of the over
design concept. It is suggested that a modest number (see
footnote, page 53) of additional samples be taken at randomly
located sites in the stratum where the highest concentrations are
expected. These high concentration areas are normally identified
on the basis of the exploratory study data. The data should be
analyzed for that stratum both with and without the additional
samples and the two results compared. The comparisons should
give some indication as to whether or not the desired levels of
precision and confidence were actually achieved by the original
design.
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CHAPTER 6
SAMPLE COLLECTION
INTRODUCTION
An important segment of the definitive studies QA/QC plan
deals with sample collection. Sample collection has been covered
by Mason (1983), Cline (1944) and Ford et al. (1983). This
aspect of the definitive studies must be designed to meet the
specific objectives. Improperly collected samples can void the
entire study. The final protocol must provide guidance on such
matters as sampling methods, equipment, locations for sampling,
and compositing; dealing with non-soil portions of samples;
dealing with the existence of animal burrows, root channels and
other such anomalies in the soil being sampled; and the selection
of the depth or depths that should be sampled.
The environmental scientist should be able to estimate the
components of the variance, or error, associated with each
element of the sample collection methods and procedures used from
the data generated by the study. Evidence from the exploratory
study pertinent to this estimation process should be taken into
consideration. It is recommended that a minimum adequate
approach be sought consistent with the objectives of the study,
the resources available and the designated required levels of
precision and confidence. Also an effort should be made to
establish some criteria or procedures for estimating, after the
fact, whether or not the sample collection elements of the QA/QC
plan and objectives were satisfactorily achieved.
SIZE OF SAMPLES AND METHODS OF COLLECTION
Generally, the minimum sample volume is specified by the
analytical laboratory on the basis of the selected method and
required sensitivity of analysis. Of course, enough sample must
be collected so that the final soil sample remaining after any
non-soil materials are discarded will be adequate to meet the
requirements of the analysis. Sufficient information should be
available from the exploratory study to provide guidelines on
65
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approximately what percentage of the collected sample will be
discarded during the analytical sample preparation process.
The method of collecting samples must take into
consideration the required depth of sampling as well as required
amounts. The data obtained from the exploratory study on soil
concentrations at various depths should be adequate to allow a
specification of required depths of sampling for the final study.
The sample collection device must be adequate to obtain samples
to the required depth. Mason (1983) and Ford et al. (1983)
provide information on available sampling devices and procedures.
The sampling device must be carefully cleaned between each use to
avoid cross contamination of samples. Suggested cleaning methods
are given in USEPA (Love Canal 1982, 1984). The type of device
selected should be one that provides the most cost effective
sample.
Frequently when collecting soil samples anomalies such as
animal burrows, root channels, sand lenses, desiccation cracks
and/or other factors that can alter the sample, or the collecting
procedure, and affect pollutant migration will be encountered.
These anomalies should be documented and noted on coring logs, in
sample log books, and on sampling site description forms.
BORING LOG
When subsurface samples are being collected a boring or core
log should be prepared. The log should indicate soil structural
changes, stratigraphy changes, the presence of rock, sand and
gravel lenses, root channels, animal burrows, debris and other
factors that may be useful in interpreting the likely avenues of
contaminant migration.
The forms for these logs can be designed by the investigator
or can be copied from most geological field sampling texts. The
form should present both a graphic and a verbal description of
the soil lying below the surface.
Quality assurance can be maintained by periodic audit of the
forms and by proper training of the personnel preparing the forms.
Properly prepared boring logs are one of the most valuable
interpretive tools developed during an investigation.
FREQUENCY OF SAMPLING
The required frequency of sampling depends on the objectives
of the study, the sources of pollution, the pollutants of
66
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interest, transport rates, and disappearance rates (physical,
chemical or biological transformations as well as dilution or
the determination of dispersion). Sampling frequency may be
related to changes over time, season, or precipitation. Normally
little information will be obtained on sampling frequency from
the exploratory study but in those cases where temporal changes
are expected the final study should incorporate sampling
frequency into the design. It is not uncommon for many
definitive studies to be conducted over a period of one year or
more.
The changes expected in the concentration of pollutants in
soil are normally associated with precipitation. Precipitation
may influence the movement of chemical pollutants downward and
aids in decomposition. Sampling frequency associated with either
major rainfall events or with an accumulated amount of rainfall
can often provide valuable information on changes that are
occurring.
Monitoring studies are often designed to measure the effects
of some remedial measure on the site. Trends are important in
these cases. The frequency of sampling should be designed to
measure the changes. One approach used successfully has been to
provide intensive initial sampling early in the study, then to
decrease sampling frequency as the levels begin to drop. One
recommended procedure would be to sample monthly for the first
year, quarterly for the second year, semi annually for the next
two to three years then annually thereafter.
Evaluation of the trend of the data should allow the
environmental scientist to determine when the sampling frequency
can be reduced or halted completely. Monthly data may provide
the needed data for performing statistical tests and for
determining the yearly variation within the data base.
Samples collected for evaluating trends can usually be
obtained on some subset of the initial year's sampling. The
major focus is mainly on the highly contaminated and on the
immediately adjacent areas. The environmental scientist is
primarily interested in detecting changes in these adjacent areas
in order to provide early warning of a breakdown of the remedial
measures.
QUALITY ASSURANCE ASPECTS
QA/QC procedures of the sample collection effort must
identify and determine the magnitude of errors associated with
characterizing soil contamination introduced through the sample
collection effort. Audits (see Chapter 9) are perhaps the most
67
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effective tool to insure that the sampling is done correctly.
Factors likely to influence the magnitude of the sample
collection error are sample size, collection methods, and
frequency of sampling. The most important of these are the
methods of collection and the frequency of sampling.
The tools used for collecting soil samples are limited and
are not likely to be sources of error. The errors most likely
occur in the use made of the tool. Proper replication will
insure that the precision of the procedure meets the QA/QC
objectives.
Techniques such as trend line analysis or interdiction
analysis will provide a means of evaluating the effectiveness of
the data obtained from sampling frequency studies. The methods
outlined in Chapter 4 for evaluating possible errors from
compositing can prove to be a valuable tool for evaluating the
use of the composite sample.
A comparison between the first samples taken and the most
recent should show a decrease in pollutant concentrations unless
there is a new source of pollutants, there is migration into the
sampled soil or there is an error in the data. This test becomes
a better indicator of errors the longer the study runs.
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CHAPTER 7
SAMPLE HANDLING AND DOCUMENTATION
INTRODUCTION
The goal is to define the segment of the QA/QC plan dealing
with all aspects of sample handling including the transfer of the
sample from the collecting device to a suitable container,
transportation of the sample, and the preparation of the sample
for analysis. The importance of all these aspects of sample
handling and possible errors introduced thereby will naturally
vary with the sampling methods, monitoring objectives,
characteristics of the soil being sampled and the physical and
chemical properties of the pollutants of concern.
CONTAINER PREPARATION, LABELING, PRESERVATION, AND SAMPLE
PREPARATION
The sampling protocol and the QA/QC plan must address the
following factors.
o Type of container material, its size, shape and the type
of lid.
o Cleaning procedures for the containers
o Decontamination procedures for sampling instruments.
o Decontamination procedures for sample bank equipment.
o Labeling scheme and log book entries
o Chain of custody procedures
o Sample preparation procedures in the field
o Sample preparation procedures at the sample bank
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Due to a lack of specifically tested and recommended methods
dealing with the storage, handling, construction and types of
containers, cleaning and decontamination of containers, and
suggested materials for container lids for soil samples it is
suggested that the specifications and methods identified in
OSEPA, Federal Register Vol. 44 No. 233 (1979) be utilized.
