v>EPA
          United States
          Environmental Protection
          Agency
            Office of Air Quality
            Planning and Standards
            Research Triangle Park NC 27711
EPA-451/R-93-002
March 1993
          Air/Superfund
AIR/SUPERFUND
NATIONAL TECHNICAL
GUIDANCE  STUDY SERIES
          Air  Emissions from  Area Sources:
          Estimating Soil and  Soil-Gas
          Sample  Number Requirements

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                                DISCLAIMER
      This report was prepared for the U.S.  Environmental  Protection Agency
under Contract Number 68D00124, Work Assignment No.  11-147.  The contents are
reproduced as received  from the contractor.  The contents do not necessarily
reflect  the  views  and policies  of  the  Agency,  neither  does mention  of
commercial products or trade names constitute endorsement  or recommendation
for use.

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                                           TABLE OF CONTENTS

             DISCLAIMER	   ii
7            LIST OF TABLES	   iv
I)           LIST OF FIGURES	   iv

                                                                                     Page
               1.0  INTRODUCTION   	 1
               2.0  BASIC  CONCEPTS   	 3
                    2.1    DIVIDING  THE AREA INTO ZONES	3
                    2.2    RANDOM  SAMPLING 	 3
                    2.3    VARIANCE,  STANDARD DEVIATION,  AND COEFFICIENT OF VARIATION   . 4
                    2.4    CONFIDENCE LIMITS AND THE CONFIDENCE INTERVAL 	 5
                    2.5    COMBINING ZONE DATA INTO AREA DATA	6

               3.0  PROCEDURES  SUITABLE FOR DESK-TOP CALCULATIONS 	 8
                    3.1    ESTIMATING SAMPLE NUMBER REQUIREMENTS 	 8
                          3.1.1 Preliminary Estimate  	 7
                          3.1.2 Example Applications  	   11
                    3.2    ANALYZING COLLECTED DATA	14
                          3.2.1 Analyzing the Data	14
                          3.2.2 Analyzing Multi-Component  Data  	   17
                    3.3    ANALYZING LOGNORMALLY DISTRIBUTED DATA  	   21

               4.0  USING  THE COMPUTER SOFTWARE 	   23
                    4.1    INSTALLATION AND EXECUTION  	   23
                          4.1.1 Using  a Floppy Disk	23
                          4.1.2 Installing on a Hard Drive	23
                    4.2    USING THE SOFTWARE	24
                          4.2.1 Functions Available at the Main Menu	24
                          4.2.2 Example Application 	   39
                    4.3    ANALYZING  LOGNORMALLY DISTRIBUTED DATA  	   42
                                       U.S. Environmental Protection Agency
                                       Region 5, Library (PL-12J)
                                       77 West Jackson Boulevard, 12th Floor
                                       Chicago, IL  60604-3590

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                               LIST  OF  TABLES
Table                                                                  Page
  1   Relevant Values Based on Student's t-Distribution 	  10
  2   Preliminary Data for Example 4	18
  3   Preliminary Estimates for TCE	19
  4   Preliminary Estimates for PCE	19
  5   Final  Zone Data for Example 4	20
  6   Area Statistics for Example 4	20
  7   H-statistics for use with Lognormal Distributions and
      95 Percent Confidence Limits  	  22
                              LIST OF FIGURES
Figure                                                                 Page
  1   Main Menu Screen	25
  2   Site Catalog Screen	26
  3   Add a New Site Screen	27
  4   Add a New Zone Screen	29
  5   Zone List Screen	30
  6   Screening Data Entry Screen 	  31
  7   Edit an Existing Site Screen	32
  8   Sample Measurement Entry Screen 	  34
  9   Review Sampling Plan Site Catalog Screen  	  35
 10   Sampling Plan Screens	37
 11   Statistics Report for Vinyl Chloride  	  43
                                     iv

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                                 SECTION  1

                                INTRODUCTION
   Soil  sampling  and  soil-gas  surveys are  frequently used  techniques to
estimate  air emissions  from  Superfund sites  such  as  landfills  and spill
areas.   In  performing these  surveys,  it  is  important that  the sampling
strategy generate data that are an adequate statistical represention of the
area source.  These data are necessary in  performing Air Risk Assessments at
the confidence level stipulated in the Risk Assessment  Guidance  for Superfund
(EPA 1989).

   The  purpose of  this Manual  is to  provide  guidance  as  to  the  necessary
number of soil gas  or soil  samples needed to estimate air emissions from area
sources.   The Manual  relies  heavily  on  statistical   methods  discussed in
Appendix C  of Volume II  of Air/Superfund  National  Technical  Guidance Study
Series (EPA 1990) and Chapter 9 of SW-846  (EPA  1986).   These methods utilize
the arithmetic mean  as is  specified in EPA Publication 9285.7-081, "Supple-
mental Guidance to  RAGS: Calculating the Concentration Term".

   If samples  are taken over the entire  surface of an area source using random
sampling techniques,  EPA experience shows that most of these data sets will
be lognormally distributed.    That is,  some of the sample results  will  be
either so much higher or lower than the mean of  all samples that the plot of
number of samples versus concentration will  be significantly skewed from the
normal  or   "bell   shaped"   distribution.   Stated  another  way, a  lognormal
distribution suggests the area  has one or more "hot or  cold  spots", or zones,
in which the  pollutant concentration differs significantly from the average
concentration throughout the rest of the area.

   The  techniques  in this manual  are  based on recognizing  this inhomgeniety
in the area,  by observation or screening samples, before samples  are taken.
Each  of the   identified  zones  are  then  sampled,  using  random  sampling
techniques,  and   statistics  calculated  separately  for each  zone  before
combining the  statistics  to  provide  an estimate for  the entire area.   The
assumption  is that  zoning  can  be effected such that  each zone   is  reasonably
normally distributed even when the overall area is lognormally distributed.
If the zoning  does  not satisfy this  assumption,  the methods  in this manual
will  fail.

   It must be  recognized that lognormal data cannot be  "zoned" after the fact
and analyzed by the techniques  in this manual.   It is extremely  unlikely that
such data  would  represent random samples  for each  zone,  and,   thus,  the
statistics  would  be  biased.   The techniques,  and  computer  software,  can
however, be used  to assist with the analysis of lognormally distributed data
by the  procedures  given  in the  above referenced EPA publication.   This
application is discussed in Sections 3.3 and 4.3.

   The  statistical   techniques  presented may also be   used  to  analyze other
types of  data and  provide measures  such  as  mean,  variance,   and standard

                                     1

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deviation.  The methods presented  in  this  Manual  are  based  on small  sample
methods.  Application of the methods to data which  are appropriately analyzed
by large  sample methods or to data which  is  not  normally  distributed will
give erroneous results.

   Section 2 provides a brief overview of concepts  and statistical techniques;
used in this document.  Section 3 provides  step-by-step procedures which can
be used for desk-top calculations.   Section 4 provides an  overview  of the
computer software  which accompanies this Manual.  The software  can be used to
perform all  procedures  described in Section 3.

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                                 SECTION 2

                               BASIC CONCEPTS
2.1   DIVIDING THE AREA INTO ZONES

   The number of samples that must be obtained to estimate the mean concentra-
tion of  an area  is strongly  dependent on  the heterogeneity  of  chemical
distribution (for constant confidence and confidence interval).  Thus, for an
area with uniform chemical distribution, very few samples would  be needed to
provide  good   characterization.    Conversely,  areas  with  widely  varying
concentrations could require a great number of samples.

   For  areas with non-uniform  distribution of  chemical  contamination,  the
total  number   of  samples  required for adequate  characterization  can  be
dramatically  reduced  by   subdividing   the  area  into  zones  with  similar
contamination   levels.  This situation  is commonly  encountered at Superfund
sites.  Such areas may be identified by variations in vegetation  stress,  area
source records, or results of preliminary screening.

   The  maximum benefit  in  sample  number reduction  is  obtained  by  defining
zones within the  area such  that the concentrations within any particular zone
are as uniform as possible.  As  many zones  as  is practical may be defined to
accomplish this objective.  Zones do not have to be  of similar  size or shape.
The area of each  zone must be determined.

2.2   RANDOM SAMPLING

   To  use the  statistical  methods  in  the Manual,   it  is  necessary  that  the
locations to  be  sampled within each zone  be selected  in a  random  manner.
Random does not  imply  haphazard.   One  way haphazard  sampling may  occur is
when sampling  points are simply selected based on personal judgement that the
points selected are  random.  There  is no assurance  with this  procedure  that
sampling  points  are not  selected  with  a  conscious or  subconscious  bias.
Samples collected from points selected haphazardly may not be statistically
representative of the area.

