Lookup tables can be used to determine the confidence limits on the median (50 th percentile). For example, see Conover (1999, Table A3) or Gilbert (1987, Table A14). In general, when the sample size is very small (e. g., less than about nine or ten samples) and the required level of confidence is high (e. g., 95 to 99 percent), the tables will designate the maximum value in the data set as the upper confidence limit. Conover (1999, page 143) gives a large sample approximation for a confidence interval on a proportion (quantile). Methods also are given in Gilbert (1987, page 173), Hahn and Meeker (1991, page 83), and USEPA (1992i, page 5 30). Appendix F 253 F. 3 Tests for a Proportion or Percentile Some RCRA standards represent concentrations that should rarely or never be exceeded for the waste or media to comply with the standard. To measure compliance with such a standard, a waste handler may want to know with some specified level of confidence that a high proportion of the waste complies with the standard (or conversely, that at most only a small proportion of all possible samples could exceed the standard). Two approaches are given for measuring compliance with such a standard:

1. Under the assumption of a normal distribution, use a parametric UCL on a percentile to demonstrate that the true pth percentile (xp) concentration in the set of all possible samples is less than the concentration standard. The method is given below in Section F. 3.1.

2. By far, the simplest method for testing proportions is to use an "exceedance rule" in which the proportion of the population with concentrations less than the standard can be estimated based on the total number of sample values and the number of those (if any) that exceed the standard. The exceedance rule method is given below in Section F. 3.2.

If the number of samples is relatively large, then a "one sample proportion test" also can be used to test a proportion against a fixed standard. The one sample proportion test is described in Section <IP_ADDRESS> in Guidance for Data Quality Assessment, EPA QA/ G 9 (QA00 Update) (USEPA 2000d).

F. 3.1 Parametric Upper Confidence Limits for an Upper Percentile If the study objective is to demonstrate that the true pth percentile (xp) concentration in the set of all possible samples (of a given sample support) is less than the applicable standard or Action Level, then a UCL on the upper percentile can be used to determine attainment of the standard.

Requirements and Assumptions The formulas for constructing parametric UCL on an upper percentile assume that the data are at least approximately normally distributed. Therefore, such a limit should be constructed only if the data pass a test of normality. If the data are best fit by a lognormal distribution instead, the observations should first be transformed to the log scale. Unlike confidence limits for a lognormal mean, no special equations are required to construct similar limits on an upper percentile. The same formula used when the data are normally distributed can be applied to the log scale data. The only additional step is that the confidence interval limits must be reexponentiated before comparing them against the regulatory standard.

It is strongly recommended that a confidence limit not be constructed with less than four measurements, and preferably more (the actual number, however, should be determined during Step Seven of the DQO Process). There are three reasons for this: (1) the formula for a normal based confidence interval on an upper percentile involves calculation of the sample standard deviation, s, which is used as an estimate of the underlying population standard deviation. This estimate may not be accurate when fewer than four samples are used. (2) The confidence interval formula also involves a special factor (" kappa"), which depends on both   Appendix F 254 the desired confidence level ( ) and the number of samples, n, used in the calculation. 1      When n is quite small, the factor is more extreme, leading to a much wider confidence   interval than would be expected with a larger n. For example, at a confidence level of 90 percent, the appropriate factor for an upper one sided limit on the 99th percentile is =     18.50 when n = 2, = 5.438 when n = 4, and = 3.783 when n = 8. (3) The third reason is     that the power of the test for normality or lognormality is very low with a small number of samples.

Procedure Step 1. First test the data for normality on the original scale. If a test of normality is passed, calculate the limit on the raw measurements. If the data violate the assumption of normality, but pass a test of lognormality, calculate the limit using the log scale data.

Step 2. If the data are normal, compute the mean and standard deviation of the raw data. If the data are consistent with lognormality instead, compute the mean and standard deviation after first transforming the data to the log scale.

Step 3. Given the percentile (p) being estimated, the sample size (n), and the desired confidence level ( ), use Table G 2 (in Appendix G) to determine the 1        factor( s) needed to construct the appropriate UCL. A one sided upper confidence bound is then computed with the formula UL x x s p p 1 1     = +        () , Equation F. 6 where is the upper factor for the pth percentile with n sample     1    , p 1      measurements.

Again, if the data are lognormal instead of normal, the same formula would be used but with the log scale mean and standard deviation substituted for the rawscale values. Then the limit must be exponentiated to get the final upper confidence bound, as in the following formula for an upper bound with confidence: () 1 100%     [ ] UL x y s p yp 1 1     = +        () exp , Equation F. 7 Step 4. Compare the upper confidence bound against the fixed standard. () 1 100%     If the upper limit exceeds the standard, then the standard is not met.

An example calculation of the UCL on a percentile is given in Box F. 4. Appendix F 255 F. 3.2 Using a Simple Exceedance Rule Method for Determining Compliance With A Fixed Standard Some RCRA standards represent concentration limits that should never or rarely be exceeded or waste properties that should never or rarely be exhibited for the waste to comply with the standard. One of the simplest nonparametric methods for determining compliance with such a standard is to use an "exceedance rule" (USEPA 1989a). To apply this method, simply require that a number of samples be acquired and that zero or a small number (e. g., one) of the concentration measurements be allowed to exceed the standard. This kind of rule is easy to implement and evaluate once the data are collected. It only requires specification of a number of samples and the number of exceedances allowed (usually zero, for example, for compliance with the LDR concentration level treatment standards). Alternately, one can specify the statistical performance criteria in advance and then determine the number of samples required. Box F. 4. Example Calculation of a UCL on an Upper Percentile To Classify a Solid Waste A secondary lead smelter produces a slag that under some operating conditions exhibits the Toxicity Characteristic (TC) for lead. The facility owner needs to classify a batch of waste as either hazardous or nonhazardous at the point of waste generation. During the planning process, the owner determined based on previous sampling studies that the constituent of interest is lead, TCLP results for lead tend to exhibit a normal distribution, and a sample size of ten 200 gram samples (not including QC samples) should satisfy the study objectives. The TC regulatory level for lead is 5 mg/ L. The owner wants to determine, with 90 percent confidence, whether a large proportion (e. g., at least 95 percent) of all possible samples of the waste will be below the regulatory limit.

At the point of waste generation, the facility representative takes a series of systematic samples of the waste. The following sample analysis results were generated for ten samples analyzed for lead via the TCLP and SW846 Method 6010B: <0. 5, 0.55, 0.60, 0.80, 0.90, 1.00, 1.50, 1.80, 2.00, and 3.00 mg/ L.

Calculate a 90 percent upper confidence limit on the 95 th percentile.

Solution Step 1. Based on the shape of the histogram and normal probability plot, the data were judged to exhibit a normal distribution. Therefore, we proceed with the calculation on the original (untransformed) scale.

Step 2. One value (10% of the measurements) is reported below the quantitation limit of 0.5 mg/ L so we replace that value with half the quantitation limit (0.25 mg/ L) (see also Section F. 4). The mean and standard deviation of the data set are then calculated as mg/ L and . x = 124 . s = 0836 .

Step 3. Use Table G 2 (in Appendix G) to determine the factor for n = 10 needed to construct a 90 percent   UCL on the 95 th percentile. The table indicates . Plug , , and into Equation F. 6,  = 2568 . x s   as follows:

UL x 0 90 095 124 0 836 2 568 3 39 3 4 .. ().(.)(.).. = + =   mg / L Step 4. All of the sample analysis results are less than the TC regulatory limit of 5 mg/ L TCLP for lead, and the owner concludes that the waste is a nonhazardous waste under RCRA. The owner also can conclude with at least 90 percent confidence that at least 95 percent of all possible sample analysis results representing the batch of waste in the roll off bin are nonhazardous. Appendix F 256 Requirements and Assumptions for Use of an Exceedance Rule The method given here is a simple nonparametric method and requires only the ability to identify the number of samples in the data set and whether each sample analysis result complies with the applicable standard or does not comply with the standard. Unfortunately, this ease of use comes with a price. Compared to parametric methods that assume underlying normality or lognormality of the data, the nonparametric method given here requires significantly more samples to achieve the same level of confidence.

Procedure Step 1: Specify the degree of confidence desired, , and the proportion (p) ( ) 100 1      % of the population that must comply with the standard.

Step 2: If the decision rule permits no exceedance of the standard for any single sample in a set of samples, then obtain and analyze the number of samples (n) indicated in Table G 3a in Appendix G.

If the decision rule permits a single exceedance of the standard in a set of samples, then obtain and analyze the number of samples (n) indicated in Table G 3b in Appendix G.

Step 3: Based on the number of samples obtained and the statistical performance required, determine whether the applicable standard has been attained.

An example application of the exceedance rule is Box F. 5.

Box F. 5: Example Application of a Simple Exceedance Rule A facility has treated nonwastewater F003 solvent waste containing carbon disulfide to attain the LDR UTS. Samples of the treatment residue are obtained systematically as the waste treatment is completed. The treater wants to have at least 90% confidence that at least 90% of the batch of treated waste attains the standard. To comply with the LDR regulations, no samples can exceed the UTS. TCLP analyses for carbon disulfide in the treated waste are required to measure compliance with the treatment standard of 4.8 mg/ L TCLP.

From Table G 3a we find that for a confidence level ( ) of .90 (or 90%) and a proportion of .90, at least 22 1      samples are required. All sample analysis results must be less than or equal to the UTS of 4.8 mg/ L TCLP for the statistical performance criteria to be achieved.

If only 9 samples are obtained (with all sample analysis results less than or equal to the standard), what level of confidence can the treater have that at least 90 percent (or p = 0.90) of all possible samples drawn from the waste meet the treatment standard?

From Table G 3a we find for p = 0.90 and n = 9, = 0.60. Therefore, the confidence level 1     100 1 ()%     equals only 60 percent. Appendix F 2 Additional experience and research for EPA supporting development of guidance on the statistical analysis of ground water monitoring data indicates that if the percentage of nondetects is as high as 20 to 25 percent, the results of parametric statistical tests may not be substantially affected if the nondetects are replaced with half their detection limits (Cameron 1999).

257 F. 4 Treatment of Nondetects in Statistical Tests Data generated from chemical analysis may fall below a limit of detection of the analytical procedure. These measurement data generally are described as "nondetects", (rather than as zero or not present) and the appropriate limit of detection  such as a quantitation limit  usually is reported. Data sets that include both detected and nondetected results are called "censored" data in the statistical literature.

If a relatively small proportion of the data are reported below detection limit values, replacing the nondetects with a small number (between zero and the detection limit) and proceeding with the usual analysis may be satisfactory. For moderate amounts of data below the detection limit, a more detailed adjustment is appropriate. In situations in which relatively large amounts of data below the detection limit exist, one may need only to consider whether the chemical was detected as above some level or not.

F. 4.1 Recommendations If no more than approximately 15 percent of the sample analysis results are nondetect for a given constituent, then the results of parametric statistical tests will not be substantially affected if nondetects are replaced by half their detection limits (USEPA 1992b). 2 When more than approximately 15 percent of the samples are nondetect, however, the handling of nondetects is more crucial to the outcome of statistical procedures. Indeed, simple substitution methods tend to perform poorly in statistical tests when the nondetect percentage is substantial (Gilliom and Helsel 1986). If the percentage of nondetects is between approximately 15 percent and 50 percent, we recommend use of Cohen's Adjustment (see method below).

The conditions for use of Cohen's method, however, are limited (see method given below) and numerous alternative techniques for imputing left censored data should be considered if the conditions for use of Cohen's method do not apply. Other methods available include iterative techniques, regression on order statistics (ROS) methods, bias corrected maximum likelihood estimator (MLE), restricted MLE, modified probability plotting, Winsorization, and lognormalized statistics (EPA Delta log). A modified probability plotting method called Helsel's Robust Method (Helsel 1990) is a popular method that should be considered. Most of the above methods can be performed using publicly available software entitled UnCensor© v. 4.0 (Newman et al. 1995). Although EPA's Office of Solid Waste has not reviewed or tested this software, users of this guidance may be interested in investigating its use.

If the percentage of nondetects is greater than 50 percent, then the regression on order statistics method or Helsel's Robust Method should be considered. As an alternative, EPA's Guidance for Data Quality Assessment EPA QA/ G 9 (USEPA 2000d) suggests the use of a test for proportions when the percentage of nondetects is in the range of greater than 50 percent to 90 percent.

This guidance does not advocate a specific method for imputing or replacing values that lie Appendix F 258 below the limit of detection, however, whichever method is selected should be adequately supported. Table F 3 provides a summary of approaches for handling nondetects in statistical intervals.

Table F 3. Guidance for Handling Nondetects In Statistical Intervals Percentage of Data Reported as "Nondetect" Recommended Treatment of Data Set < 15% Replace nondetects with DL/ 2 15% to 50% Cohen's adjustment, regression order statistics, or Helsel's Robust Method > 50% Regression on order statistics, Helsel's Robust Method, or a test for proportions Even with a small proportion of nondetects, care should be taken when choosing which value should be used as the "detection limit". There are important differences between the method detection limit and the quantitation limit (QL) in characterizing "nondetect" concentrations. Many nondetects are characterized by analytical laboratories with one of three data qualifier flags: "U," "J," or "E." Samples with a "U" data qualifier represent "undetected" measurements, meaning that the signal characteristic of that analyte could not be observed or distinguished from "background noise" during lab analysis. Inorganic samples with an "E" flag and organic samples with a "J" flag may or may not be reported with an estimated concentration. If no concentration estimate is reported, these samples represent "detected but not quantified" measurements. In this case, the actual concentration is assumed to be positive, falling somewhere between zero and the QL. Because the actual concentration is unknown, the suggested substitution for parametric statistical procedures is to replace each nondetect qualified with an "E" or "J" with one half the QL. Note, however, that "E" and "J" samples reported with estimated concentrations should be treated, for statistical purposes, as valid measurements. In other words, substitution of one half the QL is not recommended for samples for which an estimated concentration is provided.

As a general rule, nondetect concentrations should not be assumed to be bounded above by the MDL. The MDL is usually estimated on the basis of ideal laboratory conditions with analyte samples that may or may not account for matrix or other interferences encountered when analyzing specific, actual field samples. For this reason, the QL typically should be taken as the most reasonable upper bound for nondetects when imputing specific concentration values to these measurements.

If a constituent is reported only as "not detected" and a detection limit is not provided, then review the raw data package to determine if a detection limit was provided. If not, identify the analytical method used and consult a qualified chemist for guidance on an appropriate QL.

F. 4.2 Cohen's Adjustment If a confidence limit is used to compare waste concentrations to a fixed standard, and a significant fraction of the observed measurements in the data set are reported as nondetects, simple substitution techniques (such as putting in half the detection limit for each nondetect) can lead to biased estimates of the mean or standard deviation and inaccurate confidence limits. Appendix F 259 By using the detection limit and the pattern seen in the detected values, Cohen's method (Cohen 1959) attempts to reconstruct the key features of the original population, providing explicit estimates of the population mean and standard deviation. These, in turn, can be used to calculate confidence intervals, where Cohen's adjusted estimates are used as replacements for the sample mean and sample standard deviation.