Table 7-1 provides general information on recommended
containers, preservation requirements, and holding times for
measuring selected contaminants. Even though these procedures
and methods were specifically designed and tested for water
samples, they are applicable for soil sampling studies.
For sampling studies that require a large number of samples
and/or extensive preanalytical sample preparation a sample bank
may be established. The sample bank is the element that operates
between the field sampling effort and the analytical laboratory.
However, for smaller studies the sample banks responsibilities
are often incorporated into the responsibilities of the field
sampling team or the analytical laboratory.
If a sample bank is established, sample bank personnel can
assume responsibility for the following procedures:
o Custodian for all records pertaining to the sampling,
sample preparation as required, and shipment of soil
samples to analytical laboratories.
o Responsibility for record filing and storing, for
storing and preparation of soil samples, and for
dispensing containers, sampling equipment and all
custody documents such as chain-of-custody forms and
sample collection and analytical tags, as required.
o Responsibility for updating and maintaining the
projects' master log book, auditing the records as
required, generating sample bank QC sample blanks,
accepting QA/QC samples for inclusion into the
analytical scheme, and for scheduling the collection of
field sample blanks.
o Responsibility for completing, as required, analysis
data reporting forms and for assuring that all
chai n-of-custody requirements pertaining to all
field sampling, shipping and sample bank operations,
are adhered to.
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Table 7-1 Sampling Containers, Preservation Requirements, and Holding Tines for Soil Samples
CONTAMINANT CONTA1N£R PRESERVATION HOLDING TIME
Acidity
Alkalinity
Aaaonia
Sulfate
Sulfide
Sulfite
Nitrate
Nitrate-Mitrite
Nitrite
Oil and Grease
Organic Carbon
Metals
Chromium VI
Mercury
Metals except above
Organic Compounds
Extractables (including
phthalates, nittosamines
org%nochlorine pesticides,
PCB'e nitroaromaticn,
isophorone, Polynuclear
aromatic hydrocarbons,
haloethers, chlorinated
hydrocarbons and TCOO)
Extractables (phenols)
Purgables (halocarbona
and aroma tics)
Purgables (acrolein and
acrylooitrate)
Ortbophosphate
Pesticides
Phenols
Phosphorus (elemental)
Phosphorus, total
Chlorinated organic
coapounds
P.G
P.G
P,G
P.G
P.G
P.G
P.G
P.G
P.G
G
P.G
P.G
P.G
P.G
Cool, 4°C
Cool, 4°C
Cool, 4°C
Cool, 4°C
Cool, 4°C
Cool, 4°C
Cool, 4°C
Cool, 4°C
Cool, 4°
Cool, 4°C
Cool, 4°C
Cool, 4°C
G, teflon-lined Cool, 4°C
cap
G, teflon-lined
cap
G, teflon-lined
aeptum
G, teflon-lined
septua
P,G
G, teflon-lined
cap
P,G
G
P.G
G, teflon-lined
cap
Cool, 4°C
Cool, 4°C
Cool, 4°C
Cool, 4°C
Cool, 4°C
Cool, 4°C
Cool, 4°C
Cool, 4°C
Cool, 4°C
14 days
14 days
28 days
28 days
28 days
48 hours
48 hours
28 days
48 hours
28 days
28 days
48 hours
28 days
6 Months
7 days (until extraction)
30 days (after extraction)
7 days (until extraction)
30 days (after extraction)
14 days
3 days
48 hours
7 days (until extraction)
30 dsys (after extraction)
28 days
48 hours
28 days
7 days (until extraction)
30 days (after extraction)
Polyethylene(P) or Glass(G)
Sample preservation should be performed immediately upon sample collection. For composite samples
each aliquot £Jiould be preserved at the time of collection. When impossible to preserve each
aliquot, then samples may be preserved by maintaining at 4°C until compositing ond sample splitting
is completed.
Samplea should be analyzed as soon as possible after collection. The times listed are the maximum
times that samples may be held before analysis and still considered valid. Samples may be held for
longer periods only if the aialytical laboratory has data on file to show that the specific types of
samples under study are stable for the longer time.
For additional information see Ford et al (1983).
71
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The following sample bank procedures have been used
successfully on a number of soil monitoring studies.
A. Issuing Supplies:
(1) The sample bank issues as required sample
containers, sample collection tags, chain-of-custody
forms and site description forms to the sampling
teams. Sample collection tags and chain-of-custody
forms are normally accountable documents; the sample
bank will log the forms by numerical lot identifying
the team and/or the individual responsible for the
temporary custody of these documents.
(2) The sample bank may be required to store sampling
equipment in a suitable environment. If sampling
equipment is stored at the sample bank, issuing this
equipment to the sampling teams as required will be
necessary.
B. Accepting and Logging Samples:
(1) Transfer of sample custody from the sampler to
sample bank personnel will normally occur at the
sample bank.
(2) Before accepting custody of any samples, sample bank
personnel must check all tags and forms for
legibility and completeness.
(a) All individual samples must have a completely
filled out sample collection tag attached.
(b) Every sample must be identified on the
chain-of-custody form.
(c) Each site sampled must have a completely filled
out site description form.
(d) Any discrepancy will be corrected before sample
bank personnel will assume custody. If a
discrepancy exists that cannot be resolved to
the satisfaction of the sample bank personnel,
resampling, filling out additional tags and
forms, and/or revisiting the site to obtain
necessary documentation may be required.
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(e) All unused accountable documents as shown in
Table 7-2 must be returned to the sample bank
on a daily basis. However, depending upon
circumstances such as a sampling team's
schedule and route, accountable documents may
be retained by the sampling team leader. The
sample bank supervisor, however, must be aware
of the situation.
(3) After the sampler relinquishes custody and the
sample bank personnel assumes custody of the
samples, each sample must be logged into the master
log book.
Preparation of soil samples for analysis may require sample
bank personnel to dry, sieve, mix and aliquot samples
appropriately. The preparation procedures selected are
determined by the contaminant to be measured and the analytical
requirements. Various techniques and methods for mixing and
compositing soils have been described by Oregon State University
(1971), USEPA (1984), and Peterson and Calvin (1965).
It is inappropriate to initiate a sampling study without
first consulting with analytical personnel. Collecting samples
that cannot be suitably analyzed will not provide data necessary
for satisfying the sampling objectives.
The possibility of errors being introduced in sample
preparation procedures involving the discarding of non-soil
material or of non-sieved material as well as possible losses
during any grinding or drying operation has been briefly
discussed in Chapter 4. The definitive study decisions
concerning the non-soil fraction must be made on the basis of the
data obtained from the exploratory study. For example, available
data may indicate that significant contamination is in the
discarded portion. If so, it is recommended that the discarded
portion from ten percent of the samples collected from the area
having the highest concentrations be analyzed. An estimate can
then be made of the total amount of contamination being discarded
by multiplying the measured concentration in the discarded
material by the total amount of the discarded material. Assuming
that this amount is uniformly distributed through the soil sample
remaining after non-soil materials and non-sieved materials have
been discarded, one can then calculate an estimated value for the
potential soil sample total concentration if none of the
contamination had been discarded. Comparison of this potential
concentration to the actual measured concentration will enable an
estimate of the possible error to be made.