   Random sampling requires  a plan to  ensure that  each  potential  sampling
location has an equal chance  of being selected.  One method (but  not the only
method) to accomplish this is as  follows.   Define  an imaginary square  grid
for each  zone.   The grid  may  be  marked  off  in  feet,  yards,  meters,  or
whatever unit  is  convenient so  long as the  number of points where grid lines
intersect exceeds the  estimated number  of samples required   by  at  least  a
factor of two  (allowing additional samples to  be  collected  if necessary).
Neither  the directional  orientation of  the  grid  nor the selection  of  the
reference point from which all grid lines are  measured  are significant (grids
should  be established  independently  for  each  zone.)   Number the  grid
intersections  sequentially from 1  to X.   The  actual  points on  the grid to be
sampled are selected using a table of random numbers (available in  any  book
on statistics).  No grid point may be selected for sampling  more than once.

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2.3   VARIANCE, STANDARD DEVIATION, AND COEFFICIENT OF VARIATION

   The variance is simply the average of the squared deviations from the mean
of the data.   For the small  sample  methods used in area source sampling, the
sum of  the  squared  deviations are  divided by  the total number  of samples
minus one to obtain this average.

   The standard deviation  is the  square root of the variance.  Approximately
two-thirds of all sample data  will  fall within a range defined by the mean ±
standard  deviation.   Large  standard deviations  are  indicative  of  highly
variable concentrations within the area sampled and/or an inadequate number
of samples.

   The coefficient of variation  (sometimes  referred  to as relative standard
deviation or precision)  is the standard deviation divided by the mean of the
samples  and multiplied  by  100%.  By  expressing the  standard deviation as a
percentage of the mean,  it  is generally easier to grasp just  how variable the
data are.  For example,  if the coefficient  of variation is  20 percent, two-
thirds of the sample data fall within 20 percent  of the mean.

   The variance is calculated  from:
   where,

      SK2    =     variance for zone K
      nK    =     number of samples from zone K
      X,-    =     value of sample i from zone K

      Xk    =     mean of sample values from zone K


The standard deviation is the square root of the variance:


                                                                     (2-2)

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The coefficient of variation is calculated from


                               cv= 10°* (g*}                         (2-3)
2.4   CONFIDENCE LIMITS AND THE CONFIDENCE INTERVAL

   By definition confidence limits are the limits  between which the true mean
will fall  with  a specified probability  (or  confidence).   For  example,  if
calculations are made on a particular set  of data from an area source at the
95  percent  confidence  level,  a range is  established within which  the true
mean of the area source concentration will  fall 95 percent of the time.  The
upper 95 percent confidence limit  is  thus  simply the highest mean value from
this range.  Note that  because the true  mean  could  just  as  likely  be below
the lower confidence limit as above the upper  limit,  the probability that the
true mean might exceed the 95% UCL is only 5%/2 = 2.5 percent.

   The confidence interval  is the range of possible values for the true mean
which lie between the upper limit and the lower limit.  It shows how small  or
wide is  the range of possible values  for  the true mean based on the sampling
data collected.   The confidence interval  becomes  smaller as  the variability
in the sample data becomes less and as the number  of  samples increases.  Note
that the value of the upper confidence limit is dependent on both the mean  of
the sample data and the confidence interval.

   The impact of  this relationship is  simple and  straight forward:

      •   The 95% upper confidence limit can be calculated for  any  data set
         containing  more than one  data point.
      •   The value  at the 95% UCL  is  dependent on the confidence  interval.
      •   The confidence  interval  is  dependent  on   the  variability  in  the
         sample  data and the number of samples.

   The number of  samples  to collect cannot be meaningfully specified without
also specifying  the  confidence interval that is acceptable for the particular
purpose.    If  it is  only of  interest  to  know that  the  true  mean  area
concentration is no more than  an order  of magnitude  below the 95%  UCL,  a
large confidence interval is appropriate and  few  samples  need  be collected.
Conversely, if it is of interest to know the true mean area concentration  is
no more than 10  percent below  the 95% UCL, a  small confidence  interval  is
appropriate and many more samples would be required.

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   The  95%  confidence  limits  for  a  zone  (i.e., k) are calculated from:



                        95% LCLk  = !Tk  - r0-05 -A                   (2-4)
                        95% UCLk = Xk + T0.05  -                     (2-5)
                                                fn,
                                                 k
Note that tabulated values for the Student's t-distribution are for the sum
of the  probabilities  that the true mean  could  be either greater  than the
upper confidence limit or less than the lower confidence limit (i.e.,a two -
tailed test).   Thus,  the tabulated t-values for a 95%  confidence  interval
(0.05 probability) are the same as those for a one-tailed test with a  0.025
probability.  Thus,  if is only required  to know with 95% confidence that the
true  mean  does  not  exceed  the  sample mean  (i.e.,  a  one-tailed  test),
tabulated values for t0 1 should be used.

  The  confidence  interval  is:

      CIk   =     95% UCLk -  95% LCLk                              (2 - 6)


2.5   COMBINING ZONE DATA INTO AREA DATA

  After adequate data have been obtained for each of the zones in the source
area, the zone data must  be  combined  to represent  the overall  area.   These
data are combined based on the weighted areas of the  zones as follows:

  The  overall  mean  is  calculated  from:


                               X = £ wxx~K                         (2-7)
   where,

      VL    =     area zone K divided by total area

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   The  overall  variance is calculated from:
                               S2 = t Wr S\                         (2-8)
                                    Jf=l
   The  overall  standard deviation is calculated from:
  And  the  overall  95% UCL is calculated from:
                           95% UCL = X+ T0 05 —                     (2-10)
where,
   n   =  total  number of samples from all  zones.

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                                 SECTION 3

               PROCEDURES SUITABLE FOR DESK-TOP CALCULATIONS
   The procedures in this Section assume  that the area source has been divided
into zones within  which it is  expected that  concentrations are reasonably
uniform  and  that  a  plan   to  randomly  select sample  locations  has  been
formulated as discussed in  Section 2.   All calculations in this Section are
predicated on  the  assumption that  the  95% UCL on  the zone  and  area  mean
concentrations are desired.  It  is quite simple to  make calculations at other
confidence levels as will  be indicated  in the text.
3.1   ESTIMATING SAMPLE NUMBER REQUIREMENTS

3.1.1    Preliminary Estimate

   An  estimate of  sample  number requirements  can  be made  if  a reasonable
estimate can  be  made  for  the zone  variabilities.   The  number  of samples
required for any  zone will depend on the variability of concentrations within
that zone and on the confidence interval desired.  This relationship can be
expressed mathematically as:
                                                                     (3-D
                                         P2
                                         c
where,
   nK     =  samples required for zone K
   TO.05   =  °-05 percentage point of a Student's t-distribution
            with nK-l  degrees of freedom
   CVK    =  coefficient of variation of data from zone K
   P      =  acceptable percent variation between sample mean and true mean at
            stated confidence level

This  equation  can  be readily  derived  by  substituting  equation  2-3  into
Equation 2-5 and defining P as:


                                  (95%  UCLk - !Tk)
                         P = 100	—
[Note that T0 05 indicates we are calculating the 95% confidence limits.  By
simply replacing T0 05 with appropriate values from the Student's
                                     8

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t-distribution, calculations can  be made  at  any  desired confidence.   Thus,
for 90% confidence limits,  use tabulated values for  T0 10. for 99% confidence
limits use tabulated values  for Toor  Tabulated   values  for the Student's t-
distribution can  be found  in  any general statistics  textbook.]   Table 1
contains values of n, T0 05 and n/T20 05 for use with  Equation  3-1.

   Because  the  parameter  P specifies how close the 95% UCL should  be to be to
the sample  mean,  it can, and  should,  be specified before any  sampling is
done.    Thus,  if P is given  a  value of 20 percent, enough samples  must be
taken that  the sample  mean  will  be no  more  than 20 percent  below  the 95%
upper confidence limit.

   The value of the coefficient of variation,  CV,  will not be known until the
samples are analyzed.   If preliminary  screening  sample  data  are available,
these data can be used to calculate CV and a preliminary estimate of nK can
be made using Equation 3-1.

   Estimates of CV  can  also  be  made based on  experience  with  similar sites.
That is,  if a  previously  investigated site  has  a waste disposal  pattern
similar to  that suspected  for the site  to  be  investigated,  it would be
reasonable to  expect  similarities in  the relative  spatial distribution of
chemical concentrations.  Because  CV  is  a measure  of that  distribution, it
would be reasonable for the  CVs of the sites  to  also be  similar.   If the CV
has been calculated, or could be readily calculated from the  data using the
relationships of Section 2.3, it could be used in Equation  3-1 for planning
purposes.

   If no preliminary data for the site are available and no  estimate for CV
can be made, a  crude estimate of  the number of samples required in each zone
can be obtained from:


                          Nk = 6 + y^Zone area                     (3-2)
where,
  y  = 0.15  for zone  areas  in  square meters, or
  y  = 0.046 for zone areas  in  square  feet.

