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Appendix H - Data Statistics
Appendix H - Data Statistics
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A B C D E F G H I J K L
Assuming Gamma Distribution
95% Approximate Gamma UCL (use when n>=50)) 87.29 95% Adjusted Gamma UCL (use when n<50) 89.11
Adjusted Level of Significance 0.0437 Adjusted Chi Square Value 16.01
MLE Mean (bias corrected) 52.36 MLE Sd (bias corrected) 88.58
Approximate Chi Square Value (0.05) 16.34
Theta hat (MLE) 145.5 Theta star (bias corrected MLE) 149.9
nu hat (MLE) 28.07 nu star (bias corrected) 27.25
Gamma Statistics
k hat (MLE) 0.36 k star (bias corrected MLE) 0.349
5% K-S Critical Value 0.152 Data Not Gamma Distributed at 5% Significance Level
Data Not Gamma Distributed at 5% Significance Level
5% A-D Critical Value 0.844 Data Not Gamma Distributed at 5% Significance Level
K-S Test Statistic 0.288 Kolmogorov-Smirnov Gamma GOF Test
Gamma GOF Test
A-D Test Statistic 4.171 Anderson-Darling Gamma GOF Test
95% Student's-t UCL 100.5 95% Adjusted-CLT UCL (Chen-1995) 126.8
95% Modified-t UCL (Johnson-1978) 104.8
Data Not Normal at 5% Significance Level
Assuming Normal Distribution
95% Normal UCL 95% UCLs (Adjusted for Skewness)
Lilliefors Test Statistic 0.387 Lilliefors GOF Test
5% Lilliefors Critical Value 0.14 Data Not Normal at 5% Significance Level
Normal GOF Test
Shapiro Wilk Test Statistic 0.308 Shapiro Wilk GOF Test
5% Shapiro Wilk Critical Value 0.939 Data Not Normal at 5% Significance Level
Coefficient of Variation 3.403 Skewness 5.646
Maximum 1100 Median 5.6
SD 178.2 Std. Error of Mean 28.53
Number of Missing Observations 715
Minimum 1.1 Mean 52.36
General Statistics
Total Number of Observations 39 Number of Distinct Observations 35
Number of Bootstrap Operations 2000
Perfluoro-n-octanoic acid (PFOA)
From File Tindal_Soil for ProUCL_Less than 0.5_20180606.xls
Full Precision OFF
Confidence Coefficient 95%
UCL Statistics for Uncensored Full Data Sets
User Selected Options
Date/Time of Computation ProUCL 5.16/6/2018 8:52:29 AM
Coffey Appendix H - Data Statistics
RAAF Base Tindal PFAS Ecological Risk Assessment
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A B C D E F G H I J K L
5% Lilliefors Critical Value 0.0429 Data Not Normal at 5% Significance Level
Data Not Normal at 5% Significance Level
5% Shapiro Wilk P Value 0 Data Not Normal at 5% Significance Level
Lilliefors Test Statistic 0.44 Lilliefors GOF Test
Normal GOF Test
Shapiro Wilk Test Statistic 0.159 Shapiro Wilk GOF Test
SD 1409 Std. Error of Mean 67.54
Coefficient of Variation 6.647 Skewness 14.98
Minimum 0.2 Mean 211.9
Maximum 26000 Median 12
Total Number of Observations 435 Number of Distinct Observations 184
Number of Missing Observations 319
Perfluoro-n-octane sulfonic acid (PFOS)
General Statistics
Note: Suggestions regarding the selection of a 95% UCL are provided to help the user to select the most appropriate 95% UCL.
Recommendations are based upon data size, data distribution, and skewness.
These recommendations are based upon the results of the simulation studies summarized in Singh, Maichle, and Lee (2006).
However, simulations results will not cover all Real World data sets; for additional insight the user may want to consult a statistician.
Suggested UCL to Use
95% Chebyshev (Mean, Sd) UCL 176.7
90% Chebyshev(Mean, Sd) UCL 137.9 95% Chebyshev(Mean, Sd) UCL 176.7
97.5% Chebyshev(Mean, Sd) UCL 230.5 99% Chebyshev(Mean, Sd) UCL 336.2
95% Hall's Bootstrap UCL 248.7 95% Percentile Bootstrap UCL 106.3
95% BCA Bootstrap UCL 152
95% CLT UCL 99.28 95% Jackknife UCL 100.5
95% Standard Bootstrap UCL 97.78 95% Bootstrap-t UCL 242
Nonparametric Distribution Free UCL Statistics
Data do not follow a Discernible Distribution (0.05)
Nonparametric Distribution Free UCLs
95% Chebyshev (MVUE) UCL 78.77 97.5% Chebyshev (MVUE) UCL 99.59
99% Chebyshev (MVUE) UCL 140.5
Assuming Lognormal Distribution
95% H-UCL 81.11 90% Chebyshev (MVUE) UCL 63.78
Maximum of Logged Data 7.003 SD of logged Data 1.676
Lognormal Statistics
Minimum of Logged Data 0.0953 Mean of logged Data 2.098
5% Lilliefors Critical Value 0.14 Data Not Lognormal at 5% Significance Level
Data Not Lognormal at 5% Significance Level
5% Shapiro Wilk Critical Value 0.939 Data Not Lognormal at 5% Significance Level
Lilliefors Test Statistic 0.171 Lilliefors Lognormal GOF Test
Lognormal GOF Test
Shapiro Wilk Test Statistic 0.894 Shapiro Wilk Lognormal GOF Test
Coffey Appendix H - Data Statistics
RAAF Base Tindal PFAS Ecological Risk Assessment
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A B C D E F G H I J K L
Note: Suggestions regarding the selection of a 95% UCL are provided to help the user to select the most appropriate 95% UCL.
Recommendations are based upon data size, data distribution, and skewness.
These recommendations are based upon the results of the simulation studies summarized in Singh, Maichle, and Lee (2006).
However, simulations results will not cover all Real World data sets; for additional insight the user may want to consult a statistician.
Suggested UCL to Use
95% Chebyshev (Mean, Sd) UCL 506.3
90% Chebyshev(Mean, Sd) UCL 414.6 95% Chebyshev(Mean, Sd) UCL 506.3
97.5% Chebyshev(Mean, Sd) UCL 633.7 99% Chebyshev(Mean, Sd) UCL 884
95% Hall's Bootstrap UCL 720.8 95% Percentile Bootstrap UCL 328
95% BCA Bootstrap UCL 397.9
95% CLT UCL 323 95% Jackknife UCL 323.3
95% Standard Bootstrap UCL 322.9 95% Bootstrap-t UCL 473.1
Nonparametric Distribution Free UCL Statistics
Data do not follow a Discernible Distribution (0.05)
Nonparametric Distribution Free UCLs
95% Chebyshev (MVUE) UCL 254.1 97.5% Chebyshev (MVUE) UCL 304.6
99% Chebyshev (MVUE) UCL 403.9
Assuming Lognormal Distribution
95% H-UCL 200.9 90% Chebyshev (MVUE) UCL 217.6
Maximum of Logged Data 10.17 SD of logged Data 2.242
Lognormal Statistics
Minimum of Logged Data -1.609 Mean of logged Data 2.428
5% Lilliefors Critical Value 0.0429 Data Not Lognormal at 5% Significance Level
Data Not Lognormal at 5% Significance Level
5% Shapiro Wilk P Value 3.1859E-9 Data Not Lognormal at 5% Significance Level
Lilliefors Test Statistic 0.0612 Lilliefors Lognormal GOF Test
Lognormal GOF Test
Shapiro Wilk Test Statistic 0.962 Shapiro Wilk Lognormal GOF Test
Assuming Gamma Distribution
95% Approximate Gamma UCL (use when n>=50)) 250.6 95% Adjusted Gamma UCL (use when n<50) 250.7
Adjusted Level of Significance 0.0494 Adjusted Chi Square Value 179
MLE Mean (bias corrected) 211.9 MLE Sd (bias corrected) 429.5
Approximate Chi Square Value (0.05) 179.1
Theta hat (MLE) 870 Theta star (bias corrected MLE) 870.5
nu hat (MLE) 211.9 nu star (bias corrected) 211.8
Data Not Gamma Distributed at 5% Significance Level
Gamma Statistics
k hat (MLE) 0.244 k star (bias corrected MLE) 0.243
K-S Test Statistic 0.238 Kolmogorov-Smirnov Gamma GOF Test
5% K-S Critical Value 0.0479 Data Not Gamma Distributed at 5% Significance Level
Gamma GOF Test
A-D Test Statistic 41.54 Anderson-Darling Gamma GOF Test
5% A-D Critical Value 0.899 Data Not Gamma Distributed at 5% Significance Level
95% Modified-t UCL (Johnson-1978) 331.4
Assuming Normal Distribution
95% Normal UCL 95% UCLs (Adjusted for Skewness)
95% Student's-t UCL 323.3 95% Adjusted-CLT UCL (Chen-1995) 374.9
Coffey Appendix H - Data Statistics
RAAF Base Tindal PFAS Ecological Risk Assessment
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A B C D E F G H I J K L
5% Lilliefors Critical Value 0.234 Data appear Lognormal at 5% Significance Level
Data appear Lognormal at 5% Significance Level
5% Shapiro Wilk Critical Value 0.866 Data appear Lognormal at 5% Significance Level
Lilliefors Test Statistic 0.196 Lilliefors Lognormal GOF Test
Lognormal GOF Test
Shapiro Wilk Test Statistic 0.915 Shapiro Wilk Lognormal GOF Test
Assuming Gamma Distribution
95% Approximate Gamma UCL (use when n>=50)) 108.3 95% Adjusted Gamma UCL (use when n<50) 121.9
Adjusted Level of Significance 0.0301 Adjusted Chi Square Value 5.416
MLE Mean (bias corrected) 49.63 MLE Sd (bias corrected) 69.39
Approximate Chi Square Value (0.05) 6.097
Theta hat (MLE) 82.93 Theta star (bias corrected MLE) 97.01
nu hat (MLE) 15.56 nu star (bias corrected) 13.3
Gamma Statistics
k hat (MLE) 0.598 k star (bias corrected MLE) 0.512
5% K-S Critical Value 0.248 Detected data appear Gamma Distributed at 5% Significance Level
Detected data appear Gamma Distributed at 5% Significance Level
5% A-D Critical Value 0.782 Detected data appear Gamma Distributed at 5% Significance Level
K-S Test Statistic 0.208 Kolmogorov-Smirnov Gamma GOF Test
Gamma GOF Test
A-D Test Statistic 0.446 Anderson-Darling Gamma GOF Test
95% Student's-t UCL 78.53 95% Adjusted-CLT UCL (Chen-1995) 82.15
95% Modified-t UCL (Johnson-1978) 79.44
Data appear Approximate Normal at 5% Significance Level
Assuming Normal Distribution
95% Normal UCL 95% UCLs (Adjusted for Skewness)
Lilliefors Test Statistic 0.227 Lilliefors GOF Test
5% Lilliefors Critical Value 0.234 Data appear Normal at 5% Significance Level
Normal GOF Test
Shapiro Wilk Test Statistic 0.821 Shapiro Wilk GOF Test
5% Shapiro Wilk Critical Value 0.866 Data Not Normal at 5% Significance Level
Coefficient of Variation 1.178 Skewness 1.217
Maximum 180 Median 22
SD 58.46 Std. Error of Mean 16.21
Number of Missing Observations 58
Minimum 1.2 Mean 49.63
General Statistics
Total Number of Observations 13 Number of Distinct Observations 13
Number of Bootstrap Operations 2000
Perfluoro-n-octanoic acid (PFOA) (fire station)
From File Tindal_Soil for ProUCL_Less than 0.5_20180606.xls
Full Precision OFF
Confidence Coefficient 95%
UCL Statistics for Uncensored Full Data Sets
User Selected Options
Date/Time of Computation ProUCL 5.16/6/2018 8:49:59 AM
Coffey Appendix H - Data Statistics
RAAF Base Tindal PFAS Ecological Risk Assessment
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A B C D E F G H I J K L
95% Student's-t UCL 136.5 95% Adjusted-CLT UCL (Chen-1995) 180.7
95% Modified-t UCL (Johnson-1978) 143.9
Data Not Normal at 5% Significance Level
Assuming Normal Distribution
95% Normal UCL 95% UCLs (Adjusted for Skewness)
Lilliefors Test Statistic 0.489 Lilliefors GOF Test
5% Lilliefors Critical Value 0.177 Data Not Normal at 5% Significance Level
Normal GOF Test
Shapiro Wilk Test Statistic 0.268 Shapiro Wilk GOF Test
5% Shapiro Wilk Critical Value 0.916 Data Not Normal at 5% Significance Level
Coefficient of Variation 3.87 Skewness 4.735
Maximum 1100 Median 5.05
SD 224.5 Std. Error of Mean 45.83
Number of Missing Observations 40
Minimum 1.1 Mean 58.01
Perfluoro-n-octanoic acid (PFOA) (fire training area)
General Statistics
Total Number of Observations 24 Number of Distinct Observations 22
Recommendations are based upon data size, data distribution, and skewness.
These recommendations are based upon the results of the simulation studies summarized in Singh, Maichle, and Lee (2006).
However, simulations results will not cover all Real World data sets; for additional insight the user may want to consult a statistician.
When a data set follows an approximate (e.g., normal) distribution passing one of the GOF test
When applicable, it is suggested to use a UCL based upon a distribution (e.g., gamma) passing both GOF tests in ProUCL
Note: Suggestions regarding the selection of a 95% UCL are provided to help the user to select the most appropriate 95% UCL.
Suggested UCL to Use
95% Student's-t UCL 78.53
90% Chebyshev(Mean, Sd) UCL 98.27 95% Chebyshev(Mean, Sd) UCL 120.3
97.5% Chebyshev(Mean, Sd) UCL 150.9 99% Chebyshev(Mean, Sd) UCL 211
95% Hall's Bootstrap UCL 87.77 95% Percentile Bootstrap UCL 75.34
95% BCA Bootstrap UCL 81.66
95% CLT UCL 76.3 95% Jackknife UCL 78.53
95% Standard Bootstrap UCL 74.97 95% Bootstrap-t UCL 91.13
Nonparametric Distribution Free UCL Statistics
Data appear to follow a Discernible Distribution at 5% Significance Level
Nonparametric Distribution Free UCLs
95% Chebyshev (MVUE) UCL 217.1 97.5% Chebyshev (MVUE) UCL 283.1
99% Chebyshev (MVUE) UCL 412.6
Assuming Lognormal Distribution
95% H-UCL 692.2 90% Chebyshev (MVUE) UCL 169.6
Maximum of Logged Data 5.193 SD of logged Data 1.75
Lognormal Statistics
Minimum of Logged Data 0.182 Mean of logged Data 2.872
Coffey Appendix H - Data Statistics
RAAF Base Tindal PFAS Ecological Risk Assessment
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A B C D E F G H I J K L
Note: Suggestions regarding the selection of a 95% UCL are provided to help the user to select the most appropriate 95% UCL.
Recommendations are based upon data size, data distribution, and skewness.
These recommendations are based upon the results of the simulation studies summarized in Singh, Maichle, and Lee (2006).
However, simulations results will not cover all Real World data sets; for additional insight the user may want to consult a statistician.
Suggested UCL to Use
95% Chebyshev (Mean, Sd) UCL 257.8
90% Chebyshev(Mean, Sd) UCL 195.5 95% Chebyshev(Mean, Sd) UCL 257.8
97.5% Chebyshev(Mean, Sd) UCL 344.2 99% Chebyshev(Mean, Sd) UCL 514
95% Hall's Bootstrap UCL 1105 95% Percentile Bootstrap UCL 144.7
95% BCA Bootstrap UCL 234.6
95% CLT UCL 133.4 95% Jackknife UCL 136.5
95% Standard Bootstrap UCL 133.5 95% Bootstrap-t UCL 2838
Nonparametric Distribution Free UCL Statistics
Data do not follow a Discernible Distribution (0.05)
Nonparametric Distribution Free UCLs
95% Chebyshev (MVUE) UCL 49.26 97.5% Chebyshev (MVUE) UCL 62.68
99% Chebyshev (MVUE) UCL 89.06
Assuming Lognormal Distribution
95% H-UCL 59.4 90% Chebyshev (MVUE) UCL 39.58
Maximum of Logged Data 7.003 SD of logged Data 1.55
Lognormal Statistics
Minimum of Logged Data 0.0953 Mean of logged Data 1.799
5% Lilliefors Critical Value 0.177 Data Not Lognormal at 5% Significance Level
Data Not Lognormal at 5% Significance Level
5% Shapiro Wilk Critical Value 0.916 Data Not Lognormal at 5% Significance Level
Lilliefors Test Statistic 0.193 Lilliefors Lognormal GOF Test
Lognormal GOF Test
Shapiro Wilk Test Statistic 0.797 Shapiro Wilk Lognormal GOF Test
Assuming Gamma Distribution
95% Approximate Gamma UCL (use when n>=50)) 123.1 95% Adjusted Gamma UCL (use when n<50) 130.2
Adjusted Level of Significance 0.0392 Adjusted Chi Square Value 6.289
MLE Mean (bias corrected) 58.01 MLE Sd (bias corrected) 107
Approximate Chi Square Value (0.05) 6.647
Theta hat (MLE) 190.7 Theta star (bias corrected MLE) 197.3
nu hat (MLE) 14.6 nu star (bias corrected) 14.11
Gamma Statistics
k hat (MLE) 0.304 k star (bias corrected MLE) 0.294
5% K-S Critical Value 0.193 Data Not Gamma Distributed at 5% Significance Level
Data Not Gamma Distributed at 5% Significance Level
5% A-D Critical Value 0.85 Data Not Gamma Distributed at 5% Significance Level
K-S Test Statistic 0.393 Kolmogorov-Smirnov Gamma GOF Test
Gamma GOF Test
A-D Test Statistic 4.708 Anderson-Darling Gamma GOF TestCoffey Appendix H - Data Statistics
RAAF Base Tindal PFAS Ecological Risk Assessment
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A B C D E F G H I J K L
95% Student's-t UCL 1497 95% Adjusted-CLT UCL (Chen-1995) 1839
95% Modified-t UCL (Johnson-1978) 1552
Data Not Normal at 5% Significance Level
Assuming Normal Distribution
95% Normal UCL 95% UCLs (Adjusted for Skewness)
Lilliefors Test Statistic 0.401 Lilliefors GOF Test
5% Lilliefors Critical Value 0.107 Data Not Normal at 5% Significance Level
Normal GOF Test
Shapiro Wilk Test Statistic 0.276 Shapiro Wilk GOF Test
5% Shapiro Wilk P Value 0 Data Not Normal at 5% Significance Level
Coefficient of Variation 3.948 Skewness 6.876
Maximum 26000 Median 69
SD 3297 Std. Error of Mean 396.9
Number of Missing Observations 2
Minimum 5.3 Mean 834.9
General Statistics
Total Number of Observations 69 Number of Distinct Observations 57
If possible, compute and collect Data Quality Objectives (DQO) based sample size and analytical results.
Perfluoro-n-octane sulfonic acid (PFOS) (fire station)
Warning: This data set only has 2 observations!
Data set is too small to compute reliable and meaningful statistics and estimates!
The data set for variable Perfluoro-n-octanoic acid (PFOA) (offbase) was not processed!
It is suggested to collect at least 8 to 10 observations before using these statistical methods!
Maximum 3.4 Median 2.25
Number of Missing Observations 193
Minimum 1.1 Mean 2.25
Perfluoro-n-octanoic acid (PFOA) (offbase)
General Statistics
Total Number of Observations 2 Number of Distinct Observations 2
It is suggested to collect at least 8 to 10 observations before using these statistical methods!
If possible, compute and collect Data Quality Objectives (DQO) based sample size and analytical results.
Warning: This data set only has 0 observations!
Data set is too small to compute reliable and meaningful statistics and estimates!
The data set for variable Perfluoro-n-octanoic acid (PFOA) (non-source area) was not processed!
Minimum N/A Mean N/A
Maximum N/A Median N/A
Total Number of Observations 0 Number of Distinct Observations 0
Number of Missing Observations 424
Perfluoro-n-octanoic acid (PFOA) (non-source area)
General Statistics
Coffey Appendix H - Data Statistics
RAAF Base Tindal PFAS Ecological Risk Assessment
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ProUCL computes and outputs H-statistic based UCLs for historical reasons only.
H-statistic often results in unstable (both high and low) values of UCL95 as shown in examples in the Technical Guide.
It is therefore recommended to avoid the use of H-statistic based 95% UCLs.
Use of nonparametric methods are preferred to compute UCL95 for skewed data sets which do not follow a gamma distribution.
Note: Suggestions regarding the selection of a 95% UCL are provided to help the user to select the most appropriate 95% UCL.
Recommendations are based upon data size, data distribution, and skewness.
These recommendations are based upon the results of the simulation studies summarized in Singh, Maichle, and Lee (2006).
However, simulations results will not cover all Real World data sets; for additional insight the user may want to consult a statistician.
Suggested UCL to Use
95% H-UCL 1045
90% Chebyshev(Mean, Sd) UCL 2026 95% Chebyshev(Mean, Sd) UCL 2565
97.5% Chebyshev(Mean, Sd) UCL 3313 99% Chebyshev(Mean, Sd) UCL 4784
95% Hall's Bootstrap UCL 3523 95% Percentile Bootstrap UCL 1566
95% BCA Bootstrap UCL 2099
95% CLT UCL 1488 95% Jackknife UCL 1497
95% Standard Bootstrap UCL 1473 95% Bootstrap-t UCL 3067
Nonparametric Distribution Free UCL Statistics
Data appear to follow a Discernible Distribution at 5% Significance Level
Nonparametric Distribution Free UCLs
95% Chebyshev (MVUE) UCL 1273 97.5% Chebyshev (MVUE) UCL 1602
99% Chebyshev (MVUE) UCL 2249
Assuming Lognormal Distribution
95% H-UCL 1045 90% Chebyshev (MVUE) UCL 1036
Maximum of Logged Data 10.17 SD of logged Data 1.9
Lognormal Statistics
Minimum of Logged Data 1.668 Mean of logged Data 4.501
5% Lilliefors Critical Value 0.107 Data appear Lognormal at 5% Significance Level
Data appear Approximate Lognormal at 5% Significance Level
5% Shapiro Wilk P Value 0.00576 Data Not Lognormal at 5% Significance Level
Lilliefors Test Statistic 0.0794 Lilliefors Lognormal GOF Test
Lognormal GOF Test
Shapiro Wilk Test Statistic 0.942 Shapiro Wilk Lognormal GOF Test
Assuming Gamma Distribution
95% Approximate Gamma UCL (use when n>=50)) 1246 95% Adjusted Gamma UCL (use when n<50) 1257
Adjusted Level of Significance 0.0465 Adjusted Chi Square Value 27.93
MLE Mean (bias corrected) 834.9 MLE Sd (bias corrected) 1513
Approximate Chi Square Value (0.05) 28.18
Theta hat (MLE) 2708 Theta star (bias corrected MLE) 2741
nu hat (MLE) 42.56 nu star (bias corrected) 42.04
Gamma Statistics
k hat (MLE) 0.308 k star (bias corrected MLE) 0.305
5% K-S Critical Value 0.116 Data Not Gamma Distributed at 5% Significance Level
Data Not Gamma Distributed at 5% Significance Level
5% A-D Critical Value 0.863 Data Not Gamma Distributed at 5% Significance Level
K-S Test Statistic 0.242 Kolmogorov-Smirnov Gamma GOF Test
Gamma GOF Test
A-D Test Statistic 6.337 Anderson-Darling Gamma GOF TestCoffey Appendix H - Data Statistics
RAAF Base Tindal PFAS Ecological Risk Assessment
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A B C D E F G H I J K L
95% Chebyshev (MVUE) UCL 964.8 97.5% Chebyshev (MVUE) UCL 1198
99% Chebyshev (MVUE) UCL 1657
Assuming Lognormal Distribution
95% H-UCL 779.1 90% Chebyshev (MVUE) UCL 796.7
Maximum of Logged Data 8.882 SD of logged Data 1.65
Lognormal Statistics
Minimum of Logged Data 1.974 Mean of logged Data 4.74
5% Lilliefors Critical Value 0.111 Data Not Lognormal at 5% Significance Level
Data Not Lognormal at 5% Significance Level
5% Shapiro Wilk P Value 0.00784 Data Not Lognormal at 5% Significance Level
Lilliefors Test Statistic 0.123 Lilliefors Lognormal GOF Test
Lognormal GOF Test
Shapiro Wilk Test Statistic 0.941 Shapiro Wilk Lognormal GOF Test
Assuming Gamma Distribution
95% Approximate Gamma UCL (use when n>=50)) 684.9 95% Adjusted Gamma UCL (use when n<50) 690.5
Adjusted Level of Significance 0.0462 Adjusted Chi Square Value 38.67
MLE Mean (bias corrected) 485.2 MLE Sd (bias corrected) 734.1
Approximate Chi Square Value (0.05) 38.99
Theta hat (MLE) 1084 Theta star (bias corrected MLE) 1111
nu hat (MLE) 56.39 nu star (bias corrected) 55.04
Data Not Gamma Distributed at 5% Significance Level
Gamma Statistics
k hat (MLE) 0.448 k star (bias corrected MLE) 0.437
K-S Test Statistic 0.209 Kolmogorov-Smirnov Gamma GOF Test
5% K-S Critical Value 0.12 Data Not Gamma Distributed at 5% Significance Level
Gamma GOF Test
A-D Test Statistic 3.583 Anderson-Darling Gamma GOF Test
5% A-D Critical Value 0.829 Data Not Gamma Distributed at 5% Significance Level
95% Modified-t UCL (Johnson-1978) 735
Assuming Normal Distribution
95% Normal UCL 95% UCLs (Adjusted for Skewness)
95% Student's-t UCL 722.2 95% Adjusted-CLT UCL (Chen-1995) 801
5% Lilliefors Critical Value 0.111 Data Not Normal at 5% Significance Level
Data Not Normal at 5% Significance Level
5% Shapiro Wilk P Value 0 Data Not Normal at 5% Significance Level
Lilliefors Test Statistic 0.336 Lilliefors GOF Test
Normal GOF Test
Shapiro Wilk Test Statistic 0.469 Shapiro Wilk GOF Test
SD 1127 Std. Error of Mean 141.9
Coefficient of Variation 2.322 Skewness 4.311
Minimum 7.2 Mean 485.2
Maximum 7200 Median 81
Total Number of Observations 63 Number of Distinct Observations 53
Number of Missing Observations 1
Perfluoro-n-octane sulfonic acid (PFOS) (fire training area)
General Statistics
Coffey Appendix H - Data Statistics
RAAF Base Tindal PFAS Ecological Risk Assessment
336
337
338
339
340
341
342
343
344
345
346
347
348
349
350
351
352
353
354
355
356
357
358
359
360
361
362
363
364
365
366
367
368
369
370
371
372
373
374
375
376
377
378
379
380
381
382
383
384
385
386
387
388
389
390
391
392
A B C D E F G H I J K L
Adjusted Level of Significance 0.0489 Adjusted Chi Square Value 178.6
MLE Mean (bias corrected) 9.918 MLE Sd (bias corrected) 14.31
Approximate Chi Square Value (0.05) 178.8
Theta hat (MLE) 20.49 Theta star (bias corrected MLE) 20.64
nu hat (MLE) 213 nu star (bias corrected) 211.4
Data Not Gamma Distributed at 5% Significance Level
Gamma Statistics
k hat (MLE) 0.484 k star (bias corrected MLE) 0.481
K-S Test Statistic 0.158 Kolmogorov-Smirnov Gamma GOF Test
5% K-S Critical Value 0.065 Data Not Gamma Distributed at 5% Significance Level
Gamma GOF Test
A-D Test Statistic 7.721 Anderson-Darling Gamma GOF Test
5% A-D Critical Value 0.825 Data Not Gamma Distributed at 5% Significance Level
95% Modified-t UCL (Johnson-1978) 12.08
Assuming Normal Distribution
95% Normal UCL 95% UCLs (Adjusted for Skewness)
95% Student's-t UCL 12.03 95% Adjusted-CLT UCL (Chen-1995) 12.33
5% Lilliefors Critical Value 0.0602 Data Not Normal at 5% Significance Level
Data Not Normal at 5% Significance Level
5% Shapiro Wilk P Value 0 Data Not Normal at 5% Significance Level
Lilliefors Test Statistic 0.304 Lilliefors GOF Test
Normal GOF Test
Shapiro Wilk Test Statistic 0.553 Shapiro Wilk GOF Test
SD 18.92 Std. Error of Mean 1.276
Coefficient of Variation 1.908 Skewness 3.435
Minimum 0.2 Mean 9.918
Maximum 120 Median 2
Total Number of Observations 220 Number of Distinct Observations 95
Number of Missing Observations 204
Perfluoro-n-octane sulfonic acid (PFOS) (non-source area)
General Statistics
Note: Suggestions regarding the selection of a 95% UCL are provided to help the user to select the most appropriate 95% UCL.