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TABLE 7-2. ACCOUNTABLE DOCUMENT CONTROL REQUIREMENTS
Documentation
Iifued by
Numbering
Interim
Responsibility
Fin* I
Responsibility
Sanple Collection Teg*
Custody Records
Field Logbook*
Site Description fora*
Analytical Sample Tags
Laboratory Notebook*
Analytical Data Sheet*
Sample Bank
Sample Bank
Sanple Bank
Sample Bank
Sanple Bank
Laboratory
Staple Bank
Praaerialiied
Preaerialiied
Preaerialiced
Sampling Teaaj
Sanpling Tea*
Sampling Tea*
Sanpling Te«»
Sanple Bank
Analytical Laboratory
Analytical Laboratory
Sanple Bank
Sample Bank
Sample Bank
Sanple Bank
Analytical Laboratory
Sanple Bank
Sanple Bank
-------
If the error estimated by this process exceeds acceptable
limits specified in the QA/QC plan, it might be necessary to
modify sample preparation procedures for the definitive study.
One might consider a sample preparation procedure in which the
entire collected sample (soil and non-soil materials) is
extracted in the analytical laboratory. The analytical results
could then be reported as amounts of contaminant per gram of
mixed material. At present there is no acceptable method for
proceeding in cases such as these. One problem is the lack of
standard reference materials for determining and measuring errors
in extraction efficiency. One solution may be to try different
methods of extraction and compare the results. The final
interpretation of the data must then take into consideration
these estimated errors.
QUALITY ASSURANCE ASPECTS
The problem is to quantitate overall errors. The
recommended procedure for verifying that the QA/QC plan is being
carried out properly for this chapter's factors is a periodic
audit, combined with a modest amount of extra samples and
analyses related to factors discussed above.
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CHAPTER 8
ANALYSIS AND INTERPRETATION OF QA/QC DATA
INTRODUCTION
One goal in the analysis and interpretation of data is to
show how all aspects of QA/QC for a soil monitoring study combine
to give an overall level of precision and confidence for the data
resulting from the study. Another goal may be to determine
whether all QA/QC procedures which were used were necessary and
adequate and should definitely be incorporated into future
studies of the same type. This entire evaluation must be closely
linked to the objectives of the study. In summary the important
questions to be answered are, "What is the quality of the data
(maximum accuracy attainable)?" and also," Could the same
objective have been achieved through an improved QA/QC design
which may have required fewer resources?"
PRESENTATION OF DATA SUMMARIES
It is desirable to provide summarized tables of validated
QA/QC data in the final report. For example, QA/QC data
validation procedures used in a number of soil sampling studies
reported by Brown and Black (1983) included validation of sample
data sets by checking and assessing the accompanying QA/QC data.
The criteria for QA/QC samples and procedures used to validate
all data included:
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Samples and Procedures
Example Criteria
1. Reagent Blanks
2. Calibration Check
Standards
3. Laboratory Control
Standards
Concentrations had to be less
than 0.25 g/ml"1.
Recovery must be between 95% and
105% of the known value for
either the first analysis or the
first re-check analysis.
Recovery must be between 90% and
110% of the known value for
either the first analysis or the
first re-check analysis.
Data produced by any sampling and analyzing system are
affected by two types of errors; random and systematic. The
accuracy of any one result then, is a function of the bias (due
to systematic error) and precision (due to
collection and analysis methodology.
components, associated with extraction and
and is assessed by the mean recovery
Standards and Laboratory Control Standards
random error) of the
Bias has at least two
instrument efficiency,
of Calibration Check
(LCS). The LCS check
overall bias
determines the
for the system;
instrumental bias.
the Calibration Check Standard
Total random error can be assessed by analyzing duplicate
samples, but it includes errors due to sample collection, sample
homogeneity, sample extraction, sample composition (matrix
effects) and instrumental reproducibility. These errors can be
evaluated by the use of the other QC procedures stated above and
are assessed by calculating the standard deviations of the
various analyses.
The accuracy of analysis, i.e
evaluated separately below for the two
the following equations:
. , bias and precision, are
types of samples, using
Recovery = Amount Found/Known Amount
(1)
Bias (B)
Recovery - 1
(2)
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Difference (D) = | x^ - x2| where x^ and X2 are the analytical
results of paired analyses and the average is:
n
(3)
and the precision is:
s_=Precision = 0.8862 D
(4)
where 0.8862 converts the range of two results to the standard
deviation (Natrella, 1963).
then
If component errors are used to assess total random error,
+ D2 +
)/n and
(5)
precision - [0.8862 (D].2 + D22
) +
s 2
I1/2-
Equation (3) is suitable for use on results where the
concentration varies over a very narrow range. If the
concentrations found vary by an order of magnitude or more, then
the difference should be normalized by dividing by the average of
the two values and the precision is expressed as the coefficient
of variation (CV) which is s/x
Z
n n
D_ L, I I X ~ X I »
_ - _ ( | 1 2h )
(6)
r ix - x
2 z I i 2
n .
CV = 0.8862 D
(7)
n
One of the studies discussed by Brown and Black (1983)
involved lead contaminated soils. The use and evaluation of the
QC analyses for this soil monitoring study was presented as
follows:
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The limit of detection, approximately 0.25 yg ml~l, was tested on
about 10 blank analyses using a more sensitive absorbance
wavelength for lead on an AAS. The result was less than 0.1 yg
ml"1, or 2 yg g~l for sample analysis. This suggests that most
of the blank analyses were less than 2 yg g~l, but this cannot be
stated with any confidence. The results of the QC analyses were
as follows:
QC Sample
Calibration Check Standard
Laboratory Control Standard
Field Blank (yg ml"1)
Sample Bank Blank (yg ml~l)
Reagent Blank (yg ml~l)
Re-extraction Analysis
Total Recoverable
Split Extract (CV)
Spiked Extract
Spiked Sample
Duplicate Aliquot (CV)
Duplicate Sample (CV)
Triplicate Analysis (CV)
No.
150
147
76
77
148
17
144
147
147
147
134
129
220
Mean
101.5%
101.2%
<0.25
<0.25
<0.25
1.7%
99.8%
0.0089
99.4%
100.4%
0.053
0.189
0.144
S
2.6%
4.1%
1.4%
8.0%
0.0079
5.0%
5.1%
0.047
0.168
0.128
(1) Bias: The percent recoveries indicated above for the
Calibration Check Standards and LCS's suggest a small positive
bias for the method of soil analysis, due principally to
instrument reproducibility. The result, using Equation (2), is:
Bias = Recovery - 1 = 1.012 - 1 = 0.012.
(2) Precision: The recovery of the analyte by the analytical
method compared to the "total" recoverable method was essentially
equal and re-extraction of the residue left from the initial
extraction indicated an additional 1.7 ±1.4 percent recovery,
also essentially equivalent. Furthermore, the results of the
three types of blank analyses indicate no measurable
contamination from reagents, sample collection, or sample
preparation. The remaining random errors are evaluated below.
Because of the wide range of concentration of lead in the
samples, the coefficient of variation is used, Equation (7).
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Precision (total random error) from Duplicate Sample
Analysis:
CV - 0.168 or 16.8% of sample concentration.
The component random errors, summed as per Equation (5), are:
sx m (0.00792 + 0.052 + 0.0512 + 0.0472)1/2 = 0.085.
These random errors suggest that reproducibility
errors(0.0079) are small and that extract matrix, sample matrix,
and sample homogeneity errors are equivalent. The sum of these
errors is about half the total random error so the sampling error
is essentially equal to all other errors combined.