  This arbitrary  relationship,  which  appears  in  Appendix C of Volume II of
the NTGS document referred  to  in  Section  1, assumes  that CV increases as a
function of the size  of the contaminated  zone.   This assumption may or may
not  be true  and   significant  over  or under  forecasts  of  sample  number
requirements  may  result  from  its  use.   For example,  for  a  20  percent
difference  between   the  95% UCL  and  the sample  mean,  the  corresponding
coefficients of variation calculated using this relationship range from 19%
for areas less than  -10 m2  (-110 ft2),  i.e.,  those requiring no more than 6
samples, to 48% percent for areas  up to -28,000 m2 (300,000  ft2),  i.e., those
requiring up to 25 samples.

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TABLE 1.  RELEVANT VALUES BASED ON STUDENT'S t-DISTRIBUTION
Degrees
Freedom
i
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
A = 0.05
12.706
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
n/T*
0.012
0.162
0.395
0.649
0.908
1.169
1.430
1.692
1.954
2.216
2.477
2.738
3.001
3.260
3.523
3.782
4.043
4.304
4.566
4.826
5.085
5.347
5.606
5.868
6.127
6.387
6.650
6.914
7.174
7.434
n = No. Samples
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
31
NOTES:
• Degrees freedom is maximum number of variates that can be freely assigned before the rest are
determined; generally, one less than the total number of samples.
• Values listed under A = 0.05 are T006 values for a two-tailed test at 95 percent confidence for the
listed degrees of freedom.
• Values for n/T2are provided for convenience when using Equation 3-1 . They were obtained by
dividing the square of the values in the column headed A = 0.05 into one more than the associated
degree of freedom.
• Values under column headed n = number samples are the values used for n in the column headed
n/T2.
                             10

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  Regardless  of the method used to estimate  the  number of samples, it  is
recommended that  a few  extra  samples be  collected  and  stored  for later
analysis just in case the sample variability  is  greater  than estimated.


3.1.2    Example Applications

Example 1.   Assume the mean concentration of zone 1 (1,000 m2) of the  area
            source is needed within  20 percent of  the UCL  at the 95  percent
            confidence level  and no  preliminary  site  data  is available.
            Based on past experience with  similar sites, we guess most of the
            samples will  be within  40  percent  of the mean.

  The  parameters  for  use in the analysis  are:
      Zone area   = 1,000 m2
         CVk       = 40
         P         =20

  Using  Equation  3-1


                                n  .  (40)2_1
                              T2      (20) 2
   From Table  1, the  smallest number of samples for which n/T20 05  is greater
than 4 is n = 18.

   Using  Equation  3-2:
                       Nk  = 6  +  0 .15v/Zone area,  m2
the number of samples required for this  zone is  estimated  as:
                          n = 6 + 0.15v/l7ooo m2

                          n = 11
Thus,  experience  indicates  at least 18  samples  should be taken from  this
zone.


Example 2.  Make  the  same  assumptions  as  example  one  except  that  four
            preliminary screening data  points  are available for the  zone.
            These data are 30, 33, 41,  37 units.

                                     11

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  The zone mean  is:

  X   =   30 +  33  +  41  +  37  =   35
               4
  The variance  is:


                                            A ,  30+33+41+37
             1   4-1



         =    1  [5,039 - 4,970]
             3

         =   23

  The standard deviation  is:
    =  4.8

  The coefficient of variation is:

  CV   =  100  (4.8)
             35

            13.7 percent

  From Equation 3-1

     n     =   (13.7)2
     T2       (20)2

          =   0.469

  and from  Table 1,

  n  = 5

  The preliminary data indicate the zone  is fairly homogeneous and only five
samples  are  required.   Several  additional  samples should be collected  and
stored  for  later  analysis in case  the  site is  not  as homogeneous as  the
preliminary data indicate.

Example  3.  Assume an area source has been divided into  two zones.  Zone 1 is
            100 m2 and expected to contain high  concentrations.   Zone 2 is
            400 m2  and  expected to have  much lower concentrations.   In each

                                    12

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            zone  4  preliminary screening samples had been  taken  haphazardly
            (i.e.,  not  using  random selection techniques).   The  project
            required that we determine the 95% upper  confidence limit for the
            area  such  that  the mean  concentration was within 20  percent of
            the 95% upper confidence limit.
  The initial screening data was:

  ZONE 1                           Zone 2
  16                               5.2
  18                               3.6
  15                               4.4
  13                               3.3

Using Equation 3-2  we  estimate the number of samples needed  as:

  Zone 1:   n = 6 + 0.15  (100)* = 7.5
            n = 8
  Zone 2:   n = 6 + 0.15  (400)'/2 = 9
            n = 9

Using Equation 3-1  we  estimate the number of samples needed  as follows:
  Zone 1:   Mean,  X   ==  (16 +  18 + 15 + 13)/4 = 15.5
                     Variance, S2 = -i- [Ex2 - 4 X2}
                                     4-1
                                    =    1  [974  -  961]
                                         3
                             S2     =   4.3
                     Standard Deviation,  S = /4 . 3
               Coefficient of Variation,  CV =
                                              2.1


                                                100 (2.1)
                                                   15.5
                                 CV      =   13.5 percent

                                         =   (13.5)2     =   0.46
                              TYo5
                        n  (from  Table 1)  =   5

                                    13

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Thus, we opt  to  collect and analyze 5 samples and  collect  and store three
(3)extra samples just in case the samples are more variable than estimated.

      Zone 2:
                  Mean  =      4.1
                  S2    =      0.73
                  S     =      0.85
                  CV    =     20.8

                   n	   =  (20.8)2
                              1.08

                              7
      Thus, for  Zone  2 we  opt  to collect  7  samples for analysis  and two
extras in case the zone is more variable than we estimate.
3.2  ANALYZING COLLECTED DATA

   In  the proceeding  section methods  for making  initial   estimates  were
presented.  In this section methods to verify an adequate number of samples
were collected and calculation of the 95 percent upper confidence limit are
given.

3.2.1  Analyzing The Data

   As  indicated  in the  previous Section,  because  we  do  not  know  before
samples are collected and analyzed just how variable site concentrations are,
the best we can hope for in making preliminary estimates of required sample
numbers is that  we estimated  enough  samples  so that the  final  confidence
interval will  be  small enough to satisfy the particular need.  After the data
are available calculations  can be made to  determine if, in fact, an adequate
number of samples were collected and, if not,  how many more are needed.  In
either case,  the confidence interval  and  95%  upper confidence  limit  can be
calculated for that data set.

   Let  us  continue with the project  described  in  Example 3 above.   After
collecting random samples from each zone,  the analytical  results are:

   Zone 1                       Zone  2
    11.3                         3.4
    21.2                         4.4
    15.6                         4.8
    17.1                         3.6
    14.6                         2.9
                                 3.1
3 samples held in reserve        3.9
                              2 samples held in reserve

                                     14

-------
Calculations for Zone  1

   Mean     =     15.96
   S2       =     13.11
   S        =      3.62
   CV       =     22.7  percent

     n      =     (22.7)2

     °'°5    =      1.288

   Thus, from Table 1, 8 samples should be analyzed.  The three samples held
in reserve are analyzed and yield results of 17.5, 14.3, 15.1.

   For this set of 8 data points

   Mean     =     15.8
   S2       =      8.31
   S        =      2.88
   CV       =     18.2

   Because the new CV  is less than for the set  of  6 samples  (i.e., 22.7), we
know that no more samples are needed.

   We  can  now  calculate  final  statistics  for  Zone   1.    The  95%  upper
confidence limit can be found,  using Equation 2-5, from:

   T0.05     =     (UCL - X) (n)%
                       O

where UCL  is  the highest  value for  the  true  mean  for  Zone 1  at  the 95%
confidence level.  From Table 1  for 8 samples  (7 degrees of  freedom), T0 05 =
2.365.  Thus,

   2.365 =  (UCL - 15.8) (8)'/2
               2.88

   95% UCL  =     15.8 + 2.4  = 18.2

   This value is the 95% upper confidence  limit for a data  set with the limit
within 20% or less of  the mean.  The mean for Zone 1 is within

            (100)(2.4)/15.8 = 15.2 percent.
                                     15

-------
Calculations For Zone 2

   Mean     =     3.7
   S2       =     0.47
   S        =     0.69
   CV       =     18.6 percent
    _n	   =     (18.6)2  =  0.865

    ^0.05
(20)2
   Since n from Table 1 is 6 and we analyzed 7  samples,  no  additional  sample
analysis is required.

   The 95% upper confidence  limit  is  then  (T0 05  for  7 samples, 6 degrees  of
freedom):

   2.477    =     (UCL - 3.7U7)'/;
                         0.69

   UCL      -     3.7 + 0.65
   UCL      =     4.4

and the UCL is within 100  (0.65)/3.7  =  17.6  percent  of  the mean for Zone  2.