Requirements and Assumptions Cohen's Adjustment assumes that the common underlying population is normal. As such, the technique should only be used when the observed sample data approximately fit a normal model. Because the presence of a large fraction of nondetects will make explicit normality testing difficult, if not impossible, the most helpful diagnostic aid may be to construct a censored probability plot on the detected measurements. If the censored probability plot is clearly linear on the original measurement scale but not on the log scale, assume normality for purposes of computing Cohen's Adjustment. If, however, the censored probability plot is clearly linear on the log scale, but not on the original scale, assume the common underlying population is lognormal instead; then compute Cohen's Adjustment to the estimated mean and standard deviation on the log scale measurements and construct the desired statistical interval using the algorithm for lognormally distributed observations (see also Gilbert 1987, page 182).

When more than 50 percent of the observations are nondetect, the accuracy of Cohen's method breaks down substantially, getting worse as the percentage of nondetects increases. Because of this drawback, EPA does not recommend the use of Cohen's adjustment when more than half the data are nondetect. In such circumstances, one should consider an alternate statistical method (see Section F. 4.1).

One other requirement of Cohen's method is that there be just a single censoring point. As discussed previously, data sets with multiple detection or quantitation limits may require a more sophisticated treatment.

Procedure Step 1. Divide the data set into two groups: detects and nondetects. If the total sample size equals n, let m represent the number of detects and (n  m) represent the number of nondetects. Denote the ith detected measurement by , then xi compute the mean and sample variance of the group of detects (i. e., above the quantitation limit data) using the following formulas:

x m x d i i m = =   1 1 Equation F. 8 and s m x mx d id i m 2 22 1 1 1 =                 =   Equation F. 9 Appendix F 260 Step 2. Denote the single censoring point (e. g., the quantitation limit) by QL. Then compute the two intermediate quantities, h and , necessary to derive Cohen's   adjustment via the following equations:

h nmn =   () Equation F. 10 and   =   s xQL d d 2 2 () Equation F. 11 Step 3. Use the intermediate quantities, h and to determine Cohen's adjustment   parameter from Table G 7 in Appendix G. For example, if h = 0.4 and = $     0.30, then = 0.6713. $   Step 4. Using the adjustment parameter found in step 3, compute adjusted estimates $   of the mean and standard deviation with the following formulas:

x x xQL d d =     $ ()   Equation F. 12 and s s xQL d d = +   2 2 $ ()   Equation F. 13 Step 5. Once the adjusted estimates for the population mean and standard deviation are derived, these values can be substituted for the sample mean and standard deviation in formulas for the desired confidence limit.

An example calculation using Cohen's method is given in Box F. 6. Appendix F 261 Box F. 6. An Example of Cohen's Method To determine attainment of a cleanup standard at SWMU, 24 random soil samples were obtained and analyzed for pentachlorophenol. Eight of the 24 values (33%) were below the matrix/ laboratory specific quantitation limit of 1 mg/ L. The 24 values are <1. 0, <1. 0, <1.0, <1.0, <1.0, <1.0, <1.0, <1.0, 1.1, 1.5, 1.9, 2.0, 2.5, 2.6, 3.1, 3.3, 3.2, 3.2, 3.3, 3.4, 3.5, 3.8, 4.5, 5.8 mg/ L. Cohen's Method will be used to adjust the sample mean and standard deviation for use in constructing a UCL on the mean to determine if the cleanup has attained the site specific risk based cleanup standard of 5.0 mg/ kg.

Solution Step 1: The sample mean of the m = 16 values greater than the quantitation limit is = 3.044 xd Step 2: The sample variance of the 16 quantified values is = 1.325. sd 2 Step 3: h = (24  16) / 24 = 0.333 and = 1.325 / (3.044  1.0) 2 = 0.317   Step 4: Table G 7 of Appendix G was used for h = 0.333 and = 0.317 to find the value of . Since the   $   table does not contain these entries exactly, double linear interpolation was used to estimate = $   0.5223.

Step 5: The adjusted sample mean and standard deviation are then estimated as follows:

= 3.044  0.5223 (3.044  1.0) = 1.976 2.0 and x   s = +   =   1325 0 5223 3 044 10 1873 19 2 ..(..).. 262 This page intentionally left blank 263 APPENDIX G STATISTICAL TABLES Table G 1. Critical Values of Student's t Distribution (One Tailed)

1     t() 1      Degrees of Freedom (see note) values for ( ) or ( ) t 1      1      0.70 0.75 0.80 0.85 0.90 0.95 0.975 0.99 0.995 1 0. 727 1.000 1.376 1.963 3.078 6.314 12.706 31.821 63.657 2 0. 617 0.816 1.061 1.386 1.886 2.920 4.303 6.965 9.925 3 0. 584 0.765 0.978 1.250 1.638 2.353 3.182 4.541 5.841 4 0. 569 0.741 0.941 1.190 1.533 2.132 2.776 3.747 4.604 5 0. 559 0.727 0.920 1.156 1.476 2.015 2.571 3.365 4.032 6 0. 553 0.718 0.906 1.134 1.440 1.943 2.447 3.143 3.707 7 0. 549 0.711 0.896 1.119 1.415 1.895 2.365 2.998 3.499 8 0. 546 0.706 0.889 1.108 1.397 1.860 2.306 2.896 3.355 9 0. 543 0.703 0.883 1.100 1.383 1.833 2.262 2.821 3.250 10 0.542 0.700 0.879 1.093 1.372 1.812 2.228 2.764 3.169 11 0.540 0.697 0.876 1.088 1.363 1.796 2.201 2.718 3.106 12 0.539 0.695 0.873 1.083 1.356 1.782 2.179 2.681 3.055 13 0.538 0.694 0.870 1.079 1.350 1.771 2.160 2.650 3.012 14 0.537 0.692 0.868 1.076 1.345 1.761 2.145 2.624 2.977 15 0.536 0.691 0.866 1.074 1.340 1.753 2.131 2.602 2.947 16 0.535 0.690 0.865 1.071 1.337 1.746 2.120 2.583 2.921 17 0.534 0.689 0.863 1.069 1.333 1.740 2.110 2.567 2.898 18 0.534 0.688 0.862 1.067 1.330 1.734 2.101 2.552 2.878 19 0.533 0.688 0.861 1.066 1.328 1.729 2.093 2.539 2.861 20 0.533 0.687 0.860 1.064 1.325 1.725 2.086 2.528 2.845 21 0.532 0.686 0.859 1.063 1.323 1.721 2.080 2.518 2.831 22 0.532 0.686 0.858 1.061 1.321 1.717 2.074 2.508 2.819 23 0.532 0.685 0.858 1.060 1.319 1.714 2.069 2.500 2.807 24 0.531 0.685 0.857 1.059 1.318 1.711 2.064 2.492 2.797 25 0.531 0.684 0.856 1.058 1.316 1.708 2.060 2.485 2.787 26 0.531 0.684 0.856 1.058 1.315 1.706 2.056 2.479 2.779 27 0.531 0.684 0.855 1.057 1.314 1.703 2.052 2.473 2.771 28 0.530 0.683 0.855 1.056 1.313 1.701 2.048 2.467 2.763 29 0.530 0.683 0.854 1.055 1.311 1.699 2.045 2.462 2.756 30 0.530 0.683 0.854 1.055 1.310 1.697 2.042 2.457 2.750 40 0.529 0.681 0.851 1.050 1.303 1.684 2.021 2.423 2.704 60 0.527 0.679 0.848 1.046 1.296 1.671 2.000 2.390 2.660 120 0.526 0.677 0.845 1.041 1.289 1.658 1.980 2.358 2.617   0.524 0.674 0.842 1.036 1.282 1.645 1.960 2.326 2.576 Note: For simple random or systematic sampling, degrees of freedom ( ) are equal to the number of samples ( ) df n collected from a solid waste and analyzed, less one (in other words, ). If stratified random sampling is df n =   1 used, calculate using Equation 12 or 14 in Section <IP_ADDRESS>. df The last row of the table ( degrees of freedom) gives the critical values for a standard normal distribution ( ).   z For example, the value for where is found in the last row as 1.282. z 1       = 010 . Appendix G 264 Table G 2. Factors ( ) for Parametric Upper Confidence Bounds on Upper Percentiles ( )   p n p = 0.80 p = 0.90 1      0.800 0.900 0.950 0.975 0.990 0.800 0.900 0.950 0.975 0.990 2 3.417 6.987 14.051 28.140 70.376 5.049 10.253 20.581 41.201 103.029 3 2.016 3.039 4.424 6.343 10.111 2.871 4.258 6.155 8.797 13.995 4 1.675 2.295 3.026 3.915 5.417 2.372 3.188 4.162 5.354 7.380 5 1.514 1.976 2.483 3.058 3.958 2.145 2.742 3.407 4.166 5.362 6 1.417 1.795 2.191 2.621 3.262 2.012 2.494 3.006 3.568 4.411 7 1.352 1.676 2.005 2.353 2.854 1.923 2.333 2.755 3.206 3.859 8 1.304 1.590 1.875 2.170 2.584 1.859 2.219 2.582 2.960 3.497 9 1.266 1.525 1.779 2.036 2.391 1.809 2.133 2.454 2.783 3.240 10 1.237 1.474 1.703 1.933 2.246 1.770 2.066 2.355 2.647 3.048 11 1.212 1.433 1.643 1.851 2.131 1.738 2.011 2.275 2.540 2.898 12 1.192 1.398 1.593 1.784 2.039 1.711 1.966 2.210 2.452 2.777 13 1.174 1.368 1.551 1.728 1.963 1.689 1.928 2.155 2.379 2.677 14 1.159 1.343 1.514 1.681 1.898 1.669 1.895 2.109 2.317 2.593 15 1.145 1.321 1.483 1.639 1.843 1.652 1.867 2.068 2.264 2.521 16 1.133 1.301 1.455 1.603 1.795 1.637 1.842 2.033 2.218 2.459 17 1.123 1.284 1.431 1.572 1.753 1.623 1.819 2.002 2.177 2.405 18 1.113 1.268 1.409 1.543 1.716 1.611 1.800 1.974 2.141 2.357 19 1.104 1.254 1.389 1.518 1.682 1.600 1.782 1.949 2.108 2.314 20 1.096 1.241 1.371 1.495 1.652 1.590 1.765 1.926 2.079 2.276 21 1.089 1.229 1.355 1.474 1.625 1.581 1.750 1.905 2.053 2.241 22 1.082 1.218 1.340 1.455 1.600 1.572 1.737 1.886 2.028 2.209 23 1.076 1.208 1.326 1.437 1.577 1.564 1.724 1.869 2.006 2.180 24 1.070 1.199 1.313 1.421 1.556 1.557 1.712 1.853 1.985 2.154 25 1.065 1.190 1.302 1.406 1.537 1.550 1.702 1.838 1.966 2.129 26 1.060 1.182 1.291 1.392 1.519 1.544 1.691 1.824 1.949 2.106 27 1.055 1.174 1.280 1.379 1.502 1.538 1.682 1.811 1.932 2.085 28 1.051 1.167 1.271 1.367 1.486 1.533 1.673 1.799 1.917 2.065 29 1.047 1.160 1.262 1.355 1.472 1.528 1.665 1.788 1.903 2.047 30 1.043 1.154 1.253 1.344 1.458 1.523 1.657 1.777 1.889 2.030 31 1.039 1.148 1.245 1.334 1.445 1.518 1.650 1.767 1.877 2.014 32 1.035 1.143 1.237 1.325 1.433 1.514 1.643 1.758 1.865 1.998 33 1.032 1.137 1.230 1.316 1.422 1.510 1.636 1.749 1.853 1.984 34 1.029 1.132 1.223 1.307 1.411 1.506 1.630 1.740 1.843 1.970 35 1.026 1.127 1.217 1.299 1.400 1.502 1.624 1.732 1.833 1.957 36 1.023 1.123 1.211 1.291 1.391 1.498 1.618 1.725 1.823 1.945 37 1.020 1.118 1.205 1.284 1.381 1.495 1.613 1.717 1.814 1.934 38 1.017 1.114 1.199 1.277 1.372 1.492 1.608 1.710 1.805 1.922 39 1.015 1.110 1.194 1.270 1.364 1.489 1.603 1.704 1.797 1.912 40 1.013 1.106 1.188 1.263 1.356 1.486 1.598 1.697 1.789 1.902 41 1.010 1.103 1.183 1.257 1.348 1.483 1.593 1.691 1.781 1.892 42 1.008 1.099 1.179 1.251 1.341 1.480 1.589 1.685 1.774 1.883 43 1.006 1.096 1.174 1.246 1.333 1.477 1.585 1.680 1.767 1.874 44 1.004 1.092 1.170 1.240 1.327 1.475 1.581 1.674 1.760 1.865 45 1.002 1.089 1.165 1.235 1.320 1.472 1.577 1.669 1.753 1.857 46 1.000 1.086 1.161 1.230 1.314 1.470 1.573 1.664 1.747 1.849 47 0.998 1.083 1.157 1.225 1.308 1.468 1.570 1.659 1.741 1.842 48 0.996 1.080 1.154 1.220 1.302 1.465 1.566 1.654 1.735 1.835 49 0.994 1.078 1.150 1.216 1.296 1.463 1.563 1.650 1.730 1.828 50 0.993 1.075 1.146 1.211 1.291 1.461 1.559 1.646 1.724 1.821 55 0.985 1.063 1.130 1.191 1.266 1.452 1.545 1.626 1.700 1.790 60 0.978 1.052 1.116 1.174 1.245 1.444 1.532 1.609 1.679 1.764 65 0.972 1.043 1.104 1.159 1.226 1.437 1.521 1.594 1.661 1.741 70 0.967 1.035 1.094 1.146 1.210 1.430 1.511 1.581 1.645 1.722 75 0.963 1.028 1.084 1.135 1.196 1.425 1.503 1.570 1.630 1.704 80 0.959 1.022 1.076 1.124 1.183 1.420 1.495 1.559 1.618 1.688 85 0.955 1.016 1.068 1.115 1.171 1.415 1.488 1.550 1.606 1.674 90 0.951 1.011 1.061 1.106 1.161 1.411 1.481 1.542 1.596 1.661 95 0.948 1.006 1.055 1.098 1.151 1.408 1.475 1.534 1.586 1.650 100 0.945 1.001 1.049 1.091 1.142 1.404 1.470 1.527 1.578 1.639 Appendix G 265 Table G 2. Factors ( ) for Parametric Upper Confidence Bounds on Upper Percentiles ( ) (continued)   p n p = 0.95 p = 0.99 1      0.800 0.900 0.950 0.975 0.990 0.800 0.900 0.950 0.975 0.990 2 6.464 13.090 26.260 52.559 131.426 9.156 18.500 37.094 74.234 185.617 3 3.604 5.311 7.656 10.927 17.370 5.010 7.340 10.553 15.043 23.896 4 2.968 3.957 5.144 6.602 9.083 4.110 5.438 7.042 9.018 12.387 5 2.683 3.400 4.203 5.124 6.578 3.711 4.666 5.741 6.980 8.939 6 2.517 3.092 3.708 4.385 5.406 3.482 4.243 5.062 5.967 7.335 7 2.407 2.894 3.399 3.940 4.728 3.331 3.972 4.642 5.361 6.412 8 2.328 2.754 3.187 3.640 4.285 3.224 3.783 4.354 4.954 5.812 9 2.268 2.650 3.031 3.424 3.972 3.142 3.641 4.143 4.662 5.389 10 2.220 2.568 2.911 3.259 3.738 3.078 3.532 3.981 4.440 5.074 11 2.182 2.503 2.815 3.129 3.556 3.026 3.443 3.852 4.265 4.829 12 2.149 2.448 2.736 3.023 3.410 2.982 3.371 3.747 4.124 4.633 13 2.122 2.402 2.671 2.936 3.290 2.946 3.309 3.659 4.006 4.472 14 2.098 2.363 2.614 2.861 3.189 2.914 3.257 3.585 3.907 4.337 15 2.078 2.329 2.566 2.797 3.102 2.887 3.212 3.520 3.822 4.222 16 2.059 2.299 2.524 2.742 3.028 2.863 3.172 3.464 3.749 4.123 17 2.043 2.272 2.486 2.693 2.963 2.841 3.137 3.414 3.684 4.037 18 2.029 2.249 2.453 2.650 2.905 2.822 3.105 3.370 3.627 3.960 19 2.016 2.227 2.423 2.611 2.854 2.804 3.077 3.331 3.575 3.892 20 2.004 2.208 2.396 2.576 2.808 2.789 3.052 3.295 3.529 3.832 21 1.993 2.190 2.371 2.544 2.766 2.774 3.028 3.263 3.487 3.777 22 1.983 2.174 2.349 2.515 2.729 2.761 3.007 3.233 3.449 3.727 23 1.973 2.159 2.328 2.489 2.694 2.749 2.987 3.206 3.414 3.681 24 1.965 2.145 2.309 2.465 2.662 2.738 2.969 3.181 3.382 3.640 25 1.957 2.132 2.292 2.442 2.633 2.727 2.952 3.158 3.353 3.601 26 1.949 2.120 2.275 2.421 2.606 2.718 2.937 3.136 3.325 3.566 27 1.943 2.109 2.260 2.402 2.581 2.708 2.922 3.116 3.300 3.533 28 1.936 2.099 2.246 2.384 2.558 2.700 2.909 3.098 3.276 3.502 29 1.930 2.089 2.232 2.367 2.536 2.692 2.896 3.080 3.254 3.473 30 1.924 2.080 2.220 2.351 2.515 2.684 2.884 3.064 3.233 3.447 31 1.919 2.071 2.208 2.336 2.496 2.677 2.872 3.048 3.213 3.421 32 1.914 2.063 2.197 2.322 2.478 2.671 2.862 3.034 3.195 3.398 33 1.909 2.055 2.186 2.308 2.461 2.664 2.852 3.020 3.178 3.375 34 1.904 2.048 2.176 2.296 2.445 2.658 2.842 3.007 3.161 3.354 35 1.900 2.041 2.167 2.284 2.430 2.652 2.833 2.995 3.145 3.334 36 1.895 2.034 2.158 2.272 2.415 2.647 2.824 2.983 3.131 3.315 37 1.891 2.028 2.149 2.262 2.402 2.642 2.816 2.972 3.116 3.297 38 1.888 2.022 2.141 2.251 2.389 2.637 2.808 2.961 3.103 3.280 39 1.884 2.016 2.133 2.241 2.376 2.632 2.800 2.951 3.090 3.264 40 1.880 2.010 2.125 2.232 2.364 2.627 2.793 2.941 3.078 3.249 41 1.877 2.005 2.118 2.223 2.353 2.623 2.786 2.932 3.066 3.234 42 1.874 2.000 2.111 2.214 2.342 2.619 2.780 2.923 3.055 3.220 43 1.871 1.995 2.105 2.206 2.331 2.615 2.773 2.914 3.044 3.206 44 1.868 1.990 2.098 2.198 2.321 2.611 2.767 2.906 3.034 3.193 45 1.865 1.986 2.092 2.190 2.312 2.607 2.761 2.898 3.024 3.180 46 1.862 1.981 2.086 2.183 2.303 2.604 2.756 2.890 3.014 3.168 47 1.859 1.977 2.081 2.176 2.294 2.600 2.750 2.883 3.005 3.157 48 1.857 1.973 2.075 2.169 2.285 2.597 2.745 2.876 2.996 3.146 49 1.854 1.969 2.070 2.163 2.277 2.594 2.740 2.869 2.988 3.135 50 1.852 1.965 2.065 2.156 2.269 2.590 2.735 2.862 2.980 3.125 55 1.841 1.948 2.042 2.128 2.233 2.576 2.713 2.833 2.943 3.078 60 1.832 1.933 2.022 2.103 2.202 2.564 2.694 2.807 2.911 3.038 65 1.823 1.920 2.005 2.082 2.176 2.554 2.677 2.785 2.883 3.004 70 1.816 1.909 1.990 2.063 2.153 2.544 2.662 2.765 2.859 2.974 75 1.810 1.899 1.976 2.047 2.132 2.536 2.649 2.748 2.838 2.947 80 1.804 1.890 1.964 2.032 2.114 2.528 2.638 2.733 2.819 2.924 85 1.799 1.882 1.954 2.019 2.097 2.522 2.627 2.719 2.802 2.902 90 1.794 1.874 1.944 2.006 2.082 2.516 2.618 2.706 2.786 2.883 95 1.790 1.867 1.935 1.995 2.069 2.510 2.609 2.695 2.772 2.866 100 1.786 1.861 1.927 1.985 2.056 2.505 2.601 2.684 2.759 2.850 Appendix G 266 Table G 3a. Sample Size Required to Demonstrate With At Least Confidence That At Least 100 1 ()%     of a Lot or Batch of Waste Complies With the Applicable Standard (No Samples Exceeding the Standard) 100p%