Recommendations are based upon data size, data distribution, and skewness.
These recommendations are based upon the results of the simulation studies summarized in Singh, Maichle, and Lee (2006).
However, simulations results will not cover all Real World data sets; for additional insight the user may want to consult a statistician.
Suggested UCL to Use
95% Chebyshev (Mean, Sd) UCL 1104
90% Chebyshev(Mean, Sd) UCL 911 95% Chebyshev(Mean, Sd) UCL 1104
97.5% Chebyshev(Mean, Sd) UCL 1372 99% Chebyshev(Mean, Sd) UCL 1897
95% Hall's Bootstrap UCL 1503 95% Percentile Bootstrap UCL 736.1
95% BCA Bootstrap UCL 816.5
95% CLT UCL 718.6 95% Jackknife UCL 722.2
95% Standard Bootstrap UCL 716.1 95% Bootstrap-t UCL 884.7
Nonparametric Distribution Free UCL Statistics
Data do not follow a Discernible Distribution (0.05)
Nonparametric Distribution Free UCLs
Coffey Appendix H - Data Statistics
RAAF Base Tindal PFAS Ecological Risk Assessment
393
394
395
396
397
398
399
400
401
402
403
404
405
406
407
408
409
410
411
412
413
414
415
416
417
418
419
420
421
422
423
424
425
426
427
428
429
430
431
432
433
434
435
436
437
438
439
440
441
442
443
444
445
446
447
448
449
A B C D E F G H I J K L
5% Lilliefors Critical Value 0.0974 Data Not Normal at 5% Significance Level
Data Not Normal at 5% Significance Level
5% Shapiro Wilk P Value 0 Data Not Normal at 5% Significance Level
Lilliefors Test Statistic 0.235 Lilliefors GOF Test
Normal GOF Test
Shapiro Wilk Test Statistic 0.717 Shapiro Wilk GOF Test
SD 20.7 Std. Error of Mean 2.272
Coefficient of Variation 0.939 Skewness 2.444
Minimum 5.3 Mean 22.06
Maximum 120 Median 15
Total Number of Observations 83 Number of Distinct Observations 53
Number of Missing Observations 112
Perfluoro-n-octane sulfonic acid (PFOS) (offbase)
General Statistics
Note: Suggestions regarding the selection of a 95% UCL are provided to help the user to select the most appropriate 95% UCL.
Recommendations are based upon data size, data distribution, and skewness.
These recommendations are based upon the results of the simulation studies summarized in Singh, Maichle, and Lee (2006).
However, simulations results will not cover all Real World data sets; for additional insight the user may want to consult a statistician.
Suggested UCL to Use
95% Chebyshev (Mean, Sd) UCL 15.48
90% Chebyshev(Mean, Sd) UCL 13.75 95% Chebyshev(Mean, Sd) UCL 15.48
97.5% Chebyshev(Mean, Sd) UCL 17.89 99% Chebyshev(Mean, Sd) UCL 22.61
95% Hall's Bootstrap UCL 12.27 95% Percentile Bootstrap UCL 12.05
95% BCA Bootstrap UCL 12.27
95% CLT UCL 12.02 95% Jackknife UCL 12.03
95% Standard Bootstrap UCL 12.02 95% Bootstrap-t UCL 12.59
Nonparametric Distribution Free UCL Statistics
Data do not follow a Discernible Distribution (0.05)
Nonparametric Distribution Free UCLs
95% Chebyshev (MVUE) UCL 18.55 97.5% Chebyshev (MVUE) UCL 21.97
99% Chebyshev (MVUE) UCL 28.68
Assuming Lognormal Distribution
95% H-UCL 14.86 90% Chebyshev (MVUE) UCL 16.09
Maximum of Logged Data 4.787 SD of logged Data 1.677
Lognormal Statistics
Minimum of Logged Data -1.609 Mean of logged Data 0.976
5% Lilliefors Critical Value 0.0602 Data Not Lognormal at 5% Significance Level
Data Not Lognormal at 5% Significance Level
5% Shapiro Wilk P Value 7.421E-12 Data Not Lognormal at 5% Significance Level
Lilliefors Test Statistic 0.0924 Lilliefors Lognormal GOF Test
Lognormal GOF Test
Shapiro Wilk Test Statistic 0.936 Shapiro Wilk Lognormal GOF Test
Assuming Gamma Distribution
95% Approximate Gamma UCL (use when n>=50)) 11.73 95% Adjusted Gamma UCL (use when n<50) 11.74
Coffey Appendix H - Data Statistics
RAAF Base Tindal PFAS Ecological Risk Assessment
450
451
452
453
454
455
456
457
458
459
460
461
462
463
464
465
466
467
468
469
470
471
472
473
474
475
476
477
478
479
480
481
482
483
484
485
486
487
488
489
490
491
492
493
494
495
496
497
498
499
500
501
502
503
504
505
506
A B C D E F G H I J K L
Note: Suggestions regarding the selection of a 95% UCL are provided to help the user to select the most appropriate 95% UCL.
Recommendations are based upon data size, data distribution, and skewness.
These recommendations are based upon the results of the simulation studies summarized in Singh, Maichle, and Lee (2006).
However, simulations results will not cover all Real World data sets; for additional insight the user may want to consult a statistician.
Suggested UCL to Use
95% Chebyshev (Mean, Sd) UCL 31.96
90% Chebyshev(Mean, Sd) UCL 28.87 95% Chebyshev(Mean, Sd) UCL 31.96
97.5% Chebyshev(Mean, Sd) UCL 36.25 99% Chebyshev(Mean, Sd) UCL 44.67
95% Hall's Bootstrap UCL 26.64 95% Percentile Bootstrap UCL 26.03
95% BCA Bootstrap UCL 26.47
95% CLT UCL 25.8 95% Jackknife UCL 25.84
95% Standard Bootstrap UCL 25.74 95% Bootstrap-t UCL 26.76
Nonparametric Distribution Free UCL Statistics
Data do not follow a Discernible Distribution (0.05)
Nonparametric Distribution Free UCLs
95% Chebyshev (MVUE) UCL 29.39 97.5% Chebyshev (MVUE) UCL 32.91
99% Chebyshev (MVUE) UCL 39.82
Assuming Lognormal Distribution
95% H-UCL 25.06 90% Chebyshev (MVUE) UCL 26.86
Maximum of Logged Data 4.787 SD of logged Data 0.721
Lognormal Statistics
Minimum of Logged Data 1.668 Mean of logged Data 2.801
5% Lilliefors Critical Value 0.0974 Data Not Lognormal at 5% Significance Level
Data Not Lognormal at 5% Significance Level
5% Shapiro Wilk P Value 5.4195E-4 Data Not Lognormal at 5% Significance Level
Lilliefors Test Statistic 0.13 Lilliefors Lognormal GOF Test
Lognormal GOF Test
Shapiro Wilk Test Statistic 0.936 Shapiro Wilk Lognormal GOF Test
Assuming Gamma Distribution
95% Approximate Gamma UCL (use when n>=50)) 25.38 95% Adjusted Gamma UCL (use when n<50) 25.44
Adjusted Level of Significance 0.0471 Adjusted Chi Square Value 258.7
MLE Mean (bias corrected) 22.06 MLE Sd (bias corrected) 16.45
Approximate Chi Square Value (0.05) 259.3
Theta hat (MLE) 11.88 Theta star (bias corrected MLE) 12.27
nu hat (MLE) 308.1 nu star (bias corrected) 298.3
Data Not Gamma Distributed at 5% Significance Level
Gamma Statistics
k hat (MLE) 1.856 k star (bias corrected MLE) 1.797
K-S Test Statistic 0.179 Kolmogorov-Smirnov Gamma GOF Test
5% K-S Critical Value 0.0995 Data Not Gamma Distributed at 5% Significance Level
Gamma GOF Test
A-D Test Statistic 2.841 Anderson-Darling Gamma GOF Test
5% A-D Critical Value 0.766 Data Not Gamma Distributed at 5% Significance Level
95% Modified-t UCL (Johnson-1978) 25.94
Assuming Normal Distribution
95% Normal UCL 95% UCLs (Adjusted for Skewness)
95% Student's-t UCL 25.84 95% Adjusted-CLT UCL (Chen-1995) 26.45
Coffey Appendix H - Data Statistics
RAAF Base Tindal PFAS Ecological Risk Assessment
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43
44
45
46
47
48
49
50
51
52
53
54
55
A B C D E F G H I J K L
5% K-S Critical Value 0.156 Data Not Gamma Distributed at 5% Significance Level
Data Not Gamma Distributed at 5% Significance Level
5% A-D Critical Value 0.843 Data Not Gamma Distributed at 5% Significance Level
K-S Test Statistic 0.282 Kolmogorov-Smirnov Gamma GOF Test
Gamma GOF Test
A-D Test Statistic 3.819 Anderson-Darling Gamma GOF Test
95% Student's-t UCL 105.8 95% Adjusted-CLT UCL (Chen-1995) 133.5
95% Modified-t UCL (Johnson-1978) 110.3
Data Not Normal at 5% Significance Level
Assuming Normal Distribution
95% Normal UCL 95% UCLs (Adjusted for Skewness)
Lilliefors Test Statistic 0.384 Lilliefors GOF Test
5% Lilliefors Critical Value 0.144 Data Not Normal at 5% Significance Level
Normal GOF Test
Shapiro Wilk Test Statistic 0.315 Shapiro Wilk GOF Test
5% Shapiro Wilk Critical Value 0.936 Data Not Normal at 5% Significance Level
Coefficient of Variation 3.317 Skewness 5.502
Maximum 1100 Median 6.3
SD 182.6 Std. Error of Mean 30.03
Number of Missing Observations 522
Minimum 1.1 Mean 55.06
General Statistics
Total Number of Observations 37 Number of Distinct Observations 34
If possible, compute and collect Data Quality Objectives (DQO) based sample size and analytical results.
Perfluoro-n-octanoic acid (PFOA) (onbase)
Warning: This data set only has 2 observations!
Data set is too small to compute reliable and meaningful statistics and estimates!
The data set for variable Perfluoro-n-octanoic acid (PFOA) (offbase) was not processed!
It is suggested to collect at least 8 to 10 observations before using these statistical methods!
Maximum 3.4 Median 2.25
Number of Missing Observations 193
Minimum 1.1 Mean 2.25
General Statistics
Total Number of Observations 2 Number of Distinct Observations 2
Number of Bootstrap Operations 2000
Perfluoro-n-octanoic acid (PFOA) (offbase)
From File Data_Tindal_Soil for ProUCL_Less than 0.5_20180606.xls
Full Precision OFF
Confidence Coefficient 95%
UCL Statistics for Uncensored Full Data Sets
User Selected Options
Date/Time of Computation ProUCL 5.16/7/2018 1:17:44 PM
Coffey Appendix H - Data Statistics
RAAF Base Tindal PFAS Ecological Risk Assessment
56
57
58
59
60
61
62
63
64
65
66
67
68
69
70
71
72
73
74
75
76
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80
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95
96
97
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99
100
101
102
103
104
105
106
107
108
109
110
111
112
A B C D E F G H I J K L
SD 20.7 Std. Error of Mean 2.272
Coefficient of Variation 0.939 Skewness 2.444
Minimum 5.3 Mean 22.06
Maximum 120 Median 15
Total Number of Observations 83 Number of Distinct Observations 53
Number of Missing Observations 112
Perfluoro-n-octane sulfonic acid (PFOS) (offbase)
General Statistics
Note: Suggestions regarding the selection of a 95% UCL are provided to help the user to select the most appropriate 95% UCL.
Recommendations are based upon data size, data distribution, and skewness.
These recommendations are based upon the results of the simulation studies summarized in Singh, Maichle, and Lee (2006).
However, simulations results will not cover all Real World data sets; for additional insight the user may want to consult a statistician.
Suggested UCL to Use
95% Chebyshev (Mean, Sd) UCL 185.9
90% Chebyshev(Mean, Sd) UCL 145.1 95% Chebyshev(Mean, Sd) UCL 185.9
97.5% Chebyshev(Mean, Sd) UCL 242.6 99% Chebyshev(Mean, Sd) UCL 353.8
95% Hall's Bootstrap UCL 260.9 95% Percentile Bootstrap UCL 111.3
95% BCA Bootstrap UCL 145.6
95% CLT UCL 104.5 95% Jackknife UCL 105.8
95% Standard Bootstrap UCL 103.8 95% Bootstrap-t UCL 243.8
Nonparametric Distribution Free UCL Statistics
Data do not follow a Discernible Distribution (0.05)
Nonparametric Distribution Free UCLs
95% Chebyshev (MVUE) UCL 86.73 97.5% Chebyshev (MVUE) UCL 109.9
99% Chebyshev (MVUE) UCL 155.3
Assuming Lognormal Distribution
95% H-UCL 90.44 90% Chebyshev (MVUE) UCL 70.07
Maximum of Logged Data 7.003 SD of logged Data 1.681
Lognormal Statistics
Minimum of Logged Data 0.0953 Mean of logged Data 2.176
5% Lilliefors Critical Value 0.144 Data Not Lognormal at 5% Significance Level
Data Not Lognormal at 5% Significance Level
5% Shapiro Wilk Critical Value 0.936 Data Not Lognormal at 5% Significance Level
Lilliefors Test Statistic 0.173 Lilliefors Lognormal GOF Test
Lognormal GOF Test
Shapiro Wilk Test Statistic 0.898 Shapiro Wilk Lognormal GOF Test
Assuming Gamma Distribution
95% Approximate Gamma UCL (use when n>=50)) 92.96 95% Adjusted Gamma UCL (use when n<50) 95.15
Adjusted Level of Significance 0.0431 Adjusted Chi Square Value 15.12
MLE Mean (bias corrected) 55.06 MLE Sd (bias corrected) 92.68
Approximate Chi Square Value (0.05) 15.47
Theta hat (MLE) 151.1 Theta star (bias corrected MLE) 156
nu hat (MLE) 26.98 nu star (bias corrected) 26.12
Gamma Statistics
k hat (MLE) 0.365 k star (bias corrected MLE) 0.353Coffey Appendix H - Data Statistics
RAAF Base Tindal PFAS Ecological Risk Assessment
113
114
115
116
117
118
119
120
121
122
123
124
125
126
127
128
129
130
131
132
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166
167
168
169
170
171
172
173
174
175
176
177
A B C D E F G H I J K L
Note: Suggestions regarding the selection of a 95% UCL are provided to help the user to select the most appropriate 95% UCL.
Recommendations are based upon data size, data distribution, and skewness.
These recommendations are based upon the results of the simulation studies summarized in Singh, Maichle, and Lee (2006).
However, simulations results will not cover all Real World data sets; for additional insight the user may want to consult a statistician.
Suggested UCL to Use
95% Chebyshev (Mean, Sd) UCL 31.96
90% Chebyshev(Mean, Sd) UCL 28.87 95% Chebyshev(Mean, Sd) UCL 31.96
97.5% Chebyshev(Mean, Sd) UCL 36.25 99% Chebyshev(Mean, Sd) UCL 44.67
95% Hall's Bootstrap UCL 26.99 95% Percentile Bootstrap UCL 25.97
95% BCA Bootstrap UCL 26.31
95% CLT UCL 25.8 95% Jackknife UCL 25.84
95% Standard Bootstrap UCL 25.88 95% Bootstrap-t UCL 26.95
Nonparametric Distribution Free UCL Statistics
Data do not follow a Discernible Distribution (0.05)
Nonparametric Distribution Free UCLs
95% Chebyshev (MVUE) UCL 29.39 97.5% Chebyshev (MVUE) UCL 32.91
99% Chebyshev (MVUE) UCL 39.82
Assuming Lognormal Distribution
95% H-UCL 25.06 90% Chebyshev (MVUE) UCL 26.86
Maximum of Logged Data 4.787 SD of logged Data 0.721
Lognormal Statistics
Minimum of Logged Data 1.668 Mean of logged Data 2.801
5% Lilliefors Critical Value 0.0974 Data Not Lognormal at 5% Significance Level
Data Not Lognormal at 5% Significance Level
5% Shapiro Wilk P Value 5.4195E-4 Data Not Lognormal at 5% Significance Level
Lilliefors Test Statistic 0.13 Lilliefors Lognormal GOF Test
Lognormal GOF Test
Shapiro Wilk Test Statistic 0.936 Shapiro Wilk Lognormal GOF Test
Assuming Gamma Distribution
95% Approximate Gamma UCL (use when n>=50)) 25.38 95% Adjusted Gamma UCL (use when n<50) 25.44
Adjusted Level of Significance 0.0471 Adjusted Chi Square Value 258.7
MLE Mean (bias corrected) 22.06 MLE Sd (bias corrected) 16.45
Approximate Chi Square Value (0.05) 259.3
Theta hat (MLE) 11.88 Theta star (bias corrected MLE) 12.27
nu hat (MLE) 308.1 nu star (bias corrected) 298.3
Data Not Gamma Distributed at 5% Significance Level
Gamma Statistics
k hat (MLE) 1.856 k star (bias corrected MLE) 1.797
K-S Test Statistic 0.179 Kolmogorov-Smirnov Gamma GOF Test
5% K-S Critical Value 0.0995 Data Not Gamma Distributed at 5% Significance Level
Gamma GOF Test
A-D Test Statistic 2.841 Anderson-Darling Gamma GOF Test
5% A-D Critical Value 0.766 Data Not Gamma Distributed at 5% Significance Level
95% Modified-t UCL (Johnson-1978) 25.94
Assuming Normal Distribution
95% Normal UCL 95% UCLs (Adjusted for Skewness)
95% Student's-t UCL 25.84 95% Adjusted-CLT UCL (Chen-1995) 26.45
5% Lilliefors Critical Value 0.0974 Data Not Normal at 5% Significance Level
Data Not Normal at 5% Significance Level
5% Shapiro Wilk P Value 0 Data Not Normal at 5% Significance Level
Lilliefors Test Statistic 0.235 Lilliefors GOF Test
Normal GOF Test
Shapiro Wilk Test Statistic 0.717 Shapiro Wilk GOF TestCoffey Appendix H - Data Statistics
RAAF Base Tindal PFAS Ecological Risk Assessment
178
179
180
181
182
183
184
185
186
187
188
189
190
191
192
193
194
195
196
197
198
199
200
201
202
203
204
205
206
207
208
209
210
211
212
213
214
215
216
217
218
219
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221
222
223
224
225
226
227
228
229
230
231
232
233
234
235
236
237
238
A B C D E F G H I J K L
Nonparametric Distribution Free UCL Statistics
Data do not follow a Discernible Distribution (0.05)
95% Chebyshev (MVUE) UCL 433.6 97.5% Chebyshev (MVUE) UCL 531.6
99% Chebyshev (MVUE) UCL 724.1
Assuming Lognormal Distribution
95% H-UCL 343.2 90% Chebyshev (MVUE) UCL 363
Maximum of Logged Data 10.17 SD of logged Data 2.46
Lognormal Statistics
Minimum of Logged Data -1.609 Mean of logged Data 2.341
5% Lilliefors Critical Value 0.0476 Data Not Lognormal at 5% Significance Level
Data Not Lognormal at 5% Significance Level
5% Shapiro Wilk P Value 1.069E-10 Data Not Lognormal at 5% Significance Level
Lilliefors Test Statistic 0.0638 Lilliefors Lognormal GOF Test
Lognormal GOF Test
Shapiro Wilk Test Statistic 0.955 Shapiro Wilk Lognormal GOF Test
Assuming Gamma Distribution
95% Approximate Gamma UCL (use when n>=50)) 312 95% Adjusted Gamma UCL (use when n<50) 312.3
Adjusted Level of Significance 0.0493 Adjusted Chi Square Value 130.3
MLE Mean (bias corrected) 256.7 MLE Sd (bias corrected) 541
Approximate Chi Square Value (0.05) 130.4
Theta hat (MLE) 1140 Theta star (bias corrected MLE) 1140
nu hat (MLE) 158.5 nu star (bias corrected) 158.5
Data Not Gamma Distributed at 5% Significance Level
Gamma Statistics
k hat (MLE) 0.225 k star (bias corrected MLE) 0.225
K-S Test Statistic 0.215 Kolmogorov-Smirnov Gamma GOF Test
5% K-S Critical Value 0.0536 Data Not Gamma Distributed at 5% Significance Level
Gamma GOF Test
A-D Test Statistic 30.35 Anderson-Darling Gamma GOF Test
5% A-D Critical Value 0.908 Data Not Gamma Distributed at 5% Significance Level
95% Modified-t UCL (Johnson-1978) 404.1
Assuming Normal Distribution
95% Normal UCL 95% UCLs (Adjusted for Skewness)
95% Student's-t UCL 394.1 95% Adjusted-CLT UCL (Chen-1995) 457.8
5% Lilliefors Critical Value 0.0476 Data Not Normal at 5% Significance Level
Data Not Normal at 5% Significance Level
5% Shapiro Wilk P Value 0 Data Not Normal at 5% Significance Level
Lilliefors Test Statistic 0.435 Lilliefors GOF Test
Normal GOF Test
Shapiro Wilk Test Statistic 0.178 Shapiro Wilk GOF Test
SD 1563 Std. Error of Mean 83.31
Coefficient of Variation 6.089 Skewness 13.49
Minimum 0.2 Mean 256.7
Maximum 26000 Median 11
Total Number of Observations 352 Number of Distinct Observations 166
Number of Missing Observations 207
Perfluoro-n-octane sulfonic acid (PFOS) (onbase)
General Statistics
Coffey Appendix H - Data Statistics
RAAF Base Tindal PFAS Ecological Risk Assessment
239
240
241
242
243
244
245
246
247
248
249
250
251
252
253
254
A B C D E F G H I J K L
Note: Suggestions regarding the selection of a 95% UCL are provided to help the user to select the most appropriate 95% UCL.
Recommendations are based upon data size, data distribution, and skewness.
These recommendations are based upon the results of the simulation studies summarized in Singh, Maichle, and Lee (2006).
However, simulations results will not cover all Real World data sets; for additional insight the user may want to consult a statistician.
Suggested UCL to Use
95% Chebyshev (Mean, Sd) UCL 619.8
90% Chebyshev(Mean, Sd) UCL 506.6 95% Chebyshev(Mean, Sd) UCL 619.8
97.5% Chebyshev(Mean, Sd) UCL 777 99% Chebyshev(Mean, Sd) UCL 1086
95% Hall's Bootstrap UCL 887.3 95% Percentile Bootstrap UCL 416.3
95% BCA Bootstrap UCL 483.3
95% CLT UCL 393.7 95% Jackknife UCL 394.1
95% Standard Bootstrap UCL 389.4 95% Bootstrap-t UCL 564.2
Nonparametric Distribution Free UCLs
Coffey Appendix H - Data Statistics
RAAF Base Tindal PFAS Ecological Risk Assessment
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
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A B C D E F G H I J K L
5% Lilliefors Critical Value 0.18 Data Not Lognormal at 5% Significance Level
Data Not Lognormal at 5% Significance Level
5% Shapiro Wilk Critical Value 0.914 Data Not Lognormal at 5% Significance Level
Lilliefors Test Statistic 0.257 Lilliefors Lognormal GOF Test
Lognormal GOF Test
Shapiro Wilk Test Statistic 0.878 Shapiro Wilk Lognormal GOF Test
Assuming Gamma Distribution
95% Approximate Gamma UCL (use when n>=50)) 0.0301 95% Adjusted Gamma UCL (use when n<50) 0.0308
Adjusted Level of Significance 0.0389 Adjusted Chi Square Value 45.35
MLE Mean (bias corrected) 0.0219 MLE Sd (bias corrected) 0.0186
Approximate Chi Square Value (0.05) 46.42
Theta hat (MLE) 0.014 Theta star (bias corrected MLE) 0.0158
nu hat (MLE) 71.83 nu star (bias corrected) 63.8
Gamma Statistics
k hat (MLE) 1.562 k star (bias corrected MLE) 1.387
5% K-S Critical Value 0.185 Data Not Gamma Distributed at 5% Significance Level
Detected data follow Appr. Gamma Distribution at 5% Significance Level
5% A-D Critical Value 0.759 Detected data appear Gamma Distributed at 5% Significance Level
K-S Test Statistic 0.216 Kolmogorov-Smirnov Gamma GOF Test
Gamma GOF Test
A-D Test Statistic 0.674 Anderson-Darling Gamma GOF Test
95% Student's-t UCL 0.0275 95% Adjusted-CLT UCL (Chen-1995) 0.0279
95% Modified-t UCL (Johnson-1978) 0.0276
Data appear Normal at 5% Significance Level
Assuming Normal Distribution
95% Normal UCL 95% UCLs (Adjusted for Skewness)
Lilliefors Test Statistic 0.174 Lilliefors GOF Test
5% Lilliefors Critical Value 0.18 Data appear Normal at 5% Significance Level
Normal GOF Test
Shapiro Wilk Test Statistic 0.92 Shapiro Wilk GOF Test
5% Shapiro Wilk Critical Value 0.914 Data appear Normal at 5% Significance Level
Coefficient of Variation 0.717 Skewness 0.84
Maximum 0.062 Median 0.02
SD 0.0157 Std. Error of Mean 0.00327
Number of Missing Observations 141
Minimum 0.002 Mean 0.0219
General Statistics
Total Number of Observations 23 Number of Distinct Observations 9
Number of Bootstrap Operations 2000
Perfluoro-n-octanoate acid (PFOA) (off-base)
From File Data_Tindal_SW_for ProUCL Analysis_20180605_a.xls
Full Precision OFF
Confidence Coefficient 95%
UCL Statistics for Uncensored Full Data Sets
User Selected Options
Date/Time of Computation ProUCL 5.17/9/2018 9:40:12 AM
Coffey Appendix H - Data Statistics
RAAF Base Tindal PFAS Ecological Risk Assessment
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A B C D E F G H I J K L
Data Not Gamma Distributed at 5% Significance Level
K-S Test Statistic 0.177 Kolmogorov-Smirnov Gamma GOF Test
5% K-S Critical Value 0.118 Data Not Gamma Distributed at 5% Significance Level
Gamma GOF Test
A-D Test Statistic 3.388 Anderson-Darling Gamma GOF Test
5% A-D Critical Value 0.789 Data Not Gamma Distributed at 5% Significance Level
95% Modified-t UCL (Johnson-1978) 0.151
Assuming Normal Distribution
95% Normal UCL 95% UCLs (Adjusted for Skewness)
95% Student's-t UCL 0.145 95% Adjusted-CLT UCL (Chen-1995) 0.177
5% Lilliefors Critical Value 0.113 Data Not Normal at 5% Significance Level
Data Not Normal at 5% Significance Level
5% Shapiro Wilk P Value 0 Data Not Normal at 5% Significance Level
Lilliefors Test Statistic 0.375 Lilliefors GOF Test
Normal GOF Test
Shapiro Wilk Test Statistic 0.271 Shapiro Wilk GOF Test
SD 0.254 Std. Error of Mean 0.0325
Coefficient of Variation 2.784 Skewness 7.325
Minimum 0.01 Mean 0.0912
Maximum 2 Median 0.04
Total Number of Observations 61 Number of Distinct Observations 21
Number of Missing Observations 38
Perfluoro-n-octanoate acid (PFOA) (on-base)
General Statistics
Note: Suggestions regarding the selection of a 95% UCL are provided to help the user to select the most appropriate 95% UCL.
Recommendations are based upon data size, data distribution, and skewness.
These recommendations are based upon the results of the simulation studies summarized in Singh, Maichle, and Lee (2006).
However, simulations results will not cover all Real World data sets; for additional insight the user may want to consult a statistician.