Calculations for the Area  Source

   Using the relationships of Section  2.5,  the mean value for the entire  area
is calculated as the weighted sum  of  the Zone means:

Overall mean = area Zone 1 x Zone  1 mean + area  Zone 2  x Zone 2 mean
               Total area                   Total  area

            100 x 15.8 + 400 x  3.7
            500          500
   X area =  6.12

The overall variance is calculated similarly as


   S2area    "     °'2  t8'31) + °'8 (

   S'area    -     2.038

The overall standard deviation is
                                  /O2     _  -I
                                   ^ area     J- .
                                     16

-------
   The overall 95% upper confidence limit is  (T0 05 for the 15 total samples,
14 degrees of freedom) :

   2.145    =     (UCL - 6.12H15)*
                         1.428

   95% UCL  =     6.12 + 0.79
                  6.91

   and the UCL is within 100 (0.79)/6.12 = 12.9 percent of the area mean.

Therefore, we report the statistics for the area source as:

  mean                  =     6.12 ± 0.79
  variance              =     2.04
  standard deviation    =     1.43
  95% UCL               =     6.91


3.2.2 Analyzing Multi -Component Data

   In the preceding sections,  simple cases  for  one or two zones and only one
contaminant were considered.  In this section,  a more complex case, represen-
tative of situations likely to be encountered,  is presented.

Example 4.  A landfill,  approximately 12 acres, is divided  into 5 zones based
            on an  inspection  that revealed leachate seeps,  eroded covers,
            fracture traces, vegetation breaching the cap, etc.   There are
            three compounds of  interest at the site: vinyl chloride, TCE, and
            PCE.  A varying number of preliminary samples have been taken in
            each  zone  for each  of the  compounds.   We  wish to  determine
            whether these samples are adequate  to calculate the 95% UCLs for
            each zone and the overall area under the constraint that the mean
            determined for each zone be within  20 percent of the 95% UCL for
            that zone.   If they  are not,  we  must determine the  number of
            additional samples  needed for each compound  in each zone, collect
            and analyze those  samples and determine final statistics for the
            zones and the landfill.

Given in Table 2 are the areas, estimated CVs based  on  prior  investigations
of similar sites, and the preliminary sample data.

Vinyl Chloride

   For Zone  1,  there  is  no sample data;  only  an estimate of the  CV.   Thus
the number of samples required is estimated from Equation  3-1 as:
    T2o.os
2  =
                         =  1
and from Table 1, 7 samples should be taken (Equation 3-2 would estimate 17
samples should be taken).

                                     17

-------
                  Table 2. Preliminary Data for Example 4
Contaminant
Area, m2
Estimated CV
Vinyl Chloride,
ppm
TCE, ppm
PCE, ppm
Zone 1
5,000
20
No data
101
98
120
105
101
105
98
103
Zone 2
7,000
20
11.5
38
26
30
55
50
46
52
Zone 3
10,000
35
11.5
12.1
15
19
1,000
975
1,050
1,025
Zone 4
12,000
25
101.5
112.1
93.1
1,175
860
10.1
11.5
9.9
10.4
Zone 5
15,000
30
51.5
52.1
53.1
52.5
480
390
530
615
1.1
1.3
0.9
1.0
   For Zone 2 there is one data point.   As this is statistically meaningless
(degrees of  freedom  equal zero),  the  number of samples  required are also
calculated from Equation  3-1.   Because the estimated CV  for  Zone 2 is the
same as Zone 1, 7  samples  are  also estimated to  be  required for this Zone.
Thus, if the preliminary sample is considered a valid sample, only six more
should be needed.
   For Zone 3,  there are two data points.
the standard deviation  is 0.42, and  the
n/T:
    0.05
is 0.0317,  and,  from Table  1,  3
already have,  are required based on this preliminary data.
 For these  data,  the mean  is  11.8,
CV  is 3.56%.   From Equation 3-1,
 samples,  or only  1 more  than we
   For Zone 4, there are 3 data points.  For these data, the mean is 102.2,
the standard  deviation  is 9.52,  and the CV  is  9.3%.    From  Equation  3-1,
n/T20 05 is 0.216, and, from Table 1,  4 samples, or only 1 more than we already
have,' are required based on this preliminary data.
   For Zone 5, there are  4  data  points.   For these data, the mean is 52.3,
the standard deviation  is 0.673, and  the  CV is 1.3%.   From Equation 3-1,
n/T2q05 is 0.004, and,  from Table 1, 2 samples are  required based on this
preliminary data.  Because we already have 4 samples, no additional samples
are needed.

TCE and PCE

   Following the same procedures, the estimates shown in Tables 3 and 4 can
be obtained for these compounds.
                                     18

-------
                   Table  3.  Preliminary  Estimates  for  TCE
Parameter
Mean
SD
CV
n/Vos
Samples
Needed
Samples
Taken
Additional
Needed
Zone 1
106.0
9.76
9.2
0.212
4
4
0
Zone 2
31.33
6.11
19.5
0.951
7
3
4
Zone 3
17.0
2.83
16.6
0.689
6
2
4
Zone 4
1017.5
222.7
21.9
1.199
8
2
6
Zone 5
503.75
94.11
18.7
0.874
6
4
2
                   Table  4.  Preliminary  Estimates  for  PCE
Parameter
Mean
SD
CV
"/Vos
Samples
Needed
Samples
Taken
Additional
Needed
Zone 1
101.75
2.99
2.9
0.021
3
4
0
Zone 2
51.25
2.99
5.8
0.084
3
4
0
Zone 3
1012.5
32.27
3.2
0.026
3
4
0
Zone 4
10.475
0.714
6.8
0.116
3
4
0
Zone 5
1.15
0.129
11.2
0.314
4
4
0
   Note that no additional samples are required in Zone 1 for TCE and no
additional samples are required in any Zone for PCE.

   Because in this case, the preliminary samples are also considered valid
for final statistics, only the number of additional samples required are
obtained and analyzed.  The sample analytical  results and Zone statistics
are given in Table 5.  Note that the precision for all  zones and all
compounds equals or is better than the stated goal of 20 percent.  Thus, no
additional samples are required and the Zone statistics meet our objective
and can now be combined into area statistics.   These statistics are
calculated as described in Section 2.5 and Example 3 above.  The results
are given in Table 6.
                                     19

-------
Table 5. Final Zone Data for Example 4
Contaminant
Vinyl Chloride,
ppm
Mean
SD
CV
95% UCL
Precision
TCE, ppm
Mean
SD
CV
95% UCL
Precision
PCE, ppm
Mean
SD
CV
95% UCL
Precision
Zone 1
1076
982
1117
991
1215
905
1036
1046
101.3
9.7
1139
9.0
101
98
120
105
106
9.76
9.2
121.5
15
101
105
98
103
101.8
2.99
2.9
106.5
4.7
Zone 2
11.5
10.5
12.6
13.1
10.9
12.2
9.9
11.53
1.17
10.1
12.6
9.4
38
26
30
33
29
37
35
32.57
4.43
13.6
36.7
13
55
50
46
52
51.3
2.99
5.8
56.0
9.3
Zone 3
11.5
12.1
11.9
11.83
0.31
2.6
12.6
6.4
15
19
21
16
18
15
17.3
2.42
14.0
19.9
15
1,000
975
1,050
1,025
1012.5
32.3
3.2
1063.8
5.1
Zone 4
101.5
112.1
93.1
105.1
102.95
7.91
7.7
115.5
12
1,175
860
1050
976
990
1125
890
945
1001.4
109.6
10.9
1093
9.2
10.1
11.5
9.9
10.4
10.48
0.71
6.8
11.6
11
Zone 5
51.5
52.1
53.1
52.5
52.3
0.67
1.3
53.4
2
480
390
530
615
450
555
503.3
15.9
15.9
587.4
17
1.1
1.3
0.9
1.0
1.15
0.13
11.2
1.36
18
Table 6. Area Statistics for Example 4
Statistic | Vinyl Chloride
Mean
SD
CV
95% UCL
Precision
152.0
32.6
21.5
165.5
8.9
PCE
418.3
70.2
16.8
444.1
6.2
TCE |
222.3
14.7
6.5
234.1
3.0
                  20

-------
3.3   ANALYZING LOGNORMALLY DISTRIBUTED DATA

   EPA Publication 9285.7-081 provides guidance  for  calculating statistics
for lognormally distributed data.   The methods previously  illustrated  for
calculating the mean and standard  deviation may  be used  to assist  with
calculating those statistics.

   The first step is to calculate  the natural  logarithm  of each data point
(i.e., calculate ln(x), where x is the data point).   The resulting values
are referred to as transformed data.

   Calculate the mean and standard deviation  of  the  transformed data.
Determine the H-statistic for the  number of data points  being  analyzed,  the
standard deviation of the data, and the confidence level desired.   Table 7
provides tabulated H-statistics for the 95 percent confidence  level  for  a
number of combinations of sample numbers and  standard deviations.   Note
that it is necessary to use the H-statistic for  the  standard deviation
calculated from the transformed data.