p 1      0.50 0.55 0.60 0.65 0.70 0.75 0.80 0.85 0.90 0.95 0.99 0.50 1 2 222233 4 57 0.55 2 2 223334 4 68 0.60 2 2 233344 5 610 0.65 2 2 333445 6 711 0.70 2 3 334456 7 913 0.75 3 3 44556791117 0.80 4 4 5 5 6 7 8 9 11 14 21 0.85 5 5 6 7 8 9 10 12 15 19 29 0.90 7 8 9 10 12 14 16 19 22 29 44 0.95 14 16 18 21 24 28 32 37 45 59 90 0.99 69 80 92 105 120 138 161 189 230 299 459 Table G 3b. Sample Size Required to Demonstrate With At Least Confidence That At Least 100 1 ()%     of a Lot or Batch of Waste Complies With the Applicable Standard (One Sample Exceeding the Standard) 100p%

p 1      0.50 0.55 0.60 0.65 0.70 0.75 0.80 0.85 0.90 0.95 0.99 0.50 3 4 445556 7 811 0.55 4 4 455667 8 912 0.60 4 5 55667891014 0.65 5 5 6 6 7 7 8 9 10 12 16 0.70 6677 8 9910 12 1420 0.75 7 7 8 9 9 10 11 13 15 18 24 0.80 9 9 10 11 12 13 14 16 18 22 31 0.85 11 12 13 15 16 18 19 22 25 30 42 0.90 17 19 20 22 24 27 29 33 38 46 64 0.95 34 37 40 44 49 53 59 67 77 93 130 0.99 168 184 202 222 244 269 299 337 388 473 662 Appendix G 267 Table G 4. Coefficients for the Shapiro Wilk Test for Normality [] an i   + 1 i \ n 2 3 4 5 6 7 8 910 1 .7071 .7071 .6872 .6646 .6431 .6233 .6052 .5888 .5739 2 .0000 .1677 .2413 .2806 .3031 .3164 .3244 .3291 3 .0000 .0875 .1401 .1743 .1976 .2141 4 .0000 .0561 .0947 .1224 5 .0000 .0399 i \ n 11 12 13 14 15 16 17 18 19 20 1 .5601 .5475 .5359 .5251 .5150 .5056 .4968 .4886 .4808 .4734 2 .3315 .3325 .3325 .3318 .3306 .3290 .3273 .3253 .3232 .3211 3 .2260 .2347 .2412 .2460 .2495 .2521 .2540 .2553 .2561 .2565 4 .1429 .1586 .1707 .1802 .1878 .1939 .1988 .2027 .2059 .2085 5 .0695 .0922 .1099 .1240 .1353 .1447 .1524 .1587 .1641 .1686 6 .0000 .0303 .0539 .0727 .0880 .1005 .1109 .1197 .1271 .1334 7 .0000 .0240 .0433 .0593 .0725 .0837 .0932 .1013 8 .0000 .0196 .0359 .0496 .0612 .0711 9 .0000 .0163 .0303 .0422 10 .0000 .0140 i \ n 21 22 23 24 25 26 27 28 29 30 1 .4643 .4590 .4542 .4493 .4450 .4407 .4366 .4328 .4291 .4254 2 .3185 .3156 .3126 .3098 .3069 .3043 .3018 .2992 .2968 .2944 3 .2578 .2571 .2563 .2554 .2543 .2533 .2522 .2510 .2499 .2487 4 .2119 .2131 .2139 .2145 .2148 .2151 .2152 .2151 .2150 .2148 5 .1736 .1764 .1787 .1807 .1822 .1836 .1848 .1857 .1864 .1870 6 .1399 .1443 .1480 .1512 .1539 .1563 .1584 .1601 .1616 .1630 7 .1092 .1150 .1201 .1245 .1283 .1316 .1346 .1372 .1395 .1415 8 .0804 .0878 .0941 .0997 .1046 .1089 .1128 .1162 .1192 .1219 9 .0530 .0618 .0696 .0764 .0823 .0876 .0923 .0965 .1002 .1036 10 .0263 .0368 .0459 .0539 .0610 .0672 .0728 .0778 .0822 .0862 11 .0000 .0122 .0228 .0321 .0403 .0476 .0540 .0598 .0650 .0697 12 .0000 .0107 .0200 .0284 .0358 .0424 .0483 .0537 13 .0000 .0094 .0178 .0253 .0320 .0381 14 .0000 .0084 .0159 .0227 15 .0000 .0076 Source: After Shapiro and Wilk (1965) Appendix G 268 Table G 4. Coefficients for the Shapiro Wilk Test for Normality (Continued) [] an i   + 1 i \ n 31 32 33 34 35 36 37 38 39 40 1 .4220 .4188 .4156 .4127 .4096 .4068 .4040 .4015 .3989 .3964 2 .2921 .2898 .2876 .2854 .2834 .2813 .2794 .2774 .2755 .2737 3 .2475 .2463 .2451 .2439 .2427 .2415 .2403 .2391 .2380 .2368 4 .2145 .2141 .2137 .2132 .2127 .2121 .2116 .2110 .2104 .2098 5 .1874 .1878 .1880 .1882 .1883 .1883 .1883 .1881 .1880 .1878 6 .1641 .1651 .1660 .1667 .1673 .1678 .1683 .1686 .1689 .1691 7 .1433 .1449 .1463 .1475 .1487 .1496 .1505 .1513 .1520 .1526 8 .1243 .1265 .1284 .1301 .1317 .1331 .1344 .1356 .1366 .1376 9 .1066 .1093 .1118 .1140 .1160 .1179 .1196 .1211 .1225 .1237 10 .0899 .0931 .0961 .0988 .1013 .1036 .1056 .1075 .1092 .1108 11 .0739 .0777 .0812 .0844 .0873 .0900 .0924 .0947 .0967 .0986 12 .0585 .0629 .0669 .0706 .0739 .0770 .0798 .0824 .0848 .0870 13 .0435 .0485 .0530 .0572 .0610 .0645 .0677 .0706 .0733 .0759 14 .0289 .0344 .0395 .0441 .0484 .0523 .0559 .0592 .0622 .0651 15 .0144 .0206 .0262 .0314 .0361 .0404 .0444 .0481 .0515 .0546 16 .0000 .0068 .0131 .0187 .0239 .0287 .0331 .0372 .0409 .0444 17 .0000 .0062 .0119 .0172 .0220 .0264 .0305 .0343 18 .0000 .0057 .0110 .0158 .0203 .0244 19 .0000 .0053 .0101 .0146 20 .0000 .0049 i \ n 41 42 43 44 45 46 47 48 49 50 1 .3940 .3917 .3894 .3872 .3850 .3830 .3808 .3789 .3770 .3751 2 .2719 .2701 .2628 .2667 .2651 .2635 .2620 .2604 .2589 .2574 3 .2357 .2345 .2334 .2323 .2313 .2302 .2291 .2281 .2271 .2260 4 .2091 .2085 .2078 .2072 .2065 .2058 .2052 .2045 .2038 .2032 5 .1876 .1874 .1871 .1868 .1865 .1862 .1859 .1855 .1851 .1847 6 .1693 .1694 .1695 .1695 .1695 .1695 .1695 .1693 .1692 .1691 7 .1531 .1535 .1539 .1542 .1545 .1548 .1550 .1551 .1553 .1554 8 .1384 .1392 .1398 .1405 .1410 .1415 .1420 .1423 .1427 .1430 9 .1249 .1259 .1269 .1278 .1286 .1293 .1300 .1306 .1312 .1317 10 .1123 .1136 .1149 .1160 .1170 .1180 .1189 .1197 .1205 .1212 11 .1004 .1020 .1035 .1049 .1062 .1073 .1085 .1095 .1105 .1113 12 .0891 .0909 .0927 .0943 .0959 .0972 .0986 .0998 .1010 .1020 13 .0782 .0804 .0824 .0842 .0860 .0876 .0892 .0906 .0919 .0932 14 .0677 .0701 .0724 .0745 .0775 .0785 .0801 .0817 .0832 .0846 15 .0575 .0602 .0628 .0651 .0673 .0694 .0713 .0731 .0748 .0764 16 .0476 .0506 .0534 .0560 .0584 .0607 .0628 .0648 .0667 .0685 17 .0379 .0411 .0442 .0471 .0497 .0522 .0546 .0568 .0588 .0608 18 .0283 .0318 .0352 .0383 .0412 .0439 .0465 .0489 .0511 .0532 19 .0188 .0227 .0263 .0296 .0328 .0357 .0385 .0411 .0436 .0459 20 .0094 .0136 .0175 .0211 .0245 .0277 .0307 .0335 .0361 .0386 21 .0000 .0045 .0087 .0126 .0163 .0197 .0229 .0259 .0288 .0314 22 .0000 .0042 .0081 .0118 .0153 .0185 .0215 .0244 23 .0000 .0039 .0076 .0111 .0143 .0174 24 .0000 .0037 .0071 .0104 25 .0000 .0035 Appendix G 269 Table G 5. Level Critical Points for the Shapiro Wilk Test   n   0.01 0.05 3 0. 753 0.767 4 0. 687 0.748 5 0. 686 0.762 6 0. 713 0.788 7 0. 730 0.803 8 0. 749 0.818 9 0. 764 0.829 10 0.781 0.842 11 0.792 0.850 12 0.805 0.859 13 0.814 0.866 14 0.825 0.874 15 0.835 0.881 16 0.844 0.887 17 0.851 0.892 18 0.858 0.897 19 0.863 0.901 20 0.868 0.905 21 0.873 0.908 22 0.878 0.911 23 0.881 0.914 24 0.884 0.916 25 0.888 0.918 26 0.891 0.920 27 0.894 0.923 28 0.896 0.924 29 0.898 0.926 30 0.900 0.927 31 0.902 0.929 32 0.904 0.930 33 0.906 0.931 34 0.908 0.933 35 0.910 0.934 36 0.912 0.935 37 0.914 0.936 38 0.916 0.938 39 0.917 0.939 40 0.919 0.940 41 0.920 0.941 42 0.922 0.942 43 0.923 0.943 44 0.924 0.944 45 0.926 0.945 46 0.927 0.945 47 0.928 0.946 48 0.929 0.947 49 0.929 0.947 50 0.930 0.947 Source: After Shapiro and Wilk (1965) Appendix G 270 Table G 6. Values of for Calculating a One Sided 90 Percent UCL on a Lognormal Mean H H 1 090   =   .