Suggested UCL to Use
95% Student's-t UCL 0.0275
90% Chebyshev(Mean, Sd) UCL 0.0317 95% Chebyshev(Mean, Sd) UCL 0.0361
97.5% Chebyshev(Mean, Sd) UCL 0.0423 99% Chebyshev(Mean, Sd) UCL 0.0544
95% Hall's Bootstrap UCL 0.028 95% Percentile Bootstrap UCL 0.0274
95% BCA Bootstrap UCL 0.0276
95% CLT UCL 0.0272 95% Jackknife UCL 0.0275
95% Standard Bootstrap UCL 0.0271 95% Bootstrap-t UCL 0.0281
Nonparametric Distribution Free UCL Statistics
Data appear to follow a Discernible Distribution at 5% Significance Level
Nonparametric Distribution Free UCLs
95% Chebyshev (MVUE) UCL 0.0496 97.5% Chebyshev (MVUE) UCL 0.0604
99% Chebyshev (MVUE) UCL 0.0817
Assuming Lognormal Distribution
95% H-UCL 0.0432 90% Chebyshev (MVUE) UCL 0.0417
Maximum of Logged Data -2.781 SD of logged Data 0.997
Lognormal Statistics
Minimum of Logged Data -6.215 Mean of logged Data -4.176
Coffey Appendix H - Data Statistics
RAAF Base Tindal PFAS Ecological Risk Assessment
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A B C D E F G H I J K L
Perfluoro-n-octane sulfonic acid (PFOS) (off-base)
ProUCL computes and outputs H-statistic based UCLs for historical reasons only.
H-statistic often results in unstable (both high and low) values of UCL95 as shown in examples in the Technical Guide.
It is therefore recommended to avoid the use of H-statistic based 95% UCLs.
Use of nonparametric methods are preferred to compute UCL95 for skewed data sets which do not follow a gamma distribution.
Note: Suggestions regarding the selection of a 95% UCL are provided to help the user to select the most appropriate 95% UCL.
Recommendations are based upon data size, data distribution, and skewness.
These recommendations are based upon the results of the simulation studies summarized in Singh, Maichle, and Lee (2006).
However, simulations results will not cover all Real World data sets; for additional insight the user may want to consult a statistician.
Suggested UCL to Use
95% H-UCL 0.0979
90% Chebyshev(Mean, Sd) UCL 0.189 95% Chebyshev(Mean, Sd) UCL 0.233
97.5% Chebyshev(Mean, Sd) UCL 0.294 99% Chebyshev(Mean, Sd) UCL 0.414
95% Hall's Bootstrap UCL 0.343 95% Percentile Bootstrap UCL 0.154
95% BCA Bootstrap UCL 0.191
95% CLT UCL 0.145 95% Jackknife UCL 0.145
95% Standard Bootstrap UCL 0.143 95% Bootstrap-t UCL 0.302
Nonparametric Distribution Free UCL Statistics
Data appear to follow a Discernible Distribution at 5% Significance Level
Nonparametric Distribution Free UCLs
95% Chebyshev (MVUE) UCL 0.12 97.5% Chebyshev (MVUE) UCL 0.141
99% Chebyshev (MVUE) UCL 0.182
Assuming Lognormal Distribution
95% H-UCL 0.0979 90% Chebyshev (MVUE) UCL 0.105
Maximum of Logged Data 0.693 SD of logged Data 1.007
Lognormal Statistics
Minimum of Logged Data -4.605 Mean of logged Data -3.125
5% Lilliefors Critical Value 0.113 Data appear Lognormal at 5% Significance Level
Data appear Approximate Lognormal at 5% Significance Level
5% Shapiro Wilk P Value 0.0044 Data Not Lognormal at 5% Significance Level
Lilliefors Test Statistic 0.111 Lilliefors Lognormal GOF Test
Lognormal GOF Test
Shapiro Wilk Test Statistic 0.936 Shapiro Wilk Lognormal GOF Test
Assuming Gamma Distribution
95% Approximate Gamma UCL (use when n>=50)) 0.118 95% Adjusted Gamma UCL (use when n<50) 0.118
Adjusted Level of Significance 0.0461 Adjusted Chi Square Value 73.53
MLE Mean (bias corrected) 0.0912 MLE Sd (bias corrected) 0.103
Approximate Chi Square Value (0.05) 73.99
Theta hat (MLE) 0.112 Theta star (bias corrected MLE) 0.116
nu hat (MLE) 99.07 nu star (bias corrected) 95.53
Gamma Statistics
k hat (MLE) 0.812 k star (bias corrected MLE) 0.783
Coffey Appendix H - Data Statistics
RAAF Base Tindal PFAS Ecological Risk Assessment
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A B C D E F G H I J K L
Nonparametric Distribution Free UCL Statistics
Data do not follow a Discernible Distribution (0.05)
95% Chebyshev (MVUE) UCL 0.316 97.5% Chebyshev (MVUE) UCL 0.373
99% Chebyshev (MVUE) UCL 0.486
Assuming Lognormal Distribution
95% H-UCL 0.255 90% Chebyshev (MVUE) UCL 0.274
Maximum of Logged Data 0.405 SD of logged Data 1.306
Lognormal Statistics
Minimum of Logged Data -4.962 Mean of logged Data -2.539
5% Lilliefors Critical Value 0.0867 Data Not Lognormal at 5% Significance Level
Data Not Lognormal at 5% Significance Level
5% Shapiro Wilk P Value 1.3795E-4 Data Not Lognormal at 5% Significance Level
Lilliefors Test Statistic 0.104 Lilliefors Lognormal GOF Test
Lognormal GOF Test
Shapiro Wilk Test Statistic 0.94 Shapiro Wilk Lognormal GOF Test
Assuming Gamma Distribution
95% Approximate Gamma UCL (use when n>=50)) 0.229 95% Adjusted Gamma UCL (use when n<50) 0.23
Adjusted Level of Significance 0.0477 Adjusted Chi Square Value 117.4
MLE Mean (bias corrected) 0.187 MLE Sd (bias corrected) 0.225
Approximate Chi Square Value (0.05) 117.7
Theta hat (MLE) 0.266 Theta star (bias corrected MLE) 0.271
nu hat (MLE) 147.4 nu star (bias corrected) 144.5
Data Not Gamma Distributed at 5% Significance Level
Gamma Statistics
k hat (MLE) 0.702 k star (bias corrected MLE) 0.688
K-S Test Statistic 0.164 Kolmogorov-Smirnov Gamma GOF Test
5% K-S Critical Value 0.0919 Data Not Gamma Distributed at 5% Significance Level
Gamma GOF Test
A-D Test Statistic 4.38 Anderson-Darling Gamma GOF Test
5% A-D Critical Value 0.8 Data Not Gamma Distributed at 5% Significance Level
95% Modified-t UCL (Johnson-1978) 0.234
Assuming Normal Distribution
95% Normal UCL 95% UCLs (Adjusted for Skewness)
95% Student's-t UCL 0.233 95% Adjusted-CLT UCL (Chen-1995) 0.24
5% Lilliefors Critical Value 0.0867 Data Not Normal at 5% Significance Level
Data Not Normal at 5% Significance Level
5% Shapiro Wilk P Value 0 Data Not Normal at 5% Significance Level
Lilliefors Test Statistic 0.309 Lilliefors GOF Test
Normal GOF Test
Shapiro Wilk Test Statistic 0.617 Shapiro Wilk GOF Test
SD 0.286 Std. Error of Mean 0.0279
Coefficient of Variation 1.533 Skewness 2.398
Minimum 0.007 Mean 0.187
Maximum 1.5 Median 0.09
Total Number of Observations 105 Number of Distinct Observations 39
Number of Missing Observations 59
General Statistics
Coffey Appendix H - Data Statistics
RAAF Base Tindal PFAS Ecological Risk Assessment
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Assuming Gamma Distribution
95% Approximate Gamma UCL (use when n>=50)) 2.378 95% Adjusted Gamma UCL (use when n<50) 2.388
Adjusted Level of Significance 0.0475 Adjusted Chi Square Value 66.16
MLE Mean (bias corrected) 1.818 MLE Sd (bias corrected) 2.715
Approximate Chi Square Value (0.05) 66.43
Theta hat (MLE) 3.992 Theta star (bias corrected MLE) 4.057
nu hat (MLE) 88.32 nu star (bias corrected) 86.92
Data Not Gamma Distributed at 5% Significance Level
Gamma Statistics
k hat (MLE) 0.455 k star (bias corrected MLE) 0.448
K-S Test Statistic 0.126 Kolmogorov-Smirnov Gamma GOF Test
5% K-S Critical Value 0.0967 Data Not Gamma Distributed at 5% Significance Level
Gamma GOF Test
A-D Test Statistic 2.668 Anderson-Darling Gamma GOF Test
5% A-D Critical Value 0.829 Data Not Gamma Distributed at 5% Significance Level
95% Modified-t UCL (Johnson-1978) 3.046
Assuming Normal Distribution
95% Normal UCL 95% UCLs (Adjusted for Skewness)
95% Student's-t UCL 2.942 95% Adjusted-CLT UCL (Chen-1995) 3.597
5% Lilliefors Critical Value 0.0902 Data Not Normal at 5% Significance Level
Data Not Normal at 5% Significance Level
5% Shapiro Wilk P Value 0 Data Not Normal at 5% Significance Level
Lilliefors Test Statistic 0.394 Lilliefors GOF Test
Normal GOF Test
Shapiro Wilk Test Statistic 0.243 Shapiro Wilk GOF Test
SD 6.671 Std. Error of Mean 0.677
Coefficient of Variation 3.67 Skewness 9.052
Minimum 0.02 Mean 1.818
Maximum 65 Median 0.57
Total Number of Observations 97 Number of Distinct Observations 61
Number of Missing Observations 2
Perfluoro-n-octane sulfonic acid (PFOS) (on-base)
General Statistics
Note: Suggestions regarding the selection of a 95% UCL are provided to help the user to select the most appropriate 95% UCL.
Recommendations are based upon data size, data distribution, and skewness.
These recommendations are based upon the results of the simulation studies summarized in Singh, Maichle, and Lee (2006).
However, simulations results will not cover all Real World data sets; for additional insight the user may want to consult a statistician.
Suggested UCL to Use
95% Chebyshev (Mean, Sd) UCL 0.308
90% Chebyshev(Mean, Sd) UCL 0.27 95% Chebyshev(Mean, Sd) UCL 0.308
97.5% Chebyshev(Mean, Sd) UCL 0.361 99% Chebyshev(Mean, Sd) UCL 0.464
95% Hall's Bootstrap UCL 0.24 95% Percentile Bootstrap UCL 0.235
95% BCA Bootstrap UCL 0.238
95% CLT UCL 0.233 95% Jackknife UCL 0.233
95% Standard Bootstrap UCL 0.233 95% Bootstrap-t UCL 0.246
Nonparametric Distribution Free UCLs
Coffey Appendix H - Data Statistics
RAAF Base Tindal PFAS Ecological Risk Assessment
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A B C D E F G H I J K L
Note: Suggestions regarding the selection of a 95% UCL are provided to help the user to select the most appropriate 95% UCL.
Recommendations are based upon data size, data distribution, and skewness.
These recommendations are based upon the results of the simulation studies summarized in Singh, Maichle, and Lee (2006).
However, simulations results will not cover all Real World data sets; for additional insight the user may want to consult a statistician.
Suggested UCL to Use
95% Chebyshev (Mean, Sd) UCL 4.77
90% Chebyshev(Mean, Sd) UCL 3.849 95% Chebyshev(Mean, Sd) UCL 4.77
97.5% Chebyshev(Mean, Sd) UCL 6.047 99% Chebyshev(Mean, Sd) UCL 8.557
95% Hall's Bootstrap UCL 7.035 95% Percentile Bootstrap UCL 3.119
95% BCA Bootstrap UCL 3.886
95% CLT UCL 2.932 95% Jackknife UCL 2.942
95% Standard Bootstrap UCL 2.967 95% Bootstrap-t UCL 6.06
Nonparametric Distribution Free UCL Statistics
Data do not follow a Discernible Distribution (0.05)
Nonparametric Distribution Free UCLs
95% Chebyshev (MVUE) UCL 3.88 97.5% Chebyshev (MVUE) UCL 4.763
99% Chebyshev (MVUE) UCL 6.497
Assuming Lognormal Distribution
95% H-UCL 3.245 90% Chebyshev (MVUE) UCL 3.244
Maximum of Logged Data 4.174 SD of logged Data 1.711
Lognormal Statistics
Minimum of Logged Data -3.912 Mean of logged Data -0.818
5% Lilliefors Critical Value 0.0902 Data Not Lognormal at 5% Significance Level
Data Not Lognormal at 5% Significance Level
5% Shapiro Wilk P Value 0.0118 Data Not Lognormal at 5% Significance Level
Lilliefors Test Statistic 0.098 Lilliefors Lognormal GOF Test
Lognormal GOF Test
Shapiro Wilk Test Statistic 0.956 Shapiro Wilk Lognormal GOF TestCoffey Appendix H - Data Statistics
RAAF Base Tindal PFAS Ecological Risk Assessment
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A B C D E F G H I J K L
Note: Sample size is small (e.g., <10), if data are collected using ISM approach, you should use
guidance provided in ITRC Tech Reg Guide on ISM (ITRC, 2012) to compute statistics of interest.
For example, you may want to use Chebyshev UCL to estimate EPC (ITRC, 2012).
Chebyshev UCL can be computed using the Nonparametric and All UCL Options of ProUCL 5.1
Coefficient of Variation 0.644 Skewness -0.0328
Maximum 0.01 Median 0.0065
SD 0.00403 Std. Error of Mean 0.00142
Number of Missing Observations 21
Minimum 0.002 Mean 0.00625
General Statistics
Total Number of Observations 8 Number of Distinct Observations 3
If possible, compute and collect Data Quality Objectives (DQO) based sample size and analytical results.
Perfluoro-n-octanoate acid (PFOA) (kr-3)
Warning: This data set only has 0 observations!
Data set is too small to compute reliable and meaningful statistics and estimates!
The data set for variable Perfluoro-n-octanoate acid (PFOA) (kr-2) was not processed!
It is suggested to collect at least 8 to 10 observations before using these statistical methods!
Maximum N/A Median N/A
Number of Missing Observations 62
Minimum N/A Mean N/A
General Statistics
Total Number of Observations 0 Number of Distinct Observations 0
If possible, compute and collect Data Quality Objectives (DQO) based sample size and analytical results.
Perfluoro-n-octanoate acid (PFOA) (kr-2)
Warning: This data set only has 0 observations!
Data set is too small to compute reliable and meaningful statistics and estimates!
The data set for variable Perfluoro-n-octanoate acid (PFOA) (kr-1) was not processed!
It is suggested to collect at least 8 to 10 observations before using these statistical methods!
Maximum N/A Median N/A
Number of Missing Observations 26
Minimum N/A Mean N/A
General Statistics
Total Number of Observations 0 Number of Distinct Observations 0
Number of Bootstrap Operations 2000
Perfluoro-n-octanoate acid (PFOA) (kr-1)
From File Tindal_SW_for ProUCL Analysis_20180605_a.xls
Full Precision OFF
Confidence Coefficient 95%
UCL Statistics for Uncensored Full Data Sets
User Selected Options
Date/Time of Computation ProUCL 5.16/6/2018 8:32:30 AM
Coffey Appendix H - Data Statistics
RAAF Base Tindal PFAS Ecological Risk Assessment
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These recommendations are based upon the results of the simulation studies summarized in Singh, Maichle, and Lee (2006).
However, simulations results will not cover all Real World data sets; for additional insight the user may want to consult a statistician.
Note: For highly negatively-skewed data, confidence limits (e.g., Chen, Johnson, Lognormal, and Gamma) may not be
reliable. Chen's and Johnson's methods provide adjustments for positvely skewed data sets.
Recommended UCL exceeds the maximum observation
Note: Suggestions regarding the selection of a 95% UCL are provided to help the user to select the most appropriate 95% UCL.
Recommendations are based upon data size, data distribution, and skewness.
Suggested UCL to Use
95% Chebyshev (Mean, Sd) UCL 0.0125
90% Chebyshev(Mean, Sd) UCL 0.0105 95% Chebyshev(Mean, Sd) UCL 0.0125
97.5% Chebyshev(Mean, Sd) UCL 0.0151 99% Chebyshev(Mean, Sd) UCL 0.0204
95% Hall's Bootstrap UCL N/A 95% Percentile Bootstrap UCL N/A
95% BCA Bootstrap UCL N/A
95% CLT UCL 0.00859 95% Jackknife UCL 0.00895
95% Standard Bootstrap UCL N/A 95% Bootstrap-t UCL N/A
Nonparametric Distribution Free UCL Statistics
Data do not follow a Discernible Distribution (0.05)
Nonparametric Distribution Free UCLs
95% Chebyshev (MVUE) UCL 0.014 97.5% Chebyshev (MVUE) UCL 0.0173
99% Chebyshev (MVUE) UCL 0.0238
Assuming Lognormal Distribution
95% H-UCL 0.0153 90% Chebyshev (MVUE) UCL 0.0116
Maximum of Logged Data -4.605 SD of logged Data 0.767
Lognormal Statistics
Minimum of Logged Data -6.215 Mean of logged Data -5.309
5% Lilliefors Critical Value 0.283 Data Not Lognormal at 5% Significance Level
Data Not Lognormal at 5% Significance Level
5% Shapiro Wilk Critical Value 0.818 Data Not Lognormal at 5% Significance Level
Lilliefors Test Statistic 0.32 Lilliefors Lognormal GOF Test
Lognormal GOF Test
Shapiro Wilk Test Statistic 0.752 Shapiro Wilk Lognormal GOF Test
Assuming Gamma Distribution
95% Approximate Gamma UCL (use when n>=50)) 0.0108 95% Adjusted Gamma UCL (use when n<50) 0.0125
Adjusted Level of Significance 0.0195 Adjusted Chi Square Value 12.15
MLE Mean (bias corrected) 0.00625 MLE Sd (bias corrected) 0.00507
Approximate Chi Square Value (0.05) 14.07
Theta hat (MLE) 0.00272 Theta star (bias corrected MLE) 0.00412
nu hat (MLE) 36.73 nu star (bias corrected) 24.29
Gamma Statistics
k hat (MLE) 2.296 k star (bias corrected MLE) 1.518
5% K-S Critical Value 0.297 Data Not Gamma Distributed at 5% Significance Level
Data Not Gamma Distributed at 5% Significance Level
5% A-D Critical Value 0.723 Data Not Gamma Distributed at 5% Significance Level
K-S Test Statistic 0.338 Kolmogorov-Smirnov Gamma GOF Test
Gamma GOF Test
A-D Test Statistic 1.088 Anderson-Darling Gamma GOF Test
95% Student's-t UCL 0.00895 95% Adjusted-CLT UCL (Chen-1995) 0.00857
95% Modified-t UCL (Johnson-1978) 0.00894
Data Not Normal at 5% Significance Level
Assuming Normal Distribution
95% Normal UCL 95% UCLs (Adjusted for Skewness)
Lilliefors Test Statistic 0.324 Lilliefors GOF Test
5% Lilliefors Critical Value 0.283 Data Not Normal at 5% Significance Level
Normal GOF Test
Shapiro Wilk Test Statistic 0.711 Shapiro Wilk GOF Test
5% Shapiro Wilk Critical Value 0.818 Data Not Normal at 5% Significance Level
Coffey Appendix H - Data Statistics
RAAF Base Tindal PFAS Ecological Risk Assessment
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A B C D E F G H I J K L
Note: Suggestions regarding the selection of a 95% UCL are provided to help the user to select the most appropriate 95% UCL.
Recommendations are based upon data size, data distribution, and skewness.
These recommendations are based upon the results of the simulation studies summarized in Singh, Maichle, and Lee (2006).
However, simulations results will not cover all Real World data sets; for additional insight the user may want to consult a statistician.
Suggested UCL to Use
95% Adjusted Gamma UCL 0.0743
90% Chebyshev(Mean, Sd) UCL 0.0807 95% Chebyshev(Mean, Sd) UCL 0.0923
97.5% Chebyshev(Mean, Sd) UCL 0.109 99% Chebyshev(Mean, Sd) UCL 0.14
95% Hall's Bootstrap UCL 0.0719 95% Percentile Bootstrap UCL 0.0696
95% BCA Bootstrap UCL 0.0704
95% CLT UCL 0.0691 95% Jackknife UCL 0.0696
95% Standard Bootstrap UCL 0.0688 95% Bootstrap-t UCL 0.0732
Nonparametric Distribution Free UCL Statistics
Data appear to follow a Discernible Distribution at 5% Significance Level
Nonparametric Distribution Free UCLs
95% Chebyshev (MVUE) UCL 0.104 97.5% Chebyshev (MVUE) UCL 0.124
99% Chebyshev (MVUE) UCL 0.164
Assuming Lognormal Distribution
95% H-UCL 0.0864 90% Chebyshev (MVUE) UCL 0.0889
Maximum of Logged Data -1.661 SD of logged Data 0.898
Lognormal Statistics
Minimum of Logged Data -4.605 Mean of logged Data -3.256
5% Lilliefors Critical Value 0.164 Data appear Lognormal at 5% Significance Level
Data appear Lognormal at 5% Significance Level
5% Shapiro Wilk Critical Value 0.924 Data appear Lognormal at 5% Significance Level
Lilliefors Test Statistic 0.149 Lilliefors Lognormal GOF Test
Lognormal GOF Test
Shapiro Wilk Test Statistic 0.926 Shapiro Wilk Lognormal GOF Test
Assuming Gamma Distribution
95% Approximate Gamma UCL (use when n>=50) 0.073 95% Adjusted Gamma UCL (use when n<50) 0.0743
Adjusted Level of Significance 0.0404 Adjusted Chi Square Value 58.49
MLE Mean (bias corrected) 0.055 MLE Sd (bias corrected) 0.0463
Approximate Chi Square Value (0.05) 59.53
Theta hat (MLE) 0.0354 Theta star (bias corrected MLE) 0.039
nu hat (MLE) 87 nu star (bias corrected) 79.01
Detected data appear Gamma Distributed at 5% Significance Level
Gamma Statistics
k hat (MLE) 1.554 k star (bias corrected MLE) 1.411
K-S Test Statistic 0.157 Kolmogorov-Smirnov Gamma GOF Test
5% K-S Critical Value 0.168 Detected data appear Gamma Distributed at 5% Significance Level
Gamma GOF Test
A-D Test Statistic 0.687 Anderson-Darling Gamma GOF Test
5% A-D Critical Value 0.762 Detected data appear Gamma Distributed at 5% Significance Level
95% Modified-t UCL (Johnson-1978) 0.0699
Assuming Normal Distribution
95% Normal UCL 95% UCLs (Adjusted for Skewness)
95% Student's-t UCL 0.0696 95% Adjusted-CLT UCL (Chen-1995) 0.0711
5% Lilliefors Critical Value 0.164 Data Not Normal at 5% Significance Level
Data Not Normal at 5% Significance Level
5% Shapiro Wilk Critical Value 0.924 Data Not Normal at 5% Significance Level
Lilliefors Test Statistic 0.209 Lilliefors GOF Test
Normal GOF Test
Shapiro Wilk Test Statistic 0.86 Shapiro Wilk GOF Test
SD 0.0453 Std. Error of Mean 0.00857
Coefficient of Variation 0.824 Skewness 1.168
Minimum 0.01 Mean 0.055
Maximum 0.19 Median 0.035
Total Number of Observations 28 Number of Distinct Observations 12
Number of Missing Observations 22
Perfluoro-n-octanoate acid (PFOA) (on-base drain)
General Statistics
Coffey Appendix H - Data Statistics
RAAF Base Tindal PFAS Ecological Risk Assessment
205
206
207
208
209
210
211
212
213
214
215
216
217
218
219
220
221
222
223
224
225
226
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228
229
230
231
232
233
234
235
236
237
238
239
240
241
242
243
244
245
246
247
248
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251
252
253
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257
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261
262
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268
269
270
271
272
273
274
275
276
277
278
279
280
A B C D E F G H I J K L
Note: Suggestions regarding the selection of a 95% UCL are provided to help the user to select the most appropriate 95% UCL.
Recommendations are based upon data size, data distribution, and skewness.
These recommendations are based upon the results of the simulation studies summarized in Singh, Maichle, and Lee (2006).
However, simulations results will not cover all Real World data sets; for additional insight the user may want to consult a statistician.
Suggested UCL to Use
99% Chebyshev (Mean, Sd) UCL 1.6
90% Chebyshev(Mean, Sd) UCL 0.643 95% Chebyshev(Mean, Sd) UCL 0.83
97.5% Chebyshev(Mean, Sd) UCL 1.09 99% Chebyshev(Mean, Sd) UCL 1.6
95% Hall's Bootstrap UCL 1.41 95% Percentile Bootstrap UCL 0.493
95% BCA Bootstrap UCL 0.646
95% CLT UCL 0.456 95% Jackknife UCL 0.473
95% Standard Bootstrap UCL 0.444 95% Bootstrap-t UCL 1.389
Nonparametric Distribution Free UCL Statistics
Data appear to follow a Discernible Distribution at 5% Significance Level
Nonparametric Distribution Free UCLs
95% Chebyshev (MVUE) UCL 0.584 97.5% Chebyshev (MVUE) UCL 0.754
99% Chebyshev (MVUE) UCL 1.086
Assuming Lognormal Distribution
95% H-UCL 1.125 90% Chebyshev (MVUE) UCL 0.462
Maximum of Logged Data 0.693 SD of logged Data 1.54
Lognormal Statistics
Minimum of Logged Data -4.605 Mean of logged Data -2.675
5% Lilliefors Critical Value 0.226 Data appear Lognormal at 5% Significance Level
Data appear Lognormal at 5% Significance Level
5% Shapiro Wilk Critical Value 0.874 Data appear Lognormal at 5% Significance Level
Lilliefors Test Statistic 0.16 Lilliefors Lognormal GOF Test
Lognormal GOF Test
Shapiro Wilk Test Statistic 0.91 Shapiro Wilk Lognormal GOF Test
Assuming Gamma Distribution
95% Approximate Gamma UCL (use when n>=50)) 0.508 95% Adjusted Gamma UCL (use when n<50) 0.569
Adjusted Level of Significance 0.0312 Adjusted Chi Square Value 5.188
MLE Mean (bias corrected) 0.229 MLE Sd (bias corrected) 0.338
Approximate Chi Square Value (0.05) 5.804
Theta hat (MLE) 0.437 Theta star (bias corrected MLE) 0.499
nu hat (MLE) 14.68 nu star (bias corrected) 12.87
Data Not Gamma Distributed at 5% Significance Level
Gamma Statistics
k hat (MLE) 0.524 k star (bias corrected MLE) 0.46
K-S Test Statistic 0.26 Kolmogorov-Smirnov Gamma GOF Test
5% K-S Critical Value 0.241 Data Not Gamma Distributed at 5% Significance Level
Gamma GOF Test
A-D Test Statistic 1.002 Anderson-Darling Gamma GOF Test
5% A-D Critical Value 0.791 Data Not Gamma Distributed at 5% Significance Level
95% Modified-t UCL (Johnson-1978) 0.495
Assuming Normal Distribution
95% Normal UCL 95% UCLs (Adjusted for Skewness)
95% Student's-t UCL 0.473 95% Adjusted-CLT UCL (Chen-1995) 0.597
5% Lilliefors Critical Value 0.226 Data Not Normal at 5% Significance Level
Data Not Normal at 5% Significance Level
5% Shapiro Wilk Critical Value 0.874 Data Not Normal at 5% Significance Level
Lilliefors Test Statistic 0.436 Lilliefors GOF Test
Normal GOF Test
Shapiro Wilk Test Statistic 0.428 Shapiro Wilk GOF Test
SD 0.515 Std. Error of Mean 0.138
Coefficient of Variation 2.248 Skewness 3.596
Minimum 0.01 Mean 0.229
Maximum 2 Median 0.105
Total Number of Observations 14 Number of Distinct Observations 10
Number of Missing Observations 0
Perfluoro-n-octanoate acid (PFOA) (source area)
General Statistics
Coffey Appendix H - Data Statistics
RAAF Base Tindal PFAS Ecological Risk Assessment
281
282
283
284
285
286
287
288
289
290
291
292
293
294
295
296
297
298
299
300
301
302
303
304
305
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308
309
310
311
312
313
314
315
316
317
318
319
320
321
322
323
324
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326
327
328
329
330
331
332
333
334
335
336
337
338
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341
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345
346
347
348
349
350
351
352
353
354
355
356
357
358
359
A B C D E F G H I J K L
Recommendations are based upon data size, data distribution, and skewness.
These recommendations are based upon the results of the simulation studies summarized in Singh, Maichle, and Lee (2006).
However, simulations results will not cover all Real World data sets; for additional insight the user may want to consult a statistician.
When a data set follows an approximate (e.g., normal) distribution passing one of the GOF test
When applicable, it is suggested to use a UCL based upon a distribution (e.g., gamma) passing both GOF tests in ProUCL
Note: Suggestions regarding the selection of a 95% UCL are provided to help the user to select the most appropriate 95% UCL.