   Calculate the upper confidence  using equation 3-3:


                   UCL  =  e (* + 0<5 s2 + SH/\/^~I)              (3-3)
where:
   e  =   constant (base of natural  log,  equal  to  2.718)

   x  =   mean of the transformed data
   s  =   standard deviation of the  transformed data
   H  =   H-statistic from Table 7
                                     21

-------


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-------
THIS PAGE INTENTIONALLY LEFT BLANK

-------
                                 SECTION 4

                        USING THE COMPUTER SOFTWARE
   The calculations of Section 3 may also be made using the computer soft-
ware accompanying this manual.  The algorithm was developed using IF® data-
base management system.  It is not necessary to have this software to run
the program.  The algorithm has been compiled and should be executable on
any IBM compatible computer.  The reports generated are written directly to
the printer in an ASCII format at the time of creation.  Disk copies of the
reports are not created.  The reports should print on all printers.

   The software has been named Area Source Analysis Program (ASAP).  There
are three files basic to the program:
   ASAP.EXE
   FOXPRO.ESL
   FOXPRO.ESO

   These files must not be deleted or altered.  ASAP.EXE is fairly small
but contains all the algorithm code.  The two IF® files (FOXPRO.ESL and
FOXPRO.ESO) are larger but contain only file structure and display informa-
tion.  Because ASAP is provided with the examples in this manual already
programmed to give the first time user an easy orientation, several addi-
tional files have been created.  The size of these files will  change as
additional data is entered or deleted.   There should be three Site_Cat
files, two Zones files and two Samples files.  As supplied, the software
occupies 1.4 kilobytes of disk space.

   ASAP may be run from either the floppy disk or from a hard drive.  How-
ever, because the execution from the floppy disk is quite slow (due to
display screen generation), it is strongly recommended that it be installed
on a hard drive.

4.1   INSTALLATION AND EXECUTION

4.1.1 Using a Floppy Disk

   Place the read/write protect tab in the unprotect mode (tab on 3^ inch
disks should be placed so that the hole is covered).  Place the disk in the
disk drive and change the computer prompt to that drive.  Type in ASAP and
press the Enter or Return key.  It will take 30 seconds or more for the
first screen to appear.  The program will read and write to the floppy
disk.

4.1.2 Installing on a Hard Drive

   ASAP will perform most satisfactorily if installed on a hard drive.
The files should be installed in a separate directory.   (Consult with your
system manager for installation on other than a personal use computer.)

                                     23

-------
The following assumes your hard drive is designated "C" and the floppy disk
drive is "A".

   At the C prompt enter:
   MKDIR ASAP (It is not necessary to name the directory ASAP)
   CD ASAP (To place the computer in the newly created directory)

   Place the floppy disk protect tab in the PROTECT mode.  Place the flop-
py disk containing the ASAP files in drive A.   Enter A: so the computer
will  read the floppy disk placed in drive A.

   Enter Copy *.* C: to copy all files from the floppy disk into the ASAP
directory on the hard drive.  Enter C: to transfer execution to the hard
drive.  Remove the floppy disk and put it in a safe place.

   ASAP can now be run from the hard disk by typing in ASAP and pressing
the enter or return key.

4.2   USING THE SOFTWARE

4.2.1 Functions Available at the Main Menu

   The first screen that appears upon execution of ASAP is the Main Menu
(see Figure 1).  The options may be executed by pressing the number of the
option, clicking on it with a mouse, or highlighting it with the up and
down arrow keys and pressing the enter key.  All  options except number 6,
Review Sampling Plan, are also available at different screens within the
program.

Option 1. List all Available Sites -- Selection of this option takes you
directly to the Site Catalog screen (Figure 2).  This screen lists, in
alphabetical order, all sites that have been entered into the program, the
number of zones in each site, and the total area of all zones.  Note that
if the number of zones is zero for any site, it means either that no zone
information was added or that the entered data has not been analyzed (Op-
tion 7) to generate a sampling plan or analyze screening or actual data.
This screen is updated only when the analyze routine is executed.  Thus, if
site zone descriptions are added, edited or deleted, the screen will be
incorrect until the new data is analyzed.  Many functions are available
directly from this screen by holding down the ALT key and pressing a second
key.  Use the up and down arrow keys to select the site for which informa-
tion is desired.

Option 2. Add a New Site -- Selection of this option takes you to the "Add
a New Site" screen (Figure 3).  At this screen, enter the descriptive name
for the site, the confidence level  (e.g., 95%) desired, and the precision
desired.  As described in Sections 2 and 3, the latter two are key drivers
for sample number requirements.  Note that the program does not check for
duplication and will accept multiple sites with the same name.  The screen
also requests whether or not you plan to input screening data.  Neither
selection prevents you from changing your mind later.  The last entry on
the screen requests the units for data entry.  ASAP does not make unit

                                     24

-------
  Area Source Analysis  Program
1.  List all available sites
2.  Add a new site
3.  Edit or Delete existing site
4.  Enter or edit screening data
5.  Enter or edit actual  data
6.  Review Sampling Plan
7.  Analyze data
8.  Quit program and return to  DOS
   Figure 1  Main Menu Screen
               25

-------
                         Area Source Analysis Program
                                 Site Catalog
Site Name
Example 1
Example 2
Example 3
Example 4
Example 4
Example 4
or Description



- PCE
- TCE
- Vinyl chloride
f Zones
1
1
2
5
5
5
Area
1000
1000
500
-19000
49000
49000
Alt-M=Main Menu
t J=Select
Alt-Z=Zone List
Alt-N=New
Alt-A=Analyze Data
Alt-E=Edit
Alt-Q=Quit Program
Alt-D=Delete
                                  Figure 2  Site  Catalog Screen
                                                 26

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                          Area Source  Analysis  Program
                                 Add a  New Site
Site Name or Description

Desired Confidence Level (80%,  90%,  95%,  99%)   0
Desired Precision (%)   0
Is screening data available? (Y/N)  N
Enter the concentration units for all samples  (ppm,  ug/m2,  etc.)
Esc=Cancel          Enter=Accept
                          Figure 3  Add a New  Site Screen
                                         27

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conversions.  It uses this field only for reporting purposes.  After the
last entry, a new screen (Figure 4) will appear for entry of zone informa-
tion.

   At the  "Add a New Zone" screen, enter a descriptive label for one of
the site zones and the area, in square meters, for that zone.  Enter an
estimate of the coefficient of variation for this zone if desired.  If you
leave this field blank, sample number requirements will be estimated based
on area of the zone, or screening data if entered in the next steps.  This
screen will continue to appear until  you  press the ESC(ape) key indicating
you have entered descriptions for all zones.

   A Zone  List screen (Figure 5) will now appear and will list all zones
and zone areas for the new site.  You may edit the entries,  if incorrect,
by using the arrow keys to select the zone and pressing the  ALT and E keys.
If you wish to enter screening data now for one or more zones,  select the
zone and press ALT-S.  [DO NOT enter actual data (defined as the sample
results you want to use for final site statistics) at this time even if
available.  Data entry will be much easier after a sample plan is generat-
ed.]  If you do not wish to enter screening data, press ALT-C to return to
the Site Catalog screen or ALT-M to return to the Main Menu.

   Pressing the ALT-S keys takes you to the screening data entry screen
(Figure 6).  By default, there are 15 numbered positions for data entry.
Type in the screening data and, using either the arrow keys  or enter (re-
turn) key, move down the list until all  screening data for that zone has
been entered.  You may move up and down the list to review or change en-
tered data.  Editing works in the insert mode rather than overwrite mode,
therefore  incorrect data must be deleted with the backspace  or delete keys.
Use the ALT-Z keys to return to the Zone List and select additional zones
for screening data entry.  Screening data does not have to be entered for
all zones.  After you have completed all entries, press ALT-C to return to
the Site Catalog or ALT-M to return to the Main Menu.  Data  processing may
be done from either screen (Option 7 returns directly to the Site Catalog).

Data processing to generate a sampling plan is addressed under Option 7.