sy n 3 5 7 10 12 15 21 31 51 101 0.10 1.686 1.438 1.381 1.349 1.338 1.328 1.317 1.308 1.301 1.295 0.20 1.885 1.522 1.442 1.396 1.380 1.365 1.348 1.335 1.324 1.314 0.30 2.156 1.627 1.517 1.453 1.432 1.411 1.388 1.370 1.354 1.339 0.40 2.521 1.755 1.607 1.523 1.494 1.467 1.437 1.412 1.390 1.371 0.50 2.990 1.907 1.712 1.604 1.567 1.532 1.494 1.462 1.434 1.409 0.60 3.542 2.084 1.834 1.696 1.650 1.606 1.558 1.519 1.485 1.454 0.70 4.136 2.284 1.970 1.800 1.743 1.690 1.631 1.583 1.541 1.504 0.80 4.742 2.503 2.119 1.914 1.845 1.781 1.710 1.654 1.604 1.560 0.90 5.349 2.736 2.280 2.036 1.955 1.880 1.797 1.731 1.672 1.621 1.00 5.955 2.980 2.450 2.167 2.073 1.985 1.889 1.812 1.745 1.686 1.25 7.466 3.617 2.904 2.518 2.391 2.271 2.141 2.036 1.946 1.866 1.50 8.973 4.276 3.383 2.896 2.733 2.581 2.415 2.282 2.166 2.066 1.75 10.48 4.944 3.877 3.289 3.092 2.907 2.705 2.543 2.402 2.279 2.00 11.98 5.619 4.380 3.693 3.461 3.244 3.005 2.814 2.648 2.503 2.50 14.99 6.979 5.401 4.518 4.220 3.938 3.629 3.380 3.163 2.974 3.00 18.00 8.346 6.434 5.359 4.994 4.650 4.270 3.964 3.697 3.463 3.50 21.00 9.717 7.473 6.208 5.778 5.370 4.921 4.559 4.242 3.965 4.00 24.00 11.09 8.516 7.062 6.566 6.097 5.580 5.161 4.796 4.474 4.50 27.01 12.47 9.562 7.919 7.360 6.829 6.243 5.763 5.354 4.989 5.00 30.01 13.84 10.61 8.779 8.155 7.563 6.909 6.379 5.916 5.508 6.00 36.02 16.60 12.71 10.50 9.751 9.037 8.248 7.607 7.048 6.555 7.00 42.02 19.35 14.81 12.23 11.35 10.52 9.592 8.842 8.186 7.607 8.00 48.03 22.11 16.91 13.96 12.96 12.00 10.94 10.08 9.329 8.665 9.00 54.03 24.87 19.02 15.70 14.56 13.48 12.29 11.32 10.48 9.725 10.0 60.04 27.63 21.12 17.43 16.17 14.97 13.64 12.56 11.62 10.79 Source: Land (1975) Appendix G 271 Table G 7. Values of the Parameter for Cohen's Adjustment for Nondetected Values $     h .01 .02 .03 .04 .05 .06 .07 .08 .09 .10 .15 .20 .00 .010100 .020400 .030902 .041583 .052507 .063625 .074953 .08649 .09824 .11020 .17342 .24268 .05 .010551 .021294 .032225 .043350 .054670 .066159 .077909 .08983 .10197 .11431 .17925 .25033 .10 .010950 .022082 .033398 .044902 .056596 .068483 .080563 .09285 .10534 .11804 .18479 .25741 .15 .011310 .022798 .034466 .046318 .058356 .070586 .083009 .09563 .10845 .12148 .18985 .26405 .20 .011642 .023459 .035453 .047829 .059990 .072539 .085280 .09822 .11135 .12469 .19460 .27031 .25 .011952 .024076 .036377 .048858 .061522 .074372 .087413 .10065 .11408 .12772 .19910 .27626 .30 .012243 .024658 .037249 .050018 .062969 .076106 .089433 .10295 .11667 .13059 .20338 .28193 .35 .012520 .025211 .038077 .051120 .064345 .077736 .091355 .10515 .11914 .13333 .20747 .28737 .40 .012784 .025738 .038866 .052173 .065660 .079332 .093193 .10725 .12150 .13595 .21129 .29250 .45 .013036 .026243 .039624 .053182 .066921 .080845 .094958 .10926 .12377 .13847 .21517 .29765 .50 .013279 .026728 .040352 .054153 .068135 .082301 .096657 .11121 .12595 .14090 .21882 .30253 .55 .013513 .027196 .041054 .055089 .069306 .083708 .098298 .11208 .12806 .14325 .22225 .30725 .60 .013739 .027849 .041733 .055995 .070439 .085068 .099887 .11490 .13011 .14552 .22578 .31184 .65 .013958 .028087 .042391 .056874 .071538 .086388 .10143 .11666 .13209 .14773 .22910 .31630 .70 .014171 .028513 .043030 .057726 .072505 .087670 .10292 .11837 .13402 .14987 .23234 .32065 .75 .014378 .029927 .043652 .058556 .073643 .088917 .10438 .12004 .13590 .15196 .23550 .32489 .80 .014579 .029330 .044258 .059364 .074655 .090133 .10580 .12167 .13775 .15400 .23858 .32903 .85 .014773 .029723 .044848 .060153 .075642 .091319 .10719 .12225 .13952 .15599 .24158 .33307 .90 .014967 .030107 .045425 .060923 .075606 .092477 .10854 .12480 .14126 .15793 .24452 .33703 .95 .015154 .030483 .045989 .061676 .077549 .093611 .10987 .12632 .14297 .15983 .24740 .34091 1.00 .015338 .030850 .046540 .062413 .078471 .094720 .11116 .12780 .14465 .16170 .25022 .34471 Appendix G 272 Table G 7. Values of the Parameter for Cohen's Adjustment for Nondetected Values (Continued) $     h .25 .30 .35 .40 .45 .50 .55 .60 .65 .70 .80 .90 .05 .32793 .4130 .5066 .6101 .7252 .8540 .9994 1.166 1.358 1.585 2.203 3.314 .10 .33662 .4233 .5184 .6234 .7400 .8703 1.017 1.185 1.379 1.608 2.229 3.345 .15 .34480 .4330 .5296 .6361 .7542 .8860 1.035 1.204 1.400 1.630 2.255 3.376 .20 .35255 .4422 .5403 .6483 .7673 .9012 1.051 1.222 1.419 1.651 2.280 3.405 .25 .35993 .4510 .5506 .6600 .7810 .9158 1.067 1.240 1.439 1.672 2.305 3.435 .30 .36700 .4595 .5604 .6713 .7937 .9300 1.083 1.257 1.457 1.693 2.329 3.464 .35 .37379 .4676 .5699 .6821 .8060 .9437 1.098 1.274 1.475 1.713 2.353 3.492 .40 .38033 .4735 .5791 .6927 .8179 .9570 1.113 1.290 1.494 1.732 2.376 3.520 .45 .38665 .4831 .5880 .7029 .8295 .9700 1.127 1.306 1.511 1.751 2.399 3.547 .50 .39276 .4904 .5967 .7129 .8408 .9826 1.141 1.321 1.528 1.770 2.421 3.575 .55 .39679 .4976 .6061 .7225 .8517 .9950 1.155 1.337 1.545 1.788 2.443 3.601 .60 .40447 .5045 .6133 .7320 .8625 1.007 1.169 1.351 1.561 1.806 2.465 3.628 .65 .41008 .5114 .6213 .7412 .8729 1.019 1.182 1.368 1.577 1.824 2.486 3.654 .70 .41555 .5180 .6291 .7502 .8832 1.030 1.195 1.380 1.593 1.841 2.507 3.679 .75 .42090 .5245 .6367 .7590 .8932 1.042 1.207 1.394 1.608 1.851 2.528 3.705 .80 .42612 .5308 .6441 .7676 .9031 1.053 1.220 1.408 1.624 1.875 2.548 3.730 .85 .43122 .5370 .6515 .7781 .9127 1.064 1.232 1.422 1.639 1.892 2.568 3.754 .90 .43622 .5430 .6586 .7844 .9222 1.074 1.244 1.435 1.653 1.908 2.588 3.779 .95 .44112 .5490 .6656 .7925 .9314 1.085 1.255 1.448 1.668 1.924 2.607 3.803 1.00 .44592 .5548 .6724 .8005 .9406 1.095 1.287 1.461 1.882 1.940 2.626 3.827 273 APPENDIX H STATISTICAL SOFTWARE Since publication of Chapter Nine (" Sampling Plan") of SW 846 in 1986, great advances have been made in desktop computer hardware and software. In implementing the procedures recommended in this chapter, you should take advantage of the powerful statistical software now available for low cost or no cost. A number of useful "freeware" packages are available from EPA and other organizations, and many are downloadable from the Internet. Commercially available software also may be used.

This appendix provides a list of software that you might find useful. EPA Guidance for Quality Assurance Project Plans, EPA QA/ G 5 (USEPA 1998a) also provides an extensive list of software that can assist you in developing and preparing a quality assurance project plan.

Sampling Design Software Title Description Decision Error Feasibility Trials (DEFT)* This software package allows quick generation of cost information about several simple sampling designs based on DQO constraints, which can be evaluated to determine their appropriateness and feasibility before the sampling and analysis design is finalized. This software supports the Guidance for the Data Quality Objectives Process EPA QA/ G 4 (USEPA 2000b), which provides general guidance to organizations developing data quality criteria and performance specifications for decision making. The Data Quality Objectives Decision Error Feasibility Trials Software (DEFT)  User's Guide (EPA/ 240/ B 01/ 007) contains detailed instructions on how to use DEFT software and provides background information on the sampling designs that the software uses.

Download from EPA's World Wide Web site at: http:// www. epa. gov/ quality/ qa_ docs. html.

GeoEAS* Geostatistical Environmental Assessment Software (GeoEAS) (USEPA 1991b) is a collection of interactive software tools for performing twodimensional geostatistical analyses of spatially distributed data. Programs are provided for data file management, data transformations, univariate statistics, variogram analysis, cross validation, kriging, contour mapping, post plots, and line/ scatter plots. Users may alter parameters and re calculate results or reproduce graphs, providing a "what if" analysis capability.

GeoEAS Version 1.2.1 (April 1989) software and documentation is available from EPA's Web site at http:// www. epa. gov/ ada/ csmos/ models/ geoeas. html * Also available on EPA's CD ROM Site Characterization Library Volume 1 (Release 2) (USEPA 1998c) Appendix H 274 Sampling Design Software (Continued)

Title Description ELIPGRID PC ELIPGRID PC is a program for the design and analysis of sampling grids for locating elliptical targets (e. g., contamination "hot spots"). It computes the probability of success in locating targets based on the assumed size, shape, and orientation of the targets, as well as the specified grid spacing. It also can be used to compute a grid spacing from a specified success probability, compute cost information associated with specified sampling grids, determine the size of the smallest "hot spot" detected given a particular grid, and create graphs of the results.

Information, software, and user's guide are available on the World Wide Web at: http:// dqo. pnl. gov/ software/ elipgrid. htm The site is operated for the U. S. Department of Energy Office of Environmental Management by the Pacific Northwest National Laboratory.

DQO PRO This software comprises a series of programs with a user interface such as a common calculator and it is accessed using Microsoft Windows. DQO PRO provides answers for three objectives:

1. Determining the rate at which an event occurs 2. Determining an estimate of an average within a tolerable error 3. Determining the sampling grid necessary to detect "hot spots."

DQO PRO facilitates understanding the significance of DQOs by showing the relationships between numbers of samples and DQO parameters, such as (1) confidence levels versus numbers of false positive or negative conclusions; (2) tolerable error versus analyte concentration, standard deviation, etc., and (3) confidence levels versus sampling area grid size. The user has only to type in his or her requirements and the calculator instantly provides the answers.

Contact: Information and software are available on the Internet at the American Chemical Society, Division of Environmental Chemistry Web site at http:// www. acs envchem. duq. edu/ dqopro. htm Visual Sample Plan (VSP) VSP provides statistical solutions for optimizing the sampling design. The software can answer two important questions in sample planning: (1) How many samples are needed? VSP can quickly calculate the number of samples needed for various scenarios at different costs. (2) Where should the samples be taken? Sample placement based on personal judgment is prone to bias. VSP provides random or grided sampling locations overlaid on the site map.

Information and software available at http:// dqo. pnl. gov/ VSP/ Index. htm VSP was developed in part by Department of Energy's (DOE's) National Analytical Management Program (NAMP) and through a joint effort between Pacific Northwest National Laboratory (PNNL) and Advanced Infrastructure Management Technologies (AIMTech). Appendix H 275 Data Quality Assessment Software Title Description DataQUEST This software tool is designed to provide a quick and easy way for managers and analysts to perform baseline Data Quality Assessment. The goal of the system is to allow those not familiar with standard statistical packages to review data and verify assumptions that are important in implementing the DQA Process. This software supports the Guidance for Data Quality Assessment, EPA QA/ G 9 (USEPA 2000d) which demonstrates the use of the DQA Process in evaluating environmental data sets.

Download from EPA's World Wide Web site at http:// www. epa. gov/ quality/ qa_ docs. html ASSESS 1.01a* This software tool was designed to calculate variances for quality assessment samples in a measurement process. The software performs the following functions: (1) transforming the entire data set, (2) producing scatter plots of the data, (3) displaying error bar graphs that demonstrate the variance, and (4) generating reports of the results and header information.

Available on EPA's CD ROM Site Characterization Library Volume 1 (Release 2) (USEPA 1998c)

MTCAStat This software package is published by the Washington Department of Ecology and can be used to calculate sample sizes (for both normal and lognormal distributions), basic statistical quantities, and confidence intervals. Requires MS Excel 97.

The USEPA Office of Solid Waste has not evaluated this software for use in connection with RCRA programs, however, users of this guidance may wish to review the software for possible application to some of the concepts described in this document.

Available from Washington Department of Ecology's "Site Cleanup, Sediments, and Underground Storage Tanks" World Wide Web site at http:// www. ecy. wa. gov/ programs/ tcp/ tools/ toolmain. html * Also available on EPA's CD ROM Site Characterization Library Volume 1 (Release 2) (USEPA 1998c) 276 This page intentionally left blank 277 APPENDIX I EXAMPLES OF PLANNING, IMPLEMENTATION, AND ASSESSMENT FOR RCRA WASTE SAMPLING This appendix presents the following two hypothetical examples of planning, implementation, and assessment for RCRA waste sampling:

Example 1: Sampling soil in a RCRA Solid Waste Management Unit (SWMU) to confirm attainment of the cleanup standard (using the mean to measure compliance with a standard)

Example 2: Sampling of a process waste to make a hazardous waste determination (using a maximum or upper percentile to measure compliance with a standard).