Suggested UCL to Use
95% Student's-t UCL 0.0503
90% Chebyshev(Mean, Sd) UCL 0.0559 95% Chebyshev(Mean, Sd) UCL 0.0619
97.5% Chebyshev(Mean, Sd) UCL 0.0702 99% Chebyshev(Mean, Sd) UCL 0.0866
95% Hall's Bootstrap UCL 0.0513 95% Percentile Bootstrap UCL 0.0501
95% BCA Bootstrap UCL 0.0501
95% CLT UCL 0.0499 95% Jackknife UCL 0.0503
95% Standard Bootstrap UCL 0.0497 95% Bootstrap-t UCL 0.0515
Nonparametric Distribution Free UCL Statistics
Data appear to follow a Discernible Distribution at 5% Significance Level
Nonparametric Distribution Free UCLs
95% Chebyshev (MVUE) UCL 0.066 97.5% Chebyshev (MVUE) UCL 0.0759
99% Chebyshev (MVUE) UCL 0.0953
Assuming Lognormal Distribution
95% H-UCL 0.0555 90% Chebyshev (MVUE) UCL 0.0589
Maximum of Logged Data -2.501 SD of logged Data 0.508
Lognormal Statistics
Minimum of Logged Data -4.605 Mean of logged Data -3.262
5% Lilliefors Critical Value 0.197 Data Not Lognormal at 5% Significance Level
Data appear Approximate Lognormal at 5% Significance Level
5% Shapiro Wilk Critical Value 0.901 Data appear Lognormal at 5% Significance Level
Lilliefors Test Statistic 0.218 Lilliefors Lognormal GOF Test
Lognormal GOF Test
Shapiro Wilk Test Statistic 0.92 Shapiro Wilk Lognormal GOF Test
Assuming Gamma Distribution
95% Approximate Gamma UCL (use when n>=50)) 0.052 95% Adjusted Gamma UCL (use when n<50) 0.053
Adjusted Level of Significance 0.0369 Adjusted Chi Square Value 124.2
MLE Mean (bias corrected) 0.0427 MLE Sd (bias corrected) 0.0212
Approximate Chi Square Value (0.05) 126.4
Theta hat (MLE) 0.00894 Theta star (bias corrected MLE) 0.0105
nu hat (MLE) 181.3 nu star (bias corrected) 154
Detected data appear Gamma Distributed at 5% Significance Level
Gamma Statistics
k hat (MLE) 4.772 k star (bias corrected MLE) 4.054
K-S Test Statistic 0.19 Kolmogorov-Smirnov Gamma GOF Test
5% K-S Critical Value 0.199 Detected data appear Gamma Distributed at 5% Significance Level
Gamma GOF Test
A-D Test Statistic 0.531 Anderson-Darling Gamma GOF Test
5% A-D Critical Value 0.743 Detected data appear Gamma Distributed at 5% Significance Level
95% Modified-t UCL (Johnson-1978) 0.0504
Assuming Normal Distribution
95% Normal UCL 95% UCLs (Adjusted for Skewness)
95% Student's-t UCL 0.0503 95% Adjusted-CLT UCL (Chen-1995) 0.0506
5% Lilliefors Critical Value 0.197 Data Not Normal at 5% Significance Level
Data appear Approximate Normal at 5% Significance Level
5% Shapiro Wilk Critical Value 0.901 Data appear Normal at 5% Significance Level
Lilliefors Test Statistic 0.24 Lilliefors GOF Test
Normal GOF Test
Shapiro Wilk Test Statistic 0.927 Shapiro Wilk GOF Test
SD 0.0192 Std. Error of Mean 0.00441
Coefficient of Variation 0.45 Skewness 0.617
Minimum 0.01 Mean 0.0427
Maximum 0.082 Median 0.04
Total Number of Observations 19 Number of Distinct Observations 9
Number of Missing Observations 16
Perfluoro-n-octanoate acid (PFOA) (tc-1)
General Statistics
Coffey Appendix H - Data Statistics
RAAF Base Tindal PFAS Ecological Risk Assessment
360
361
362
363
364
365
366
367
368
369
370
371
372
373
374
375
376
377
378
379
380
381
382
383
384
385
386
387
388
389
390
391
392
393
394
395
396
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398
399
400
401
402
403
404
405
406
407
408
409
410
411
412
413
414
415
416
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418
419
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422
423
424
425
426
427
428
429
430
431
432
433
434
435
436
437
A B C D E F G H I J K L
Note: Suggestions regarding the selection of a 95% UCL are provided to help the user to select the most appropriate 95% UCL.
Recommendations are based upon data size, data distribution, and skewness.
These recommendations are based upon the results of the simulation studies summarized in Singh, Maichle, and Lee (2006).
However, simulations results will not cover all Real World data sets; for additional insight the user may want to consult a statistician.
Suggested UCL to Use
95% Student's-t UCL 0.036 or 95% Modified-t UCL 0.0362
90% Chebyshev(Mean, Sd) UCL 0.0401 95% Chebyshev(Mean, Sd) UCL 0.0446
97.5% Chebyshev(Mean, Sd) UCL 0.0509 99% Chebyshev(Mean, Sd) UCL 0.0632
95% Hall's Bootstrap UCL 0.0386 95% Percentile Bootstrap UCL 0.0357
95% BCA Bootstrap UCL 0.0371
95% CLT UCL 0.0356 95% Jackknife UCL 0.036
95% Standard Bootstrap UCL 0.0354 95% Bootstrap-t UCL 0.0386
Nonparametric Distribution Free UCL Statistics
Data do not follow a Discernible Distribution (0.05)
Nonparametric Distribution Free UCLs
95% Chebyshev (MVUE) UCL 0.0431 97.5% Chebyshev (MVUE) UCL 0.0487
99% Chebyshev (MVUE) UCL 0.0598
Assuming Lognormal Distribution
95% H-UCL 0.0368 90% Chebyshev (MVUE) UCL 0.039
Maximum of Logged Data -2.781 SD of logged Data 0.378
Lognormal Statistics
Minimum of Logged Data -3.912 Mean of logged Data -3.572
5% Lilliefors Critical Value 0.22 Data Not Lognormal at 5% Significance Level
Data Not Lognormal at 5% Significance Level
5% Shapiro Wilk Critical Value 0.881 Data Not Lognormal at 5% Significance Level
Lilliefors Test Statistic 0.246 Lilliefors Lognormal GOF Test
Lognormal GOF Test
Shapiro Wilk Test Statistic 0.837 Shapiro Wilk Lognormal GOF Test
Assuming Gamma Distribution
95% Approximate Gamma UCL (use when n>=50)) 0.0364 95% Adjusted Gamma UCL (use when n<50) 0.0373
Adjusted Level of Significance 0.0324 Adjusted Chi Square Value 139.7
MLE Mean (bias corrected) 0.0302 MLE Sd (bias corrected) 0.0126
Approximate Chi Square Value (0.05) 143
Theta hat (MLE) 0.00424 Theta star (bias corrected MLE) 0.00526
nu hat (MLE) 213.8 nu star (bias corrected) 172.4
Gamma Statistics
k hat (MLE) 7.126 k star (bias corrected MLE) 5.745
5% K-S Critical Value 0.222 Data Not Gamma Distributed at 5% Significance Level
Data Not Gamma Distributed at 5% Significance Level
5% A-D Critical Value 0.738 Data Not Gamma Distributed at 5% Significance Level
K-S Test Statistic 0.251 Kolmogorov-Smirnov Gamma GOF Test
Gamma GOF Test
A-D Test Statistic 1.065 Anderson-Darling Gamma GOF Test
95% Student's-t UCL 0.036 95% Adjusted-CLT UCL (Chen-1995) 0.0369
95% Modified-t UCL (Johnson-1978) 0.0362
Data Not Normal at 5% Significance Level
Assuming Normal Distribution
95% Normal UCL 95% UCLs (Adjusted for Skewness)
Lilliefors Test Statistic 0.24 Lilliefors GOF Test
5% Lilliefors Critical Value 0.22 Data Not Normal at 5% Significance Level
Normal GOF Test
Shapiro Wilk Test Statistic 0.799 Shapiro Wilk GOF Test
5% Shapiro Wilk Critical Value 0.881 Data Not Normal at 5% Significance Level
Coefficient of Variation 0.425 Skewness 1.353
Maximum 0.062 Median 0.03
SD 0.0128 Std. Error of Mean 0.00331
Number of Missing Observations 32
Minimum 0.02 Mean 0.0302
Perfluoro-n-octanoate acid (PFOA) (tc-2)
General Statistics
Total Number of Observations 15 Number of Distinct Observations 6
Coffey Appendix H - Data Statistics
RAAF Base Tindal PFAS Ecological Risk Assessment
438
439
440
441
442
443
444
445
446
447
448
449
450
451
452
453
454
455
456
457
458
459
460
461
462
463
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466
467
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469
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471
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473
474
475
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477
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481
482
483
484
485
486
487
488
489
490
491
492
493
494
495
496
497
498
499
500
501
502
503
504
505
506
507
508
509
510
511
512
513
514
515
516
517
518
A B C D E F G H I J K L
Note: Suggestions regarding the selection of a 95% UCL are provided to help the user to select the most appropriate 95% UCL.
Recommendations are based upon data size, data distribution, and skewness.
These recommendations are based upon the results of the simulation studies summarized in Singh, Maichle, and Lee (2006).
However, simulations results will not cover all Real World data sets; for additional insight the user may want to consult a statistician.
Recommended UCL exceeds the maximum observation
When a data set follows an approximate (e.g., normal) distribution passing one of the GOF test
When applicable, it is suggested to use a UCL based upon a distribution (e.g., gamma) passing both GOF tests in ProUCL
Suggested UCL to Use
95% Student's-t UCL 0.0231
90% Chebyshev(Mean, Sd) UCL 0.0233 95% Chebyshev(Mean, Sd) UCL 0.0279
97.5% Chebyshev(Mean, Sd) UCL 0.0341 99% Chebyshev(Mean, Sd) UCL 0.0465
95% Hall's Bootstrap UCL N/A 95% Percentile Bootstrap UCL N/A
95% BCA Bootstrap UCL N/A
95% CLT UCL 0.0188 95% Jackknife UCL N/A
95% Standard Bootstrap UCL N/A 95% Bootstrap-t UCL N/A
Nonparametric Distribution Free UCL Statistics
Data appear to follow a Discernible Distribution at 5% Significance Level
Nonparametric Distribution Free UCLs
95% Chebyshev (MVUE) UCL 0.0264 97.5% Chebyshev (MVUE) UCL 0.0321
99% Chebyshev (MVUE) UCL 0.0432
Assuming Lognormal Distribution
95% H-UCL 0.0598 90% Chebyshev (MVUE) UCL 0.0223
Maximum of Logged Data -3.912 SD of logged Data 0.4
Lognormal Statistics
Minimum of Logged Data -4.605 Mean of logged Data -4.374
5% Lilliefors Critical Value 0.425 Data appear Lognormal at 5% Significance Level
Data appear Approximate Lognormal at 5% Significance Level
5% Shapiro Wilk Critical Value 0.767 Data Not Lognormal at 5% Significance Level
Lilliefors Test Statistic 0.385 Lilliefors Lognormal GOF Test
Lognormal GOF Test
Shapiro Wilk Test Statistic 0.75 Shapiro Wilk Lognormal GOF Test
Assuming Gamma Distribution
95% Approximate Gamma UCL (use when n>=50)) N/A 95% Adjusted Gamma UCL (use when n<50) N/A
Adjusted Level of Significance N/A Adjusted Chi Square Value N/A
MLE Mean (bias corrected) N/A MLE Sd (bias corrected) N/A
Approximate Chi Square Value (0.05) N/A
Theta hat (MLE) 0.00148 Theta star (bias corrected MLE) N/A
nu hat (MLE) 53.95 nu star (bias corrected) N/A
Gamma GOF Test
Not Enough Data to Perform GOF Test
Gamma Statistics
k hat (MLE) 8.992 k star (bias corrected MLE) N/A
95% Modified-t UCL (Johnson-1978) 0.0236
Assuming Normal Distribution
95% Normal UCL 95% UCLs (Adjusted for Skewness)
95% Student's-t UCL 0.0231 95% Adjusted-CLT UCL (Chen-1995) 0.0224
5% Lilliefors Critical Value 0.425 Data appear Normal at 5% Significance Level
Data appear Approximate Normal at 5% Significance Level
5% Shapiro Wilk Critical Value 0.767 Data Not Normal at 5% Significance Level
Lilliefors Test Statistic 0.385 Lilliefors GOF Test
Normal GOF Test
Shapiro Wilk Test Statistic 0.75 Shapiro Wilk GOF Test
Note: Sample size is small (e.g., <10), if data are collected using ISM approach, you should use
guidance provided in ITRC Tech Reg Guide on ISM (ITRC, 2012) to compute statistics of interest.
For example, you may want to use Chebyshev UCL to estimate EPC (ITRC, 2012).
Chebyshev UCL can be computed using the Nonparametric and All UCL Options of ProUCL 5.1
SD 0.00577 Std. Error of Mean 0.00333
Coefficient of Variation 0.433 Skewness 1.732
Minimum 0.01 Mean 0.0133
Maximum 0.02 Median 0.01
Total Number of Observations 3 Number of Distinct Observations 2
Number of Missing Observations 23
Perfluoro-n-octane sulfonic acid (PFOS) (kr-1)
General StatisticsCoffey Appendix H - Data Statistics
RAAF Base Tindal PFAS Ecological Risk Assessment
519
520
521
522
523
524
525
526
527
528
529
530
531
532
533
534
535
536
537
538
539
540
541
542
543
544
545
546
547
548
549
550
551
552
553
554
555
556
557
558
559
560
561
562
563
564
565
566
567
568
569
570
571
572
573
574
575
576
577
578
579
580
581
582
583
584
585
586
587
588
589
590
591
592
593
594
595
A B C D E F G H I J K L
Note: Suggestions regarding the selection of a 95% UCL are provided to help the user to select the most appropriate 95% UCL.
Recommendations are based upon data size, data distribution, and skewness.
These recommendations are based upon the results of the simulation studies summarized in Singh, Maichle, and Lee (2006).
However, simulations results will not cover all Real World data sets; for additional insight the user may want to consult a statistician.
Suggested UCL to Use
95% Chebyshev (Mean, Sd) UCL 0.0935
90% Chebyshev(Mean, Sd) UCL 0.0831 95% Chebyshev(Mean, Sd) UCL 0.0935
97.5% Chebyshev(Mean, Sd) UCL 0.108 99% Chebyshev(Mean, Sd) UCL 0.136
95% Hall's Bootstrap UCL 0.0748 95% Percentile Bootstrap UCL 0.0725
95% BCA Bootstrap UCL 0.0734
95% CLT UCL 0.0727 95% Jackknife UCL 0.0729
95% Standard Bootstrap UCL 0.0724 95% Bootstrap-t UCL 0.0741
Nonparametric Distribution Free UCL Statistics
Data do not follow a Discernible Distribution (0.05)
Nonparametric Distribution Free UCLs
95% Chebyshev (MVUE) UCL 0.103 97.5% Chebyshev (MVUE) UCL 0.121
99% Chebyshev (MVUE) UCL 0.157
Assuming Lognormal Distribution
95% H-UCL 0.0851 90% Chebyshev (MVUE) UCL 0.0902
Maximum of Logged Data -1.561 SD of logged Data 0.909
Lognormal Statistics
Minimum of Logged Data -4.962 Mean of logged Data -3.191
5% Lilliefors Critical Value 0.132 Data Not Lognormal at 5% Significance Level
Data Not Lognormal at 5% Significance Level
5% Shapiro Wilk Critical Value 0.944 Data Not Lognormal at 5% Significance Level
Lilliefors Test Statistic 0.159 Lilliefors Lognormal GOF Test
Lognormal GOF Test
Shapiro Wilk Test Statistic 0.928 Shapiro Wilk Lognormal GOF Test
Assuming Gamma Distribution
95% Approximate Gamma UCL (use when n>=50)) 0.0751 95% Adjusted Gamma UCL (use when n<50) 0.0757
Adjusted Level of Significance 0.0445 Adjusted Chi Square Value 96.49
MLE Mean (bias corrected) 0.06 MLE Sd (bias corrected) 0.051
Approximate Chi Square Value (0.05) 97.23
Theta hat (MLE) 0.0409 Theta star (bias corrected MLE) 0.0434
nu hat (MLE) 129.2 nu star (bias corrected) 121.7
Data Not Gamma Distributed at 5% Significance Level
Gamma Statistics
k hat (MLE) 1.468 k star (bias corrected MLE) 1.383
K-S Test Statistic 0.201 Kolmogorov-Smirnov Gamma GOF Test
5% K-S Critical Value 0.136 Data Not Gamma Distributed at 5% Significance Level
Gamma GOF Test
A-D Test Statistic 1.477 Anderson-Darling Gamma GOF Test
5% A-D Critical Value 0.768 Data Not Gamma Distributed at 5% Significance Level
95% Modified-t UCL (Johnson-1978) 0.0731
Assuming Normal Distribution
95% Normal UCL 95% UCLs (Adjusted for Skewness)
95% Student's-t UCL 0.0729 95% Adjusted-CLT UCL (Chen-1995) 0.0739
5% Lilliefors Critical Value 0.132 Data Not Normal at 5% Significance Level
Data Not Normal at 5% Significance Level
5% Shapiro Wilk Critical Value 0.944 Data Not Normal at 5% Significance Level
Lilliefors Test Statistic 0.245 Lilliefors GOF Test
Normal GOF Test
Shapiro Wilk Test Statistic 0.844 Shapiro Wilk GOF Test
SD 0.051 Std. Error of Mean 0.00768
Coefficient of Variation 0.849 Skewness 1.029
Minimum 0.007 Mean 0.06
Maximum 0.21 Median 0.03
Total Number of Observations 44 Number of Distinct Observations 20
Number of Missing Observations 18
Perfluoro-n-octane sulfonic acid (PFOS) (kr-2)
General Statistics
Coffey Appendix H - Data Statistics
RAAF Base Tindal PFAS Ecological Risk Assessment
596
597
598
599
600
601
602
603
604
605
606
607
608
609
610
611
612
613
614
615
616
617
618
619
620
621
622
623
624
625
626
627
628
629
630
631
632
633
634
635
636
637
638
639
640
641
642
643
644
645
646
647
648
649
650
651
652
653
654
655
656
657
658
659
660
661
662
663
664
665
666
667
668
669
670
671
A B C D E F G H I J K L
Note: Suggestions regarding the selection of a 95% UCL are provided to help the user to select the most appropriate 95% UCL.
Recommendations are based upon data size, data distribution, and skewness.
These recommendations are based upon the results of the simulation studies summarized in Singh, Maichle, and Lee (2006).
However, simulations results will not cover all Real World data sets; for additional insight the user may want to consult a statistician.
Suggested UCL to Use
95% Student's-t UCL 0.115
90% Chebyshev(Mean, Sd) UCL 0.125 95% Chebyshev(Mean, Sd) UCL 0.137
97.5% Chebyshev(Mean, Sd) UCL 0.153 99% Chebyshev(Mean, Sd) UCL 0.184
95% Hall's Bootstrap UCL 0.115 95% Percentile Bootstrap UCL 0.114
95% BCA Bootstrap UCL 0.112
95% CLT UCL 0.114 95% Jackknife UCL 0.115
95% Standard Bootstrap UCL 0.114 95% Bootstrap-t UCL 0.116
Nonparametric Distribution Free UCL Statistics
Data appear to follow a Discernible Distribution at 5% Significance Level
Nonparametric Distribution Free UCLs
95% Chebyshev (MVUE) UCL 0.145 97.5% Chebyshev (MVUE) UCL 0.164
99% Chebyshev (MVUE) UCL 0.201
Assuming Lognormal Distribution
95% H-UCL 0.123 90% Chebyshev (MVUE) UCL 0.131
Maximum of Logged Data -1.772 SD of logged Data 0.444
Lognormal Statistics
Minimum of Logged Data -3.507 Mean of logged Data -2.386
5% Lilliefors Critical Value 0.188 Data appear Lognormal at 5% Significance Level
Data appear Lognormal at 5% Significance Level
5% Shapiro Wilk Critical Value 0.908 Data appear Lognormal at 5% Significance Level
Lilliefors Test Statistic 0.126 Lilliefors Lognormal GOF Test
Lognormal GOF Test
Shapiro Wilk Test Statistic 0.934 Shapiro Wilk Lognormal GOF Test
Assuming Gamma Distribution
95% Approximate Gamma UCL (use when n>=50)) 0.118 95% Adjusted Gamma UCL (use when n<50) 0.119
Adjusted Level of Significance 0.0383 Adjusted Chi Square Value 186.1
MLE Mean (bias corrected) 0.1 MLE Sd (bias corrected) 0.0435
Approximate Chi Square Value (0.05) 188.5
Theta hat (MLE) 0.0163 Theta star (bias corrected MLE) 0.0189
nu hat (MLE) 257.4 nu star (bias corrected) 222
Detected data appear Gamma Distributed at 5% Significance Level
Gamma Statistics
k hat (MLE) 6.129 k star (bias corrected MLE) 5.285
K-S Test Statistic 0.124 Kolmogorov-Smirnov Gamma GOF Test
5% K-S Critical Value 0.19 Detected data appear Gamma Distributed at 5% Significance Level
Gamma GOF Test
A-D Test Statistic 0.324 Anderson-Darling Gamma GOF Test
5% A-D Critical Value 0.745 Detected data appear Gamma Distributed at 5% Significance Level
95% Modified-t UCL (Johnson-1978) 0.115
Assuming Normal Distribution
95% Normal UCL 95% UCLs (Adjusted for Skewness)
95% Student's-t UCL 0.115 95% Adjusted-CLT UCL (Chen-1995) 0.114
5% Lilliefors Critical Value 0.188 Data appear Normal at 5% Significance Level
Data appear Normal at 5% Significance Level
5% Shapiro Wilk Critical Value 0.908 Data appear Normal at 5% Significance Level
Lilliefors Test Statistic 0.167 Lilliefors GOF Test
Normal GOF Test
Shapiro Wilk Test Statistic 0.963 Shapiro Wilk GOF Test
SD 0.0388 Std. Error of Mean 0.00847
Coefficient of Variation 0.388 Skewness 0.185
Minimum 0.03 Mean 0.1
Maximum 0.17 Median 0.1
Total Number of Observations 21 Number of Distinct Observations 12
Number of Missing Observations 8
Perfluoro-n-octane sulfonic acid (PFOS) (kr-3)
General StatisticsCoffey Appendix H - Data Statistics
RAAF Base Tindal PFAS Ecological Risk Assessment
672
673
674
675
676
677
678
679
680
681
682
683
684
685
686
687
688
689
690
691
692
693
694
695
696
697
698
699
700
701
702
703
704
705
706
707
708
709
710
711
712
713
714
715
716
717
718
719
720
721
722
723
724
725
726
727
728
729
730
731
732
733
734
735
736
737
738
739
740
741
742
743
744
745
746
747
A B C D E F G H I J K L
Note: Suggestions regarding the selection of a 95% UCL are provided to help the user to select the most appropriate 95% UCL.
Recommendations are based upon data size, data distribution, and skewness.
These recommendations are based upon the results of the simulation studies summarized in Singh, Maichle, and Lee (2006).
However, simulations results will not cover all Real World data sets; for additional insight the user may want to consult a statistician.
Suggested UCL to Use
95% Chebyshev (Mean, Sd) UCL 2.071
90% Chebyshev(Mean, Sd) UCL 1.755 95% Chebyshev(Mean, Sd) UCL 2.071
97.5% Chebyshev(Mean, Sd) UCL 2.51 99% Chebyshev(Mean, Sd) UCL 3.373
95% Hall's Bootstrap UCL 1.673 95% Percentile Bootstrap UCL 1.466
95% BCA Bootstrap UCL 1.571
95% CLT UCL 1.439 95% Jackknife UCL 1.447
95% Standard Bootstrap UCL 1.437 95% Bootstrap-t UCL 1.619
Nonparametric Distribution Free UCL Statistics
Data appear to follow a Discernible Distribution at 5% Significance Level
Nonparametric Distribution Free UCLs
95% Chebyshev (MVUE) UCL 2.944 97.5% Chebyshev (MVUE) UCL 3.682
99% Chebyshev (MVUE) UCL 5.131
Assuming Lognormal Distribution
95% H-UCL 2.715 90% Chebyshev (MVUE) UCL 2.413
Maximum of Logged Data 2.152 SD of logged Data 1.624
Lognormal Statistics
Minimum of Logged Data -3.507 Mean of logged Data -1.046
5% Lilliefors Critical Value 0.126 Data appear Lognormal at 5% Significance Level
Data appear Approximate Lognormal at 5% Significance Level
5% Shapiro Wilk Critical Value 0.947 Data Not Lognormal at 5% Significance Level
Lilliefors Test Statistic 0.0865 Lilliefors Lognormal GOF Test
Lognormal GOF Test
Shapiro Wilk Test Statistic 0.943 Shapiro Wilk Lognormal GOF Test
Assuming Gamma Distribution
95% Approximate Gamma UCL (use when n>=50)) 1.499 95% Adjusted Gamma UCL (use when n<50) 1.515
Adjusted Level of Significance 0.0451 Adjusted Chi Square Value 37.23
MLE Mean (bias corrected) 1.056 MLE Sd (bias corrected) 1.43
Approximate Chi Square Value (0.05) 37.63
Theta hat (MLE) 1.865 Theta star (bias corrected MLE) 1.937
nu hat (MLE) 55.48 nu star (bias corrected) 53.42
Data Not Gamma Distributed at 5% Significance Level
Gamma Statistics
k hat (MLE) 0.566 k star (bias corrected MLE) 0.545
K-S Test Statistic 0.135 Kolmogorov-Smirnov Gamma GOF Test
5% K-S Critical Value 0.133 Data Not Gamma Distributed at 5% Significance Level
Gamma GOF Test
A-D Test Statistic 1.005 Anderson-Darling Gamma GOF Test
5% A-D Critical Value 0.808 Data Not Gamma Distributed at 5% Significance Level
95% Modified-t UCL (Johnson-1978) 1.462
Assuming Normal Distribution
95% Normal UCL 95% UCLs (Adjusted for Skewness)
95% Student's-t UCL 1.447 95% Adjusted-CLT UCL (Chen-1995) 1.536
5% Lilliefors Critical Value 0.126 Data Not Normal at 5% Significance Level
Data Not Normal at 5% Significance Level
5% Shapiro Wilk Critical Value 0.947 Data Not Normal at 5% Significance Level
Lilliefors Test Statistic 0.265 Lilliefors GOF Test
Normal GOF Test
Shapiro Wilk Test Statistic 0.667 Shapiro Wilk GOF Test
SD 1.63 Std. Error of Mean 0.233
Coefficient of Variation 1.544 Skewness 2.722
Minimum 0.03 Mean 1.056
Maximum 8.6 Median 0.31
Total Number of Observations 49 Number of Distinct Observations 38
Number of Missing Observations 1
Perfluoro-n-octane sulfonic acid (PFOS) (on-base drain)
General StatisticsCoffey Appendix H - Data Statistics
RAAF Base Tindal PFAS Ecological Risk Assessment
748
749
750
751
752
753
754
755
756
757
758
759
760
761
762
763
764
765
766
767
768
769
770
771
772
773
774
775
776
777
778
779
780
781
782
783
784
785
786
787
788
789
790
791
792
793
794
795
796
797
798
799
800
801
802
803
804
805
806
807
808
809
810
811
812
813
814
815
816
817
818
819
820
821
822
823
A B C D E F G H I J K L
Note: Suggestions regarding the selection of a 95% UCL are provided to help the user to select the most appropriate 95% UCL.
Recommendations are based upon data size, data distribution, and skewness.
These recommendations are based upon the results of the simulation studies summarized in Singh, Maichle, and Lee (2006).
However, simulations results will not cover all Real World data sets; for additional insight the user may want to consult a statistician.