Option 3.  Edit or Delete Existing Site -- Selection of this  option enters
the Site Catalog screen.  Select the site to be edited or deleted and press
the appropriate key combination shown at the bottom of the screen.  The
delete selection removes all site data, including samples and zones.  Be-
fore completing the deletion, the program prompts for confirmation.  Selec-
tion of the edit option transfer to an edit screen (Figure 7) which allows
you only to edit the overall site information (description,  confidence
level, precision desired, and units).  However, individual zone descrip-
tions can  be added, edited, or the entire zone deleted, after pressing ALT-
Z at the Site Catalog screen to access the zone list.  Note  that the site
catalog does not automatically update if zones are added or deleted.  Chan-
ges will be made to that screen only after data analysis (Option 7 or ALT-A
in the Site catalog) has been executed.  Also, individual screening or
actual data for zones can edited from the zone list.
                                     28

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                          Area Source Analysis  Program
                        SITE:  Example 4  - Vinyl  Chloride

                                 Add a New Zone
Zone Description
Area (square meters)
Estimated coefficient of variation (%)   0
Leave blank if using screening data
Esc=Cancel
Enter=Accept
                       Figure  4  Add a New Zone Screen
                                       29

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                          Area Source Analysis Program
                        SITE:  Example  4  - Vinyl  Chloride
                                   Zone  List
Zone Description
Zone 1
Zone 2
Zone 3
Zone 4
Zone 5
Area
5000
7000
10000
12000
15000






Alt-S=Screening data  Alt-D=Delete
ti=Select             Alt-N=New
Alt-A=Actual data
Alt-E=£dit
Alt-C=Site Catalog
Alt-M=Main Menu
                                 Figure  5   Zone List  Screen
                                              30

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                         Area Source Analysis Program

Sample









SITE
Number
1
2
3
4
5
6
7
8
9
Measured
51.5
52.1
53 . 1
52.5





: Example 4 - Vinyl Chloride
ZONE: Zone 5
Screening Data
concentration/flux (ppm)



















Alt-Z=Zone List
U=Select
Alt-C=Site Catalog  Alt-M=Main Menu
                    Figure  6   Screening Data  Entry Screen
                                        31

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                          Area  Source  Analysis Program
                             Edit an  Existing  Site
Site Name or Description
Example 4 - Vinyl Chloride
Desired Confidence Level (80%,  90%,  95%,  99%)  95

Desired Precision (%)  20

Is screening data available? (Y/N)  Y

Enter the concentration units for all samples (ppm,  ug/mj,  etc.)
ppm
Esc=Cancel          Enter=Accept
                          Figure 7   Edit an Existing Site  Screen
                                             32

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Option 4. Enter or Edit Screening Data -- Selection of this option enters
the Site catalog screen.  Select the site for which data is to be entered
or edited and press the zone list keys (ALT-Z).  At the zone list screen,
select the zone for which data is to be entered or edited and press ALT-S
to access the screening data entry screen.  Entering and editing data at
this screen was discussed under Option 2, above.

Option 5. Enter or Edit Actual Data -- Selection of this option enters the
Site catalog screen.  If there is a zero in the Zones column, no sampling
plan has been generated.  In this case, select the site and press ALT-A to
analyze the data previously entered (minimum required is zone areas).
Within a few seconds, a sampling plan will appear which you may review and
print or simply press the D(one) key and n(o) for printout.  This returns
directly to the Site Catalog with the site highlighted.  Press the zone
list keys (ALT-Z) and, at the zone list screen, select the zone for which
data is to be entered or edited and press ALT-A to access the Sample Mea-
surements data entry screen (Figure 8).  First entry to the screen is at
the bottom (subsequent zones accessed while in this mode are at the top of
the data list).  Press the page-up or use the arrow keys to move to the top
of the listed data. Editing is similar to that for screening data.  If
additional data points, beyond those for which the analyze function created
blank records, are needed, press the ALT-N keys.  After data entry is com-
plete, press ALT-Z to enter data for additional zones, or ALT-C or ALT-M to
return to the Site catalog or Main Menu,  respectively.

Option 6. Review Sampling Plan -- Selection of this option allows the re-
view and printing of previously created sampling plans.  Plans may be re-
viewed both before and after final sample data have been entered and final
site statistics have been calculated.  Selection of the option displays a
screen (Figure 9) similar to the Site catalog except that the options
available are limited to reviewing a plan or returning to the Main Menu.
To review a plan, select a site using the arrow keys and press ALT-R.

   ASAP does not retain the actual plan in memory, but recreates it when
the option is executed.  Therefore, if site data such as confidence and
precision requirements, zone names, zone areas, estimated CVs, or screening
data have been altered using the edit functions, a different sample plan
may be generated.  Because of this feature, a partial sampling plan can be
generated using this option, rather than Option 7, that gives the estimated
number of samples needed based on areas,  estimated CVs or screening data.
However, Option 6 does not generate a suggested sampling grid and does not
update the Site Catalog listing for number of zones and zone area.

   After ALT-R is pressed, a message appears indicating the statistics are
being recalculated.  The program ignores any data entered as "actual" mea-
surements.  A Sample Plan then appears which can be reviewed.  It gives the
number of samples needed overall and for each zone and the basis for the
estimate.  Information for each zone can be displayed by pressing the M
key.  You cannot move backwards in the display.  At any time, the D key
                                     33

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                          Area Source Analysis Program
                        SITE:  Example 4 - Vinyl Chloride
                                 ZONE: Zone 5
                              Sample Measurements
     Grid Point Measured concentration/flux  (ppm)
             57
             76
            118
51.5
52.1
53. 1
52.5
Alt-Z=Zone List
t J=Select
    Alt-C=Site Catalog
    Alt-N=New
Alt-M=Main Menu
                           Figure 8  Sample  Measurement  Entry Screen
                                                34

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                         Area  Source Analysis Program
                                 Site Catalog
Site Name
Example 1
Example 2
Example 3
Example 4
Example 4
Example 4
or Description



- PCE
- TCE
- Vinyl Chloride
# Zones
1
1
2
5
5
5
Area
1000
1000
500
49000
49000
49000
Alt-M=Main  Menu
Alt-R=Review  Plan
             Figure 9   Review Sampling  Plan Site Catalog  Screen
                                       35

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(for Done) may be pressed to terminate display and access a prompt for
printing the plan.  If Y(es) is selected and no printer is available, a
message will appear and the prompt repeated.  The screen cannot be exited
except by successfully printing the plan or selecting no print.


Option 7. Analyze Data -- Option 7 is used to analyze any information that
has been input for a site.  It is used to generate sampling plans, deter-
mine whether measurement data are adequate for site statistics, and to
calculate final site and zone statistics.  The program automatically se-
lects the function(s) to execute depending on the type of data entered.

   Selection of the option transfers to the Site Catalog display screen.
At this screen, select the site for which analysis is desired and press the
ALT-A keys.  Sampling plans are automatically created if no sampling plan
for the site has been previously created or if the only data inputted are
screening data, coefficients of variation (CV) for zones, or area of zones.
Priority for data to be used in creating the plan is actual measurement
data, screening data, estimated CVs, and zone areas.  Minimum data require-
ment are zone areas.  If no information has been entered, the program will
prompt "Nothing to Analyze" and return to the Site Catalog screen.

    If no "actual" measurement data have been entered, the program gener-
ates a simple sampling plan (Figure 10) which gives the number of samples
to collect and analyze for each zone and generates a suggested sampling
grid.   This screen will give the number of zones in the site, total area,
requested confidence level and precision, and the number of samples that
should be analyzed as well as the number of backup samples that should be
collected just in case the zones are more variable than estimated.

   Specific plan details for each zone may be accessed by pressing the M
key (for more).  You cannot move backwards in the screens.  You will have
to press this key two or three times to move from the summary to the first
zone.  The zone details include the basis for the estimated number of sam-
ples and suggestions for a sampling grid and points to samples on that
grid.  Grid points are selected using a random number generator and change
each time you run the Analyze routine.

   You may exit this screen at any time by pressing the D key  (for done).
A prompt then appears asking whether or not you want to print the report.
If you are satisfied with the results (or just want a printout), select
yes.  [If no printer is available, the prompt will be repeated until you
select no.]  If you are not satisfied with the results, select no for print
and you will be returned to the Site Catalog screen where you may initiate
changes in previous input, as previously described, and reanalyze the data.

   Selection of this Option is the preferred way to create blank data en-
try records for initial entry of "actual" data for analysis if "actual"
measurement data, rather than screening data, are to be used for plan gen-
eration.  Be aware that if the program detects even one "actual" data en-
try, it ignores all other screening and planning data for that zone.  It


                                     36

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11/21/92                SUMMARY  OF  SAMPLING PLAN FOR SITE

SITE:  Example 1


                     Number of  Zones:          1
                          Total Area:       1000 square meters

            Desired Confidence  Level:         95 %
                   Desired Precision:         20 %

       Number of  Samples to Analyze:         18
             Number of Extra Samples:          4
                      Figure 10  Sampling Plan Screens
                                       37

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11/21/92

SITE:  Example 1

      ZONE:  Zone 1

    Desired  Precision
            Zone area
            Unit area
    SAMPLING  PLAN  FOR  ZONES
  20 %
1000 square meters
  25 square meters
Page:  1
               Number of grid points:    40
  Estimated coefficient of variation:
        Number of Samples to Analyze:
             Number of Extra Samples:

          Number of samples would be:

            Samples to Analyze

                    Grid Point
                         28
                         40
                         21
                         39
                         33
                         20
                          4
                         14
                         34
                          5
                         18
                         29
                         36
                         15
                         23
                          6
                         32
                          2

            Extra Samples

                    Grid Point
                          12
                           8
                          31
                          16
                40 %
                18 based  on  estimated C.V.
                 4                 •

                11 if based  on  zone area.
               Concentration/Flux  (ppm)
               Concentration/Flux (ppm)
                       Figure 10  Sampling Plan  Screens (cont'd)
                                            38

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will calculate the number of samples needed for other zones based on the
planning and screening data.