Inter laboratory precision as calculated from the results of
triplicate analyses, using Equation (7) is:
Precision * CV « 0.128 or 12.8% of sample concentration,
(3) Uncertainty: The data for bias and precision can be
combined to yield the uncertainty for any reported concentration
by use of the following equation:
U - (1 + B + 2 C) (8)
where B is the bias, C is the standard deviation or coefficient
of variation as appropriate, and 2 converts these to the 95
percent confidence limits. For soil analyses, using Equation (8)
and the bias and CV derived above, the 95% confidence bounds on a
reported value, x, are:
Soil result will lie between 0.676x and 1.348x yg g"1.
It is required that the QA/QC plan ensure and document that
all data collected, whether used for research or for monitoring
purposes, is scientifically valid, defensible and of known
precision and accuracy. The described presentation of QC data,
though designed for analysis of lead in soil, can be used as a
80
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guide for other sampling and data analysis protocols and/or QA/QC
plans.
Presentation of QA/QC data allows readers to verify
conclusions drawn as to the reliability of the data. Such an
approach also contributes to the building of a body of QA/QC and
monitoring experimental data in the literature which allow
comparisons to be made between and among studies. Procedures
used to validate the individual data points should be presented
and where some points are discarded arguments should be presented
to support these decisions.
PRESENTATION OF RESULTS AND CONCLUSIONS
Special emphasis should be placed on how overall levels of
precision and confidence were derived from the data. Great care
must be exercised to insure that, in determining results and
conclusions, assumptions are not made which were not part of the
study design and which cannot be tested by data derived from the
study. If portions of the study results are ambiguous and
supportable conclusions cannot be drawn with regard to the total
reliability of the data, that situation must be clearly stated.
In that event it is desirable to include recommendations for
conducting an improved study in such a way as to clarify the
observed ambiguities.
QUALITY ASSURANCE ASPECTS
The adequacy of all aspects of the QA/QC plan should be
examined in detail with emphasis on defining for future studies
an appropriate minimum adequate plan. Some aspects of the plan
actually used may have been too restrictive, some may not have
been restrictive enough. Appropriate analyses and interpretation
of the data should identify the actual situation.
Future soil monitoring studies should have checks and
balances built into the QA/QC plan which will identify early in
the study whether the plan is adequate and if necessary, allow
for corrective action to be taken before the study continues.
This is one of the major advantages of conducting an exploratory
study along the lines outlined in this report. If there are
problems with the QA/QC plan, they will often be identified in
the exploratory study and be corrected before major resources are
expended.
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There is insufficient knowledge dealing with soil monitoring
studies to state with confidence which portions of the QA/QC plan
will be generally applicable to all soil monitoring studies and
which portions must be varied depending on site-specific factors.
As experience is gained, it may be possible to provide more
adequate guidance on this subject. In the meantime it is
recommended that the best approach is to assume that important
factors of QA/QC plans are site-specific and to conduct an
appropriate exploratory study at each new study site to verify
that various aspects of the QA/QC plan are adequate to meet
program objectives prior to proceeding with the final definitive
study.
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CHAPTER 9
SYSTEM AUDITS AND TRAINING
INTRODUCTION
The material for this chapter has been obtained primarily
from USEPA Kellogg Idaho Study (1984). The first phase of an
auditing program for soil monitoring projects should be the
preparation of standard operating procedures (SOP) that identify
the methods and techniques necessary to perform all aspects of
the required audit. The SOP must be adequate to perform onsite
sampling and sample bank (where applicable) audits. The second
phase should then be the actual conduct of the required field
audit. Audits are conducted by appropriate elements of agencies
or organizations having cognizance over the monitoring project.
The frequency of auditing should be determined by the project
officer. Juran et al. (1979) state that, "the activities subject
to audit should include any that affect quality regardless of the
internal organizational location."
A system audit is an overall evaluation of a project to:
o Verify that sampling methodology is being performed in
accordance with program requirements
o Check on the use of appropriate QA/QC measures
o Check methods of .sample handling, i.e., packaging,
labeling, preserving, transporting, and archiving in
accordance with progam requirements
o Identify any existing quality problems
o Check program documentation, i.e., records (site
description, chain-of-custody collection and analytical
tags, field and sample bank log books and field work
sheets)
o Initiate corrective action if a problem is identified
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o Asssss personnel experience and qualifications if
required
o Follow-up on any corrective action previously
implemented
o Provide onsite debrief ings for sampling team and sample
bank personnel.
o Provide a written evaluation of the sampling and sample
bank program
The purpose of the system audit is to ensure that the QA/QC
system planned for the project is in place and functioning well.
The auditor first must review Work Plans, Protocols, Test
Plans, QA/QC Project Plan, and all Program Reports. A discussion
of the current status of the project, and the identity of any
problems encountered, with the project officer is suggested
before conducting the onsite sampling audit. Sample
chain-of-custody procedures and raw data are checked as
appropriate and results of blind QC samples routinely inserted in
the sample load by sample bank personnel are reviewed.
Spot-checks of sampling methods and techniques, sampling and
analysis calculations, and data transcription are performed.
SAMPLE BANK AUDIT
The primary objective is to determine the status of all
Sample Bank documentation and archived samples. Emphasis is
placed on:
o Verifying that the documentation is in order and
sufficient to establish the disposition of any sample
collected
*
o Determining any discrepancies that currently exist and
initiating corrective action as appropriate
o Verifying that the recording of QA/QC measures (blanks,
duplicate spikes, blinds) is in accordance with the
QA/QC Plan
o Establishing procedures for final disposition and
mechanics of transfer of all Sample Bank holdings upon
termination of the operation.
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The first step of the audit is to inventory the Sample Bank
records and archived samples. The records that must be inspected
are:
o Chain-of-custody forms
- Field forms
- Analysis forms
o Sample tags
- Field tags
- Analysis tags
o Analysis forms
- Individual samples
- Batch sheets
o Shipment forms
o Logbooks
- Soils
- Daily log
The operational procedures inspected should include:
o Preparation Procedures (sample bank or analytical
laboratory)
- Drying (if used)
- Sieving
Mixing
- Packaging
- Shipping
o Housekeeping
Safety
- Decontamination
- Evaluation of Swipe Samples
o Security
- Forms (documents)
- Samples
o Storage
- Sampling equipment
- Archived samples
Check that required documentation has been maintained
in an orderly fashion, that each of the recorded items is
properly categorized, and cross-checking can be easily performed.
In addition, ensure that data recording conforms to strict
document control protocols and the program's QA/QC Plan.
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The archived samples inspected can be categorized as
follows:
o Soil
o Blanks
o Splits
o Standard Reference Materials (SRM )
o Non-Soil Materials Collected with the Soil Sample
Conduct an audit of the archived samples. Verify that
appropriate samples exist for each entry in the logbook. Field
sample tags should be replaced by the appropriate analytical
tags, and chain-of-custody forms are prepared in order to
transfer the samples. Detailed sample bank procedures are
presented by USEPA Dallas Lead Study (1984).
DAILY LOG
Check for clear, concise entries detailing events of the day
(such as numbers of samples processed), problems encountered, and
actions taken to solve them. This log can provide excellent
documentation of the operation of the Sample Bank.
SAMPLE BANK LOGS
Review these logs for complete sample information entered.
Changes made should be by crossing out so the original entry is
still visible, and initialing. In addition checks for the
identification and documentation of split and duplicate samples,
and field and Sample Bank blanks must be performed.