Suggested UCL to Use
99% Chebyshev (Mean, Sd) UCL 51.78
90% Chebyshev(Mean, Sd) UCL 20.53 95% Chebyshev(Mean, Sd) UCL 26.64
97.5% Chebyshev(Mean, Sd) UCL 35.12 99% Chebyshev(Mean, Sd) UCL 51.78
95% Hall's Bootstrap UCL 46.25 95% Percentile Bootstrap UCL 15.91
95% BCA Bootstrap UCL 20.75
95% CLT UCL 14.44 95% Jackknife UCL 15.01
95% Standard Bootstrap UCL 14.14 95% Bootstrap-t UCL 54.49
Nonparametric Distribution Free UCL Statistics
Data appear to follow a Discernible Distribution at 5% Significance Level
Nonparametric Distribution Free UCLs
95% Chebyshev (MVUE) UCL 16.77 97.5% Chebyshev (MVUE) UCL 21.61
99% Chebyshev (MVUE) UCL 31.13
Assuming Lognormal Distribution
95% H-UCL 31.8 90% Chebyshev (MVUE) UCL 13.28
Maximum of Logged Data 4.174 SD of logged Data 1.53
Lognormal Statistics
Minimum of Logged Data -1.47 Mean of logged Data 0.697
5% Lilliefors Critical Value 0.226 Data appear Lognormal at 5% Significance Level
Data appear Lognormal at 5% Significance Level
5% Shapiro Wilk Critical Value 0.874 Data appear Lognormal at 5% Significance Level
Lilliefors Test Statistic 0.128 Lilliefors Lognormal GOF Test
Lognormal GOF Test
Shapiro Wilk Test Statistic 0.942 Shapiro Wilk Lognormal GOF Test
Assuming Gamma Distribution
95% Approximate Gamma UCL (use when n>=50)) 15.88 95% Adjusted Gamma UCL (use when n<50) 17.81
Adjusted Level of Significance 0.0312 Adjusted Chi Square Value 4.925
MLE Mean (bias corrected) 7.046 MLE Sd (bias corrected) 10.57
Approximate Chi Square Value (0.05) 5.524
Theta hat (MLE) 13.95 Theta star (bias corrected MLE) 15.85
nu hat (MLE) 14.15 nu star (bias corrected) 12.45
Data Not Gamma Distributed at 5% Significance Level
Gamma Statistics
k hat (MLE) 0.505 k star (bias corrected MLE) 0.445
K-S Test Statistic 0.253 Kolmogorov-Smirnov Gamma GOF Test
5% K-S Critical Value 0.242 Data Not Gamma Distributed at 5% Significance Level
Gamma GOF Test
A-D Test Statistic 1.049 Anderson-Darling Gamma GOF Test
5% A-D Critical Value 0.793 Data Not Gamma Distributed at 5% Significance Level
95% Modified-t UCL (Johnson-1978) 15.73
Assuming Normal Distribution
95% Normal UCL 95% UCLs (Adjusted for Skewness)
95% Student's-t UCL 15.01 95% Adjusted-CLT UCL (Chen-1995) 19.11
5% Lilliefors Critical Value 0.226 Data Not Normal at 5% Significance Level
Data Not Normal at 5% Significance Level
5% Shapiro Wilk Critical Value 0.874 Data Not Normal at 5% Significance Level
Lilliefors Test Statistic 0.423 Lilliefors GOF Test
Normal GOF Test
Shapiro Wilk Test Statistic 0.41 Shapiro Wilk GOF Test
SD 16.82 Std. Error of Mean 4.495
Coefficient of Variation 2.387 Skewness 3.635
Minimum 0.23 Mean 7.046
Maximum 65 Median 2.55
Total Number of Observations 14 Number of Distinct Observations 14
Number of Missing Observations 0
Perfluoro-n-octane sulfonic acid (PFOS) (source area)
General StatisticsCoffey Appendix H - Data Statistics
RAAF Base Tindal PFAS Ecological Risk Assessment
824
825
826
827
828
829
830
831
832
833
834
835
836
837
838
839
840
841
842
843
844
845
846
847
848
849
850
851
852
853
854
855
856
857
858
859
860
861
862
863
864
865
866
867
868
869
870
871
872
873
874
875
876
877
878
879
880
881
882
883
884
885
886
887
888
889
890
891
892
893
894
895
896
897
898
899
900
901
902
A B C D E F G H I J K L
Recommendations are based upon data size, data distribution, and skewness.
These recommendations are based upon the results of the simulation studies summarized in Singh, Maichle, and Lee (2006).
However, simulations results will not cover all Real World data sets; for additional insight the user may want to consult a statistician.
When a data set follows an approximate (e.g., normal) distribution passing one of the GOF test
When applicable, it is suggested to use a UCL based upon a distribution (e.g., gamma) passing both GOF tests in ProUCL
Note: Suggestions regarding the selection of a 95% UCL are provided to help the user to select the most appropriate 95% UCL.
Suggested UCL to Use
95% Adjusted Gamma UCL 1.139
90% Chebyshev(Mean, Sd) UCL 1.132 95% Chebyshev(Mean, Sd) UCL 1.3
97.5% Chebyshev(Mean, Sd) UCL 1.532 99% Chebyshev(Mean, Sd) UCL 1.989
95% Hall's Bootstrap UCL 0.982 95% Percentile Bootstrap UCL 0.959
95% BCA Bootstrap UCL 0.975
95% CLT UCL 0.965 95% Jackknife UCL 0.971
95% Standard Bootstrap UCL 0.963 95% Bootstrap-t UCL 0.984
Nonparametric Distribution Free UCL Statistics
Data appear to follow a Discernible Distribution at 5% Significance Level
Nonparametric Distribution Free UCLs
95% Chebyshev (MVUE) UCL 2.883 97.5% Chebyshev (MVUE) UCL 3.647
99% Chebyshev (MVUE) UCL 5.147
Assuming Lognormal Distribution
95% H-UCL 3.058 90% Chebyshev (MVUE) UCL 2.333
Maximum of Logged Data 0.788 SD of logged Data 1.617
Lognormal Statistics
Minimum of Logged Data -3.912 Mean of logged Data -1.114
5% Lilliefors Critical Value 0.15 Data Not Lognormal at 5% Significance Level
Data Not Lognormal at 5% Significance Level
5% Shapiro Wilk Critical Value 0.933 Data Not Lognormal at 5% Significance Level
Lilliefors Test Statistic 0.198 Lilliefors Lognormal GOF Test
Lognormal GOF Test
Shapiro Wilk Test Statistic 0.866 Shapiro Wilk Lognormal GOF Test
Assuming Gamma Distribution
95% Approximate Gamma UCL (use when n>=50) 1.117 95% Adjusted Gamma UCL (use when n<50) 1.139
Adjusted Level of Significance 0.0422 Adjusted Chi Square Value 30.58
MLE Mean (bias corrected) 0.762 MLE Sd (bias corrected) 0.93
Approximate Chi Square Value (0.05) 31.17
Theta hat (MLE) 1.066 Theta star (bias corrected MLE) 1.135
nu hat (MLE) 48.63 nu star (bias corrected) 45.67
Detected data follow Appr. Gamma Distribution at 5% Significance Level
Gamma Statistics
k hat (MLE) 0.715 k star (bias corrected MLE) 0.672
K-S Test Statistic 0.154 Kolmogorov-Smirnov Gamma GOF Test
5% K-S Critical Value 0.157 Detected data appear Gamma Distributed at 5% Significance Level
Gamma GOF Test
A-D Test Statistic 1.159 Anderson-Darling Gamma GOF Test
5% A-D Critical Value 0.791 Data Not Gamma Distributed at 5% Significance Level
95% Modified-t UCL (Johnson-1978) 0.973
Assuming Normal Distribution
95% Normal UCL 95% UCLs (Adjusted for Skewness)
95% Student's-t UCL 0.971 95% Adjusted-CLT UCL (Chen-1995) 0.979
5% Lilliefors Critical Value 0.15 Data Not Normal at 5% Significance Level
Data Not Normal at 5% Significance Level
5% Shapiro Wilk Critical Value 0.933 Data Not Normal at 5% Significance Level
Lilliefors Test Statistic 0.173 Lilliefors GOF Test
Normal GOF Test
Shapiro Wilk Test Statistic 0.865 Shapiro Wilk GOF Test
SD 0.719 Std. Error of Mean 0.123
Coefficient of Variation 0.943 Skewness 0.613
Minimum 0.02 Mean 0.762
Maximum 2.2 Median 0.665
Total Number of Observations 34 Number of Distinct Observations 24
Number of Missing Observations 1
Perfluoro-n-octane sulfonic acid (PFOS) (tc-1)
General StatisticsCoffey Appendix H - Data Statistics
RAAF Base Tindal PFAS Ecological Risk Assessment
903
904
905
906
907
908
909
910
911
912
913
914
915
916
917
918
919
920
921
922
923
924
925
926
927
928
929
930
931
932
933
934
935
936
937
938
939
940
941
942
943
944
945
946
947
948
949
950
951
952
953
954
955
956
957
958
959
960
961
962
963
964
965
966
967
968
969
970
971
972
973
974
975
976
977
A B C D E F G H I J K L
Note: Suggestions regarding the selection of a 95% UCL are provided to help the user to select the most appropriate 95% UCL.
Recommendations are based upon data size, data distribution, and skewness.
These recommendations are based upon the results of the simulation studies summarized in Singh, Maichle, and Lee (2006).
However, simulations results will not cover all Real World data sets; for additional insight the user may want to consult a statistician.
Suggested UCL to Use
95% Chebyshev (Mean, Sd) UCL 0.686
90% Chebyshev(Mean, Sd) UCL 0.597 95% Chebyshev(Mean, Sd) UCL 0.686
97.5% Chebyshev(Mean, Sd) UCL 0.81 99% Chebyshev(Mean, Sd) UCL 1.053
95% Hall's Bootstrap UCL 0.518 95% Percentile Bootstrap UCL 0.506
95% BCA Bootstrap UCL 0.515
95% CLT UCL 0.508 95% Jackknife UCL 0.511
95% Standard Bootstrap UCL 0.506 95% Bootstrap-t UCL 0.525
Nonparametric Distribution Free UCL Statistics
Data appear to follow a Discernible Distribution at 5% Significance Level
Nonparametric Distribution Free UCLs
95% Chebyshev (MVUE) UCL 1.294 97.5% Chebyshev (MVUE) UCL 1.621
99% Chebyshev (MVUE) UCL 2.263
Assuming Lognormal Distribution
95% H-UCL 1.231 90% Chebyshev (MVUE) UCL 1.058
Maximum of Logged Data 0.405 SD of logged Data 1.513
Lognormal Statistics
Minimum of Logged Data -4.605 Mean of logged Data -1.702
5% Lilliefors Critical Value 0.144 Data appear Lognormal at 5% Significance Level
Data appear Approximate Lognormal at 5% Significance Level
5% Shapiro Wilk Critical Value 0.936 Data Not Lognormal at 5% Significance Level
Lilliefors Test Statistic 0.135 Lilliefors Lognormal GOF Test
Lognormal GOF Test
Shapiro Wilk Test Statistic 0.899 Shapiro Wilk Lognormal GOF Test
Assuming Gamma Distribution
95% Approximate Gamma UCL (use when n>=50)) 0.57 95% Adjusted Gamma UCL (use when n<50) 0.579
Adjusted Level of Significance 0.0431 Adjusted Chi Square Value 36.66
MLE Mean (bias corrected) 0.401 MLE Sd (bias corrected) 0.474
Approximate Chi Square Value (0.05) 37.23
Theta hat (MLE) 0.528 Theta star (bias corrected MLE) 0.56
nu hat (MLE) 56.17 nu star (bias corrected) 52.95
Gamma Statistics
k hat (MLE) 0.759 k star (bias corrected MLE) 0.716
5% K-S Critical Value 0.151 Data Not Gamma Distributed at 5% Significance Level
Data Not Gamma Distributed at 5% Significance Level
5% A-D Critical Value 0.788 Data Not Gamma Distributed at 5% Significance Level
K-S Test Statistic 0.153 Kolmogorov-Smirnov Gamma GOF Test
Gamma GOF Test
A-D Test Statistic 0.931 Anderson-Darling Gamma GOF Test
95% Student's-t UCL 0.511 95% Adjusted-CLT UCL (Chen-1995) 0.518
95% Modified-t UCL (Johnson-1978) 0.513
Data Not Normal at 5% Significance Level
Assuming Normal Distribution
95% Normal UCL 95% UCLs (Adjusted for Skewness)
Lilliefors Test Statistic 0.197 Lilliefors GOF Test
5% Lilliefors Critical Value 0.144 Data Not Normal at 5% Significance Level
Normal GOF Test
Shapiro Wilk Test Statistic 0.839 Shapiro Wilk GOF Test
5% Shapiro Wilk Critical Value 0.936 Data Not Normal at 5% Significance Level
Coefficient of Variation 0.996 Skewness 0.86
Maximum 1.5 Median 0.21
SD 0.399 Std. Error of Mean 0.0656
Number of Missing Observations 10
Minimum 0.01 Mean 0.401
Perfluoro-n-octane sulfonic acid (PFOS) (tc-2)
General Statistics
Total Number of Observations 37 Number of Distinct Observations 26
Coffey Appendix H - Data Statistics
RAAF Base Tindal PFAS Ecological Risk Assessment
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43
44
45
46
47
48
49
50
51
52
53
54
55
56
57
58
A B C D E F G H I J K L
If possible, compute and collect Data Quality Objectives (DQO) based sample size and analytical results.
Warning: This data set only has 0 observations!
Data set is too small to compute reliable and meaningful statistics and estimates!
The data set for variable Perfluoro-n-octanoate acid (PFOA) (kr-2 dry) was not processed!
It is suggested to collect at least 8 to 10 observations before using these statistical methods!
Maximum N/A Median N/A
Number of Missing Observations 34
Minimum N/A Mean N/A
General Statistics
Total Number of Observations 0 Number of Distinct Observations 0
If possible, compute and collect Data Quality Objectives (DQO) based sample size and analytical results.
Perfluoro-n-octanoate acid (PFOA) (kr-2 dry)
Warning: This data set only has 0 observations!
Data set is too small to compute reliable and meaningful statistics and estimates!
The data set for variable Perfluoro-n-octanoate acid (PFOA) (kr-1 wet) was not processed!
It is suggested to collect at least 8 to 10 observations before using these statistical methods!
Maximum N/A Median N/A
Number of Missing Observations 14
Minimum N/A Mean N/A
General Statistics
Total Number of Observations 0 Number of Distinct Observations 0
If possible, compute and collect Data Quality Objectives (DQO) based sample size and analytical results.
Perfluoro-n-octanoate acid (PFOA) (kr-1 wet)
Warning: This data set only has 0 observations!
Data set is too small to compute reliable and meaningful statistics and estimates!
The data set for variable Perfluoro-n-octanoate acid (PFOA) (kr-1 dry) was not processed!
It is suggested to collect at least 8 to 10 observations before using these statistical methods!
Maximum N/A Median N/A
Number of Missing Observations 12
Minimum N/A Mean N/A
General Statistics
Total Number of Observations 0 Number of Distinct Observations 0
Number of Bootstrap Operations 2000
Perfluoro-n-octanoate acid (PFOA) (kr-1 dry)
From File Tindal_SW_for ProUCL Analysis_20180605_a.xls
Full Precision OFF
Confidence Coefficient 95%
UCL Statistics for Uncensored Full Data Sets
User Selected Options
Date/Time of Computation ProUCL 5.16/6/2018 8:29:09 AM
Coffey Appendix H - Data Statistics
RAAF Base Tindal PFAS Ecological Risk Assessment
59
60
61
62
63
64
65
66
67
68
69
70
71
72
73
74
75
76
77
78
79
80
81
82
83
84
85
86
87
88
89
90
91
92
93
94
95
96
97
98
99
100
101
102
103
104
105
106
107
108
109
110
111
112
A B C D E F G H I J K L
5% K-S Critical Value 0.297 Data Not Gamma Distributed at 5% Significance Level
Data Not Gamma Distributed at 5% Significance Level
5% A-D Critical Value 0.723 Data Not Gamma Distributed at 5% Significance Level
K-S Test Statistic 0.338 Kolmogorov-Smirnov Gamma GOF Test
Gamma GOF Test
A-D Test Statistic 1.088 Anderson-Darling Gamma GOF Test
95% Student's-t UCL 0.00895 95% Adjusted-CLT UCL (Chen-1995) 0.00857
95% Modified-t UCL (Johnson-1978) 0.00894
Data Not Normal at 5% Significance Level
Assuming Normal Distribution
95% Normal UCL 95% UCLs (Adjusted for Skewness)
Lilliefors Test Statistic 0.324 Lilliefors GOF Test
5% Lilliefors Critical Value 0.283 Data Not Normal at 5% Significance Level
Normal GOF Test
Shapiro Wilk Test Statistic 0.711 Shapiro Wilk GOF Test
5% Shapiro Wilk Critical Value 0.818 Data Not Normal at 5% Significance Level
Note: Sample size is small (e.g., <10), if data are collected using ISM approach, you should use
guidance provided in ITRC Tech Reg Guide on ISM (ITRC, 2012) to compute statistics of interest.
For example, you may want to use Chebyshev UCL to estimate EPC (ITRC, 2012).
Chebyshev UCL can be computed using the Nonparametric and All UCL Options of ProUCL 5.1
Coefficient of Variation 0.644 Skewness -0.0328
Maximum 0.01 Median 0.0065
SD 0.00403 Std. Error of Mean 0.00142
Number of Missing Observations 9
Minimum 0.002 Mean 0.00625
General Statistics
Total Number of Observations 8 Number of Distinct Observations 3
If possible, compute and collect Data Quality Objectives (DQO) based sample size and analytical results.
Perfluoro-n-octanoate acid (PFOA) (kr-3 dry)
Warning: This data set only has 0 observations!
Data set is too small to compute reliable and meaningful statistics and estimates!
The data set for variable Perfluoro-n-octanoate acid (PFOA) (kr-2 wet) was not processed!
It is suggested to collect at least 8 to 10 observations before using these statistical methods!
Maximum N/A Median N/A
Number of Missing Observations 28
Minimum N/A Mean N/A
General Statistics
Total Number of Observations 0 Number of Distinct Observations 0
Perfluoro-n-octanoate acid (PFOA) (kr-2 wet)
Coffey Appendix H - Data Statistics
RAAF Base Tindal PFAS Ecological Risk Assessment
113
114
115
116
117
118
119
120
121
122
123
124
125
126
127
128
129
130
131
132
133
134
135
136
137
138
139
140
141
142
143
144
145
146
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148
149
150
151
152
153
154
155
156
157
158
159
160
161
162
163
164
A B C D E F G H I J K L
These recommendations are based upon the results of the simulation studies summarized in Singh, Maichle, and Lee (2006).
However, simulations results will not cover all Real World data sets; for additional insight the user may want to consult a statistician.
Note: For highly negatively-skewed data, confidence limits (e.g., Chen, Johnson, Lognormal, and Gamma) may not be
reliable. Chen's and Johnson's methods provide adjustments for positvely skewed data sets.
Recommended UCL exceeds the maximum observation
Note: Suggestions regarding the selection of a 95% UCL are provided to help the user to select the most appropriate 95% UCL.
Recommendations are based upon data size, data distribution, and skewness.
Suggested UCL to Use
95% Chebyshev (Mean, Sd) UCL 0.0125
90% Chebyshev(Mean, Sd) UCL 0.0105 95% Chebyshev(Mean, Sd) UCL 0.0125
97.5% Chebyshev(Mean, Sd) UCL 0.0151 99% Chebyshev(Mean, Sd) UCL 0.0204
95% Hall's Bootstrap UCL N/A 95% Percentile Bootstrap UCL N/A
95% BCA Bootstrap UCL N/A
95% CLT UCL 0.00859 95% Jackknife UCL 0.00895
95% Standard Bootstrap UCL N/A 95% Bootstrap-t UCL N/A
Nonparametric Distribution Free UCL Statistics
Data do not follow a Discernible Distribution (0.05)
Nonparametric Distribution Free UCLs
95% Chebyshev (MVUE) UCL 0.014 97.5% Chebyshev (MVUE) UCL 0.0173
99% Chebyshev (MVUE) UCL 0.0238
Assuming Lognormal Distribution
95% H-UCL 0.0153 90% Chebyshev (MVUE) UCL 0.0116
Maximum of Logged Data -4.605 SD of logged Data 0.767
Lognormal Statistics
Minimum of Logged Data -6.215 Mean of logged Data -5.309
5% Lilliefors Critical Value 0.283 Data Not Lognormal at 5% Significance Level
Data Not Lognormal at 5% Significance Level
5% Shapiro Wilk Critical Value 0.818 Data Not Lognormal at 5% Significance Level
Lilliefors Test Statistic 0.32 Lilliefors Lognormal GOF Test
Lognormal GOF Test
Shapiro Wilk Test Statistic 0.752 Shapiro Wilk Lognormal GOF Test
Assuming Gamma Distribution
95% Approximate Gamma UCL (use when n>=50)) 0.0108 95% Adjusted Gamma UCL (use when n<50) 0.0125
Adjusted Level of Significance 0.0195 Adjusted Chi Square Value 12.15
MLE Mean (bias corrected) 0.00625 MLE Sd (bias corrected) 0.00507
Approximate Chi Square Value (0.05) 14.07
Theta hat (MLE) 0.00272 Theta star (bias corrected MLE) 0.00412
nu hat (MLE) 36.73 nu star (bias corrected) 24.29
Gamma Statistics
k hat (MLE) 2.296 k star (bias corrected MLE) 1.518
Coffey Appendix H - Data Statistics
RAAF Base Tindal PFAS Ecological Risk Assessment
165
166
167
168
169
170
171
172
173
174
175
176
177
178
179
180
181
182
183
184
185
186
187
188
189
190
191
192
193
194
195
196
197
198
199
200
201
202
203
204
205
206
207
208
209
210
211
212
213
214
215
216
217
218
219
220
221
222
223
224
225
226
227
228
229
230
231
232
233
234
235
236
237
238
239
240
241
A B C D E F G H I J K L
Nonparametric Distribution Free UCL Statistics
Data appear to follow a Discernible Distribution at 5% Significance Level
95% Chebyshev (MVUE) UCL 0.0799 97.5% Chebyshev (MVUE) UCL 0.0986
99% Chebyshev (MVUE) UCL 0.135
Assuming Lognormal Distribution
95% H-UCL 0.311 90% Chebyshev (MVUE) UCL 0.0665
Maximum of Logged Data -2.996 SD of logged Data 0.478
Lognormal Statistics
Minimum of Logged Data -3.912 Mean of logged Data -3.376
5% Lilliefors Critical Value 0.425 Data appear Lognormal at 5% Significance Level
Data appear Lognormal at 5% Significance Level
5% Shapiro Wilk Critical Value 0.767 Data appear Lognormal at 5% Significance Level
Lilliefors Test Statistic 0.295 Lilliefors Lognormal GOF Test
Lognormal GOF Test
Shapiro Wilk Test Statistic 0.919 Shapiro Wilk Lognormal GOF Test
Assuming Gamma Distribution
95% Approximate Gamma UCL (use when n>=50)) N/A 95% Adjusted Gamma UCL (use when n<50) N/A
Approximate Chi Square Value (0.05) N/A
Adjusted Level of Significance N/A Adjusted Chi Square Value N/A
nu hat (MLE) 44.04 nu star (bias corrected) N/A
MLE Mean (bias corrected) N/A MLE Sd (bias corrected) N/A
k hat (MLE) 7.341 k star (bias corrected MLE) N/A
Theta hat (MLE) 0.00499 Theta star (bias corrected MLE) N/A
Gamma GOF Test
Not Enough Data to Perform GOF Test
Gamma Statistics
95% Student's-t UCL 0.0624 95% Adjusted-CLT UCL (Chen-1995) 0.0461
95% Modified-t UCL (Johnson-1978) 0.0616
Data appear Normal at 5% Significance Level
Assuming Normal Distribution
95% Normal UCL 95% UCLs (Adjusted for Skewness)
Lilliefors Test Statistic 0.253 Lilliefors GOF Test
5% Lilliefors Critical Value 0.425 Data appear Normal at 5% Significance Level
Normal GOF Test
Shapiro Wilk Test Statistic 0.964 Shapiro Wilk GOF Test
5% Shapiro Wilk Critical Value 0.767 Data appear Normal at 5% Significance Level
Note: Sample size is small (e.g., <10), if data are collected using ISM approach, you should use
guidance provided in ITRC Tech Reg Guide on ISM (ITRC, 2012) to compute statistics of interest.
For example, you may want to use Chebyshev UCL to estimate EPC (ITRC, 2012).
Chebyshev UCL can be computed using the Nonparametric and All UCL Options of ProUCL 5.1
Coefficient of Variation 0.417 Skewness -0.935
Maximum 0.05 Median 0.04
SD 0.0153 Std. Error of Mean 0.00882
Number of Missing Observations 1
Minimum 0.02 Mean 0.0367
Perfluoro-n-octanoate acid (PFOA) (on-base drain dry)
General Statistics
Total Number of Observations 3 Number of Distinct Observations 3
It is suggested to collect at least 8 to 10 observations before using these statistical methods!
If possible, compute and collect Data Quality Objectives (DQO) based sample size and analytical results.
Warning: This data set only has 0 observations!
Data set is too small to compute reliable and meaningful statistics and estimates!
The data set for variable Perfluoro-n-octanoate acid (PFOA) (kr-3 wet) was not processed!
Minimum N/A Mean N/A
Maximum N/A Median N/A
Total Number of Observations 0 Number of Distinct Observations 0
Number of Missing Observations 12
Perfluoro-n-octanoate acid (PFOA) (kr-3 wet)
General StatisticsCoffey Appendix H - Data Statistics
RAAF Base Tindal PFAS Ecological Risk Assessment
242
243
244
245
246
247
248
249
250
251
252
253
254
255
256
257
258
259
260
261
262
263
264
265
266
267
268
269
270
271
272
273
274
275
276
277
278
279
280
A B C D E F G H I J K L
5% Lilliefors Critical Value 0.173 Data Not Normal at 5% Significance Level
Data Not Normal at 5% Significance Level
5% Shapiro Wilk Critical Value 0.918 Data Not Normal at 5% Significance Level
Lilliefors Test Statistic 0.237 Lilliefors GOF Test
Normal GOF Test
Shapiro Wilk Test Statistic 0.862 Shapiro Wilk GOF Test
SD 0.0474 Std. Error of Mean 0.00948
Coefficient of Variation 0.829 Skewness 1.03
Minimum 0.01 Mean 0.0572
Maximum 0.19 Median 0.03
Total Number of Observations 25 Number of Distinct Observations 11
Number of Missing Observations 21
Perfluoro-n-octanoate acid (PFOA) (on-base drain wet)
General Statistics
These recommendations are based upon the results of the simulation studies summarized in Singh, Maichle, and Lee (2006).
However, simulations results will not cover all Real World data sets; for additional insight the user may want to consult a statistician.
Note: For highly negatively-skewed data, confidence limits (e.g., Chen, Johnson, Lognormal, and Gamma) may not be
reliable. Chen's and Johnson's methods provide adjustments for positvely skewed data sets.
Recommended UCL exceeds the maximum observation
Note: Suggestions regarding the selection of a 95% UCL are provided to help the user to select the most appropriate 95% UCL.
Recommendations are based upon data size, data distribution, and skewness.
Suggested UCL to Use
95% Student's-t UCL 0.0624
90% Chebyshev(Mean, Sd) UCL 0.0631 95% Chebyshev(Mean, Sd) UCL 0.0751
97.5% Chebyshev(Mean, Sd) UCL 0.0917 99% Chebyshev(Mean, Sd) UCL 0.124
95% Hall's Bootstrap UCL N/A 95% Percentile Bootstrap UCL N/A
95% BCA Bootstrap UCL N/A
95% CLT UCL 0.0512 95% Jackknife UCL 0.0624
95% Standard Bootstrap UCL N/A 95% Bootstrap-t UCL N/A
Nonparametric Distribution Free UCLs
Coffey Appendix H - Data Statistics
RAAF Base Tindal PFAS Ecological Risk Assessment
281
282
283
284
285
286
287
288
289
290
291
292
293
294
295
296
297
298
299
300
301
302
303
304
305
306
307
308
309
310
311
312
313
314
315
316
317
318
319
320
321
322
323
324
325
326
327
328
329
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331
332
333
334
335
336
337
338
339
340
341
342
A B C D E F G H I J K L
ProUCL computes and outputs H-statistic based UCLs for historical reasons only.
H-statistic often results in unstable (both high and low) values of UCL95 as shown in examples in the Technical Guide.
It is therefore recommended to avoid the use of H-statistic based 95% UCLs.
Use of nonparametric methods are preferred to compute UCL95 for skewed data sets which do not follow a gamma distribution.
Note: Suggestions regarding the selection of a 95% UCL are provided to help the user to select the most appropriate 95% UCL.
Recommendations are based upon data size, data distribution, and skewness.
These recommendations are based upon the results of the simulation studies summarized in Singh, Maichle, and Lee (2006).
However, simulations results will not cover all Real World data sets; for additional insight the user may want to consult a statistician.