   When using the program this way, follow the instructions above for cre-
ation of the plan.  At the printout prompt, select no print.  This returns
you to the Site Catalog with the site already highlighted.  Press the ALT-Z
keys to move to the Zone List screen and select the Zone for data entry.
Press the ALT-A keys to access the Sample Measurement screen and enter the
data.  Press the ALT-Z keys to return to the Zone List screen and repeat
the above steps until all "actual" measurement data has been entered.
Press the ALT-C keys to return to the Site Catalog and then press the ALT-A
keys to generate a sampling plan based on the entered data.

   Sampling plans generated this way provide actual statistics for the
entered data at both the overall site summary level and for each zone.  At
the bottom of the summary and for each zone, a message appears if an inade-
quate number of samples were collected.  The M(ore) key may have to be
pressed to display the message.  CAUTION: The "Actual  Precision" on the
summary may be within the tolerance specified even when an inadequate num-
ber of samples have been entered for one or more zones.  Site statistics
are not valid if the message indicates more samples are needed.

   Once a sampling plan has been generated by either of the above methods
and "actual" measurement data has been entered for all zones,  the program
analyzes the data but does not generate a new sampling plan.  The program
assumes planning is complete and analyzes and generates statistics based on
the "actual  data".  All screening data previously entered are ignored.
Screen display, messages, and prompts are the same as above for generating
plans using "actual" data.  A detailed printout is provided as part of the
following example application.


4.2.2 Example Application

   To illustrate the use of the program, the steps needed to analyze Exam-
ple 4 of Section 3 are presented.  In this case,  it is assumed that the
preliminary data are adequate for final measurements.   Thus, the steps are
somewhat different than when using only screening data.  How to plan using
only planning and screening data are illustrated, however, for the vinyl
chloride data.  This Example is already in the program and can reviewed.

   At the Main Menu, select Option 2 - Add a New Site.  At the Add a New
Site screen, enter Example 4 - Vinyl Chloride,  95 for confidence desired,
20 for precision, y for screening data, and ppm for units.  The Add A New
Zone screen will appear.   Enter Zone 1, 5000 for area, and 20 for CV.  New
screens will appear each time the CV value is entered.  In sequence,  enter

   Description    Area  CV
   Zone 2         7000  20
   Zone 3         10000 35
   Zone 4         12000 25
   Zone 5         15000 30

                                    39

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When the next blank screen appears, press the escape key.  This terminates
automatic entry of new zones and returns to the Zone List screen.

   For illustration, first treat the data as simple screening data.  Be-
cause no data is available for Zone 1, select Zone 2 using the arrow keys
and press ALT-S to enter screening data.  For sample number 1, enter 11.5
and press ALT-Z to return to the Zone List.  Select Zone 3 and press ALT-S
to enter the data.  In sequence, the following data should be entered:

            Data
            11.5, 12.1
            101.5, 112.1, 93.1
            51.5, 52.1, 53.1, 52.5

After all data has been entered, press ALT-C to go to the Site Catalog
screen.  The Example 4 - Vinyl Chloride site should be highlighted (if not,
select it).   Note that this screen shows zeros for number of zones and
total area,  indicating a sample plan has not been generated.  Press ALT-A
to analyze the data and generate a sampling plan.  The first page (Summary)
of a 6 page report appears.  Pressing D terminates review and goes directly
to the print prompt.  By pressing M a couple of times, the plan for Zone 1
is displayed.   The plan for each Zone can be reviewed by continuing to
press M.   You cannot move backwards in the screens.  For each Zone, sug-
gested grid size and grid points to sample are given.   The plan for Zones
gives the following information:

            No.  Samples Basis          No. Needed
   Zone     Needed      For Estimate   Based on Area

   17              CV             17
   27              CV             19
   3        3           Screening data    21
   4        4           Screening data    22
   5        2           Screening data    24

After review is complete, press the D(one) key and a print prompt appears.
For the current example, N(o) print is selected and return to the Site
Catalog is automatic.   This completes the illustration using only planning
and screening data.  The balance of this example is completed assuming the
preliminary data are valid "actual" samples.

   First, re-enter the vinyl chloride data as "actual" measurements.  Set-
ting up the site and Zone descriptions is the same as above.  At the Zone
List screen, however,  the data are entered using the ALT-A keys, rather
than ALT-S,  to designate the data as "actual" measurement data useable for
emission determinations.  Just as before, when data entry is complete,
return to the Site Catalog and press ALT-A to analyze the data.  A 6 page
(Summary plus 5 for Zone details) Statistics report is now available for
review and printing.

   This report gives the mean, standard deviation, actual CV, actual pre-
cision, and 95% UCL for the data entered.  A message appears at the bottom

                                     40

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of the Summary page  indicating additional samples are needed.  A review of
the individual Zone  detail pages gives the following information:
    Zone
        1
        2
        3
        4
        5
 Number
Samples
 Needed
     7
     7
     3
     4
     2
Mean

  11.5
  11.8
 102.2
  52.3
UCL

  11.
  15
 125,
  53.4
 Actual
Precision

      0
     32
     23
      2
 Extra
Samples
 Needed

     6
     1
     1
     0
   The second column  provides the  same  information generated previously.
The last column shows how many additional samples are needed to supplement
those already analyzed.  It is obvious that no more samples are required
for vinyl chloride in Zone 5.

   A sampling plan for TCE must now be generated.  Because ASAP has no
ability to copy existing site or zone descriptions, these must be created
again just as if a new site was being entered.  At the Main Menu, select
Option 2 and enter Example 4 - TCE for the site name.  Enter exactly the
same information as for vinyl chloride for the other entries on this screen
and for the 5 new zones that must  be created.  After the last zone descrip-
tion is entered, press the ALT-C keys to return to the Site Catalog (or
ALT-M to go to the Main Menu).  At the Site Catalog screen, press ALT-A to
analyze the planning data and create a preliminary sampling plan (this
inserts blank records in the Sample Measurements screen for easy entry of
"actual" data).  When the plan appears, select D(one) and N(o) for print-
ing.  This returns to the Site Catalog.  The site should be highlighted
(note that it has been alphabetically arranged before the vinyl chloride
site).  Press ALT-Z to move to the Zone list screen.  Select Zone 1 and
press ALT-A to enter the data as "actual".  After data has been entered for
all zones, go to the Site catalog  (press ALT-C) and analyze the data (press
ALT-A).  A sampling plan, complete with zone statistics, is generated simi-
lar to that for vinyl chloride.  In this case, review of the zone detail
reports indicates no additional samples are required in Zone 1, and that 4,
4, 6, and 2 additional samples are required in Zones 2, 3, 4, and 5, re-
spectively.

   To generate a sample plan for PCE, the same steps as for TCE need to be
completed.  The only difference is that Example 4 - PCE should be entered
for the site description, and the  appropriate "actual" data entered for the
zones.  Using the data presented in Section 3, the sampling plan generated
will indicate that the data are, in fact, adequate for our objectives and
that no additional samples are required.  The report generated, thus, is
the statistics report needed for PCE and should be printed.  Note that if
additional data for PCE is collected along with data needed for adequate
statistics for vinyl chloride and TCE, it can be entered into the Sample
Measurements screen using Option 5 and new statistics generated using Op-
tion 7.
                                     41

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   After the additional samples indicated are collected (including several
extras held in reserve) and analyzed, the new data can be entered and new
statistics calculated to determine whether or not the data now meet the
objective.  At the Main Menu, select Option 5 - Enter or Edit Actual  Data.
This activates the Site Catalog screen.  Highlight the appropriate site
using the arrow keys and press ALT-Z to access the Zone List screen for
that site.  At the Zone List screen, select the Zone for data input and
press ALT-A to enter the new data.  It may be necessary to add new blank
records, using ALT-N, to enter all the data.  Return to the Zone List
screen and repeat the data entry for each Zone.  When all  data has been
entered, return to the Site catalog (ALT-C) and press ALT-A to analyze the
data.  The message at the bottom of the Summary page will  indicate if addi-
tional samples are still required.  If a message does appear calling for
more samples, review the Zone detail reports to see which  zone(s) need
more data.  If no message appears on the Summary report, no additional
samples are required for any zone and the report provides all the statis-
tics needed and should be printed.

   Figure 11 is the printout that should be obtained for the site for vi-
nyl chloride.  It is comprised of a Summary Statistics Report for the site
and Detailed Statistics Reports for each of the 5 zones.  Similar reports
would be generated for TCE and PCE.

4.3   ANALYZING LOGNORMALLY DISTRIBUTED DATA

   In Section 3.3, the procedures for calculating statistics for lognorm-
ally distributed data were presented.  If the data set is small, the mean
and standard deviation may easily be calculated using desktop procedures.
However, if the data set is large, these statistics may be more easily
calculated using the computer software and the results used in Equation 3-
3.  The procedures to accomplish this follow.