SAMPLE COLLECTION AUDITS
It is recommended that an audit of the overall QA/QC plan
for sample documentation, collection, preparation, storage, and
transfer procedures be performed just before sampling starts.
The intent of this audit is to critically review the entire
sampling operation to determine the need for any corrective
action early in the program. Additional total program or partial
audits can be conducted at various times throughout the sampling
program.
It is recommended -that the Project Officer maintain a QA/QC
Coordinator onsite during sample collection to monitor the
sampling team's activities, provide technical and corrective
86
-------
action suggestions to the sampling teams, and supplement
performance audits on sampling as needed.
FIELD AUDITS
The primary objective is to determine the status of sampling
operations. Emphasis is placed on:
o Verifying that operational aspects and procedures are in
accordance with the protocols and QA/QC plan.
o Verifying the collection of all samples including
duplicates and field blanks.
o Verifying that documentation is in order and sufficient
to establish the collection location of any sample
collected.
o Determining discrepancies that exist and initiating
corrective action as appropriate.
o Collecting independent samples.
The on-site field audit is to inspect sample records and
equipment. Records inspected include:
a. Chain-of-Custody Forms
b. Sample Tags
c. Site Description Forms
d. Log Books
The operational procedures inspected should include:
o Sampling Procedures
Equipment
- Techniques
Decontamination
Collection of duplicate and field blank samples
- Security
- Sample storage and transportation
- Containers
- Contaminated waste storage and disposal
Site Description Form entries
87
-------
DATA MANAGEMENT AUDITS
An audit of the data management system by tracing the flow
of specific samples through the system should be performed. In
particular, the ability of the system to correctly identify a
sample from any one of its identification numbers should be
checked.
Entries in the sample bank's logbook will be the basis for
these performance checks. From time to time, erroneous input
information may be used to audit the system.
TRAINING
The project leader of a soil monitoring project is
responsible for ascertaining that all members of his project team
have adequate training and experience to carry out satisfactorily
their assigned missions and functions. Until a field sampling
team has worked together long enough for the project leader to
have verified this from first hand knowledge it is good practice,
in addition to any classroom training or experience, to conduct
comprehensive briefing sessions for all involved parties during
which all aspects of the sampling protocol, including the QA/QC
plan, are presented and discussed in some detail. This approach
will help the project personnel to develop into a team where each
team member knows his own job well and knows how it fits into the
overall team effort. Sufficient field training exercises should
follow the briefing sessions until each team member can
demonstrate successfully that he can perform his job routinely
well and without delay. Of course, on subsequent projects of the
same general type with the same team, the training exercises may
be reduced in' number or dispensed with as deemed appropriate by
the project leader.
In summary, the sampling effort must include classroom and
field training programs that'have provided detailed instruction
and practical experience to personnel in sample collection
techniques and procedures, labeling, preservation, documentation,
transport, and sample bank operational procedures. Also, special
training programs concerning 'procedures and program documentation
should be completed by all personnel prior to their involvement
in the conduction of any audits.
88
-------
REFERENCES
1. Allmaras, R. R. Bias. In: Methods of Soil Analysis, Part
1, Physical and Mineralogica1 Properties, including
Statistics of Measurement and Sampling. C. A. Black, et
al, ed. American Society of Agronomy, Madison, Wisconsin,
1965. pp. 24-42.
2. Bauer, Edward L. A Statistical Manual for Chemists.
Academic Press, New York, New York, 1971. 193 pp.
3. Beckett, P. H. T., and R. Webster. Soil Variability: A
Review. Soils and Fertilizers, 34:1-15. 1971.
4. Box, George, E. P. Statistics and the Environment. Journal
of the Washington Academy of Sciences, 64(2):52-59. 1974.
5. Broms, Bengt B. Soil Sampling in Europe: State-of-the-art.
Journal of the Geotechnical Engineering Div., 106:65-98.
1980.
6. Brown, K. W. and S. C. Black. Quality Assurance and Quality
Control Data Validation Procedures Used for the Love Canal
and Dallas Lead Soil Monitoring Programs. Environmental
Monitoring and Assessment, 3:113-112, 1983.
7. Buffington, J. P. Developing Recommendations to Improve
Quality Assurance for Federal Monitoring Programs. In:
Proceedings of the National Conference on Quality Assurance
of Environmental Measurements, Denver, Colorado, 1978.
8. Burgess, T. M. and R. Webster. Optimal Interpolation and
Isarithmic Mapping .of Soil Properties. I. The
Semi-variogram and Punctual Kriging. Journal of Soil
Science, 31:315-331. 1980a.
9. Burgess, T. M. and R. Webster. Optimal Interpolation and
Isarithmic Mapping of Soil Properties. II. Block Kriging.
Journal of Soil Science, 31:333-341. 1980b.
10. Campbell, James B. Spatial Variability of Soil. Annals of
the Association of American Geographers, 69(4 ) :544-556 .
1978.
11. Campbell, James B. Locating Boundaries Between Mapping
Units. Math. Geology, 10 (3 ):289-299. 1979.
89
-------
12. Cline, Marlin. Principles of Soil Sampling. Soil Science.
Vol 58:275-288. 1944.
13. Davis, John C. Statistics and Data Analysis in Geology.
John C. Wiley and Sons, Inc., New York, New York, 1973.
14. Dixon, W. J. Processing Data for Outliers. Biometrics,
9:74-89. 1953.
15. Dixon, W. J. Extraneous Values. In: Methods of Soil
Analysis. Part 1, Physical and Mineralogical Properties,
including Statistics of Measurement and Sampling. C.
A. Black, et al, ed. American Society of Agronomy, Madison,
Wisconsin, 1965. pp. 43-49.
16. Eynon, Barry and Paul Switzer. A Statistical Comparison of
Two Studies on Trace Element Composition of Coal Ash
Leachates. Final Report. Electric Power Research
Institute, Palo Alto, California. July 1983. EA-3181.
17. Flatman, G. T. Assessing Lead Contamination near Smelters:
A Case Study. Paper presented at Workshop on Environmental
Sampling. February 1-3, 1984. Las Vegas, NV.
18. Ford, Patrick J., Paul J. Turina, and Douglas E. Seely.
Characterization of Hazardous Waste SitesA Methods Manual.
Vol. II. Available Sampling Methods. EPA 600/4-83-040.
U.S. Environmental Protection Agency, Environmental
Monitoring Systems Laboratory, Las Vegas, Nv. 1983.
19. Hammond, Luther C. , William L. Pritchett, and Victor Chew.
Soil Sampling in Relation to Soil Heterogeneity. Soil
Science Society of America Proceedings, 22:548-552, 1958.
20. Heimbuch, Douglas G. Computer Software Package for the
Determination of Optimal Preliminary Sample Size in
Two-Stage Sampling for Mean Concentration. Cornell
University. Utica, NY.. 1982.
21. Hipel, Keith William, Dennis P. Lettenmaier, and A. Ian
McLeod. Assessment of Environmental Impacts Part One:
Intervention Analysis. Environmental Management,
2(6):529-535, 1978.
22. Juran, J. M. , F. M. Gryna, Jr. and R. S. Bingham Jr., eds.
Quality Control Handbook, Third Edition, McGraw Hill. 1979.