Suggested UCL to Use
95% H-UCL 0.097
90% Chebyshev(Mean, Sd) UCL 0.0856 95% Chebyshev(Mean, Sd) UCL 0.0985
97.5% Chebyshev(Mean, Sd) UCL 0.116 99% Chebyshev(Mean, Sd) UCL 0.152
95% Hall's Bootstrap UCL 0.0768 95% Percentile Bootstrap UCL 0.072
95% BCA Bootstrap UCL 0.074
95% CLT UCL 0.0728 95% Jackknife UCL 0.0734
95% Standard Bootstrap UCL 0.0726 95% Bootstrap-t UCL 0.0761
Nonparametric Distribution Free UCL Statistics
Data appear to follow a Discernible Distribution at 5% Significance Level
Nonparametric Distribution Free UCLs
95% Chebyshev (MVUE) UCL 0.114 97.5% Chebyshev (MVUE) UCL 0.138
99% Chebyshev (MVUE) UCL 0.185
Assuming Lognormal Distribution
95% H-UCL 0.097 90% Chebyshev (MVUE) UCL 0.0972
Maximum of Logged Data -1.661 SD of logged Data 0.941
Lognormal Statistics
Minimum of Logged Data -4.605 Mean of logged Data -3.241
5% Lilliefors Critical Value 0.173 Data appear Lognormal at 5% Significance Level
Data appear Approximate Lognormal at 5% Significance Level
5% Shapiro Wilk Critical Value 0.918 Data Not Lognormal at 5% Significance Level
Lilliefors Test Statistic 0.172 Lilliefors Lognormal GOF Test
Lognormal GOF Test
Shapiro Wilk Test Statistic 0.909 Shapiro Wilk Lognormal GOF Test
Assuming Gamma Distribution
95% Approximate Gamma UCL (use when n>=50)) 0.0782 95% Adjusted Gamma UCL (use when n<50) 0.08
Adjusted Level of Significance 0.0395 Adjusted Chi Square Value 46.92
MLE Mean (bias corrected) 0.0572 MLE Sd (bias corrected) 0.0499
Approximate Chi Square Value (0.05) 47.95
Theta hat (MLE) 0.0392 Theta star (bias corrected MLE) 0.0436
nu hat (MLE) 73.01 nu star (bias corrected) 65.58
Data Not Gamma Distributed at 5% Significance Level
Gamma Statistics
k hat (MLE) 1.46 k star (bias corrected MLE) 1.312
K-S Test Statistic 0.181 Kolmogorov-Smirnov Gamma GOF Test
5% K-S Critical Value 0.178 Data Not Gamma Distributed at 5% Significance Level
Gamma GOF Test
A-D Test Statistic 0.803 Anderson-Darling Gamma GOF Test
5% A-D Critical Value 0.762 Data Not Gamma Distributed at 5% Significance Level
95% Modified-t UCL (Johnson-1978) 0.0737
Assuming Normal Distribution
95% Normal UCL 95% UCLs (Adjusted for Skewness)
95% Student's-t UCL 0.0734 95% Adjusted-CLT UCL (Chen-1995) 0.0749Coffey Appendix H - Data Statistics
RAAF Base Tindal PFAS Ecological Risk Assessment
343
344
345
346
347
348
349
350
351
352
353
354
355
356
357
358
359
360
361
362
363
364
365
366
367
368
369
370
371
372
373
374
375
376
377
378
379
380
381
382
383
384
385
386
387
388
389
390
391
392
393
394
395
396
397
398
399
400
401
402
403
A B C D E F G H I J K L
Nonparametric Distribution Free UCL Statistics
Data appear to follow a Discernible Distribution at 5% Significance Level
95% Chebyshev (MVUE) UCL 0.584 97.5% Chebyshev (MVUE) UCL 0.754
99% Chebyshev (MVUE) UCL 1.086
Assuming Lognormal Distribution
95% H-UCL 1.125 90% Chebyshev (MVUE) UCL 0.462
Maximum of Logged Data 0.693 SD of logged Data 1.54
Lognormal Statistics
Minimum of Logged Data -4.605 Mean of logged Data -2.675
5% Lilliefors Critical Value 0.226 Data appear Lognormal at 5% Significance Level
Data appear Lognormal at 5% Significance Level
5% Shapiro Wilk Critical Value 0.874 Data appear Lognormal at 5% Significance Level
Lilliefors Test Statistic 0.16 Lilliefors Lognormal GOF Test
Lognormal GOF Test
Shapiro Wilk Test Statistic 0.91 Shapiro Wilk Lognormal GOF Test
Assuming Gamma Distribution
95% Approximate Gamma UCL (use when n>=50)) 0.508 95% Adjusted Gamma UCL (use when n<50) 0.569
Adjusted Level of Significance 0.0312 Adjusted Chi Square Value 5.188
MLE Mean (bias corrected) 0.229 MLE Sd (bias corrected) 0.338
Approximate Chi Square Value (0.05) 5.804
Theta hat (MLE) 0.437 Theta star (bias corrected MLE) 0.499
nu hat (MLE) 14.68 nu star (bias corrected) 12.87
Data Not Gamma Distributed at 5% Significance Level
Gamma Statistics
k hat (MLE) 0.524 k star (bias corrected MLE) 0.46
K-S Test Statistic 0.26 Kolmogorov-Smirnov Gamma GOF Test
5% K-S Critical Value 0.241 Data Not Gamma Distributed at 5% Significance Level
Gamma GOF Test
A-D Test Statistic 1.002 Anderson-Darling Gamma GOF Test
5% A-D Critical Value 0.791 Data Not Gamma Distributed at 5% Significance Level
95% Modified-t UCL (Johnson-1978) 0.495
Assuming Normal Distribution
95% Normal UCL 95% UCLs (Adjusted for Skewness)
95% Student's-t UCL 0.473 95% Adjusted-CLT UCL (Chen-1995) 0.597
5% Lilliefors Critical Value 0.226 Data Not Normal at 5% Significance Level
Data Not Normal at 5% Significance Level
5% Shapiro Wilk Critical Value 0.874 Data Not Normal at 5% Significance Level
Lilliefors Test Statistic 0.436 Lilliefors GOF Test
Normal GOF Test
Shapiro Wilk Test Statistic 0.428 Shapiro Wilk GOF Test
SD 0.515 Std. Error of Mean 0.138
Coefficient of Variation 2.248 Skewness 3.596
Minimum 0.01 Mean 0.229
Maximum 2 Median 0.105
Total Number of Observations 14 Number of Distinct Observations 10
Number of Missing Observations 0
Perfluoro-n-octanoate acid (PFOA) (source area)
General Statistics
Coffey Appendix H - Data Statistics
RAAF Base Tindal PFAS Ecological Risk Assessment
404
405
406
407
408
409
410
411
412
413
414
415
416
417
418
419
420
421
422
423
424
425
426
427
428
429
430
431
432
433
434
435
436
437
438
439
440
441
442
443
444
445
446
447
448
449
450
451
452
453
454
455
456
457
458
459
460
461
462
463
464
465
A B C D E F G H I J K L
Assuming Gamma Distribution
95% Approximate Gamma UCL (use when n>=50)) 0.0562 95% Adjusted Gamma UCL (use when n<50) 0.0595
Adjusted Level of Significance 0.0195 Adjusted Chi Square Value 94.05
MLE Mean (bias corrected) 0.045 MLE Sd (bias corrected) 0.0161
Approximate Chi Square Value (0.05) 99.65
Theta hat (MLE) 0.00366 Theta star (bias corrected MLE) 0.00579
nu hat (MLE) 196.9 nu star (bias corrected) 124.4
Detected data appear Gamma Distributed at 5% Significance Level
Gamma Statistics
k hat (MLE) 12.31 k star (bias corrected MLE) 7.776
K-S Test Statistic 0.246 Kolmogorov-Smirnov Gamma GOF Test
5% K-S Critical Value 0.294 Detected data appear Gamma Distributed at 5% Significance Level
Gamma GOF Test
A-D Test Statistic 0.388 Anderson-Darling Gamma GOF Test
5% A-D Critical Value 0.715 Detected data appear Gamma Distributed at 5% Significance Level
95% Modified-t UCL (Johnson-1978) 0.0547
Assuming Normal Distribution
95% Normal UCL 95% UCLs (Adjusted for Skewness)
95% Student's-t UCL 0.0545 95% Adjusted-CLT UCL (Chen-1995) 0.0548
5% Lilliefors Critical Value 0.283 Data appear Normal at 5% Significance Level
Data appear Normal at 5% Significance Level
5% Shapiro Wilk Critical Value 0.818 Data appear Normal at 5% Significance Level
Lilliefors Test Statistic 0.263 Lilliefors GOF Test
Normal GOF Test
Shapiro Wilk Test Statistic 0.897 Shapiro Wilk GOF Test
Note: Sample size is small (e.g., <10), if data are collected using ISM approach, you should use
guidance provided in ITRC Tech Reg Guide on ISM (ITRC, 2012) to compute statistics of interest.
For example, you may want to use Chebyshev UCL to estimate EPC (ITRC, 2012).
Chebyshev UCL can be computed using the Nonparametric and All UCL Options of ProUCL 5.1
SD 0.0141 Std. Error of Mean 0.005
Coefficient of Variation 0.314 Skewness 0.808
Minimum 0.03 Mean 0.045
Maximum 0.07 Median 0.04
Total Number of Observations 8 Number of Distinct Observations 5
Number of Missing Observations 5
Perfluoro-n-octanoate acid (PFOA) (tc-1 dry)
General Statistics
Note: Suggestions regarding the selection of a 95% UCL are provided to help the user to select the most appropriate 95% UCL.
Recommendations are based upon data size, data distribution, and skewness.
These recommendations are based upon the results of the simulation studies summarized in Singh, Maichle, and Lee (2006).
However, simulations results will not cover all Real World data sets; for additional insight the user may want to consult a statistician.
Suggested UCL to Use
99% Chebyshev (Mean, Sd) UCL 1.6
90% Chebyshev(Mean, Sd) UCL 0.643 95% Chebyshev(Mean, Sd) UCL 0.83
97.5% Chebyshev(Mean, Sd) UCL 1.09 99% Chebyshev(Mean, Sd) UCL 1.6
95% Hall's Bootstrap UCL 1.396 95% Percentile Bootstrap UCL 0.499
95% BCA Bootstrap UCL 0.644
95% CLT UCL 0.456 95% Jackknife UCL 0.473
95% Standard Bootstrap UCL 0.452 95% Bootstrap-t UCL 1.396
Nonparametric Distribution Free UCLs
Coffey Appendix H - Data Statistics
RAAF Base Tindal PFAS Ecological Risk Assessment
466
467
468
469
470
471
472
473
474
475
476
477
478
479
480
481
482
483
484
485
486
487
488
489
490
491
492
493
494
495
496
497
498
499
500
501
502
503
504
505
506
507
508
509
510
511
512
513
514
515
516
517
518
519
520
521
522
523
524
525
526
527
528
529
A B C D E F G H I J K L
Detected data appear Gamma Distributed at 5% Significance Level
K-S Test Statistic 0.191 Kolmogorov-Smirnov Gamma GOF Test
5% K-S Critical Value 0.257 Detected data appear Gamma Distributed at 5% Significance Level
Gamma GOF Test
A-D Test Statistic 0.38 Anderson-Darling Gamma GOF Test
5% A-D Critical Value 0.733 Detected data appear Gamma Distributed at 5% Significance Level
95% Modified-t UCL (Johnson-1978) 0.0537
Assuming Normal Distribution
95% Normal UCL 95% UCLs (Adjusted for Skewness)
95% Student's-t UCL 0.0534 95% Adjusted-CLT UCL (Chen-1995) 0.054
5% Lilliefors Critical Value 0.251 Data appear Normal at 5% Significance Level
Data appear Normal at 5% Significance Level
5% Shapiro Wilk Critical Value 0.85 Data appear Normal at 5% Significance Level
Lilliefors Test Statistic 0.245 Lilliefors GOF Test
Normal GOF Test
Shapiro Wilk Test Statistic 0.896 Shapiro Wilk GOF Test
SD 0.0227 Std. Error of Mean 0.00686
Coefficient of Variation 0.555 Skewness 0.778
Minimum 0.01 Mean 0.041
Maximum 0.082 Median 0.04
Total Number of Observations 11 Number of Distinct Observations 7
Number of Missing Observations 11
Perfluoro-n-octanoate acid (PFOA) (tc-1 wet)
General Statistics
Note: Suggestions regarding the selection of a 95% UCL are provided to help the user to select the most appropriate 95% UCL.
Recommendations are based upon data size, data distribution, and skewness.
These recommendations are based upon the results of the simulation studies summarized in Singh, Maichle, and Lee (2006).
However, simulations results will not cover all Real World data sets; for additional insight the user may want to consult a statistician.
Suggested UCL to Use
95% Student's-t UCL 0.0545
90% Chebyshev(Mean, Sd) UCL 0.06 95% Chebyshev(Mean, Sd) UCL 0.0668
97.5% Chebyshev(Mean, Sd) UCL 0.0762 99% Chebyshev(Mean, Sd) UCL 0.0947
95% Hall's Bootstrap UCL 0.0615 95% Percentile Bootstrap UCL 0.0525
95% BCA Bootstrap UCL 0.0538
95% CLT UCL 0.0532 95% Jackknife UCL 0.0545
95% Standard Bootstrap UCL 0.0528 95% Bootstrap-t UCL 0.0588
Nonparametric Distribution Free UCL Statistics
Data appear to follow a Discernible Distribution at 5% Significance Level
Nonparametric Distribution Free UCLs
95% Chebyshev (MVUE) UCL 0.0661 97.5% Chebyshev (MVUE) UCL 0.0752
99% Chebyshev (MVUE) UCL 0.0932
Assuming Lognormal Distribution
95% H-UCL 0.0573 90% Chebyshev (MVUE) UCL 0.0595
Maximum of Logged Data -2.659 SD of logged Data 0.304
Lognormal Statistics
Minimum of Logged Data -3.507 Mean of logged Data -3.142
5% Lilliefors Critical Value 0.283 Data appear Lognormal at 5% Significance Level
Data appear Lognormal at 5% Significance Level
5% Shapiro Wilk Critical Value 0.818 Data appear Lognormal at 5% Significance Level
Lilliefors Test Statistic 0.225 Lilliefors Lognormal GOF Test
Lognormal GOF Test
Shapiro Wilk Test Statistic 0.92 Shapiro Wilk Lognormal GOF Test
Coffey Appendix H - Data Statistics
RAAF Base Tindal PFAS Ecological Risk Assessment
530
531
532
533
534
535
536
537
538
539
540
541
542
543
544
545
546
547
548
549
550
551
552
553
554
555
556
557
558
559
560
561
562
563
564
565
566
567
568
569
570
571
572
573
574
575
576
577
578
579
580
581
582
583
584
585
586
587
588
589
590
591
592
593
594
595
596
597
598
A B C D E F G H I J K L
5% Lilliefors Critical Value 0.325 Data Not Normal at 5% Significance Level
Data appear Approximate Normal at 5% Significance Level
5% Shapiro Wilk Critical Value 0.788 Data appear Normal at 5% Significance Level
Lilliefors Test Statistic 0.345 Lilliefors GOF Test
Normal GOF Test
Shapiro Wilk Test Statistic 0.854 Shapiro Wilk GOF Test
Note: Sample size is small (e.g., <10), if data are collected using ISM approach, you should use
guidance provided in ITRC Tech Reg Guide on ISM (ITRC, 2012) to compute statistics of interest.
For example, you may want to use Chebyshev UCL to estimate EPC (ITRC, 2012).
Chebyshev UCL can be computed using the Nonparametric and All UCL Options of ProUCL 5.1
SD 0.0155 Std. Error of Mean 0.00632
Coefficient of Variation 0.416 Skewness 0.98
Minimum 0.021 Mean 0.0372
Maximum 0.062 Median 0.03
Total Number of Observations 6 Number of Distinct Observations 4
Number of Missing Observations 7
Perfluoro-n-octanoate acid (PFOA) (tc-2 dry)
General Statistics
Note: Suggestions regarding the selection of a 95% UCL are provided to help the user to select the most appropriate 95% UCL.
Recommendations are based upon data size, data distribution, and skewness.
These recommendations are based upon the results of the simulation studies summarized in Singh, Maichle, and Lee (2006).
However, simulations results will not cover all Real World data sets; for additional insight the user may want to consult a statistician.
Suggested UCL to Use
95% Student's-t UCL 0.0534
90% Chebyshev(Mean, Sd) UCL 0.0616 95% Chebyshev(Mean, Sd) UCL 0.0709
97.5% Chebyshev(Mean, Sd) UCL 0.0838 99% Chebyshev(Mean, Sd) UCL 0.109
95% Hall's Bootstrap UCL 0.0674 95% Percentile Bootstrap UCL 0.0522
95% BCA Bootstrap UCL 0.0533
95% CLT UCL 0.0523 95% Jackknife UCL 0.0534
95% Standard Bootstrap UCL 0.0518 95% Bootstrap-t UCL 0.0569
Nonparametric Distribution Free UCL Statistics
Data appear to follow a Discernible Distribution at 5% Significance Level
Nonparametric Distribution Free UCLs
95% Chebyshev (MVUE) UCL 0.0764 97.5% Chebyshev (MVUE) UCL 0.0914
99% Chebyshev (MVUE) UCL 0.121
Assuming Lognormal Distribution
95% H-UCL 0.067 90% Chebyshev (MVUE) UCL 0.0655
Maximum of Logged Data -2.501 SD of logged Data 0.617
Lognormal Statistics
Minimum of Logged Data -4.605 Mean of logged Data -3.35
5% Lilliefors Critical Value 0.251 Data appear Lognormal at 5% Significance Level
Data appear Lognormal at 5% Significance Level
5% Shapiro Wilk Critical Value 0.85 Data appear Lognormal at 5% Significance Level
Lilliefors Test Statistic 0.22 Lilliefors Lognormal GOF Test
Lognormal GOF Test
Shapiro Wilk Test Statistic 0.931 Shapiro Wilk Lognormal GOF Test
Assuming Gamma Distribution
95% Approximate Gamma UCL (use when n>=50)) 0.0578 95% Adjusted Gamma UCL (use when n<50) 0.0613
Adjusted Level of Significance 0.0278 Adjusted Chi Square Value 37.02
MLE Mean (bias corrected) 0.041 MLE Sd (bias corrected) 0.0259
Approximate Chi Square Value (0.05) 39.22
Theta hat (MLE) 0.0122 Theta star (bias corrected MLE) 0.0163
nu hat (MLE) 74.21 nu star (bias corrected) 55.31
Gamma Statistics
k hat (MLE) 3.373 k star (bias corrected MLE) 2.514Coffey Appendix H - Data Statistics
RAAF Base Tindal PFAS Ecological Risk Assessment
599
600
601
602
603
604
605
606
607
608
609
610
611
612
613
614
615
616
617
618
619
620
621
622
623
624
625
626
627
628
629
630
631
632
633
634
635
636
637
638
639
640
641
642
643
644
645
646
647
648
649
650
651
652
653
654
655
656
657
658
659
660
661
A B C D E F G H I J K L
Recommendations are based upon data size, data distribution, and skewness.
These recommendations are based upon the results of the simulation studies summarized in Singh, Maichle, and Lee (2006).
However, simulations results will not cover all Real World data sets; for additional insight the user may want to consult a statistician.
When a data set follows an approximate (e.g., normal) distribution passing one of the GOF test
When applicable, it is suggested to use a UCL based upon a distribution (e.g., gamma) passing both GOF tests in ProUCL
Note: Suggestions regarding the selection of a 95% UCL are provided to help the user to select the most appropriate 95% UCL.
Suggested UCL to Use
95% Student's-t UCL 0.0499
90% Chebyshev(Mean, Sd) UCL 0.0561 95% Chebyshev(Mean, Sd) UCL 0.0647
97.5% Chebyshev(Mean, Sd) UCL 0.0766 99% Chebyshev(Mean, Sd) UCL 0.1
95% Hall's Bootstrap UCL N/A 95% Percentile Bootstrap UCL N/A
95% BCA Bootstrap UCL N/A
95% CLT UCL 0.0476 95% Jackknife UCL 0.0499
95% Standard Bootstrap UCL N/A 95% Bootstrap-t UCL N/A
Nonparametric Distribution Free UCL Statistics
Data appear to follow a Discernible Distribution at 5% Significance Level
Nonparametric Distribution Free UCLs
95% Chebyshev (MVUE) UCL 0.0632 97.5% Chebyshev (MVUE) UCL 0.0745
99% Chebyshev (MVUE) UCL 0.0967
Assuming Lognormal Distribution
95% H-UCL 0.0576 90% Chebyshev (MVUE) UCL 0.0551
Maximum of Logged Data -2.781 SD of logged Data 0.396
Lognormal Statistics
Minimum of Logged Data -3.863 Mean of logged Data -3.36
5% Lilliefors Critical Value 0.325 Data appear Lognormal at 5% Significance Level
Data appear Lognormal at 5% Significance Level
5% Shapiro Wilk Critical Value 0.788 Data appear Lognormal at 5% Significance Level
Lilliefors Test Statistic 0.311 Lilliefors Lognormal GOF Test
Lognormal GOF Test
Shapiro Wilk Test Statistic 0.897 Shapiro Wilk Lognormal GOF Test
Assuming Gamma Distribution
95% Approximate Gamma UCL (use when n>=50)) 0.0542 95% Adjusted Gamma UCL (use when n<50) 0.0626
Adjusted Level of Significance 0.0122 Adjusted Chi Square Value 27.73
MLE Mean (bias corrected) 0.0372 MLE Sd (bias corrected) 0.0188
Approximate Chi Square Value (0.05) 32.05
Theta hat (MLE) 0.00491 Theta star (bias corrected MLE) 0.00954
nu hat (MLE) 90.8 nu star (bias corrected) 46.73
Detected data follow Appr. Gamma Distribution at 5% Significance Level
Gamma Statistics
k hat (MLE) 7.567 k star (bias corrected MLE) 3.894
K-S Test Statistic 0.339 Kolmogorov-Smirnov Gamma GOF Test
5% K-S Critical Value 0.333 Data Not Gamma Distributed at 5% Significance Level
Gamma GOF Test
A-D Test Statistic 0.52 Anderson-Darling Gamma GOF Test
5% A-D Critical Value 0.698 Detected data appear Gamma Distributed at 5% Significance Level
95% Modified-t UCL (Johnson-1978) 0.0503
Assuming Normal Distribution
95% Normal UCL 95% UCLs (Adjusted for Skewness)
95% Student's-t UCL 0.0499 95% Adjusted-CLT UCL (Chen-1995) 0.0503
Coffey Appendix H - Data Statistics
RAAF Base Tindal PFAS Ecological Risk Assessment
662
663
664
665
666
667
668
669
670
671
672
673
674
675
676
677
678
679
680
681
682
683
684
685
686
687
688
689
690
691
692
693
694
695
696
697
698
699
700
701
702
703
704
705
706
707
708
709
710
711
712
713
714
715
716
717
718
719
720
721
722
723
724
725
726
727
728
729
730
731
732
733
734
735
736
737
738
739
740
A B C D E F G H I J K L
Note: Suggestions regarding the selection of a 95% UCL are provided to help the user to select the most appropriate 95% UCL.
Recommendations are based upon data size, data distribution, and skewness.
These recommendations are based upon the results of the simulation studies summarized in Singh, Maichle, and Lee (2006).
However, simulations results will not cover all Real World data sets; for additional insight the user may want to consult a statistician.
Suggested UCL to Use
95% Student's-t UCL 0.031 or 95% Modified-t UCL 0.0312
90% Chebyshev(Mean, Sd) UCL 0.0344 95% Chebyshev(Mean, Sd) UCL 0.0384
97.5% Chebyshev(Mean, Sd) UCL 0.0439 99% Chebyshev(Mean, Sd) UCL 0.0548
95% Hall's Bootstrap UCL N/A 95% Percentile Bootstrap UCL N/A
95% BCA Bootstrap UCL N/A
95% CLT UCL 0.0304 95% Jackknife UCL 0.031
95% Standard Bootstrap UCL N/A 95% Bootstrap-t UCL N/A
Nonparametric Distribution Free UCL Statistics
Data do not follow a Discernible Distribution (0.05)
Nonparametric Distribution Free UCLs
95% Chebyshev (MVUE) UCL 0.037 97.5% Chebyshev (MVUE) UCL 0.042
99% Chebyshev (MVUE) UCL 0.0518
Assuming Lognormal Distribution
95% H-UCL 0.032 90% Chebyshev (MVUE) UCL 0.0334
Maximum of Logged Data -3.219 SD of logged Data 0.31
Lognormal Statistics
Minimum of Logged Data -3.912 Mean of logged Data -3.713
5% Lilliefors Critical Value 0.274 Data Not Lognormal at 5% Significance Level
Data Not Lognormal at 5% Significance Level
5% Shapiro Wilk Critical Value 0.829 Data Not Lognormal at 5% Significance Level
Lilliefors Test Statistic 0.406 Lilliefors Lognormal GOF Test
Lognormal GOF Test
Shapiro Wilk Test Statistic 0.662 Shapiro Wilk Lognormal GOF Test
Assuming Gamma Distribution
95% Approximate Gamma UCL (use when n>=50)) 0.0316 95% Adjusted Gamma UCL (use when n<50) 0.0331
Adjusted Level of Significance 0.0231 Adjusted Chi Square Value 103.1
MLE Mean (bias corrected) 0.0256 MLE Sd (bias corrected) 0.00938
Approximate Chi Square Value (0.05) 107.9
Theta hat (MLE) 0.00232 Theta star (bias corrected MLE) 0.00344
nu hat (MLE) 198.4 nu star (bias corrected) 133.6
Gamma Statistics
k hat (MLE) 11.02 k star (bias corrected MLE) 7.424
5% K-S Critical Value 0.279 Data Not Gamma Distributed at 5% Significance Level
Data Not Gamma Distributed at 5% Significance Level
5% A-D Critical Value 0.722 Data Not Gamma Distributed at 5% Significance Level
K-S Test Statistic 0.418 Kolmogorov-Smirnov Gamma GOF Test
Gamma GOF Test
A-D Test Statistic 1.586 Anderson-Darling Gamma GOF Test
95% Student's-t UCL 0.031 95% Adjusted-CLT UCL (Chen-1995) 0.0316
95% Modified-t UCL (Johnson-1978) 0.0312
Data Not Normal at 5% Significance Level
Assuming Normal Distribution
95% Normal UCL 95% UCLs (Adjusted for Skewness)
Lilliefors Test Statistic 0.402 Lilliefors GOF Test
5% Lilliefors Critical Value 0.274 Data Not Normal at 5% Significance Level
Normal GOF Test
Shapiro Wilk Test Statistic 0.658 Shapiro Wilk GOF Test
5% Shapiro Wilk Critical Value 0.829 Data Not Normal at 5% Significance Level
Note: Sample size is small (e.g., <10), if data are collected using ISM approach, you should use
guidance provided in ITRC Tech Reg Guide on ISM (ITRC, 2012) to compute statistics of interest.
For example, you may want to use Chebyshev UCL to estimate EPC (ITRC, 2012).
Chebyshev UCL can be computed using the Nonparametric and All UCL Options of ProUCL 5.1
Coefficient of Variation 0.345 Skewness 1.192
Maximum 0.04 Median 0.02
SD 0.00882 Std. Error of Mean 0.00294
Number of Missing Observations 25
Minimum 0.02 Mean 0.0256
Perfluoro-n-octanoate acid (PFOA) (tc-2 wet)
General Statistics
Total Number of Observations 9 Number of Distinct Observations 3
Coffey Appendix H - Data Statistics
RAAF Base Tindal PFAS Ecological Risk Assessment
741
742
743
744
745
746
747
748
749
750
751
752
753
754
755
756
757
758
759
760
761
762
763
764
765
766
767
768
769
770
771
772
773
774
775
776
777
778
779
780
781
782
783
784
785
786
787
788
789
790
791
792
793
794
795
796
797
798
799
800
801
802
803
804
805
806
807
808
809
810
811
812
813
814
815
816
817
818
819
820
821
822
A B C D E F G H I J K L
Note: Suggestions regarding the selection of a 95% UCL are provided to help the user to select the most appropriate 95% UCL.
Recommendations are based upon data size, data distribution, and skewness.
These recommendations are based upon the results of the simulation studies summarized in Singh, Maichle, and Lee (2006).
However, simulations results will not cover all Real World data sets; for additional insight the user may want to consult a statistician.