Example 1: Sampling Soil at a RCRA SWMU to Confirm Attainment of a Cleanup Standard Introduction In this example, the owner of a permitted TSDF completed removal of contaminated soil at a SWMU as required under the facility's RCRA permit under EPA's RCRA Corrective Action Program. The permit required the facility owner to conduct sampling and analysis to determine if the remaining soil attains the facility specific risk based standard specified in the permit. This hypothetical example describes how the planning, implementation, and assessment activities were conducted.

Planning Phase The planning phase included implementation of EPA's systematic planning process known as the Data Quality Objectives (DQO) Process and preparation of a quality assurance project plan (QAPP). A DQO planning team was assembled, and the DQO Process was implemented following EPA's guidance in Guidance for the Data Quality Objectives Process for Hazardous Waste Site Operations EPA QA/ G 4HW (USEPA 2000a), Guidance for the Data Quality Objectives Process EPA QA/ G 4 (USEPA 2000b), and Chapter Nine of SW 846.

The outputs of the seven steps of the DQO Process are outlined below.

DQO Step 1: Stating the Problem ° The DQO planning team included the facility owner, a technical project manager, a chemist, environmental technician (sampler), and a facility engineer familiar with statistical methods. As part of the DQO Process, the team consulted with their state regulator to determine if the State has any additional regulations or guidance that applies. A state guidance document provided recommendations for the parameter of interest and the acceptable Type I decision error rate. Appendix I Example 1 278 ° A concise description of the problem was developed as follows: The facility conducted a soil removal action at the SWMU. Soil with concentrations greater than the risk based cleanup standard of 10 mg/ kg of pentachlorophenol (PCP) was excavated for off site disposal. Removal was guided by the results of grab samples analyzed for PCP using a semi quantitative field analytical method.

° The conceptual site model (CSM) assumed that the PCP migrated downward into the soil, and that if a soil layer were found to be "clean," then the underlying soil layer also would be assumed "clean."

° The technical staff were given six weeks to complete the study and submit a draft report to the regulatory agency.

DQO Step 2: Identifying Possible Decisions ° Decision statement: The study objective was to determine if the soil remaining in the SWMU after removal of the contaminated soil attained the cleanup standard. If the standard is attained, then the area will be backfilled with clean fill and reserved for future industrial development. If the standard is not attained, then the next layer of soil within the SWMU will be removed.

DQO Step 3: Identifying Inputs to the Decision ° The sample analysis results for total PCP (in mg/ kg) in soil were used to decide whether or not the soil attained the cleanup. PCP was designated as the only constituent of concern, and its distribution within the SWMU was assumed to be random. The risk based cleanup level for PCP in soil was set at 10 mg/ kg.

° The decision was based on the concentrations in the top six inch layer of soil across the entire SWMU. The study was designed to determine whether the entire unit attains the standards, or does not.

° The chemist identified two candidate analytical methods for measuring PCP concentrations in soil: (1) SW 846 Method 4010A "Screening For Pentachlorophenol By Immunoassay" ($ 20/ analysis), and (2) SW 846 Method 8270 (and prep method 3550) ($ 110/ analysis). The project chemist confirmed that both methods were capable of achieving a quantitation limit well below the action level of 10 mg/ kg. During Step 7 of the DQO Process, the chemist revisited this step to select a final method and prepare method performance criteria as part of the overall specification of decision performance criteria.

° The planning team identified the need to specify the size, shape, and orientation of each sample to satisfy the acceptable sampling error (specified in DQO Process Step 7) and to enable selection of the appropriate sampling device (during development of the QAPP). Because the soil exists in a relatively flat stationary three dimensional unit, it was considered a series of overlapping twodimensional surfaces for the purposes of sampling. The correct orientation, size, Example 1 Appendix I 279 and shape of each sample was a vertical core capturing the full six inch thickness of the soil unit. The minimum mass of each primary field sample was determined during DQO Process Step 7 using the particle size weight relationship required to control fundamental error at an acceptable level.

DQO Step 4: Defining Boundaries ° The dimensions of the SWMU were approximately 125 feet by 80 feet (10,000 square feet). The SWMU was relatively flat. The depth of interest was limited to the top six inches of soil in the unit after removal of the contaminated soil. The spatial boundary of the SWMU was defined by the obvious excavation and by wooden stakes at the corners of the excavation.

° The soil within the study boundary was loamy sand with a maximum particle size of about 1.5 mm (0.15 cm).

° The project team planned to collect samples within a reasonable time frame, and degradation or transformation of the PCP over the investigation period was not a concern.

DQO Step 5: Developing Decision Rules ° The population parameter of interest was the mean. The mean was selected as the parameter of interest because the risk based cleanup standard (Action Level) was derived based upon long term average health effects predicted from exposures to the contaminated soil.

° The risk based action level was 10 mg/ kg total pentachlorophenol (PCP) in soil.

° The decision rule was then established as follows: "If the mean concentration for PCP in the soil is less than 10 mg/ kg, then the cleanup standard is attained. Otherwise, the SWMU will be considered contaminated and additional remedial action will be required."

DQO Step 6: Specifying Limits on Decision Errors ° The major sources of variability (measured as the relative variance) were identified as within sample unit variability ( ) (including analytical imprecision sw 2 and Gy's fundamental error) and between sample unit variability ( ) (or sb 2 population variability). The total study variance ( ) , expressed as the relative sT 2 variance, was estimated using the following relationship:

s ss s s s T bw b sa 2 22 2 22 = +

= + + Appendix I Example 1 280 where = between unit variance (population variance), = sample collection sb 2 ss 2 imprecision (estimated by Gy's fundamental error, ), and = analytical sFE 2 sa 2 imprecision (determined from the measurement of laboratory control samples with concentrations near the Action Level).

° Sample analysis results for eight samples of soil excavated from the previous lift gave a standard deviation and mean of = 7.1 and = 10.9 respectively. The s x total study relative standard deviation ( ) was then estimated as 0.65. sT ° The relative standard deviation (RSD) of the sampling error ( ) was estimated ss as 0.10 (as estimated by Gy's fundamental error), based a maximum observed particle size of approximately 1.5 mm (0.15 cm) and a sample mass of 10 grams.

° The RSD for the analytical imprecision ( ) associated with the field screening sa method (SW 846 Method 4010A  "Screening For Pentachlorophenol By Immunoassay") was estimated from replicate measurements as 0.40.

° The between unit (population) relative standard deviation ( ) was then sb estimated as:

s sss b Tsa =   +

=   + = 2 22 2 22 65 10 40 050 ()

(. ) (. . ) .

° Two potential decision errors could be made based on interpreting sampling and analytical data:

Decision Error A: Concluding that the mean PCP concentration within the SWMU was less than 10 mg/ kg when it was truly greater than 10 mg/ kg, or Decision Error B: Concluding that the mean PCP concentration within the SWMU was greater than 10 mg/ kg when it was truly less than 10 mg/ kg.

The consequences of Decision Error A, incorrectly deciding the SWMU was "clean" (mean PCP concentration less than 10 mg/ kg), would leave contaminated soil undetected and would likely increase health risks for onsite workers and pose potential future legal problems for the owner.

The consequences of Decision Error B, incorrectly deciding the SWMU was "not clean" (mean PCP concentration greater than or equal to 10 mg/ kg), would cause the needless expenditure of resources (e. g., funding, time, backhoe and operator, soil disposal, sampling crew labor, and analytical capacity) for unnecessary further remedial action. Example 1 Appendix I 281 Error A, incorrectly deciding that the mean PCP concentration is less than the action level of 10 mg/ kg, posed more severe consequences for human health plus liability and compliance concerns. Consequently, the baseline condition chosen for the SWMU was that the mean PCP concentration within the SWMU is truly greater than or equal to the action level of 10 mg/ kg.

Table I 1. Null Hypothesis and Possible Decision Errors for Example 1 "Null Hypothesis" (baseline condition) Possible Decision Errors Type I Error ( ),   False Rejection Type II Error ( ),   False Acceptance The true mean concentration of PCP in the SWMU is greater than or equal to the risk based cleanup standard (i. e., the SWMU is contaminated). Concluding the site is "clean" when, in fact, it is contaminated. Concluding the site is still contaminated when, in fact, it is "clean."

° Next, it was necessary to specify the boundaries of the gray regions. The gray region defines a range that is less than the action limit, but too close to the Action Level to be considered "clean," given uncertainty in the data. When the null hypothesis (baseline condition) assumes that the site is contaminated (as in this example), the upper limit of the gray region is bounded by the Action Level; the lower limit is determined by the decision maker. The project team sets the lower bound of the gray region at 7.5 mg/ kg, with the understanding that this bound could be modified after review of the outputs of Step 7 of the DQO Process.

° The planning team set the acceptable probability of making a Type I (false rejection) error at 5 percent ( ) based on guidance provided by the State  = 005 . regulatory agency. In other words, the team was willing to accept a 5 percent chance of concluding the SWMU was clean, if in fact it was not. While a Type II (false acceptance) error could prove to be costly to the company, environmental protection and permit compliance are judged to be most important. The planning team decides to set the Type II error rate at only 20 percent.

° The information collected in Step 6 of the DQO Process is summarized below. Appendix I Example 1 282 Table I 2. Initial Outputs of Step 6 of the DQO Process Needed Parameter Output Action Level (AL) 10 mg/ kg Gray Region 7.5  10 mg/ kg (width of gray region, = 2.5)   Relative Width of Gray Region (10  7.5)/ 7.5 = 0.33 Null Hypothesis (Ho ) Mean (PCP) 10 mg/ kg   False Rejection Decision Error Limit (probability of a Type I error)  = 005 .

False Acceptance Decision Error Limit (probability of a Type II error)  = 020 .

DQO Step 7: Optimizing the Data Collection Design 1. Review outputs from the first six steps of the DQO Process. The project team reviewed the outputs of the first six steps of the DQO Process. They expected the PCP concentration to be near the cleanup standard (Action Level); thus, it was decided that a probabilistic sampling design would be used so that the results could be stated with a known probability of making a decision error.

2. Consider various data collection designs. The objective of this step was to find cost effective design alternatives that balance the number of samples and the measurement performance, given the feasible choices for sampling designs and measurement methods. Based on characterization data from the excavated soil, the planning team assumed that the between sample unit variability or population variability would remain relatively stable at approximately , sb = 050 . independent of the sampling and analytical methods used. The planning team investigated various combinations of sampling and analytical methods (with varying associated levels of precision and cost) as a means find the optimal study design.

The planning team considered three probabilistic sampling designs: simple random, stratified random, and systematic (grid based) designs. A composite sampling strategy also was considered. All designs allowed for an estimate of the mean to be made. Because the existence of strata was not expected (although could be discovered during the investigation), the stratified design was eliminated from consideration. A simple random design is the simplest of the probabilistic sampling methods, but it may not provide very even coverage of the SWMU; thus, if spatial variability becomes a concern, then it may go undetected with a simple random design. The systematic design provides more even coverage of the SWMU and typically is easy to implement.

The practical considerations were considered for each alternative design, including site access and conditions, equipment selection/ use, experience Example 1 Appendix I 283 needed, special analytical needs, health and safety requirements, and scheduling. There were no significant practical constraints that would limit the use of either the systematic or the simple random sampling designs; however, the systematic design was preferred because it provides sampling locations that are easier to survey and locate in the field, and it provides better spatial coverage. Ultimately, two sampling designs were evaluated: a systematic sampling design and a systematic sampling design that incorporates composite sampling.

The acceptable mass of each primary field sample was determined using the particle size weight relationship required to control fundamental error. The soil in the SWMU is a granular solid, and the 95 th percentile particle size (d) was estimated at 1.5 mm (0.15 cm). To maintain the relative standard deviation of the fundamental error at 0.10, a sample mass of at least 8.2 grams was required (using Equation D. 4 in Appendix D). To maintain the relative standard deviation of the fundamental error at 0.05, a sample mass of at least 30 grams would be required. There were no practical constraints on obtaining samples of these sizes.

Next, it was necessary to estimate unit costs for sampling and analysis. Based on prior experience, the project team estimated the cost of collecting a grab sample at $40 – plus an additional $30 per sample for documentation, processing of field screening samples, and $60 per sample for documentation, processing, and shipment for samples sent for fixed laboratory analysis.

3. Select the optimal number of samples. Using the initial outputs of Step 6, the appropriate number of samples was calculated for each sampling design:

For the systematic sampling design (without compositing), the following formula was used (Equation 8 from Section 5.4.1):

n z zsz T = + +       () 1 1 2 2 2 1 2 2        where = the quantile of the standard normal distribution (from z 1      pth the last row of Table G 1, Appendix G), where is the   probability of making a Type I error (the significance level of the test) set in DQO Step 6. = the quantile of the standard normal distribution (from z1      pth the last row of Table G 1, Appendix G), where is the   probability of making a Type II error set in DQO Step 6. = an estimate of the total study relative standard deviation. sT = the width of the gray region from DQO Step 6 (expressed   as the relative error in this example). Appendix I Example 1 284 [EPA's DEFT software could be used to calculate the appropriate number of samples (see Data Quality Objectives Decision Error Feasibility Trials Software (DEFT)  User's Guide, USEPA 2001h). Note, however, that the DEFT program asks for the bounds of the gray region specified in absolute units. If the planning team uses the relative standard deviation (or coefficient of variation) in the sample size equation rather than the absolute standard deviation, then the bounds of the gray region also must be input into DEFT as relative values. Thus, the Action Level would be set equal to 1, and the other bound of the gray region would be set equal to 1  (relative width of gray region) or 1 + (relative width of gray region) depending what baseline condition is selected.]

Note that if there were more than one constituent of concern, then the appropriate number of samples would need to be calculated for each constituent using preliminary estimates of their standard deviations. The number of samples would then be determined by the highest number of samples obtained for any single constituent of concern.

The sample size for systematic composite sampling also was evaluated. In comparison to non composite sampling, composite sampling can have the effect of minimizing between sample variation, thereby reducing somewhat the total number of composite samples that must be submitted for analysis. In addition, composite samples are expected to generate normally distributed data thereby allowing the team to apply normal theory statistical methods. To estimate the sample size, the planning team again required an estimate of the standard deviation. However, since the original estimate of the standard deviation was based on available individual or "grab" sample data rather than composite samples, it was necessary to adjust the variance term in the sample size equation for the appropriate number of composite samples. In the sample size equation, the between unit (population) component of variance ( ) was sb 2 replaced with , where is the number of individual or "grab" samples s g b 2 g used to form each composite. Sample sizes were then calculated assuming . g = 4 Table I 3 and Table I 4 summarize the inputs and outputs of Step 7 of the DQO Process and provides the estimated costs for the various sampling and analysis designs evaluated. Example 1 Appendix I 285 Table I 3. Summary of Inputs for Candidate Sampling Designs Parameter Systematic Sampling  Fixed Lab Analyses Systematic Sampling  Field Analyses Systematic Composite Sampling  Fixed Lab Analyses Systematic Composite Sampling  Field Analyses Inputs Sampling Costs Collection Cost (per "grab") $40 ea. $40 ea. $40 ea. $40 ea.

Documentation, processing, shipment $60 ea. $30 ea. $60 ea. $30 ea.

Analytical Costs SW 846 Method 3550/ 8270 (fixed lab) $110 ea. $110 ea.* $110 ea. $110 ea.*

SW 846 Method 4010A (field screening) NA $20 ea. NA $20 ea.