23. Kempthorne, Oscar and R. R. Allmaras. Errors of Observation.
In: Methods of Soil Analysis. Part 1, Physical and
Mineralogical Properties including Statistics of Measurement
and Sampling. C. A. Black, et al, ed. American Society of
Agronomy, Madison, Wisconsin, 1965. pp. 1-23.
90
-------
28,
24. Ku, Harry H. Statistical Sampling and Environmental Trace
Organic Analysis. In: Trace Organic Analysis: A New
Frontier in Analytical Chemistry. Proceedings of the 9th
Materials Research Symposium, National Bureau of Standards,
Gaithersburg, Maryland, 1978.
25. Mason, Benjamin J. Preparation of Soil Sampling Protocols.
(EPA 600/4-83-020). 1983.
26. Natrella, M. G. Experimental Statistics, NBS Handbook 91,
U.S. Government Printing Office, Washington, D.C. 1963.
27. Oregon State University. Methods of Soil Analysis Used in
the Soil Testing Laboratory at Oregon State University.
Special Report 321. Corvallis, Oregon. 1971.
Peterson, R. G. and L. D. Calvin. Sampling. In: Methods
of Soil Analysis. Part 1, Physical and Mineralogical
Properties, including Statistics of Measurement and Sampling.
C. A. Black, et al, ed. American Society of Agronomy,
Madison, Wisconsin, 1965. pp. 54-71.
29. Plumb, Russell H. Jr. Procedures for Handling and Chemical
Analysis of Sediment and Water Samples. EPA-48/05-5720-10 ,
U.S. Environmental Protection Agency/Corps of Engineers
Technical Committee on Criteria for Dredged and Fill
Material, Grosse lie, Michigan, 1981.
30 Rao, P. V., P. S. C. Rao, J. M. Davidson, and L. C. Hammond.
Use of Goodness-of-Fit Tests for Characterizing the Spatial
Variability of Soil Properties. Soil Science Society of
America Journal, 3:274-278. 1979.
31 Skogerboe, R. K. and R. Koirtyohann. Accuracy Assurance in
the Analysis of Environmental Samples. Accuracy in Trace
Analysis: Sampling, Sample Handling, and Analysis Volumes
I-II. Seventh Materials Research Symposium. Edited by
Philip D. La Fleur, NBS, Gaithersburg, MD, 1976.
32 Snedecor, George W. and William G. Cochran. Statistical
Methods, Seventh Edition. The Iowa State University Press,
Ames, Iowa, 1982. 507 pp.
33 U S. Environmental Protection Agency. Guidelines
Establishing Test Procedures for the Analysis of Pollutants;
Proposed Regulations. Federal Register, 44:233, pp.
69464-69575, Washington, D.C. 1979.
34 U S. Environmenta-1 Protection Agency. Documentation of
EMSL-LV Contribution to the Kellogg Idaho Study. EPA
600/X-84-052, Environmental Monitoring Systems Laboratory,
Las Vegas, NV, 1984.
91
-------
35. U.S. Environmental Protection Agency. Quality Assurance
Handbook for Air Pollution Measurement Systems.
EPA-600/9-76-005 , Environmental Monitoring and Support
Laboratory, Research Triangle Park, N.C. 1976.
36. U.S. Environmental Protection Agency. Environmental
Monitoring at Love Canal. Volumes I - III.
EPA-600/4-82-030 a-d, Washington, D.C. 1982.
37. U.S. Environmental Protection Agency. Documentation of
EMSL-LV Contribution to Dallas Lead Study EPA-600/4-84-012.
Environmental Monitoring Systems Laboratory, Las Vegas, NV,
1984.
38. U.S. Environmental Protection Agency. National Oil and
Hazardous Substances Contingency Plan. Federal Register.
Vol 47(137):31180-31243. Washington, D.C. 1982.
39. U.S. Environmental Protection Agency. Handbook for
Analytical Quality Control in Water and Wastewater
Laboratories. EPA-600/4-79-019. U.S. Environmental
Protection Agency. Environmental Monitoring and Support
Laboratory, Cincinnati, OH. 45268. 1979.
40. U.S. Code of Federal Regulations, Land Treatment, 40 CFR,
Part 264, Subpart M, July, 1983.
41. Webster, R. and T. M. Burgess. Optimal Interpolation and
Isarithmic Mapping of Soil Properties. III. Changing Drift
and Universal Kriging. Journal of Soil Science,
31(3):505-524. 1980.
42. Youden, W. J. and E. H. Steiner. Statistical Manual of the
Association of Official Analytical Chemists. Association of
Official Analytical Chemists, Washington, D.C. 1975. 88p.
92
-------
APPENDIX A
TOOLS FOR ESTIMATING NUMBER OF SAMPLES TO ACHIEVE
SPECIFIED LEVELS OF PRECISION AND CONFIDENCE
The graph, shown as Figure A-l, can be used to determine the
number of samples required to estimate the standard deviation
within a stated percent of its true value with confidence levels
of 90, 95 and 99 percent. A series of tables are also presented
which provide estimates of the number of samples necessary to
achieve a specified level of confidence for both single-tailed
(75-99.5%)'and two-tailed (50-95%) t tests. The precision is to
be stated and it is assumed that the coefficient of variation is
known.
93
-------
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Figure A-l. Number of degrees of freedom required to estimate the Standard
Deviation within P% of its True Value with confidence level Y«
94
-------
TABLE A-l. ESTIMATED NUMBER OF SAMPLES TO ACHIEVE SPECIFIED
LEVELS OF PRECISION AND CONFIDENCE WHEN COEFFICIENT OF VARIATION
(CV) IS KNOWN.
Confidence Level
50(%): two-tailed t test
75(%): one-tailed t test
Precision p(%)
CV (%) 1 25 10 15 20 25 30 40 50 75 100
1
2
4
6
8
10
20
30
40
50
100
1
3
8
17
30
47
182
410
728
1138
4550
1
1
3
5
8
12
47
104
182
285
1138
1
1
1
2
2
3
8
17
30
47
182
1
1
1
1
1
1
3
5
8
12
47
1
1
1
1
1
1
2
3
4
6
21
1
1
1
1
1
1
1
2
3
4
12
11111 1
11111 1
11111 1
11111 1
11111 1
Confidence Level
60(%): two-tailed t test
SOU): one-tailed t test
Precision p(%)
CV (Z)
1
2
4
6
8
10
20
30
40
50
100
1
2
4
13
27
47
72
284
638
1134
1771
7084
2
1
2
4
8
13
19
72
160
284
443
1771
5
1
1
2
2
3
4
13
27
47
72
284
12
1
1
1
1
2
2
4
8
13
19
72
J_5
1
1
1
1
1
1
2
4
6
9
33
20
1
1
1
1
1
1
2
3
4
6
19
25_
1
1
1
1
1
1
2
2
3
4
13
30 40 50 75 100
1111 1
1111 1
1111 1
1111 1
1111 1
1111 1
1111 1
2111 1
2221 1
3221 1
9642 2
(Continued)
-------
TABLE A-l.