Recommended UCL exceeds the maximum observation
When a data set follows an approximate (e.g., normal) distribution passing one of the GOF test
When applicable, it is suggested to use a UCL based upon a distribution (e.g., gamma) passing both GOF tests in ProUCL
Suggested UCL to Use
95% Student's-t UCL 0.0231
90% Chebyshev(Mean, Sd) UCL 0.0233 95% Chebyshev(Mean, Sd) UCL 0.0279
97.5% Chebyshev(Mean, Sd) UCL 0.0341 99% Chebyshev(Mean, Sd) UCL 0.0465
95% Hall's Bootstrap UCL N/A 95% Percentile Bootstrap UCL N/A
95% BCA Bootstrap UCL N/A
95% CLT UCL 0.0188 95% Jackknife UCL N/A
95% Standard Bootstrap UCL N/A 95% Bootstrap-t UCL N/A
Nonparametric Distribution Free UCL Statistics
Data appear to follow a Discernible Distribution at 5% Significance Level
Nonparametric Distribution Free UCLs
95% Chebyshev (MVUE) UCL 0.0264 97.5% Chebyshev (MVUE) UCL 0.0321
99% Chebyshev (MVUE) UCL 0.0432
Assuming Lognormal Distribution
95% H-UCL 0.0598 90% Chebyshev (MVUE) UCL 0.0223
Maximum of Logged Data -3.912 SD of logged Data 0.4
Lognormal Statistics
Minimum of Logged Data -4.605 Mean of logged Data -4.374
5% Lilliefors Critical Value 0.425 Data appear Lognormal at 5% Significance Level
Data appear Approximate Lognormal at 5% Significance Level
5% Shapiro Wilk Critical Value 0.767 Data Not Lognormal at 5% Significance Level
Lilliefors Test Statistic 0.385 Lilliefors Lognormal GOF Test
Lognormal GOF Test
Shapiro Wilk Test Statistic 0.75 Shapiro Wilk Lognormal GOF Test
Assuming Gamma Distribution
95% Approximate Gamma UCL (use when n>=50)) N/A 95% Adjusted Gamma UCL (use when n<50) N/A
Adjusted Level of Significance N/A Adjusted Chi Square Value N/A
MLE Mean (bias corrected) N/A MLE Sd (bias corrected) N/A
Approximate Chi Square Value (0.05) N/A
Theta hat (MLE) 0.00148 Theta star (bias corrected MLE) N/A
nu hat (MLE) 53.95 nu star (bias corrected) N/A
Gamma GOF Test
Not Enough Data to Perform GOF Test
Gamma Statistics
k hat (MLE) 8.992 k star (bias corrected MLE) N/A
95% Modified-t UCL (Johnson-1978) 0.0236
Assuming Normal Distribution
95% Normal UCL 95% UCLs (Adjusted for Skewness)
95% Student's-t UCL 0.0231 95% Adjusted-CLT UCL (Chen-1995) 0.0224
5% Lilliefors Critical Value 0.425 Data appear Normal at 5% Significance Level
Data appear Approximate Normal at 5% Significance Level
5% Shapiro Wilk Critical Value 0.767 Data Not Normal at 5% Significance Level
Lilliefors Test Statistic 0.385 Lilliefors GOF Test
Normal GOF Test
Shapiro Wilk Test Statistic 0.75 Shapiro Wilk GOF Test
Note: Sample size is small (e.g., <10), if data are collected using ISM approach, you should use
guidance provided in ITRC Tech Reg Guide on ISM (ITRC, 2012) to compute statistics of interest.
For example, you may want to use Chebyshev UCL to estimate EPC (ITRC, 2012).
Chebyshev UCL can be computed using the Nonparametric and All UCL Options of ProUCL 5.1
SD 0.00577 Std. Error of Mean 0.00333
Coefficient of Variation 0.433 Skewness 1.732
Minimum 0.01 Mean 0.0133
Maximum 0.02 Median 0.01
Total Number of Observations 3 Number of Distinct Observations 2
Number of Missing Observations 9
Perfluoro-n-octane sulfonic acid (PFOS) (kr-1 dry)
General Statistics
Coffey Appendix H - Data Statistics
RAAF Base Tindal PFAS Ecological Risk Assessment
823
824
825
826
827
828
829
830
831
832
833
834
835
836
837
838
839
840
841
842
843
844
845
846
847
848
849
850
851
852
853
854
855
856
857
858
859
860
861
862
863
864
865
866
867
868
869
870
871
872
873
874
875
876
877
878
879
880
881
882
883
884
885
886
887
888
889
890
891
892
893
894
895
896
897
898
899
900
A B C D E F G H I J K L
Nonparametric Distribution Free UCL Statistics
Data do not follow a Discernible Distribution (0.05)
95% Chebyshev (MVUE) UCL 0.126 97.5% Chebyshev (MVUE) UCL 0.148
99% Chebyshev (MVUE) UCL 0.19
Assuming Lognormal Distribution
95% H-UCL 0.105 90% Chebyshev (MVUE) UCL 0.111
Maximum of Logged Data -1.561 SD of logged Data 0.77
Lognormal Statistics
Minimum of Logged Data -3.912 Mean of logged Data -2.855
5% Lilliefors Critical Value 0.154 Data Not Lognormal at 5% Significance Level
Data Not Lognormal at 5% Significance Level
5% Shapiro Wilk Critical Value 0.93 Data Not Lognormal at 5% Significance Level
Lilliefors Test Statistic 0.177 Lilliefors Lognormal GOF Test
Lognormal GOF Test
Shapiro Wilk Test Statistic 0.89 Shapiro Wilk Lognormal GOF Test
Assuming Gamma Distribution
95% Approximate Gamma UCL (use when n>=50)) 0.0941 95% Adjusted Gamma UCL (use when n<50) 0.0952
Adjusted Level of Significance 0.0416 Adjusted Chi Square Value 94.36
MLE Mean (bias corrected) 0.075 MLE Sd (bias corrected) 0.0548
Approximate Chi Square Value (0.05) 95.52
Theta hat (MLE) 0.0367 Theta star (bias corrected MLE) 0.0401
nu hat (MLE) 130.7 nu star (bias corrected) 119.8
Gamma Statistics
k hat (MLE) 2.042 k star (bias corrected MLE) 1.872
5% K-S Critical Value 0.158 Data Not Gamma Distributed at 5% Significance Level
Data Not Gamma Distributed at 5% Significance Level
5% A-D Critical Value 0.759 Data Not Gamma Distributed at 5% Significance Level
K-S Test Statistic 0.188 Kolmogorov-Smirnov Gamma GOF Test
Gamma GOF Test
A-D Test Statistic 1.165 Anderson-Darling Gamma GOF Test
95% Student's-t UCL 0.0905 95% Adjusted-CLT UCL (Chen-1995) 0.0912
95% Modified-t UCL (Johnson-1978) 0.0907
Data Not Normal at 5% Significance Level
Assuming Normal Distribution
95% Normal UCL 95% UCLs (Adjusted for Skewness)
Lilliefors Test Statistic 0.188 Lilliefors GOF Test
5% Lilliefors Critical Value 0.154 Data Not Normal at 5% Significance Level
Normal GOF Test
Shapiro Wilk Test Statistic 0.888 Shapiro Wilk GOF Test
5% Shapiro Wilk Critical Value 0.93 Data Not Normal at 5% Significance Level
Coefficient of Variation 0.69 Skewness 0.68
Maximum 0.21 Median 0.065
SD 0.0517 Std. Error of Mean 0.00915
Number of Missing Observations 2
Minimum 0.02 Mean 0.075
Perfluoro-n-octane sulfonic acid (PFOS) (kr-2 dry)
General Statistics
Total Number of Observations 32 Number of Distinct Observations 16
It is suggested to collect at least 8 to 10 observations before using these statistical methods!
If possible, compute and collect Data Quality Objectives (DQO) based sample size and analytical results.
Warning: This data set only has 0 observations!
Data set is too small to compute reliable and meaningful statistics and estimates!
The data set for variable Perfluoro-n-octane sulfonic acid (PFOS) (kr-1 wet) was not processed!
Minimum N/A Mean N/A
Maximum N/A Median N/A
Total Number of Observations 0 Number of Distinct Observations 0
Number of Missing Observations 14
Perfluoro-n-octane sulfonic acid (PFOS) (kr-1 wet)
General Statistics
Coffey Appendix H - Data Statistics
RAAF Base Tindal PFAS Ecological Risk Assessment
901
902
903
904
905
906
907
908
909
910
911
912
913
914
915
916
917
918
919
920
921
922
923
924
925
926
927
928
929
930
931
932
933
934
935
936
937
938
939
940
941
942
943
944
945
946
947
948
949
950
951
952
953
954
955
956
957
958
959
960
961
962
963
964
965
966
967
968
969
970
971
972
973
974
975
976
A B C D E F G H I J K L
Nonparametric Distribution Free UCL Statistics
Data appear to follow a Discernible Distribution at 5% Significance Level
95% Chebyshev (MVUE) UCL 0.0349 97.5% Chebyshev (MVUE) UCL 0.0415
99% Chebyshev (MVUE) UCL 0.0544
Assuming Lognormal Distribution
95% H-UCL 0.03 90% Chebyshev (MVUE) UCL 0.0301
Maximum of Logged Data -2.781 SD of logged Data 0.594
Lognormal Statistics
Minimum of Logged Data -4.962 Mean of logged Data -4.087
5% Lilliefors Critical Value 0.243 Data appear Lognormal at 5% Significance Level
Data appear Lognormal at 5% Significance Level
5% Shapiro Wilk Critical Value 0.859 Data appear Lognormal at 5% Significance Level
Lilliefors Test Statistic 0.217 Lilliefors Lognormal GOF Test
Lognormal GOF Test
Shapiro Wilk Test Statistic 0.91 Shapiro Wilk Lognormal GOF Test
Assuming Gamma Distribution
95% Approximate Gamma UCL (use when n>=50) 0.0284 95% Adjusted Gamma UCL (use when n<50) 0.03
Adjusted Level of Significance 0.029 Adjusted Chi Square Value 36.34
MLE Mean (bias corrected) 0.0201 MLE Sd (bias corrected) 0.0134
Approximate Chi Square Value (0.05) 38.37
Theta hat (MLE) 0.00682 Theta star (bias corrected MLE) 0.00888
nu hat (MLE) 70.63 nu star (bias corrected) 54.3
Detected data follow Appr. Gamma Distribution at 5% Significance Level
Gamma Statistics
k hat (MLE) 2.943 k star (bias corrected MLE) 2.263
K-S Test Statistic 0.259 Kolmogorov-Smirnov Gamma GOF Test
5% K-S Critical Value 0.247 Data Not Gamma Distributed at 5% Significance Level
Gamma GOF Test
A-D Test Statistic 0.721 Anderson-Darling Gamma GOF Test
5% A-D Critical Value 0.739 Detected data appear Gamma Distributed at 5% Significance Level
95% Modified-t UCL (Johnson-1978) 0.0282
Assuming Normal Distribution
95% Normal UCL 95% UCLs (Adjusted for Skewness)
95% Student's-t UCL 0.0277 95% Adjusted-CLT UCL (Chen-1995) 0.0302
5% Lilliefors Critical Value 0.243 Data Not Normal at 5% Significance Level
Data Not Normal at 5% Significance Level
5% Shapiro Wilk Critical Value 0.859 Data Not Normal at 5% Significance Level
Lilliefors Test Statistic 0.336 Lilliefors GOF Test
Normal GOF Test
Shapiro Wilk Test Statistic 0.716 Shapiro Wilk GOF Test
SD 0.0148 Std. Error of Mean 0.00426
Coefficient of Variation 0.735 Skewness 2.333
Minimum 0.007 Mean 0.0201
Maximum 0.062 Median 0.02
Total Number of Observations 12 Number of Distinct Observations 6
Number of Missing Observations 16
Perfluoro-n-octane sulfonic acid (PFOS) (kr-2 wet)
General Statistics
Note: Suggestions regarding the selection of a 95% UCL are provided to help the user to select the most appropriate 95% UCL.
Recommendations are based upon data size, data distribution, and skewness.
These recommendations are based upon the results of the simulation studies summarized in Singh, Maichle, and Lee (2006).
However, simulations results will not cover all Real World data sets; for additional insight the user may want to consult a statistician.
Suggested UCL to Use
95% Chebyshev (Mean, Sd) UCL 0.115
90% Chebyshev(Mean, Sd) UCL 0.102 95% Chebyshev(Mean, Sd) UCL 0.115
97.5% Chebyshev(Mean, Sd) UCL 0.132 99% Chebyshev(Mean, Sd) UCL 0.166
95% Hall's Bootstrap UCL 0.0911 95% Percentile Bootstrap UCL 0.0906
95% BCA Bootstrap UCL 0.0913
95% CLT UCL 0.09 95% Jackknife UCL 0.0905
95% Standard Bootstrap UCL 0.0893 95% Bootstrap-t UCL 0.0919
Nonparametric Distribution Free UCLs
Coffey Appendix H - Data Statistics
RAAF Base Tindal PFAS Ecological Risk Assessment
977
978
979
980
981
982
983
984
985
986
987
988
989
990
991
992
993
994
995
996
997
998
999
1000
1001
1002
1003
1004
1005
1006
1007
1008
1009
1010
1011
1012
1013
1014
1015
1016
1017
1018
1019
1020
1021
1022
1023
1024
1025
1026
1027
1028
1029
1030
1031
1032
1033
1034
1035
1036
1037
1038
1039
1040
1041
1042
1043
1044
1045
1046
1047
1048
1049
1050
1051
1052
1053
1054
1055
A B C D E F G H I J K L
Nonparametric Distribution Free UCL Statistics
Data appear to follow a Discernible Distribution at 5% Significance Level
95% Chebyshev (MVUE) UCL 0.166 97.5% Chebyshev (MVUE) UCL 0.189
99% Chebyshev (MVUE) UCL 0.234
Assuming Lognormal Distribution
95% H-UCL 0.141 90% Chebyshev (MVUE) UCL 0.149
Maximum of Logged Data -1.772 SD of logged Data 0.421
Lognormal Statistics
Minimum of Logged Data -3.507 Mean of logged Data -2.264
5% Lilliefors Critical Value 0.213 Data appear Lognormal at 5% Significance Level
Data appear Approximate Lognormal at 5% Significance Level
5% Shapiro Wilk Critical Value 0.887 Data Not Lognormal at 5% Significance Level
Lilliefors Test Statistic 0.179 Lilliefors Lognormal GOF Test
Lognormal GOF Test
Shapiro Wilk Test Statistic 0.846 Shapiro Wilk Lognormal GOF Test
Assuming Gamma Distribution
95% Approximate Gamma UCL (use when n>=50)) 0.133 95% Adjusted Gamma UCL (use when n<50) 0.135
Adjusted Level of Significance 0.0335 Adjusted Chi Square Value 160
MLE Mean (bias corrected) 0.111 MLE Sd (bias corrected) 0.0451
Approximate Chi Square Value (0.05) 163.2
Theta hat (MLE) 0.015 Theta star (bias corrected MLE) 0.0183
nu hat (MLE) 237.8 nu star (bias corrected) 194.5
Gamma Statistics
k hat (MLE) 7.43 k star (bias corrected MLE) 6.078
5% K-S Critical Value 0.215 Detected data appear Gamma Distributed at 5% Significance Level
Detected data appear Gamma Distributed at 5% Significance Level
5% A-D Critical Value 0.74 Detected data appear Gamma Distributed at 5% Significance Level
K-S Test Statistic 0.148 Kolmogorov-Smirnov Gamma GOF Test
Gamma GOF Test
A-D Test Statistic 0.522 Anderson-Darling Gamma GOF Test
95% Student's-t UCL 0.128 95% Adjusted-CLT UCL (Chen-1995) 0.126
95% Modified-t UCL (Johnson-1978) 0.127
Data appear Normal at 5% Significance Level
Assuming Normal Distribution
95% Normal UCL 95% UCLs (Adjusted for Skewness)
Lilliefors Test Statistic 0.182 Lilliefors GOF Test
5% Lilliefors Critical Value 0.213 Data appear Normal at 5% Significance Level
Normal GOF Test
Shapiro Wilk Test Statistic 0.954 Shapiro Wilk GOF Test
5% Shapiro Wilk Critical Value 0.887 Data appear Normal at 5% Significance Level
Coefficient of Variation 0.334 Skewness -0.272
Maximum 0.17 Median 0.1
SD 0.0371 Std. Error of Mean 0.00929
Number of Missing Observations 1
Minimum 0.03 Mean 0.111
Perfluoro-n-octane sulfonic acid (PFOS) (kr-3 dry)
General Statistics
Total Number of Observations 16 Number of Distinct Observations 9
Recommendations are based upon data size, data distribution, and skewness.
These recommendations are based upon the results of the simulation studies summarized in Singh, Maichle, and Lee (2006).
However, simulations results will not cover all Real World data sets; for additional insight the user may want to consult a statistician.
When a data set follows an approximate (e.g., normal) distribution passing one of the GOF test
When applicable, it is suggested to use a UCL based upon a distribution (e.g., gamma) passing both GOF tests in ProUCL
Note: Suggestions regarding the selection of a 95% UCL are provided to help the user to select the most appropriate 95% UCL.
Suggested UCL to Use
95% Adjusted Gamma UCL 0.03
90% Chebyshev(Mean, Sd) UCL 0.0329 95% Chebyshev(Mean, Sd) UCL 0.0387
97.5% Chebyshev(Mean, Sd) UCL 0.0467 99% Chebyshev(Mean, Sd) UCL 0.0625
95% Hall's Bootstrap UCL 0.0602 95% Percentile Bootstrap UCL 0.0275
95% BCA Bootstrap UCL 0.0308
95% CLT UCL 0.0271 95% Jackknife UCL 0.0277
95% Standard Bootstrap UCL 0.0269 95% Bootstrap-t UCL 0.0345
Nonparametric Distribution Free UCLs
Coffey Appendix H - Data Statistics
RAAF Base Tindal PFAS Ecological Risk Assessment
1056
1057
1058
1059
1060
1061
1062
1063
1064
1065
1066
1067
1068
1069
1070
1071
1072
1073
1074
1075
1076
1077
1078
1079
1080
1081
1082
1083
1084
1085
1086
1087
1088
1089
1090
1091
1092
1093
1094
1095
1096
1097
1098
1099
1100
1101
1102
1103
1104
1105
1106
1107
1108
1109
1110
1111
1112
1113
1114
1115
1116
1117
1118
1119
1120
1121
1122
1123
1124
1125
1126
1127
1128
1129
1130
1131
1132
1133
1134
1135
1136
1137
1138
1139
A B C D E F G H I J K L
Nonparametric Distribution Free UCL Statistics
Data appear to follow a Discernible Distribution at 5% Significance Level
95% Chebyshev (MVUE) UCL 0.0976 97.5% Chebyshev (MVUE) UCL 0.112
99% Chebyshev (MVUE) UCL 0.14
Assuming Lognormal Distribution
95% H-UCL 0.0883 90% Chebyshev (MVUE) UCL 0.0871
Maximum of Logged Data -2.526 SD of logged Data 0.268
Lognormal Statistics
Minimum of Logged Data -3.219 Mean of logged Data -2.775
5% Lilliefors Critical Value 0.343 Data appear Lognormal at 5% Significance Level
Data appear Lognormal at 5% Significance Level
5% Shapiro Wilk Critical Value 0.762 Data appear Lognormal at 5% Significance Level
Lilliefors Test Statistic 0.267 Lilliefors Lognormal GOF Test
Lognormal GOF Test
Shapiro Wilk Test Statistic 0.862 Shapiro Wilk Lognormal GOF Test
Assuming Gamma Distribution
95% Approximate Gamma UCL (use when n>=50)) 0.0852 95% Adjusted Gamma UCL (use when n<50) 0.0973
Adjusted Level of Significance 0.0086 Adjusted Chi Square Value 51.1
MLE Mean (bias corrected) 0.064 MLE Sd (bias corrected) 0.023
Approximate Chi Square Value (0.05) 58.35
Theta hat (MLE) 0.00335 Theta star (bias corrected MLE) 0.00824
nu hat (MLE) 190.8 nu star (bias corrected) 77.65
Gamma Statistics
k hat (MLE) 19.08 k star (bias corrected MLE) 7.765
5% K-S Critical Value 0.357 Detected data appear Gamma Distributed at 5% Significance Level
Detected data appear Gamma Distributed at 5% Significance Level
5% A-D Critical Value 0.679 Detected data appear Gamma Distributed at 5% Significance Level
K-S Test Statistic 0.282 Kolmogorov-Smirnov Gamma GOF Test
Gamma GOF Test
A-D Test Statistic 0.437 Anderson-Darling Gamma GOF Test
95% Student's-t UCL 0.0785 95% Adjusted-CLT UCL (Chen-1995) 0.0715
95% Modified-t UCL (Johnson-1978) 0.0779
Data appear Normal at 5% Significance Level
Assuming Normal Distribution
95% Normal UCL 95% UCLs (Adjusted for Skewness)
Lilliefors Test Statistic 0.254 Lilliefors GOF Test
5% Lilliefors Critical Value 0.343 Data appear Normal at 5% Significance Level
Normal GOF Test
Shapiro Wilk Test Statistic 0.914 Shapiro Wilk GOF Test
5% Shapiro Wilk Critical Value 0.762 Data appear Normal at 5% Significance Level
Note: Sample size is small (e.g., <10), if data are collected using ISM approach, you should use
guidance provided in ITRC Tech Reg Guide on ISM (ITRC, 2012) to compute statistics of interest.
For example, you may want to use Chebyshev UCL to estimate EPC (ITRC, 2012).
Chebyshev UCL can be computed using the Nonparametric and All UCL Options of ProUCL 5.1
Coefficient of Variation 0.237 Skewness -1.118
Maximum 0.08 Median 0.07
SD 0.0152 Std. Error of Mean 0.00678
Number of Missing Observations 7
Minimum 0.04 Mean 0.064
Perfluoro-n-octane sulfonic acid (PFOS) (kr-3 wet)
General Statistics
Total Number of Observations 5 Number of Distinct Observations 4
Note: For highly negatively-skewed data, confidence limits (e.g., Chen, Johnson, Lognormal, and Gamma) may not be
reliable. Chen's and Johnson's methods provide adjustments for positvely skewed data sets.
Note: Suggestions regarding the selection of a 95% UCL are provided to help the user to select the most appropriate 95% UCL.
Recommendations are based upon data size, data distribution, and skewness.
These recommendations are based upon the results of the simulation studies summarized in Singh, Maichle, and Lee (2006).
However, simulations results will not cover all Real World data sets; for additional insight the user may want to consult a statistician.
Suggested UCL to Use
95% Student's-t UCL 0.128
90% Chebyshev(Mean, Sd) UCL 0.139 95% Chebyshev(Mean, Sd) UCL 0.152
97.5% Chebyshev(Mean, Sd) UCL 0.169 99% Chebyshev(Mean, Sd) UCL 0.204
95% Hall's Bootstrap UCL 0.127 95% Percentile Bootstrap UCL 0.126
95% BCA Bootstrap UCL 0.126
95% CLT UCL 0.127 95% Jackknife UCL 0.128
95% Standard Bootstrap UCL 0.126 95% Bootstrap-t UCL 0.127
Nonparametric Distribution Free UCLs
Coffey Appendix H - Data Statistics
RAAF Base Tindal PFAS Ecological Risk Assessment
1140
1141
1142
1143
1144
1145
1146
1147
1148
1149
1150
1151
1152
1153
1154
1155
1156
1157
1158
1159
1160
1161
1162
1163
1164
1165
1166
1167
1168
1169
1170
1171
1172
1173
1174
1175
1176
1177
1178
1179
1180
1181
1182
1183
1184
1185
1186
1187
1188
1189
1190
1191
1192
1193
1194
1195
1196
1197
1198
1199
1200
1201
1202
1203
1204
1205
1206
1207
1208
1209
1210
1211
1212
1213
1214
1215
1216
1217
1218
1219
1220
A B C D E F G H I J K L
95% Chebyshev (MVUE) UCL 3.214 97.5% Chebyshev (MVUE) UCL 4.241
99% Chebyshev (MVUE) UCL 6.256
Assuming Lognormal Distribution
95% H-UCL 8366 90% Chebyshev (MVUE) UCL 2.475
Maximum of Logged Data 0.405 SD of logged Data 1.522
Lognormal Statistics
Minimum of Logged Data -2.996 Mean of logged Data -0.925
5% Lilliefors Critical Value 0.375 Data appear Lognormal at 5% Significance Level
Data appear Lognormal at 5% Significance Level
5% Shapiro Wilk Critical Value 0.748 Data appear Lognormal at 5% Significance Level
Lilliefors Test Statistic 0.228 Lilliefors Lognormal GOF Test
Lognormal GOF Test
Shapiro Wilk Test Statistic 0.916 Shapiro Wilk Lognormal GOF Test
Assuming Gamma Distribution
95% Approximate Gamma UCL (use when n>=50)) 5.142 95% Adjusted Gamma UCL (use when n<50) N/A
Adjusted Level of Significance N/A Adjusted Chi Square Value N/A
MLE Mean (bias corrected) 0.72 MLE Sd (bias corrected) 1.125
Approximate Chi Square Value (0.05) 0.459
Theta hat (MLE) 0.741 Theta star (bias corrected MLE) 1.758
nu hat (MLE) 7.771 nu star (bias corrected) 3.276
Gamma Statistics
k hat (MLE) 0.971 k star (bias corrected MLE) 0.41
5% K-S Critical Value 0.403 Detected data appear Gamma Distributed at 5% Significance Level
Detected data appear Gamma Distributed at 5% Significance Level
5% A-D Critical Value 0.667 Detected data appear Gamma Distributed at 5% Significance Level
K-S Test Statistic 0.251 Kolmogorov-Smirnov Gamma GOF Test
Gamma GOF Test
A-D Test Statistic 0.266 Anderson-Darling Gamma GOF Test
95% Student's-t UCL 1.491 95% Adjusted-CLT UCL (Chen-1995) 1.315
95% Modified-t UCL (Johnson-1978) 1.5
Data appear Normal at 5% Significance Level
Assuming Normal Distribution
95% Normal UCL 95% UCLs (Adjusted for Skewness)
Lilliefors Test Statistic 0.224 Lilliefors GOF Test
5% Lilliefors Critical Value 0.375 Data appear Normal at 5% Significance Level
Normal GOF Test
Shapiro Wilk Test Statistic 0.955 Shapiro Wilk GOF Test
5% Shapiro Wilk Critical Value 0.748 Data appear Normal at 5% Significance Level
Note: Sample size is small (e.g., <10), if data are collected using ISM approach, you should use
guidance provided in ITRC Tech Reg Guide on ISM (ITRC, 2012) to compute statistics of interest.
For example, you may want to use Chebyshev UCL to estimate EPC (ITRC, 2012).
Chebyshev UCL can be computed using the Nonparametric and All UCL Options of ProUCL 5.1
Coefficient of Variation 0.91 Skewness 0.323
Maximum 1.5 Median 0.665
SD 0.655 Std. Error of Mean 0.328
Number of Missing Observations 0
Minimum 0.05 Mean 0.72
Perfluoro-n-octane sulfonic acid (PFOS) (on-base drain dry)
General Statistics
Total Number of Observations 4 Number of Distinct Observations 4
Note: For highly negatively-skewed data, confidence limits (e.g., Chen, Johnson, Lognormal, and Gamma) may not be
reliable. Chen's and Johnson's methods provide adjustments for positvely skewed data sets.
Note: Suggestions regarding the selection of a 95% UCL are provided to help the user to select the most appropriate 95% UCL.
Recommendations are based upon data size, data distribution, and skewness.
These recommendations are based upon the results of the simulation studies summarized in Singh, Maichle, and Lee (2006).
However, simulations results will not cover all Real World data sets; for additional insight the user may want to consult a statistician.