   At the Main Menu, select option 2 to add a new site.  Enter the re-
quested information as before.  At the new zone screen, enter a coefficient
of variation sufficiently large to ensure the program will generate a suf-
ficient number of blank records to accomodate the number of data point to
analyze.  Enter data for only one zone.  Return to the Site Catalog and
execute the "Analyze data" option. If the first attempt does not indicate
as many samples are required as there are data points, edit the entry as
required.

   At the "Zone List" screen for the site, select "Enter Actual Data".
Enter the transformed data (i.e., enter the natural logarithm of the data
point).  Return to the Site Catalog screen and analyze the data.  Ignore
all screen outputs except the mean and standard deviation.  Write these
down, or obtain a printout as a check on entrys of the transformed data.

   Using the mean and standard deviation calculated by the software, com-
plete the calculation following the procedures in Section 3.3.
                                     42

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11/21/92                SUMMARY STATISTICS REPORT FOR SITE

SITE:  Example  4  -  Vinyl Chloride
                     Number  of  Zones:
                          Total Area:

            Desired  Confidence  Level:
                  Desired Precision:

          Number  of  Samples  Analyzed:

                               Mean:
                  Standard Deviation:
            Coefficient  of Variation:

          95%  Lower  Confidence  Limit:
          95%  Upper  Confidence  Limit:
                    Actual Precision:
49000 square meters

   95 %
   20 %
   25

  152.01904762
   32.60894352
   21.5 %

  138.55807573 ppm
  165.48001950 ppm
  8.9 %
             Figure 11  Statistics  Report for  Vinyl  Chloride
                                     43

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11/21/92               DETAILED  STATISTICS REPORT FOR ZONES            Page:  1

SITE:  Example  4  - Vinyl  Chloride

      ZONE:  Zone 1

            Zone area:   5000  square meters
            Unit area:     31  square meters

              Number  of grid points:   160
            Number  of  samples needed:    4


                    Grid Point          Concentration/Flux  (ppm)

                        114                   1076
                         29                   982
                         25                   1117
                        116                   991
                        107                   1215
                         68                   905
                         49                   1036


          Number of Samples  Analyzed:           7
                                Mean:        1046.00000000
                  Standard Deviation:         101.32785073
            Coefficient  of Variation:           9.7  %
          95%  Lower Confidence  Limit:         952.28399211  ppm
          95%  Upper Confidence  Limit:        1139.71600789  ppm
                    Actual Precision:           9.0  %
                 Figure 11  Statistics Report  for Vinyl  Chloride  (cont'd)
                                              44

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11/21/92               DETAILED  STATISTICS REPORT FOR ZONES

SITE:  Example  4  -  Vinyl  Chloride

      ZONE:  Zone 2
                                             Page: 2
            Zone area:
            Unit area:
7000 square meters
  44 square meters
               Number of grid  points:   160
            Number of samples  needed:    4
                    Grid Point

                        123
                        101
                         32
                         43
                         73
                        150
                        135
               Concentration/Flux  (ppm)

                     11.5
                     10.5
                     12 .6
                     13.1
                     10.9
                     12.2
                     9.9
          Number of Samples Analyzed:
                                Mean:
                  Standard Deviation:
            Coefficient of Variation:
          95%  Lower Confidence Limit:
          95%  Upper Confidence Limit:
                    Actual Precision:
                      11.52857143
                       1. 16721076
                      10. 1  %
                      10.44904263  ppm
                      12.60810023  ppm
                       9.4  %
         Figure 11   Statistics  Report for  Vinyl Chloride (cont'd)
                                      45

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11/21/92              DETAILED STATISTICS  REPORT FOR ZONES            Page: 3

SITE:  Example 4 - Vinyl Chloride

      ZONE:  Zone 3

            Zone area: 10000 square  meters
            Unit area:    63 square  meters

               Number of grid points:   160
            Number of samples needed:     3


                    Grid Point         Concentration/Flux  (ppm)

                         56                  11.5
                         40                  12.1
                         17                  11.9


          Number of Samples Analyzed:           3
                                Mean:          11.83333333
                  Standard Deviation:           0.30550505
            Coefficient of Variation:           2.6  %
          95% Lower Confidence Limit:          11.07435546  ppm
          95% Upper Confidence Limit:          12.59231120  ppm
                    Actual Precision:           6.4  %
                 Figure  11  Statistics Report  for Vinyl  Chloride  (cont'd)
                                              46

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11/21/92              DETAILED STATISTICS  REPORT FOR ZONES

SITE:  Example 4 - Vinyl Chloride

      ZONE:  Zone 4

            Zone area:  12000 square meters
            Unit area:     75 square meters

               Number of grid points:   160
            Number of samples needed:     3
                              Page: 4
                    Grid Point

                        158
                         36
                         80
                         96
Concentration/Flux  (ppm)
      101.5
      112.1
      93.1
      105.1
          Number of Samples Analyzed:
                                Mean:
                  Standard Deviation:
            Coefficient of Variation:
          95% Lower Confidence Limit:
          95% Upper Confidence Limit:
                    Actual Precision:
      102.95000000
        7.90506167
        7.7 %
       90.37304688  ppm
      115.52695312  ppm
         12 %
         Figure 11   Statistics  Report for Vinyl  Chloride  (cont'd)
                                      47

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11/21/92              DETAILED  STATISTICS REPORT FOR ZONES

SITE:  Example  4  - Vinyl  Chloride

      ZONE:  Zone 5

            Zone area: 15000  square meters
            Unit area:     94  square meters

              Number of grid points:   160
            Number  of samples needed:    2
                              Page: 5
                    Grid  Point

                         57
                         76
                        118
                          0
Concentration/Flux (ppm)

      51.5
      52.1
      53 . 1
      52.5
          Number of  Samples Analyzed:
                                Mean:
                  Standard Deviation:
            Coefficient of Variation:
          95% Lower  Confidence Limit:
          95% Upper  Confidence Limit:
                    Actual Precision:
       52.30000000
        0.67330033
        1.3 %
       51.22877917 ppm
       53.37122083 ppm
        2.0 %
                 Figure 11   Statistics  Report for  Vinyl Chloride (cont'd)
                                              48

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TECHNICAL REPORT DATA
(Pleau rtad Instructions on the revene before completing)
1. REPORT NO. 2.
EPA-451 /R-93-002
4. TITLE AND SUBTITLE
Air/Superfund National Technical Guidance Study
Series - Air Emissions From Area Sources: Estimating
Soil and Soil-Gas Sample Number Requirements
7.AUTHOR(S)
Wayne We'stbrook
9. PERFORMING ORGANIZATION NAME AND ADDRESS
Pacific Environmental Services, Inc.
560 Herndon Parkway, Suite 200
Herndon, Virginia 22070-5225
12. SPONSORING AGENCY NAME AND ADDRESS
U.S. Environmental Protection Agency
Office of Air Quality Planning and Standards
Research Triangle Park, North Carolina 27711

5. REPORT DATE
March 1993
6. PERFORMING ORGANIZATION CODE
8. PERFORMING ORGANIZATION REPORT NC
10. PROGRAM ELEMENT NO.
11. CONTRACT/GRANT NO.
13. TYPE OF REPORT AND PERIOD COVERED
Final
14. SPONSORING AGENCY CODE
15. SUPPLEMENTARY NOTES
16. ABSTRACT
        This  document provides guidance  regarding the necessary number of soil gas or soil
  samples needed to estimate air emissions from area sources.  The Manual relies heavily on
  statistical methods discussed in Appendix C of Volume II of Air/Superfund National Technical
  Guidance Study Series (EPA 1990) and Chapter 9 of SW-846 (EPA 1986).

        The techniques in this manual are based on recognizing the inhomgeniety of an area, by
  observation or screening samples, before samples are taken.  Each of the identified zones are
  then sampled, using random sampling techniques, and statistics calculated separately for each
  zone before combining the statistics to provide an estimate for the entire area.

        The statistical techniques presented may also be used to analyze other types of data and
  provide measures such as mean, variance, and standard deviation.  The methods presented in
  this Manual are based on small sample  methods. Application of the methods to data which are
  appropriately  analyzed by large sample  methods or to data which is  not normally distributed will
  give erroneous results.
17.
KEY WORDS AND DOCUMENT ANALYSIS
a. DESCRIPTORS
Air Sampling
Superfund
Soil Gas Samples
18.
DISTRIBUTION STATEMENT
b.lOENTIFIERS/OPEN ENDED TERMS

19. SECURITY CLASS (Tilts Report/
20. SECURITY CLASS (This page)
c. COSATI Field/Group

21. NO. OF PAGES
22. PRICE
EPA Form 2220-1 (R»v. 4-77)   PREVIOUS EDITION is OBSOLETE

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U.S. Environmental Protection Agency
Region 5, Library (PL-12J)
77 West Jackson Boulevard, 12th Floor
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