Confidence Level
70(%): two-tailed t test
85(%): one-tailed t test
Precision p(%)
CV (Z) 1 25 10 15 20 25 30 40 50 75 100
1 2 11111111111
2 6 21111111111
4 19 62111111111
6 42 11 321111111 1
8 74 19 422111111 1
10 115
20 430
30 967
40 1719
50 2686
100 10742
1
2
6
11
19
28
115
242
430
672
2686
1
1
2
3
4
6
19
42
74
115
430
1
1
1
2
2
2
6
11
19
28
115
1
1
1
1
2
2
3
6
9
13
52
1
1
1
1
1
2
2
4
6
8
28
1
1
1
1
1
1
2
3
4
6
19
1
1
1
1
1
1
2
2
3
4
13
Confidence Level
80(%)
90(%)
: two-tailed
: one-tailed
t
t
test
test
Precision p(%)
2
2
3
8
16
28
43
165
370
657
1027
5
1
2
2
4
6
8
28
61
107
165
10
1
1
2
2
3
3
8
16
28
43
15
1
1
1
2
2
2
4
8
13
20
20
1
1
1
1
2
2
3
5
8
12
25
1
1
1
1
1
2
2
4
6
8
30
1
1
1
1
1
1
2
3
4
6
CV (%) 1 25 10 15 20 25 30 40 50 75 100
1 3 21111111111
2 8 32111111111
4 28 82211111111
6 61 16 422111111 1
8 107 28 632211111 1
10 165
20 657
30 1479
40 2628
50 4106
100 16424 4106 657 165 75 43 28 20 12
(Continued)
96
-------
TABLE A-l.
Confidence Level
90(%): two-tailed t test
95(%): one-tailed t test
Precision p(%)
CV (X) 1 25 10 15 20 25 30 40 50 75 100
1 1
1 1
1 1
1 1
1 1
1 1
2 2
2 2
2 2
1
2
4
6
8
10
20
30
40
50
100
5
13
46
100
174
271
1083
2435
4329
6764
27055
2
5
13
27
46
70
271
609
1083
1691
6764
2
2
4
6
9
13
46
100
174
271
1083
1
2
2
3
4
5
13
27
46
70
271
1
1
2
2
3
3
7
13
21
32
121
1
1
2
2
2
3
5
8
13
19
70
1
1
1
2
2
2
3
6
9
13
46
1
1
1
2
2
2
3
5
7
10
32
1
1
1
1
2
2
2
3
5
6
19
1
1
1
1
1
2
2
3
3
5
13
Confidence Level
95(%): two-tailed t test
97.5(%): one-tailed t test
Precision p(%)
cv (%) i 2 5 J^_152025_30405025_iPJ)
1 1
1 1
1 1
1 1
2 1
2 2
2 2
3 2
3 3
4 3
9 6
97 (Continued)
1
2
4
6
8
10
20
30
40
50
100
6
18
64
139
246
385
1537
3458
6147
9604
38416
3
6
18
37
64
99
385
865
1537
2401
9604
2
3
5
8
12
18
64
139
246
385
1537
2
2
3
4
5
6
18
37
64
99
385
1
2
2
3
3
4
9
18
30
45
171
1
2
2
2
3
3
6
11
18
27
99
1
1
2
2
2
3
5
8
12
18
64
1
1
2
2
2
2
4
6
9
13
46
1
1
2
2
2
2
3
5
6
9
27
1
1
1
2
2
2
3
4
5
6
18
-------
TABLE A-l.
Confidence Level
98(%): two-tailed t test
99(2): one-tailed t test
Precision p(%)
CV (%) 1 2 5 10 15 20 25 30 40 50 75 100
2111 1
2221 1
2222 2
2222 2
2222 2
40 8659 2165 347 90 42 25 17 13 9 7 4
50 13530 3383 542 136 63 37 25 18 12 9 5
100 54119 13530 2165 542 241 136 90 63 37 25 13
1
2
4
6
8
10
20
30
8
25
90
195
347
542
2165
4871
4
9
25
52
90
136
542
1218
2
3
6
11
17
25
90
195
2
2
3
5
7
9
25
52
2
2
3
3
4
5
13
25
2
2
2
3
3
4
9
15
2
2
2
2
3
3
6
11
Confidence Level
99(%): two-tailed t test
99.5(Z): one-tailed t test
Precision p(2)
CV (2) 1 2 5 10 15 20 25 30 40 50 75 100
1
2
4
6
8
10
31
110
239
425
5
10
31
64
110
3
4
8
13
21
2
3
4
6
8
2
2
3
4
5
2
2
3
3
4
2
2
3
3
3
2
2
2
3
3
2
2
2
3
3
2
2
2
2
3
1
2
2
2
2
1
2
2
2
2
10- 664 166 31 10 6 5 4 4 3 3 2 2
20 2655 664 110 31 16 10 8 6 5 4 3 3
30 5973 1493 239 64 31 19 13 10 7 6 4 3
40 10618 2655 425 110 51 31 21 16 10 8 5 4
50 16590 4148 664 166 78 46 31 22 14 10 6 5
100 66358 16590 2655 664 295 166 110 78 46 31 16 10
98
-------
APPENDIX B
TABLES FOR USE IN CALCULATING CONFIDENCE AND TOLERANCE LIMITS
AND JUDGING THE VALIDITY OF MEASUREMENTS
A series of tables are presented which can be used to calculate
confidence intervals for averages, percentiles of the
t-distribution, the standard deviation, the tolerance interval
for individuals and critical values for discarding invalid
measurements.
99
-------
TABLE B-l. PERCENTILES OF THE t DISTRIBUTION
Confidence Level (%)
20
30
60
Confidence Level (%)
df
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
40
60
120
oc
60
.325
.289
.277
.271
.267
.265
.263
.262
.261
.260
.260
.259
.259
.258
.258
.258
.257
.257
.257
.257
.257
.256
.256
.256
.256
.256
.256
.256
.256
.256
.255
.254
.254
.253
70
.727
.617
.584
.569
.559
.553
.549
.546
.543
.542
.540
.539
.538
.537
.536
.535
.534
.534
.533
.533
.532
.532
.532
.531
.531
.531
.531
.530
.530
.530
.529
.527
.526
.524
80
1.376
1.061
.978
.941
.920
.906
.896
.889
.883
.879
.876
.873
.870
.868
.866
.865
.863
.862
.861
.860
.859
.858
.858
.857
.856
.856
.855
.855
.854
.854
.851
.848
.845
.842
:l-a/2 for two-tailed test
80
:l-a for
90
3.078
1.886
1.638
1.533
1.476
1.440
1.415
1.397
1.383
1.372
1.363
1.356
1.350
1.345
1.341
1.337
1.333
1.330
1.328
1.325
1.323
1.321
1.319
1.318
1.316
1.315
1.314
1.313
1.311
1.310
1.303
1.296
1.289
1.282
90
one-tailed
95
95
test
97.5
6.314 12.706
2.920
2.353
2.132
2.015
1.943
1.895
1.860
1.833
1.812
1.796
1.782
1.771
1.761
1.753
1.746
1.740
1.734
1.729
1.725
1.721
1.717
1.714
1.711
1.708
1.706
1.703
1.701
1.699
1.697
1.684
1.671
1.658
1.645
4.303
3.182
2.776
2.571
2.447
2.365
2.306
2.262
2.228
2.201
2.179
2.160
2.145
2.131
2.120
2.110
2.101
2.093
2.086
2.080
2.074
2.069
2.064
2.060
2.056
2.052
2.048
2.045
2.042
2.021
2.000
1.980
1.960
98
99
31.821
6.965
4.541
3.747
3.365
3.143
2.998
2.896
2.821
2.764
2.718
2.681
2.650
2.624
2.602
2.583
2.567
2.552
2.539
2.528
2.518
2.508
2.500
2.492
2.485
2.479
2.473
2.467
2.462
2.457
2.423
2.390
2.358
2.326
99
99.5
63.657
9.925
5.641
4.604
4.032
3.707
3.499
3.355
3.250
3.169
3.106
3.055
3.012
2.977
2.947
2.921
2.898
2.878
2.861
2.845
2.831
2.819
2.807
2.797
2.787
2.779
2.771
2.763
2.756
2.750
2.704
2.660
2.617
2.576
100
-------
TaMfB-2. CI=]T± A&R). Confidence Interval for Averages'
Prob.