Relative Width of Gray Region ( )   0.33 0.33 0.33 0.33 Null Hypothesis (Ho ) Mean (PCP) 10   mg/ kg Mean (PCP) 10   mg/ kg Mean (PCP) 10   mg/ kg Mean (PCP) 10   mg/ kg False Rejection Decision Error Limit  = 005 .  = 005 .  = 005 .  = 005 .

False Acceptance Decision Error Limit  = 0 20 .  = 0 20 .  = 0 20 .  = 0 20 .

Relative Std. Dev.

Sampling ( ) ss 0.10 0.10 0.10 0.10 Analytical ( ), SW sa 846 Method 8270 0.10 NA 0.10 NA Analytical ( ) SW sa 846 Method 4010A NA 0.40 NA 0.40 "Population" ( ) sb 0.50 0.50 0.50 0.50 Total Study s T s s s a s b = + + 2 2 2 0.52 0.65 0.29** 0. 48**

NA: Not applicable * Assumes 20 percent of all field analyses must be confirmed via fix laboratory method.

** For composite sampling, the total study relative standard deviation ( ) was estimated by replacing with sT sb 2 , where = the number of "grabs" per composite. s g b 2 g Appendix I Example 1 286 Table I 4. Summary of Outputs for Candidate Sampling Designs Parameter Systematic Sampling  Fixed Lab Analyses Systematic Sampling  Field Analyses Systematic Composite Sampling  Fixed Lab Analyses Systematic Composite Sampling  Field Analyses Outputs Number of Samples ( ) n 17 25 6 15 Cost Estimate "Grab" Sampling $40 x 17 $40 x 25 $40 x 4 x 6 (see note 1) $40 x 4 x 15 (see note 1)

Documentation, processing, and shipment $60 x 17 ($ 30 x 25) + ($ 60 x 5) (see note 2) $60 x 6 ($ 30 x 15) + ($ 60 x 3) (see note 2)

SW 846 Method 3550/ 8270 (fixed lab) $110 x 17 $110 x 5 (see note 2) $110 x 6 $110 x 3 (see note 2)

SW 846 Method 4010A (field screening) NA $20 x 25 NA $20 x 15 Cost $3,570 $3,100 $1,980 $3,660 1. The calculation assumes four grabs per composite sample. 2. The calculation includes costs for shipment and analysis of 20% of field screening samples for fixed laboratory analysis. NA: Not applicable 4. Select a resource effective design. It was determined that all of the systematic designs and systematic composite sampling designs would meet the statistical performance requirements for the study in estimating the mean PCP concentration in the SWMU. The project team selected the systematic composite sampling design  with fixed laboratory analysis  based on the cost savings projected over the other sampling designs.

The planning team decided that one additional field quality control sample (an equipment rinsate blank), analyzed by SW 846 Method 8720, was required to demonstrate whether the sampling equipment was free of contamination.

The outputs of the DQO Process were summarized in a memo report which was then used help prepare the QAPP.

5. Prepare a QAPP. The operational details of the sampling and analytical activities were documented in the QAPP using EPA Guidance for Quality Assurance Project Plans, EPA QA/ G 5 (USEPA 1998a) and Chapter One of SW846 for guidance. Example 1 Appendix I 287 Implementation Phase The QAPP was implemented in accordance with the schedule, sampling plan, and safety plan. The exact location of each field sample was established using a grid on a map of the SWMU. The start point for constructing the grid was selected at random.

The QAPP established the following DQOs and performance goals for the sampling equipment:

° The correct orientation and shape of each sample is a vertical core.

° Each sample must capture the full depth of interest (six inches).

° The minimum mass of each sample is 10 g.

° The device must be constructed of materials that will not alter analyte concentrations due to loss or gain of analytes via sorption, desorption, degradation, or corrosion.

° The device must be easy to use, safe, and low cost.

A sampling device was selecting using the four steps described in Figure 28 in Section 7.1.

Step 1  Identify the Medium to be Sampled The material to be sampled is a soil. Using Table 8 in Section 7.1, we find the media descriptor that most closely matches the waste in the first column of the table: "Soil and other unconsolidated geologic material."

Step 2  Select the Sample Location The second column of Table 8 in Section 7.1 provides a list of possible sampling sites (or units types) for soil (i. e., surface or subsurface). In this example, the sampling location is surface soil and "Surface" is found in the second column in the table.

Step 3  Identify Candidate Sampling Devices The third column of Table 8 in Section 7.1 provides a list of candidate sampling devices. For the waste stream in this example, the list includes bucket auger, concentric tube thief, coring type sampler, miniature core sampler, modified syringe, penetrating probe sampler, sampling scoop/ trowel/ shovel, thin walled tube, and trier.

Step 4  Select Devices Sampling devices were selected from the list of candidate sampling devices after review of Table 9 in Section 7.1. Selection of the equipment was made after consideration of the DQOs for the sample support (i. e., required volume, depth, shape, and orientation), the performance goals established for the sampling device, ease of use and decontamination, worker safety issues, cost, and any practical considerations. Appendix I Example 1 288 Table I 5 demonstrates how the DQOs and performance goals can be used together to narrow the candidate devices down to just one or two.

Table I 5. Using DQOs and Performance Goals to Select a Final Sampling Device Candidate Devices Data Quality Objectives and Performance Goals Required Depth Orientation and Shape Sample Volume Operational Considerations Desired Material of Construction 6 inches Vertical undisturbed core >10 g Device is portable, safe, & low cost? Stainless or carbon steel Bucket auger Y N Y Y Y Concentric tube thief Y NYYY Coring Type Sampler Y NYYY Miniature core sampler Y YNYN Modified syringe sampling N NNYN Penetrating Probe Sampler Y YY YY Scoop, trowel, or shovel Y NYYY Thin walled tube Y Y Y Y Y Trier Y N Y Y Y Key: Y = The device is capable of achieving the specified DQO or performance goal. N = The device is not capable of achieving the DQO or performance goal.

The "penetrating probe sampler" and the "thin walled tube" were identified as the preferred devices because they could satisfy all of the DQOs and performance goals for the sampling devices. The penetrating probe was selected because it was easy to use and was readily available to the field sampling crew.

A penetrating probe sampler was then used to take the field samples at each location on the systematic square grid (see Figure I 1). Each composite sample was formed by pooling and mixing individual samples collected from within each of four quadrants. The process was repeated until six composite samples were obtained. Because the total mass of each individual (grab) sample used to form composite samples exceeded that required by the laboratory for analysis, a field subsampling routine was used to reduce the volume of material submitted to the laboratory.

The field samples and associated field QC samples were submitted to the laboratory where a subsample was taken from each field sample for analysis. The samples were analyzed in accordance with the QAPP. Example 1 Appendix I 289 Boundary of SWMU 80 ft. 125 ft.

Field Sample No. 6 Mixture of four "grab" samples Field Subsampling 1 2 3 4 5 6 L A n ft = = =   24 20 2 10,000ft 20.4 1 2 3 4 5 6 1 2 3 4 5 6 1 2 3 4 5 6 Not to scale Figure I 1. Systematic sampling with compositing. The distance between sampling points (L) is determined using the approach described in Section 5.2.3 (Box 5). Samples with the same number are pooled and mixed to form each composite sample. A field sample is formed from each composite using one of the subsampling methods described in Section 7.3.2 (e. g., by fractional shoveling).

Assessment Phase Data Verification and Validation Sampling and analytical records were reviewed to check compliance with the QAPP. The data collected during the study met the measurement objectives. Sampling and analytical error were minimized through the use of a statistical sampling design, correct field sampling and subsampling procedures, and adherence to the requirements of the analytical methods. The soil that was sampled did not present any special problems concerning access to sampling locations, equipment usage, particle size distribution, or matrix interferences. A quantitation limit of 0.5 mg/ kg was achieved. The analytical package was verified and validated, and the data generated were judged acceptable for their intended purpose.

Data Quality Assessment (DQA)

DQA was performed using the approach outlined in Section 8.2:

1. Review DQOs and sampling design. The DQO planning team reviewed the original objectives: "If the mean concentration for PCP in the soil is less than 10 mg/ kg, then the cleanup standard is attained. Otherwise, the SWMU will be considered contaminated and additional remedial action will be required." Appendix I Example 1 290 STATISTICAL QUANTITIES Number of Observations: 6 Minimum: 6.000 Maximum: 10.500 Mean: 7. 833 Median: 7. 750 Variance: 2. 267 Std De: 1. 506 Range: 4.500 IQR: 1. 000 Coefficient of Variation: 0. 192 Coefficient of Skewness: 0. 783 Coefficient of Kurtosis: 0. 087 Percentiles: 1st: 6.000 75th: 8.000 7th: 6.000 90th: 10. 500 10th: 6. 000 95th: 10. 500 25th: 7. 000 99th: 10. 500 50th: 7. 750 (median) DataQUEST Figure I 2. Statistical quantities using DataQUEST software 2. Prepare the data for statistical analysis. The summary of the verified and validated data were received in hard copy format and an electronic data base was created by manual data entry into spreadsheet software. The data base was checked by a second person for accuracy. The results for the data collection effort are listed in Table I 6. A data file was created in a format suitable for import into EPA's DataQUEST software.

Table I 6. Soil Sample Analysis Results for PCP (mg/ kg)

Sample Identification Result (PCP, mg/ kg)

1 8. 0 2 8. 0 3 7. 0 4 6. 0 5 10.5 6 7. 5 3. Conduct preliminary analysis of data and check distributional assumptions: Using EPA's DataQUEST, statistical quantities were computed as shown in Figure I 2.

On a normal probability plot, the data plot as a straight line, indicating approximate normality (see Figure I 3). Example 1 Appendix I 291 N: 6 StDev: 1.506 Average: 7.833 10 9 8 7 6 .999 .99 .95 .80 .50 .20 .05 .01 .001 Probability PCP (mg/ kg) Normal Probability Plot Figure I 3. Normal probability plot Shapiro Wilk Test Null Hypothesis: `Data are normally distributed'

Sample Value: 0.914 Tabled Value: 0.788 There is not enough evidence to reject the assumption of normality with a 5% significance level.

DataQUEST Figure I 4. Results of the Shapiro Wilk test using EPA's DataQUEST software The data also were checked for normality by the Shapiro Wilk test. Using the DataQUEST software, the Shapiro Wilk test was performed at the 0.05 percent significant level. The Shapiro Wilk test did not reject the null hypothesis of normality (see Figure I 4). Appendix I Example 1 292 4. Select and perform the statistical test: The analysis of the data showed there were no "non detects" and a normal distribution was an acceptable model. Using the guidance in Figure 38 (Section 8.2.4), a parametric upper confidence limit (UCL) on the mean was selected as the correct statistic to compare to the regulatory level. The 95% UCL on the mean was calculated as follows:

UCL x t s n n 0. 95 0.95, 1 7 833 2 015 1506 6 91 = +

= +             =   .. .

.mg/ kg The tabulated "t value" (2.015) was obtained from Table G 1 in Appendix G and based on a 95 percent one tailed confidence interval with and 5  = 005 . degrees of freedom.

5. Draw conclusions and report results: The 95% UCL for the mean of the sample analysis results for PCP, 9.1 mg/ kg, was less than the specified cleanup level of 10 mg/ kg. Thus, the null hypothesis was rejected, and the owner made the determination that the soil remaining in the SWMU attains the cleanup standard for PCP based on the established decision rule.

A summary report including a description of all planning, implementation, and assessment activities was submitted to the regulatory agency for review. Example 2 Appendix I 293 Example 2: Sampling of a Process Waste to Make a Hazardous Waste Determination Introduction An aircraft manufacturing and maintenance facility strips paint from parts before remanufacturing them. The facility recently switched its paint stripping process from a solventbased system to use of an abrasive plastic blasting media (PBM). The waste solvent, contaminated with stripped paint, had to be managed as a hazardous waste. The facility owner changed the process to reduce  or possibly eliminate  the generation of hazardous waste from this operation and thereby reduce environmental risks and lower waste treatment and disposal costs.

The plant operators thought the spent PBM could include heavy metals such as chromium and cadmium from the paint, and therefore there was a need to make a hazardous waste determination in order to comply with the RCRA regulations at 40 CFR Part 262.11. The facility owner determined that the spent PBM is a solid waste under RCRA but not a listed hazardous waste. The facility owner then needed to determine if the solid waste exhibits any of the characteristics of hazardous waste: ignitability (§ 261.21), corrosivity (§ 261.22), reactivity (§ 261.23), or toxicity (§ 261.24). Using process and materials knowledge, the owner determined that the waste blasting media would not exhibit the characteristics of ignitability, corrosivity, or reactivity. The facility owner elected to conduct waste testing to determine if the waste blasting media exhibits the characteristic of toxicity.

This hypothetical example describes how the planning, implementation, and assessment activities were conducted.

Planning Phase The planning phase comprises the Data Quality Objectives (DQO) Process and preparation of a quality assurance project plan (QAPP) including a sampling and analysis plan. A DQO planning team was assembled and the DQO Process was implemented following EPA's guidance in Guidance for the Data Quality Objectives Process EPA QA/ G 4 (USEPA 2000b) and SW 846.

The outputs of the seven steps of the DQO Process are outlined below.

DQO Step 1: Stating the Problem ° The DQO planning team included the plant manager, a technical project manager, a consulting chemist, and the paint stripping booth operator who also served as the sampler.

° The conceptual model of the waste generation process was developed as follows: The de painting operation consists of a walk in blast booth with a reclamation floor. After blasting, the plastic blast media, mixed with paint fines, is passed through a reclamation system; the reusable media is separated out for reloading to the blast unit, while the spent media and paint waste is discharged to a container. Appendix I Example 2 294 ° A concise description of the problem was developed as follows: The problem was described as determining whether the new waste stream (the spent plastic blasting media and waste paint) should be classified as a hazardous waste that requires treatment and subsequent disposal in a RCRA Subtitle C landfill (at $300 per ton), or whether it is a nonhazardous industrial waste that can be landdisposed in an industrial landfill (at $55 per ton).

° The plant manager gave the plant staff and consultant 60 days to complete the study. The turn around time was established to minimize the amount of time that the waste was stored at the facility while the data were being generated, and to allow adequate time to have the waste shipped off site  if it were found to be a hazardous waste  within the 90 day accumulation time specified at 40 CFR Part 262.34( a).

DQO Step 2: Identifying Possible Decisions ° Decision statement: The decision statement was determining whether the spent PBM paint waste was hazardous under the RCRA regulations.

° Alternative actions: If the waste was hazardous, then treatment and subsequent disposal in a RCRA landfill would be required.

DQO Step 3: Identifying Inputs to the Decision ° The decision was to be based on the quantity of waste generated over approximately a one month period, but not to exceed the quantity placed in a single 10 cubic yard roll off box.

° Based on process and materials knowledge, the team specified cadmium and chromium as the constituents of concern.

° To resolve the decision statement, the planning team needed to determine if, using the Toxicity Characteristic Leaching Procedure (TCLP) SW 846 Method 1311, the extract from a representative sample of the waste contained the constituents of concern at concentrations equal to or greater than their regulatory levels as required by the RCRA regulations at 40 CFR 261.24. The chemist noted, however, that the TCLP method allows the following: "If a total analysis of the waste demonstrates that individual analytes are not present in the waste, or that they are present but at such low concentrations that the appropriate regulatory levels could not possibly be exceeded, the TCLP need not be run." With that flexibility in mind, the planning team identified a candidate method for total analysis (including SW 846 Method 3050B/ 6010), and noted that the TCLP would be required if the total analysis indicated TC levels could be exceeded.

° The project chemist found that SW 846 Methods 3010A (prep) and 6010B were suitable for analysis of the TCLP extracts at quantitation limits at or below the applicable regulatory levels. Example 2 Appendix I 295 ° The minimum sample "support" was determined as follows: Method 1311 (TCLP) specifies a minimum sample mass of 100 grams for analysis of nonvolatile constituents and a maximum particle size of 9.5 mm. The waste stream, composed of dry fine to medium grained plastic and paint chips, was well within the particle size requirements of the TCLP. During Step 7 of the DQO Process, the planning team revisited this step to determine whether a sample mass larger than 100 grams would be necessary to satisfy the overall decision performance criteria.

DQO Step 4: Defining Boundaries ° The paint stripping operation includes a blast booth, a PBM reclamation unit, and a waste collection roll off box that complies with the applicable container requirements of Subparts I and CC of 40 CFR part 265. The spent blast media and paint waste is discharged to the roll off box from the reclamation unit. Each discharge event was considered a "batch" for the purposes of the waste classification study.

° When testing a solid waste to determine if it exhibits a characteristic of hazardous waste, the determination must be made when management of the solid waste would potentially be subject to the RCRA hazardous waste regulations at 40 CFR Part 262 through 265. Accordingly, the planning team decided samples should be obtained at the point where the waste discharges from the reclamation unit into the roll off container (i. e., the point of generation). Until such time that the generator determined that the waste is not a hazardous waste, the generator complied with the applicable pre transport requirements at 40 CFR Part 262  Subpart C (i. e., packaging, labeling, marking, and accumulation time).

° The boundary of the decision was set as the extent of time over which the decision applies. The boundary would change only if there were a process or materials change that would alter the composition of the waste. Such a process or materials change could include, for example, a change in the composition, particle size or particle shape of the blasting media, or a significant change in the application (pressure) rate of the blast media.

DQO Step 5: Developing Decision Rules ° The planning team reviewed the RCRA regulations at for the Toxicity Characteristic at 40 CFR 261.24 and found the regulation does not specify a parameter of interest (such as the mean or a percentile). They observed, however, that the Toxicity Characteristic (TC) regulatory levels specified in Table 1 of Part 261.24 represent "maximum" concentrations that cannot be equaled or exceeded; otherwise, the solid waste must be classified as hazardous. While the regulations for hazardous waste determination do not require the use of any statistical test to make a hazardous waste determination, the planning team decided to use a high percentile value as a reasonable approximation of the maximum TCLP sample analysis result that could be obtained from a sample of the waste. Their objective was to "prove the negative"  that is, to demonstrate Appendix I Example 2 296 with a desired level of confidence that the vast majority of the waste was nonhazardous. The upper 90th percentile was selected. The team specified an additional constraint that no single sample could exceed the standard. Otherwise, there may be evidence that the waste is hazardous at least part of the time.

° The Action Levels were set at the TC regulatory limits specified in Table 1 of 40 CFR Part 261.24:

Cadmium: 1.0 mg/ L TCLP Chromium: 5. 0 mg/ L TCLP ° The decision rule was then established as follows: "If the upper 90 th percentile TCLP concentration for cadmium or chromium in the waste and all samples analysis results are less than their respective action levels of 1.0 and 5.0 mg/ L TCLP, then the waste can be classified as nonhazardous waste under RCRA; otherwise, the waste will be considered a hazardous waste."

DQO Step 6: Specifying Limits on Decision Errors ° The null hypothesis was that the waste is hazardous, i. e., the true proportion (P) of samples with concentrations of cadmium or chromium less than their regulatory thresholds is less than 0.90, or Ho: P < 0.90.

° Two potential decision errors could be made based on interpreting sampling and analytical data:

Decision Error A: Concluding that the true proportion (P) of the waste that is nonhazardous was greater than 0.90 when it was truly less than 0.90, or Decision Error B: Concluding that the true proportion (P) of the waste that is nonhazardous was less than 0.90 when it was truly greater than 0.90.

The consequences of Decision Error A  incorrectly deciding the waste was nonhazardous  would lead the facility to ship untreated hazardous waste off site for disposal in solid waste landfill, likely increase health risks for onsite workers, and pose potential future legal problems for the owner.

The consequences of Decision Error B  incorrectly deciding the waste was hazardous when in fact it is not hazardous  would cause the needless costs for treatment and disposal, but with no negative environmental consequences.

Error A, incorrectly deciding that a hazardous waste is a nonhazardous waste, posed more severe consequences for the generator in terms of liability and compliance concerns. Consequently, the baseline condition (null hypothesis) chosen was that the true proportion of waste that is nonhazardous is less than 90 percent. Example 2 Appendix I 297 Table I 7. Null Hypothesis and Possible Decision Errors for Example 2 "Null Hypothesis" (baseline condition) Possible Decision Errors Type I Error ( ),   False Rejection Type II Error ( ),   False Acceptance The true proportion (P) of waste that is nonhazardous is less than 0.90. Concluding the waste is nonhazardous when, in fact, it is hazardous. Concluding the waste is hazardous when, in fact, it is nonhazardous.

° Next, it was necessary to specify the boundaries of the gray region. When the null hypothesis (baseline condition) assumes that the waste is hazardous (as in this example), one limit of the gray region is bounded by the Action Level and the other limit is set at a point where it is desirable to control the Type II (false acceptance) error. The project team set one bound of the gray region at 0.90 (the Action Level). Since a "no exceedance" criterion is included in the decision rule, the other bound of the gray region is effectively set at 1.

° The DQO planning team then sets the acceptable probability of making a Type I (false rejection) error at 10 percent ( ). In other words, they are willing  = 010 . to accept a 10 percent chance of concluding the waste is nonhazardous when at least a portion of the waste is hazardous. The use of the exceedance rule method does not require specification of the Type II (false acceptance) error rate.

° The information collected in Step 6 of the DQO Process is summarized below.

Table I 8. Initial Outputs of Step 6 of the DQO Process  Example 2 Needed Parameter Output Action Level 0.90 Gray Region 0.90 to 1.0 ( = 0.10)   Null Hypothesis (Ho ) P < 0.90 False Rejection Decision Error Limit (probability of a Type I error)  = 010 .

False Acceptance Decision Error Limit (probability of a Type II error) Not specified Appendix I Example 2 298 DQO Step 7: Optimizing the Data Collection Design ° Review outputs from the first six steps of the DQO Process. The planning team reviewed the outputs of the first six steps of the DQO Process.

° Consider various data collection designs. The DQO planning team considered two probabilistic sampling designs: simple random and systematic (random within time intervals). Both the simple random and the systematic design would allow the facility owner to estimate whether a high percentage of the waste complies with the standard. The team also considered using an authoritative "biased" sampling design to estimate the high end or "worst case" waste characteristics.

Two analytical plans were then considered: One in which the full TCLP would be performed on each sample, and one in which TCLP concentrations could be estimated from total concentration by comparing each total sample analysis result to 20 times the TC regulatory limit (to account for the 20: 1 dilution used in the TCLP).

The laboratory requested a sample mass of at least 300 grams (per sample) to allow the laboratory to perform the preliminary analyses required by the TCLP and to provide sufficient mass to perform the full TCLP (if required).

The practical considerations were then evaluated for each alternative design, including access to sampling locations, worker safety, equipment selection/ use, experience needed, special analytical needs, and scheduling.

° Select the optimal number of samples. Since the decision rule specified no exceedance of the standard in any sample, the number of samples was determined from Table G 3a in Appendix G. The table is based on the formula . For a desired and , the number n p = log( ) log( )   p = 090 . (). 1 090   =   of samples ( ) for a simple random or systematic sampling design was 22. n The team also considered how many samples might be required if a nonprobabilistic authoritative sampling design were used. Some members of the planning team thought that significantly fewer samples (e. g., four) could be used to make a hazardous waste determination, and they pointed out that the RCRA regulations do not require statistical sampling for waste classification. On the other hand, other members of the planning team argued against the authoritative design. They argued that there was insufficient knowledge of the waste to implement authoritative sampling and noted that a few samples taken in a nonprobabilistic manner would limit their ability to quantify any possible decision errors.

° Select a resource effective design. The planning team evaluated the sampling and analytical design options and costs. The following table summarizes the estimated costs for the four sampling designs evaluated. Example 2 Appendix I 299 Table I 9. Estimated Costs for Implementing Candidate Sampling Designs Simple Random or Systematic Sampling (total metals only) Simple Random or Systematic Sampling (TCLP metals) Authoritative (Biased) Sampling (total metals only) Authoritative (Biased) Sampling (TCLP metals)

Sample collection cost (per sample) $50 $50 $50 $50 Analysis cost ° SW 846 Methods 3050B/ 6010B (total Cd and Cr) (per sample) $40 $40 ° SW 846 TCLP Method 1311. Extract analyzed by SW 846 Methods 3010A/ 6010B (per sample) $220 $220 Number of samples 22 22 4 4 Total Estimated Cost $1,980 $5,940 $360 $1,080 While the authoritative design with total metals analysis offered the least cost compared to the probabilistic designs, the team decided that they did not have sufficient knowledge of the waste, its leaching characteristics, or the process yet to use an authoritative sampling approach with total metals analysis only. Furthermore, the team needed to quantify the probability of making a decision error. The planning team selected the systematic design with total metals analysis for Cd and Cr with the condition that if any total sample analysis result indicated the maximum theoretical TCLP result could exceed the TC limit, then the TCLP would be performed for that sample. This approach was selected for its ease of implementation, it would provide adequate waste knowledge for future waste management decisions (assuming no change in the waste generation process), and would satisfy other cost and performance objectives specified by the planning team.

° Prepare a QAPP/ SAP. The operational details of the sampling and analytical activities are documented in a Quality Assurance Project Plan and Sampling and Analysis Plan (QAPP/ SAP).

Implementation Phase The QAPP/ SAP was implemented in accordance with the schedule and the facility's safety program. Based on the rate of waste generation, it was estimated that the roll off box would be filled in about 30 work days assuming one "batch" of waste was placed in the roll off box each day. It was decided to obtain one random sample from each batch as the waste was discharge from the reclamation unit to the roll off container (i. e., at the point of waste generation). See Figure I 5. Appendix I Example 2 300 Roll Off Box Blast Booth Waste Point of waste generation and sampling point If hazardous, accumulation less than 90 days prior to shipment off site per 40 CFR Part 262.34( a). Random Sampling Within Batches Batch 1 Batch 2, etc Reclaimed Blast Media Recoveryreclamation system Not to scale Figure I 5. Systematic sampling design with random sampling times selected within each batch The QAPP/ SAP established the following DQOs and performance goals for the equipment.

The sampling device must meet the following criteria:

° Be able to obtain a minimum mass of 300 grams for each sample ° Be constructed of materials that will not alter analyte concentrations due to loss or gain of analytes via sorption, desorption, degradation, or corrosion ° Be easy to use, safe, and low cost ° Be capable of obtaining increments of the waste at the discharge drop without introducing sampling bias.

The following four steps were taken to select the sampling device (from Section 7.1):

Step 1  Identify the Medium To Be Sampled Based on a prior inspection, it was known that the waste is a unconsolidated dry granular solid. Using Table 8 in Section 7.1, we find the media descriptor that most closely matches the waste in the first column of the table: "Other Solids  Unconsolidated."

Step 2  Select the Sample Location The second column of Table 8 provides a list of common sampling locations for unconsolidated solids. The discharge drop opening is four inches wide, and the waste is released downward into the collection box. "Pipe or Conveyor" found in the table is the closest match to the Example 2 Appendix I 301 configuration of the waste discharge point.

Step 3  Identify Candidate Sampling Devices The third column of Table 8 provides a list of candidate sampling devices for sampling solids from a pip or conveyor. For this waste stream, the list of devices for sampling a pipe or conveyor includes bucket, dipper, pan, sample container, miniature core sampler, scoop/ trowel/ shovel, and trier. The planning team immediately eliminated miniature core sampler, scoop/ trowel/ shovel, and trier because they are not suitable for obtaining samples from a falling stream or vertical discharge.

Step 4  Select Devices From the list of candidate sampling devices, one device was selected for use in the field from Table 9 in Section 7.1. Selection of the equipment was made after consideration of the DQOs for the sample support (i. e., required volume, width, shape, and orientation), the performance goals established for the sampling device, ease of use and decontamination, worker safety issues, cost, and any practical considerations. Table I 10 demonstrates how the DQOs and performance goals were used to narrow the candidate devices down to just one or two.

Table I 10. Using DQOs and Performance Goals To Select a Final Sampling Device Candidate Devices Data Quality Objectives and Performance Goals Required Width Orientation and Shape Sample Volume Operational Considerations Desired Material of Construction 4 inches Cross section of entire stream >300 g Device is portable, safe, and low cost? Polyethylene or PTFE Bucket Y Y Y Y Y Dipper N Y Y Y Y Pan Y Y Y Y Y Sample container N NYYY Key: Y = The device is capable of achieving the specified DQO or performance goal. N = The device is not capable of achieving the specified DQO or performance goal.

The sampling mode was "one dimensional," that is, the material is relatively linear in time and space. The ideal sampling device would obtain a sample of constant thickness and must be capable of obtaining the entire width of the stream for a fraction of the time (see discussion at Section <IP_ADDRESS>). Either a bucket or pan wide enough (preferably 3 times the width of the stream) to obtain all of the flow for a fraction of the time are identified as suitable devices because they are capable of achieving all the performance goals.

A flat 12 inch wide polyethylene pan with vertical sides was used to collect each primary field sample. Each primary field sample was approximately 2 kilograms, therefore, the field team used the "fractional shoveling" technique (see Section 7.3.2) to reduce the sample mass to a subsample of approximately 300 grams. The field samples (each in a 32 oz jar) and associated Appendix I Example 2 302 field QC samples were submitted to the laboratory in accordance with the sample handling and shipping instructions specified in the QAPP/ SAP.

A total of 30 samples were obtained by the time the roll off box was filled, so it was necessary to randomly select 22 samples from the set of 30 for laboratory analysis.

All 22 samples were first analyzed for total cadmium and chromium to determine if the maximum theoretical TCLP concentration in any one sample could exceed the applicable TC limit. Samples whose maximum theoretical TCLP value exceeded the applicable TC limit were then analyzed using the full TCLP.

For the TCLP samples, no particle size reduction was required for the sample extraction because the maximum particle size in the waste passed through a 9.5 mm sieve (the maximum particle size allowed for the TCLP). (On a small subsample of the waste, however, particle size reduction to 1 mm was required to determine the TCLP extract type (I or II)). A 100 gram subsample was taken from each field sample for TCLP analysis.

Assessment Phase Data Verification and Validation Sampling and analytical records were reviewed to check compliance with the QAPP/ SAP. The data collected during the study met the DQOs. Sampling and analytical error were minimized through the use of a statistical sampling design, correct field sampling and subsampling procedures, and adherence to the requirements of the analytical methods. The material that was sampled did not present any special problems concerning access to sampling locations, equipment usage, particle size distribution, or matrix interferences. Quantitation limits achieved for total cadmium and chromium were 5 mg/ kg and 10 mg/ kg respectively. Quantitation limits achieved for cadmium and chromium in the TCLP extract were 0.10 mg/ L and 1.0 mg/ L respectively. The analytical package was validated and the data generated were judged acceptable for their intended purpose.