0.05
0.01
0.05
0.01
0.05
0.01
0.05
0.01
0.05
0.01
0.05
0.01
0.05
0.01
0.05
0.0 1
0.05
0.01
0.05
0.01
k
1
2
3
4
5
6
7
8
9
10
2
6.36
31.9
0.879
2.11
0.360
0.660
0.210
0.350
0.140
o.::6
0.102
0.157
0.079
0.117
0.063
0.094
0.053
0.076
0.044
0.064
3
1.30
3.00
0.316
0.474
0.156
0.273
0.096
0.142
0.066
0.095
0.050
0.070
0.039
0.055
0.032
0.044
0.027
0.036
0.023
0.031
4
0.719
1.36
0.206
0.312
0.104
0.150
0.065
0.092
0.046
0.063
0.034
0.047
0.027
0.037
0.022
0.030
0.018
'0.025
0.016
0.021
5
0.505
0.865
0.154
0.227
0.079
0.112
O.OSO
0.070
0.035
0.049
0.027
0.036
0.021
0.029
0.017
0.023
0.014
0.019
"0.012
0.016
n
6
0.402
0.673
0.125
0.179
0.065
0.091
0.042
0.057
0.030
0.040
0.022
0.030
0.018
0.024
0.014
0.019
0.012
0.016
0.010
0.014
7
0.336
0.514
0.106
0.150
0.056
0.077
0.036
0.048
0.025
0.034
0.019
0.026
0.015
0.020
0.012
0.016
0.010
0.014
0.009
0.012
8
0.291
0.430
0.093
0.131
0.049
0.068
0.032
0.043
0.022
0.030
0.017
0.023
0.013
0.018
0.01 1
0.014
0.009
0.012
0.008
0.010
9
0.256
0.379
O.OS4
0.116
0.044
0.060
0.028
0.038
0.020
0.027
0.015
0.020
0.012
0.016
0.010
0.013
0.008
0.011
0.007
0.009
10
0.232
0.338
0.076
0.105
0.040
0.054
0.026
0.035
0.018
0.025
0.014
0.019
0.011
0.015
0.009
0.012
0.007
0.010
0.006
0.008
Given * subgroups of n numbers, the confidence interval is X ± A(1R).
From Bauer, 1971.
101
-------
Table B-3. Single Classification Factor (cx) to Estimate Standard
Deviation from Range, and Equivalent Degrees of Freedom (/)a
s =
k
1
2
3
4
5
6
7
8
9
10
/
1.0
1.9
2.8
3.7
4.6
5.5
64
7?
8.1
9.0
I
Ct
.41
.28
.23
71
19
18
.17
.16
.15
14
/
2.0
3.8
5.7
7.5
9.1
11.1
12.9
14.8
16.6
IF 4
I
C|
.91
.81
.77
.75
.74
.71
.72
.71
.70
69
t
f
2.9
5.7
8.4
11.2
11.9
16.6
19.4
22.1
24.9
776
1
ct
2.24
2.15
2.12
2.11
2.10
2.09
2.08
2.08
2.07
707
/
3.8
7.5
11.1
14.7
18.4
22.0
25.6
29.3
32.9
1fi5
S
C|
2.48
2.40
2.38
2.37
2.36
2.36
2.35
2.35
2.34
714
(
/
4.7
9.2
13.6
18.1
22.6
27.1
31.5
36.0
40.5
449
n
6
Cl
2.67
2.60
2.58
2.57
2.56
2.56
2.56
2.55
2.55.
7S5
/
5.5
10.8
16.0
21.3
26.6
31.9
37.1
42.4
47.7
S?9
7
Cl
2.83
2.77
2.75
2.74
2.73
2.73
2.73
2.72
2.72
2.72
/
6.3
12.3
18.3
24.4
30.4
36.4
42.5
48.5
54.5
60.6
g
c,
2.96
2.91
2.89
2.88
2.87
2.87
2.87
2.86
2.86
2.86
/
7.0
13.8
20.5
27.3
34.0
40.8
47.6
54.3
61.1
67.8
»
C|
3.08
3.02
3.01
3.00
2.99
2.99
2.98
2.98
2.98
2.98
1
/
7.7
15.1
22.6
30.1
37.5
45.0
52.4
i9.8
67.3
74.8
0
Cl
3.18
3.13
3.11
3.10
3.10
3.10
3.09
3.09
3.09
3.09
From Bauer, 1971,
102
-------
Table B-4. TI=JP ± I(LR). Tolerance Inlenalfor Individuals
Prob.
0.05
0.01
0.05
0.01
0.05
0.01
0.05
0.01
0.05
0.01
0.05
0.01
0.05
0.01
0.05
0.01
0.05
0.01
0.05
0.01
k
1
2
3
4
5
6
7
8
9
10
2
8.99
45.1
1.76
4.22
O.SS2
1.62
0.594
0.990
0.443
0.715
0.353
0.544
0.296
0.438
0.252
0.376
0.225
0.322
0.197
0.286
3
2.25
5.20
0.774
1.16
0.486
0.819
0.332
0.492
0.256
0.368
0.212
0.297
0.179
0.252
0.157
0.216
0.140
0.187
0.126
0.170
4
1.44
2.72
0.583
0.882
0.360
0.520
0.260
0.368
0.206
0.282
0.166
0.230
0.143
0.196
0.124
0:170
0.108
0.150
0.101
0.133
5
1.13
1.93
0.467
0.718
0.306
0.434
0.224
0.313
0.175
0.245
0.148
0.197
0.172
0.108
0.145
0.094
0.127
0.085
0.113
it
6
0.985
1.65
0.433
0.620
0.276
0.386
0.206
0.279
0.164
0.219
0)32
0.180
0.117
0.156
0.097
0.132
0.088
0.118
0.077
0.108
7
0.889
1.36
0.397
0.561
0.257
0.353
0.190
0.254
0.148
0.201
0.123
0.168
0.105
0.1-40
0.090
0.120
0.079
0.111
0.075
0.100
8
0.823
1-22
0.372
0.524
0.240
0.333
0.181
0.243
0.139
0.190
0.118
0.159
0.097
0.135
0.088
0.112
0.076
0.101
0.072
O.OS9
9
0.768
1.14
0.356
0.492
0.229
0.312
0.168
0.228
0.134
0.181
0.110
0.147
0.095
0.127
0.085
0.110
0.072
0.099
0.066
0.085
10
0.734
1.07
0.340
0.470
0.219
0.296
0.164
0.221
0.127
0.177
0.108
0.145
0.092
0.124
O.OSO
0.108
0.066
0.095
0.050
0.080
From Bauer, 1971.
103
-------
Table B-5. Critical
Values for Discarding
Invalid Measurements
a
3
4
5
7
8
9
10
11
12
13
14
15
20
It
1.53
1.05
0.86
0.76
0.69
0.64
. 0.60
O.S8
0.56
0.54
0.52
0.51
0.50
0.46
The probability is approximately
0.95 that if 't, = | X - X \ IK is
greater than tabulated t, the value
being investigated is invalid.
From Bauer| 1971t
104
------- |