Data Quality Assessment DQA was performed using the approach outlined in Section 9.8.2 and EPA QA/ G 9 (USEPA 2000d):

1. Review DQOs and sampling design. The DQO planning team reviewed the original objectives: "If the upper 90 th percentile TCLP concentration for cadmium or chromium in the waste and all samples analysis results are less than their respective action levels of 1.0 and 5.0 mg/ L TCLP, then the waste can be classified as nonhazardous waste under RCRA; otherwise, the waste will be considered a hazardous waste."

2. Prepare the data for statistical analysis. The summary of the verified and validated data were received in hard copy format, and summarized in a table. The table was checked by a second person for accuracy. The results for the data collection effort are listed in Table I 11. Example 2 Appendix I 303 Table I 11. Total and TCLP Sample Analysis Results Sample No. Cadmium Chromium Total (mg/ kg) Total / 20 (TC limit = 1 mg/ L) Total (mg/ kg) Total / 20 (TC limit = 5 mg/ L) 1 <5 <0.25 11 0.55 2 6 0.3 <10 <0. 5 3 29 1.45 (full TCLP = 0.72) <10 <0. 5 4 <5 <0.25 <10 <0.5 5 <5 <0.25 42 2.1 6 7 0.35 <10 <0.5 7 7 0.35 <10 <0.5 8 13 0. 65 26 1. 3 9 <5 <0.25 19 0.95 10 <5 <0. 25 <10 <0. 5 11 36 1.8 (full TCLP = 0.8) <10 <0. 5 12 <5 <0. 25 <10 <0. 5 13 <5 <0. 25 <10 <0. 5 14 <5 <0. 25 12 0. 6 15 <5 <0. 25 <10 <0. 5 16 9 0. 45 <10 <0. 5 17 <5 <0. 25 <10 <0. 5 18 <5 <0. 25 <10 <0. 5 19 <5 <0. 25 31 1. 55 20 20 1 (full TCLP = <0. 10) <10 <0. 5 21 <5 <0. 25 <10 <0. 5 22 <5 <0. 25 <10 <0. 5 3. Conduct preliminary analysis of data and check distributional assumptions. To use the nonparametric "exceedance rule" no distributional assumptions are required. The only requirements are a random sample, and that the quantitation limit is less than the applicable standard. These requirements were met.

4. Select and perform the statistical test: The maximum TCLP sample analysis results for cadmium and chromium were compared to their respective TC regulatory limits. While several of the total results indicated the maximum theoretical TCLP result could exceed the regulatory limit, subsequent analysis of the TCLP extracts from these samples indicated the TCLP concentrations were below the regulatory limits. Appendix I Example 2 1 Note that if fewer than 22 samples were analyzed  for example, due to a lost sample  and all sample analysis results indicated concentrations less than the applicable standard, then one still could conclude that 90 percent of all possible samples are less than the standard but with a lower level of confidence. See Section 5.5.2, Equation 17.

304 5. Draw conclusions and report results. All 22 sample analysis results were less than the applicable TC limits, therefore the owner concluded with at least 90 percent confidence that at least 90 percent of all possible samples of the waste would be below the TC regulatory levels. Based on the decision rule established for the study, the owner decided to manage the waste as a nonhazardous waste. 1 A summary report including a description of all planning, implementation, and assessment activities was placed in the operating record. 305 Contact ASTM For more information on ASTM or how to purchase their publications, including the standards referenced by this appendix, contact them at: ASTM, 100 Barr Harbor Drive, West Conshohocken, PA 19428 2959; telephone: 610 832 9585; World Wide Web: http:// www. astm. org. APPENDIX J SUMMARIES OF ASTM STANDARDS ASTM (the American Society for Testing and Materials) is one of the entities that can provide additional useful information on sampling. This appendix references many of the standards published by ASTM that are related to sampling.

ASTM is a not for profit organization that provides a forum for writing standards for materials, products, systems, and services. The Society develops and publishes standard test methods, specifications, practices, guides, classifications, and terminology.

Each ASTM standard is developed within the consensus principles of the Society and meets the approved requirements of its procedures. The voluntary, full consensus approach brings together people with diverse backgrounds and knowledge. The standards undergo intense round robin testing. Strict balloting and due process procedures guarantee accurate, upto date information.

To help you determine which ASTM standards may be most useful, this appendix includes text found in the scope of each standard. The standards, listed in alpha numerical order, each deal in some way with sample collection. ASTM has future plans to publish these standards together in one volume on sampling.

D 140 Standard Practice for Sampling Bituminous Materials This practice applies to the sampling of bituminous materials at points of manufacture, storage, or delivery.

D 346 Standard Practice for Collection and Preparation of Coke Samples for Laboratory Analysis This practice covers procedures for the collection and reduction of samples of coke to be used for physical tests, chemical analyses, and the determination of total moisture.

D 420 Guide to Site Characterization for Engineering, Design, and Construction Purposes This guide refers to ASTM methods by which soil, rock, and ground water conditions may be determined. The objective of the investigation should be to identify and locate, both horizontally and vertically, significant soil and rock types and ground water conditions present within a given site area and to establish the characteristics of the subsurface materials by sampling or in situ testing, or both. Appendix J 306 D 1452 Standard Practice for Soil Investigation and Sampling by Auger Borings This practice covers equipment and procedures for the use of earth augers in shallow geotechnical exploration. It does not apply to sectional continuous flight augers. This practice applies to any purpose for which disturbed samples can be used. Augers are valuable in connection with ground water level determinations, to help indicate changes in strata, and in the advancement of a hole for spoon and tube sampling.

D 1586 Standard Test Method for Penetration Test and Split Barrel Sampling of Soils This test method describes the procedure, generally known as the Standard Penetration Test, for driving a split barrel sampler. The procedure is used to obtain a representative soil sample and to measure the resistance of the soil to penetration of the sampler.

D 1587 Standard Practice for Thin Walled Tube Geotechnical Sampling of Soils This practice covers a procedure for using a thin walled metal tube to recover relatively undisturbed soil samples suitable for laboratory tests of structural properties. Thin walled tubes used in piston, plug, or rotary type samplers, such as the Denison or Pitcher sampler, should comply with the portions of this practice that describe the thin walled tubes. This practice is used when it is necessary to obtain a relatively undisturbed sample. It does not apply to liners used within the above samplers.

D 2113 Standard Practice for Diamond Core Drilling for Site Investigation This practice describes equipment and procedures for diamond core drilling to secure core samples of rock and some soils that are too hard to sample by soil sampling methods. This method is described in the context of obtaining data for foundation design and geotechnical engineering purposes rather than for mineral and mining exploration.

D 2234 Standard Practice for Collection of a Gross Sample of Coal This practice covers procedures for the collection of a gross sample of coal under various conditions of sampling. The practice describes general and special purpose sampling procedures for coals by size and condition of preparation (e. g., mechanically cleaned coal or raw coal) and by sampling characteristics. The sample is to be crushed and further prepared for analysis in accordance with ASTM Method D 2013. This practice also gives procedures for dividing large samples before any crushing.

D 3213 Standard Practices for Handling, Storing, and Preparing Soft Undisturbed Marine Soil These practices cover methods for project/ cruise reporting; and for the handling, transporting and storing of soft cohesive undisturbed marine soil. The practices also cover procedures for preparing soil specimens for triaxial strength, and procedures for consolidation testing. These practices may include the handling and transporting of sediment specimens contaminated with hazardous materials and samples subject to quarantine regulations. Appendix J 307 D 3326 Standard Practice for Preparation of Samples for Identification of Waterborne Oils This practice covers the preparation for analysis of waterborne oils recovered from water. The identification is based on the comparison of physical and chemical characteristics of the waterborne oils with oils from suspect sources. These oils may be of petroleum or vegetable/ animal origin, or both. The practice covers the following seven procedures (A through G): Procedure A, for samples of more than 50 mL volume containing significant quantities of hydrocarbons with boiling points above 280° C; Procedure B, for samples containing significant quantities of hydrocarbons with boiling points above 280° C; Procedure C, for waterborne oils containing significant amounts of components boiling below 280° C and to mixtures of these and higher boiling components; Procedure D, for samples containing both petroleum and vegetable/ animal derived oils; Procedure E, for samples of light crudes and medium distillate fuels; Procedure F, for thin films of oil on water; and Procedure G, for oil soaked samples.

D 3370 Standard Practices for Sampling Water from Closed Conduits These practices cover the equipment and methods for sampling water from closed conduits (e. g., process streams) for chemical, physical, and microbiological analyses. It provides practices for grab sampling, composite sampling, and continual sampling of closed conduits.

D 3550 Standard Practice for Ring Lined Barrel Sampling of Soils This practice covers a procedure for using a ring lined barrel sampler to obtain representative samples of soil for identification purposes and other laboratory tests. In cases in which it has been established that the quality of the sample is adequate, this practice provides shear and consolidation specimens that can be used directly in the test apparatus without prior trimming. Some types of soils may gain or lose significant shear strength or compressibility, or both, as a result of sampling. In cases like these, suitable comparison tests should be made to evaluate the effect of sample disturbance on shear strength and compressibility. This practice is not intended to be used as a penetration test; however, the force required to achieve penetration or a blow count, when driving is necessary, is recommended as supplemental information.

D 3665 Standard Practice for Random Sampling of Construction Materials This practice covers the determination of random locations (or timing) at which samples of construction materials can be taken. For the exact physical procedures for securing the sample, such as a description of the sampling tool, the number of increments needed for a sample, or the size of the sample, reference should be made to the appropriate standard method.

D 3975 Standard Practice for Development and Use (Preparation) of Samples for Collaborative Testing of Methods for Analysis of Sediments This practice establishes uniform general procedures for the development, preparation, and use of samples in the collaborative testing of methods for chemical analysis of sediments and similar materials. The principles of this practice are applicable to aqueous samples with suitable technical modifications. Appendix J 308 D 3976 Standard Practice for Preparation of Sediment Samples for Chemical Analysis This practice describes standard procedures for preparing test samples (including the removal of occluded water and moisture) of field samples collected from locations such as streams, rivers, ponds, lakes, and oceans. These procedures are applicable to the determination of volatile, semivolatile, and nonvolatile constituents of sediments.

D 3694 Standard Practices for Preparation of Sample Containers and for Preservation of Organic Constituents These practices cover the various means of (1) preparing sample containers used for collection of waters to be analyzed for organic constituents and (2) preservation of such samples from the time of sample collection until the time of analysis. The sample preservation practice depends on the specific analysis to be conducted. Preservation practices are listed with the corresponding applicable general and specific constituent test method. The preservation method for waterborne oils is given in Practice D 3325. Use of the information given will make it possible to choose the minimum number of sample preservation practices necessary to ensure the integrity of a sample designated for multiple analysis.

D 4136 Standard Practice for Sampling Phytoplankton with Water Sampling Bottles This practice covers the procedures for obtaining quantitative samples of a phytoplankton community by the use of water sampling bottles.

D 4220 Standard Practices for Preserving and Transporting Soil Samples These practices cover procedures for preserving soil samples immediately after they are obtained in the field and accompanying procedures for transporting and handling the samples. These practices are not intended to address requirements applicable to transporting of soil samples known or suspected to contain hazardous materials.

D 4342 Standard Practice for Collecting of Benthic Macroinvertebrates with Ponar Grab Sampler This practice covers the procedures for obtaining qualitative or quantitative samples of macroinvertebrates inhabiting a wide range of bottom substrate types (e. g., coarse sand, fine gravel, clay, mud, marl, and similar substrates. The Ponar grab sampler is used in freshwater lakes, rivers, estuaries, reservoirs, oceans, and similar habitats.

D 4343 Standard Practice for Collecting Benthic Macroinvertebrates with Ekman Grab Sampler This practice covers the procedures for obtaining qualitative or quantitative samples of macroinvertebrates inhabiting soft sediments. The Ekman grab sampler is used in freshwater lakes, reservoirs, and, usually, small bodies of water. Appendix J 309 D 4387 Standard Guide for Selecting Grab Sampling Devices for Collecting Benthic Macroinvertebrates This guide covers the selection of grab sampling devices for collecting benthic macroinvertebrates. Qualitative and quantitative samples of macroinvertebrates in sediments or substrates are usually taken by grab samplers. The guide discusses the advantages and limitations of the Ponar, Peterson, Ekman and other grab samplers.

D 4411 Standard Guide for Sampling Fluvial Sediment in Motion This guide covers the equipment and basic procedures for sampling to determine discharge of sediment transported by moving liquids. Equipment and procedures were originally developed to sample mineral sediments transported by rivers but they also are applicable to sampling a variety of sediments transported in open channels or closed conduits. Procedures do not apply to sediments transported by flotation. This guide does not pertain directly to sampling to determine nondischarge weighted concentrations, which in special instances are of interest. However, much of the descriptive information on sampler requirements and sediment transport phenomena is applicable in sampling for these concentrations and the guide briefly specifies suitable equipment.

D 4448 Standard Guide for Sampling Groundwater Monitoring Wells This guide covers procedures for obtaining valid representative samples from ground water monitoring wells. The scope is limited to sampling and "in the field" preservation and does not include well location, depth, well development, design and construction, screening, or analytical procedures. This guide provides a review of many of the most commonly used methods for sampling ground water quality monitoring wells and is not intended to serve as a ground water monitoring plan for any specific application. Because of the large and ever increasing number of options available, no single guide can be viewed as comprehensive. The practitioner must make every effort to ensure that the methods used, whether or not they are addressed in this guide, are adequate to satisfy the monitoring objectives at each site.

D 4489 Standard Practices for Sampling of Waterborne Oils These practices describe the procedures to be used in collecting samples of waterborne oils, oil found on adjoining shorelines, or oil soaked debris, for comparison of oils by spectroscopic and chromatographic techniques, and for elemental analyses. Two practices are described. Practice A involves "grab sampling" macro oil samples. Practice B involves sampling most types of waterborne oils and is particularly applicable in sampling thin oil films or slicks. Practice selection will be dictated by the physical characteristics and the location of the spilled oil. Specifically, the two practices are (1) Practice A, for grab sampling thick layers of oil, viscous oils or oil soaked debris, oil globules, tar balls, or stranded oil, and (2) Practice B, for TFE fluorocarbon polymer strip samplers. Each of the two practices collect oil samples with a minimum of water, thereby reducing the possibility of chemical, physical, or biological alteration by prolonged contact with water between the time of collection and analysis. Appendix J 310 D 4547 Standard Guide for Sampling Waste and Soils for Volatile Organic Compounds This guide describes recommended procedures for the collection, handling, and preparation of solid waste, soil, and sediment subsamples for subsequent determination of volatile organic compounds (VOCs). This class of compounds includes low molecular weight aromatics, hydrocarbons, halogenated hydrocarbons, ketones, acetates, nitriles, acrylates, ethers, and sulfides with boiling points below 200° C that are insoluble or slightly soluble in water. Methods of subsample collection, handling, and preparation for analysis are described. This guide does not cover the details of sampling design, laboratory preparation of containers, and the analysis of the subsamples.