Suggested UCL to Use
95% Student's-t UCL 0.0785
90% Chebyshev(Mean, Sd) UCL 0.0843 95% Chebyshev(Mean, Sd) UCL 0.0936
97.5% Chebyshev(Mean, Sd) UCL 0.106 99% Chebyshev(Mean, Sd) UCL 0.131
95% Hall's Bootstrap UCL N/A 95% Percentile Bootstrap UCL N/A
95% BCA Bootstrap UCL N/A
95% CLT UCL 0.0752 95% Jackknife UCL 0.0785
95% Standard Bootstrap UCL N/A 95% Bootstrap-t UCL N/A
Nonparametric Distribution Free UCLs
Coffey Appendix H - Data Statistics
RAAF Base Tindal PFAS Ecological Risk Assessment
1221
1222
1223
1224
1225
1226
1227
1228
1229
1230
1231
1232
1233
1234
1235
1236
1237
1238
1239
1240
1241
1242
1243
1244
1245
1246
1247
1248
1249
1250
1251
1252
1253
1254
1255
1256
1257
1258
1259
1260
1261
1262
1263
1264
1265
1266
1267
1268
1269
1270
1271
1272
1273
1274
1275
1276
1277
1278
1279
1280
A B C D E F G H I J K L
Assuming Gamma Distribution
95% Approximate Gamma UCL (use when n>=50)) 1.578 95% Adjusted Gamma UCL (use when n<50) 1.598
Adjusted Level of Significance 0.0447 Adjusted Chi Square Value 32.26
MLE Mean (bias corrected) 1.086 MLE Sd (bias corrected) 1.495
Approximate Chi Square Value (0.05) 32.67
Theta hat (MLE) 1.976 Theta star (bias corrected MLE) 2.058
nu hat (MLE) 49.45 nu star (bias corrected) 47.48
Data Not Gamma Distributed at 5% Significance Level
Gamma Statistics
k hat (MLE) 0.549 k star (bias corrected MLE) 0.528
K-S Test Statistic 0.148 Kolmogorov-Smirnov Gamma GOF Test
5% K-S Critical Value 0.139 Data Not Gamma Distributed at 5% Significance Level
Gamma GOF Test
A-D Test Statistic 1.052 Anderson-Darling Gamma GOF Test
5% A-D Critical Value 0.809 Data Not Gamma Distributed at 5% Significance Level
95% Modified-t UCL (Johnson-1978) 1.526
Assuming Normal Distribution
95% Normal UCL 95% UCLs (Adjusted for Skewness)
95% Student's-t UCL 1.509 95% Adjusted-CLT UCL (Chen-1995) 1.606
5% Lilliefors Critical Value 0.131 Data Not Normal at 5% Significance Level
Data Not Normal at 5% Significance Level
5% Shapiro Wilk Critical Value 0.945 Data Not Normal at 5% Significance Level
Lilliefors Test Statistic 0.266 Lilliefors GOF Test
Normal GOF Test
Shapiro Wilk Test Statistic 0.667 Shapiro Wilk GOF Test
SD 1.691 Std. Error of Mean 0.252
Coefficient of Variation 1.557 Skewness 2.623
Minimum 0.03 Mean 1.086
Maximum 8.6 Median 0.29
Total Number of Observations 45 Number of Distinct Observations 36
Number of Missing Observations 1
Perfluoro-n-octane sulfonic acid (PFOS) (on-base drain wet)
General Statistics
Note: Suggestions regarding the selection of a 95% UCL are provided to help the user to select the most appropriate 95% UCL.
Recommendations are based upon data size, data distribution, and skewness.
These recommendations are based upon the results of the simulation studies summarized in Singh, Maichle, and Lee (2006).
However, simulations results will not cover all Real World data sets; for additional insight the user may want to consult a statistician.
Suggested UCL to Use
95% Student's-t UCL 1.491
90% Chebyshev(Mean, Sd) UCL 1.703 95% Chebyshev(Mean, Sd) UCL 2.148
97.5% Chebyshev(Mean, Sd) UCL 2.766 99% Chebyshev(Mean, Sd) UCL 3.98
95% Hall's Bootstrap UCL N/A 95% Percentile Bootstrap UCL N/A
95% BCA Bootstrap UCL N/A
95% CLT UCL 1.259 95% Jackknife UCL 1.491
95% Standard Bootstrap UCL N/A 95% Bootstrap-t UCL N/A
Nonparametric Distribution Free UCL Statistics
Data appear to follow a Discernible Distribution at 5% Significance Level
Nonparametric Distribution Free UCLs
Coffey Appendix H - Data Statistics
RAAF Base Tindal PFAS Ecological Risk Assessment
1281
1282
1283
1284
1285
1286
1287
1288
1289
1290
1291
1292
1293
1294
1295
1296
1297
1298
1299
1300
1301
1302
1303
1304
1305
1306
1307
1308
1309
1310
1311
1312
1313
1314
1315
1316
1317
1318
1319
1320
1321
1322
1323
1324
1325
1326
1327
1328
1329
1330
1331
1332
1333
1334
1335
1336
1337
1338
1339
1340
1341
1342
1343
1344
1345
1346
1347
1348
1349
1350
1351
1352
1353
1354
1355
1356
1357
1358
1359
1360
1361
1362
1363
A B C D E F G H I J K L
5% Lilliefors Critical Value 0.226 Data appear Lognormal at 5% Significance Level
Data appear Lognormal at 5% Significance Level
5% Shapiro Wilk Critical Value 0.874 Data appear Lognormal at 5% Significance Level
Lilliefors Test Statistic 0.128 Lilliefors Lognormal GOF Test
Lognormal GOF Test
Shapiro Wilk Test Statistic 0.942 Shapiro Wilk Lognormal GOF Test
Assuming Gamma Distribution
95% Approximate Gamma UCL (use when n>=50)) 15.88 95% Adjusted Gamma UCL (use when n<50) 17.81
Adjusted Level of Significance 0.0312 Adjusted Chi Square Value 4.925
MLE Mean (bias corrected) 7.046 MLE Sd (bias corrected) 10.57
Approximate Chi Square Value (0.05) 5.524
Theta hat (MLE) 13.95 Theta star (bias corrected MLE) 15.85
nu hat (MLE) 14.15 nu star (bias corrected) 12.45
Data Not Gamma Distributed at 5% Significance Level
Gamma Statistics
k hat (MLE) 0.505 k star (bias corrected MLE) 0.445
K-S Test Statistic 0.253 Kolmogorov-Smirnov Gamma GOF Test
5% K-S Critical Value 0.242 Data Not Gamma Distributed at 5% Significance Level
Gamma GOF Test
A-D Test Statistic 1.049 Anderson-Darling Gamma GOF Test
5% A-D Critical Value 0.793 Data Not Gamma Distributed at 5% Significance Level
95% Modified-t UCL (Johnson-1978) 15.73
Assuming Normal Distribution
95% Normal UCL 95% UCLs (Adjusted for Skewness)
95% Student's-t UCL 15.01 95% Adjusted-CLT UCL (Chen-1995) 19.11
5% Lilliefors Critical Value 0.226 Data Not Normal at 5% Significance Level
Data Not Normal at 5% Significance Level
5% Shapiro Wilk Critical Value 0.874 Data Not Normal at 5% Significance Level
Lilliefors Test Statistic 0.423 Lilliefors GOF Test
Normal GOF Test
Shapiro Wilk Test Statistic 0.41 Shapiro Wilk GOF Test
SD 16.82 Std. Error of Mean 4.495
Coefficient of Variation 2.387 Skewness 3.635
Minimum 0.23 Mean 7.046
Maximum 65 Median 2.55
Total Number of Observations 14 Number of Distinct Observations 14
Number of Missing Observations 0
Perfluoro-n-octane sulfonic acid (PFOS) (source area)
General Statistics
Note: Suggestions regarding the selection of a 95% UCL are provided to help the user to select the most appropriate 95% UCL.
Recommendations are based upon data size, data distribution, and skewness.
These recommendations are based upon the results of the simulation studies summarized in Singh, Maichle, and Lee (2006).
However, simulations results will not cover all Real World data sets; for additional insight the user may want to consult a statistician.
Suggested UCL to Use
95% Chebyshev (Mean, Sd) UCL 2.184
90% Chebyshev(Mean, Sd) UCL 1.842 95% Chebyshev(Mean, Sd) UCL 2.184
97.5% Chebyshev(Mean, Sd) UCL 2.66 99% Chebyshev(Mean, Sd) UCL 3.594
95% Hall's Bootstrap UCL 1.731 95% Percentile Bootstrap UCL 1.514
95% BCA Bootstrap UCL 1.595
95% CLT UCL 1.5 95% Jackknife UCL 1.509
95% Standard Bootstrap UCL 1.494 95% Bootstrap-t UCL 1.657
Nonparametric Distribution Free UCL Statistics
Data appear to follow a Discernible Distribution at 5% Significance Level
Nonparametric Distribution Free UCLs
95% Chebyshev (MVUE) UCL 3.105 97.5% Chebyshev (MVUE) UCL 3.901
99% Chebyshev (MVUE) UCL 5.464
Assuming Lognormal Distribution
95% H-UCL 2.99 90% Chebyshev (MVUE) UCL 2.532
Maximum of Logged Data 2.152 SD of logged Data 1.649
Lognormal Statistics
Minimum of Logged Data -3.507 Mean of logged Data -1.057
5% Lilliefors Critical Value 0.131 Data appear Lognormal at 5% Significance Level
Data appear Approximate Lognormal at 5% Significance Level
5% Shapiro Wilk Critical Value 0.945 Data Not Lognormal at 5% Significance Level
Lilliefors Test Statistic 0.0861 Lilliefors Lognormal GOF Test
Lognormal GOF Test
Shapiro Wilk Test Statistic 0.942 Shapiro Wilk Lognormal GOF Test
Coffey Appendix H - Data Statistics
RAAF Base Tindal PFAS Ecological Risk Assessment
1364
1365
1366
1367
1368
1369
1370
1371
1372
1373
1374
1375
1376
1377
1378
1379
1380
1381
1382
1383
1384
1385
1386
1387
1388
1389
1390
1391
1392
1393
1394
1395
1396
1397
1398
1399
1400
1401
1402
1403
1404
1405
1406
1407
1408
1409
1410
1411
1412
1413
1414
1415
1416
1417
1418
1419
1420
1421
1422
1423
1424
1425
1426
1427
1428
1429
1430
1431
1432
1433
1434
1435
1436
1437
1438
1439
1440
1441
1442
1443
A B C D E F G H I J K L
Maximum of Logged Data 0.742 SD of logged Data 1.779
Lognormal Statistics
Minimum of Logged Data -3.912 Mean of logged Data -1.154
5% Lilliefors Critical Value 0.234 Data appear Lognormal at 5% Significance Level
Data appear Approximate Lognormal at 5% Significance Level
5% Shapiro Wilk Critical Value 0.866 Data Not Lognormal at 5% Significance Level
Lilliefors Test Statistic 0.228 Lilliefors Lognormal GOF Test
Lognormal GOF Test
Shapiro Wilk Test Statistic 0.842 Shapiro Wilk Lognormal GOF Test
Assuming Gamma Distribution
95% Approximate Gamma UCL (use when n>=50)) 1.741 95% Adjusted Gamma UCL (use when n<50) 1.951
Adjusted Level of Significance 0.0301 Adjusted Chi Square Value 5.946
MLE Mean (bias corrected) 0.821 MLE Sd (bias corrected) 1.113
Approximate Chi Square Value (0.05) 6.663
Theta hat (MLE) 1.282 Theta star (bias corrected MLE) 1.51
nu hat (MLE) 16.64 nu star (bias corrected) 14.13
Detected data appear Gamma Distributed at 5% Significance Level
Gamma Statistics
k hat (MLE) 0.64 k star (bias corrected MLE) 0.544
K-S Test Statistic 0.201 Kolmogorov-Smirnov Gamma GOF Test
5% K-S Critical Value 0.248 Detected data appear Gamma Distributed at 5% Significance Level
Gamma GOF Test
A-D Test Statistic 0.747 Anderson-Darling Gamma GOF Test
5% A-D Critical Value 0.779 Detected data appear Gamma Distributed at 5% Significance Level
95% Modified-t UCL (Johnson-1978) 1.224
Assuming Normal Distribution
95% Normal UCL 95% UCLs (Adjusted for Skewness)
95% Student's-t UCL 1.219 95% Adjusted-CLT UCL (Chen-1995) 1.222
5% Lilliefors Critical Value 0.234 Data appear Normal at 5% Significance Level
Data appear Approximate Normal at 5% Significance Level
5% Shapiro Wilk Critical Value 0.866 Data Not Normal at 5% Significance Level
Lilliefors Test Statistic 0.206 Lilliefors GOF Test
Normal GOF Test
Shapiro Wilk Test Statistic 0.853 Shapiro Wilk GOF Test
SD 0.805 Std. Error of Mean 0.223
Coefficient of Variation 0.98 Skewness 0.522
Minimum 0.02 Mean 0.821
Maximum 2.1 Median 0.76
Total Number of Observations 13 Number of Distinct Observations 11
Number of Missing Observations 0
Perfluoro-n-octane sulfonic acid (PFOS) (tc-1 dry)
General Statistics
Note: Suggestions regarding the selection of a 95% UCL are provided to help the user to select the most appropriate 95% UCL.
Recommendations are based upon data size, data distribution, and skewness.
These recommendations are based upon the results of the simulation studies summarized in Singh, Maichle, and Lee (2006).
However, simulations results will not cover all Real World data sets; for additional insight the user may want to consult a statistician.
Suggested UCL to Use
99% Chebyshev (Mean, Sd) UCL 51.78
90% Chebyshev(Mean, Sd) UCL 20.53 95% Chebyshev(Mean, Sd) UCL 26.64
97.5% Chebyshev(Mean, Sd) UCL 35.12 99% Chebyshev(Mean, Sd) UCL 51.78
95% Hall's Bootstrap UCL 46.46 95% Percentile Bootstrap UCL 15.86
95% BCA Bootstrap UCL 20.7
95% CLT UCL 14.44 95% Jackknife UCL 15.01
95% Standard Bootstrap UCL 14.41 95% Bootstrap-t UCL 54.04
Nonparametric Distribution Free UCL Statistics
Data appear to follow a Discernible Distribution at 5% Significance Level
Nonparametric Distribution Free UCLs
95% Chebyshev (MVUE) UCL 16.77 97.5% Chebyshev (MVUE) UCL 21.61
99% Chebyshev (MVUE) UCL 31.13
Assuming Lognormal Distribution
95% H-UCL 31.8 90% Chebyshev (MVUE) UCL 13.28
Maximum of Logged Data 4.174 SD of logged Data 1.53
Lognormal Statistics
Minimum of Logged Data -1.47 Mean of logged Data 0.697
Coffey Appendix H - Data Statistics
RAAF Base Tindal PFAS Ecological Risk Assessment
1444
1445
1446
1447
1448
1449
1450
1451
1452
1453
1454
1455
1456
1457
1458
1459
1460
1461
1462
1463
1464
1465
1466
1467
1468
1469
1470
1471
1472
1473
1474
1475
1476
1477
1478
1479
1480
1481
1482
1483
1484
1485
1486
1487
1488
1489
1490
1491
1492
1493
1494
1495
1496
1497
1498
1499
1500
1501
1502
1503
1504
1505
1506
1507
1508
1509
1510
1511
1512
1513
1514
1515
1516
1517
1518
1519
1520
1521
1522
1523
1524
1525
1526
1527
A B C D E F G H I J K L
95% Chebyshev (MVUE) UCL 2.804 97.5% Chebyshev (MVUE) UCL 3.583
99% Chebyshev (MVUE) UCL 5.111
Assuming Lognormal Distribution
95% H-UCL 3.652 90% Chebyshev (MVUE) UCL 2.244
Maximum of Logged Data 0.788 SD of logged Data 1.553
Lognormal Statistics
Minimum of Logged Data -3.912 Mean of logged Data -1.089
5% Lilliefors Critical Value 0.188 Data appear Lognormal at 5% Significance Level
Data appear Approximate Lognormal at 5% Significance Level
5% Shapiro Wilk Critical Value 0.908 Data Not Lognormal at 5% Significance Level
Lilliefors Test Statistic 0.188 Lilliefors Lognormal GOF Test
Lognormal GOF Test
Shapiro Wilk Test Statistic 0.892 Shapiro Wilk Lognormal GOF Test
Assuming Gamma Distribution
95% Approximate Gamma UCL (use when n>=50)) 1.187 95% Adjusted Gamma UCL (use when n<50) 1.234
Adjusted Level of Significance 0.0383 Adjusted Chi Square Value 17.21
MLE Mean (bias corrected) 0.726 MLE Sd (bias corrected) 0.871
Approximate Chi Square Value (0.05) 17.89
Theta hat (MLE) 0.937 Theta star (bias corrected MLE) 1.043
nu hat (MLE) 32.54 nu star (bias corrected) 29.23
Gamma Statistics
k hat (MLE) 0.775 k star (bias corrected MLE) 0.696
5% K-S Critical Value 0.197 Detected data appear Gamma Distributed at 5% Significance Level
Detected data appear Gamma Distributed at 5% Significance Level
5% A-D Critical Value 0.782 Detected data appear Gamma Distributed at 5% Significance Level
K-S Test Statistic 0.156 Kolmogorov-Smirnov Gamma GOF Test
Gamma GOF Test
A-D Test Statistic 0.636 Anderson-Darling Gamma GOF Test
95% Student's-t UCL 0.982 95% Adjusted-CLT UCL (Chen-1995) 0.994
95% Modified-t UCL (Johnson-1978) 0.985
Data appear Approximate Normal at 5% Significance Level
Assuming Normal Distribution
95% Normal UCL 95% UCLs (Adjusted for Skewness)
Lilliefors Test Statistic 0.171 Lilliefors GOF Test
5% Lilliefors Critical Value 0.188 Data appear Normal at 5% Significance Level
Normal GOF Test
Shapiro Wilk Test Statistic 0.885 Shapiro Wilk GOF Test
5% Shapiro Wilk Critical Value 0.908 Data Not Normal at 5% Significance Level
Coefficient of Variation 0.934 Skewness 0.698
Maximum 2.2 Median 0.57
SD 0.679 Std. Error of Mean 0.148
Number of Missing Observations 1
Minimum 0.02 Mean 0.726
Perfluoro-n-octane sulfonic acid (PFOS) (tc-1 wet)
General Statistics
Total Number of Observations 21 Number of Distinct Observations 16
Recommendations are based upon data size, data distribution, and skewness.
These recommendations are based upon the results of the simulation studies summarized in Singh, Maichle, and Lee (2006).
However, simulations results will not cover all Real World data sets; for additional insight the user may want to consult a statistician.
When a data set follows an approximate (e.g., normal) distribution passing one of the GOF test
When applicable, it is suggested to use a UCL based upon a distribution (e.g., gamma) passing both GOF tests in ProUCL
Note: Suggestions regarding the selection of a 95% UCL are provided to help the user to select the most appropriate 95% UCL.
Suggested UCL to Use
95% Student's-t UCL 1.219
90% Chebyshev(Mean, Sd) UCL 1.49 95% Chebyshev(Mean, Sd) UCL 1.794
97.5% Chebyshev(Mean, Sd) UCL 2.215 99% Chebyshev(Mean, Sd) UCL 3.041
95% Hall's Bootstrap UCL 1.165 95% Percentile Bootstrap UCL 1.188
95% BCA Bootstrap UCL 1.222
95% CLT UCL 1.188 95% Jackknife UCL 1.219
95% Standard Bootstrap UCL 1.172 95% Bootstrap-t UCL 1.231
Nonparametric Distribution Free UCL Statistics
Data appear to follow a Discernible Distribution at 5% Significance Level
Nonparametric Distribution Free UCLs
95% Chebyshev (MVUE) UCL 4.079 97.5% Chebyshev (MVUE) UCL 5.324
99% Chebyshev (MVUE) UCL 7.77
Assuming Lognormal Distribution
95% H-UCL 13.89 90% Chebyshev (MVUE) UCL 3.182
Coffey Appendix H - Data Statistics
RAAF Base Tindal PFAS Ecological Risk Assessment
1528
1529
1530
1531
1532
1533
1534
1535
1536
1537
1538
1539
1540
1541
1542
1543
1544
1545
1546
1547
1548
1549
1550
1551
1552
1553
1554
1555
1556
1557
1558
1559
1560
1561
1562
1563
1564
1565
1566
1567
1568
1569
1570
1571
1572
1573
1574
1575
1576
1577
1578
1579
1580
1581
1582
1583
1584
1585
1586
1587
1588
1589
1590
1591
1592
A B C D E F G H I J K L
Adjusted Level of Significance 0.0195 Adjusted Chi Square Value 2.82
MLE Mean (bias corrected) 0.6 MLE Sd (bias corrected) 0.775
Approximate Chi Square Value (0.05) 3.684
Theta hat (MLE) 0.727 Theta star (bias corrected MLE) 1.002
nu hat (MLE) 13.2 nu star (bias corrected) 9.585
Gamma Statistics
k hat (MLE) 0.825 k star (bias corrected MLE) 0.599
5% K-S Critical Value 0.303 Detected data appear Gamma Distributed at 5% Significance Level
Detected data appear Gamma Distributed at 5% Significance Level
5% A-D Critical Value 0.742 Detected data appear Gamma Distributed at 5% Significance Level
K-S Test Statistic 0.248 Kolmogorov-Smirnov Gamma GOF Test
Gamma GOF Test
A-D Test Statistic 0.625 Anderson-Darling Gamma GOF Test
95% Student's-t UCL 0.93 95% Adjusted-CLT UCL (Chen-1995) 0.925
95% Modified-t UCL (Johnson-1978) 0.936
Data appear Normal at 5% Significance Level
Assuming Normal Distribution
95% Normal UCL 95% UCLs (Adjusted for Skewness)
Lilliefors Test Statistic 0.139 Lilliefors GOF Test
5% Lilliefors Critical Value 0.283 Data appear Normal at 5% Significance Level
Normal GOF Test
Shapiro Wilk Test Statistic 0.943 Shapiro Wilk GOF Test
5% Shapiro Wilk Critical Value 0.818 Data appear Normal at 5% Significance Level
Note: Sample size is small (e.g., <10), if data are collected using ISM approach, you should use
guidance provided in ITRC Tech Reg Guide on ISM (ITRC, 2012) to compute statistics of interest.
For example, you may want to use Chebyshev UCL to estimate EPC (ITRC, 2012).
Chebyshev UCL can be computed using the Nonparametric and All UCL Options of ProUCL 5.1
Coefficient of Variation 0.82 Skewness 0.584
Maximum 1.5 Median 0.58
SD 0.492 Std. Error of Mean 0.174
Number of Missing Observations 5
Minimum 0.02 Mean 0.6
Perfluoro-n-octane sulfonic acid (PFOS) (tc-2 dry)
General Statistics
Total Number of Observations 8 Number of Distinct Observations 7
Recommendations are based upon data size, data distribution, and skewness.
These recommendations are based upon the results of the simulation studies summarized in Singh, Maichle, and Lee (2006).
However, simulations results will not cover all Real World data sets; for additional insight the user may want to consult a statistician.
When a data set follows an approximate (e.g., normal) distribution passing one of the GOF test
When applicable, it is suggested to use a UCL based upon a distribution (e.g., gamma) passing both GOF tests in ProUCL
Note: Suggestions regarding the selection of a 95% UCL are provided to help the user to select the most appropriate 95% UCL.
Suggested UCL to Use
95% Student's-t UCL 0.982
90% Chebyshev(Mean, Sd) UCL 1.17 95% Chebyshev(Mean, Sd) UCL 1.372
97.5% Chebyshev(Mean, Sd) UCL 1.651 99% Chebyshev(Mean, Sd) UCL 2.199
95% Hall's Bootstrap UCL 0.996 95% Percentile Bootstrap UCL 0.971
95% BCA Bootstrap UCL 0.99
95% CLT UCL 0.97 95% Jackknife UCL 0.982
95% Standard Bootstrap UCL 0.966 95% Bootstrap-t UCL 1.005
Nonparametric Distribution Free UCL Statistics
Data appear to follow a Discernible Distribution at 5% Significance Level
Nonparametric Distribution Free UCLs
Coffey Appendix H - Data Statistics
RAAF Base Tindal PFAS Ecological Risk Assessment
1593
1594
1595
1596
1597
1598
1599
1600
1601
1602
1603
1604
1605
1606
1607
1608
1609
1610
1611
1612
1613
1614
1615
1616
1617
1618
1619
1620
1621
1622
1623
1624
1625
1626
1627
1628
1629
1630
1631
1632
1633
1634
1635
1636
1637
1638
1639
1640
1641
1642
1643
1644
1645
1646
1647
1648
1649
1650
1651
1652
1653
1654
1655
1656
1657
1658
1659
1660
A B C D E F G H I J K L
Detected data follow Appr. Gamma Distribution at 5% Significance Level
K-S Test Statistic 0.166 Kolmogorov-Smirnov Gamma GOF Test
5% K-S Critical Value 0.169 Detected data appear Gamma Distributed at 5% Significance Level
Gamma GOF Test
A-D Test Statistic 0.812 Anderson-Darling Gamma GOF Test
5% A-D Critical Value 0.783 Data Not Gamma Distributed at 5% Significance Level
95% Modified-t UCL (Johnson-1978) 0.461
Assuming Normal Distribution
95% Normal UCL 95% UCLs (Adjusted for Skewness)
95% Student's-t UCL 0.459 95% Adjusted-CLT UCL (Chen-1995) 0.466
5% Lilliefors Critical Value 0.161 Data Not Normal at 5% Significance Level
Data Not Normal at 5% Significance Level
5% Shapiro Wilk Critical Value 0.926 Data Not Normal at 5% Significance Level
Lilliefors Test Statistic 0.233 Lilliefors GOF Test
Normal GOF Test
Shapiro Wilk Test Statistic 0.778 Shapiro Wilk GOF Test
SD 0.36 Std. Error of Mean 0.0668
Coefficient of Variation 1.041 Skewness 0.838
Minimum 0.01 Mean 0.346
Maximum 0.99 Median 0.18
Total Number of Observations 29 Number of Distinct Observations 21
Number of Missing Observations 5
Perfluoro-n-octane sulfonic acid (PFOS) (tc-2 wet)
General Statistics
Note: Suggestions regarding the selection of a 95% UCL are provided to help the user to select the most appropriate 95% UCL.
Recommendations are based upon data size, data distribution, and skewness.
These recommendations are based upon the results of the simulation studies summarized in Singh, Maichle, and Lee (2006).
However, simulations results will not cover all Real World data sets; for additional insight the user may want to consult a statistician.
Suggested UCL to Use
95% Student's-t UCL 0.93
90% Chebyshev(Mean, Sd) UCL 1.122 95% Chebyshev(Mean, Sd) UCL 1.359
97.5% Chebyshev(Mean, Sd) UCL 1.687 99% Chebyshev(Mean, Sd) UCL 2.332
95% Hall's Bootstrap UCL 0.983 95% Percentile Bootstrap UCL 0.876
95% BCA Bootstrap UCL 0.914
95% CLT UCL 0.886 95% Jackknife UCL 0.93
95% Standard Bootstrap UCL 0.87 95% Bootstrap-t UCL 1
Nonparametric Distribution Free UCL Statistics
Data appear to follow a Discernible Distribution at 5% Significance Level
Nonparametric Distribution Free UCLs
95% Chebyshev (MVUE) UCL 3.294 97.5% Chebyshev (MVUE) UCL 4.324
99% Chebyshev (MVUE) UCL 6.348
Assuming Lognormal Distribution
95% H-UCL 38.97 90% Chebyshev (MVUE) UCL 2.552
Maximum of Logged Data 0.405 SD of logged Data 1.708
Lognormal Statistics
Minimum of Logged Data -3.912 Mean of logged Data -1.227
5% Lilliefors Critical Value 0.283 Data Not Lognormal at 5% Significance Level
Data Not Lognormal at 5% Significance Level
5% Shapiro Wilk Critical Value 0.818 Data Not Lognormal at 5% Significance Level
Lilliefors Test Statistic 0.31 Lilliefors Lognormal GOF Test
Lognormal GOF Test
Shapiro Wilk Test Statistic 0.773 Shapiro Wilk Lognormal GOF Test
Assuming Gamma Distribution
95% Approximate Gamma UCL (use when n>=50)) 1.561 95% Adjusted Gamma UCL (use when n<50) 2.04
Coffey Appendix H - Data Statistics
RAAF Base Tindal PFAS Ecological Risk Assessment
1661
1662
1663
1664
1665
1666
1667
1668
1669
1670
1671
1672
1673
1674
1675
1676
1677
1678
1679
1680
1681
1682
1683
1684
1685
1686
1687
1688
1689
1690
1691
1692
1693
1694
1695
1696
1697
1698
1699
1700
1701
1702
1703
1704
1705
1706
1707
1708
1709
A B C D E F G H I J K L
Recommendations are based upon data size, data distribution, and skewness.
These recommendations are based upon the results of the simulation studies summarized in Singh, Maichle, and Lee (2006).
However, simulations results will not cover all Real World data sets; for additional insight the user may want to consult a statistician.
When a data set follows an approximate (e.g., normal) distribution passing one of the GOF test
When applicable, it is suggested to use a UCL based upon a distribution (e.g., gamma) passing both GOF tests in ProUCL
Note: Suggestions regarding the selection of a 95% UCL are provided to help the user to select the most appropriate 95% UCL.
Suggested UCL to Use
95% Adjusted Gamma UCL 0.53
90% Chebyshev(Mean, Sd) UCL 0.546 95% Chebyshev(Mean, Sd) UCL 0.637
97.5% Chebyshev(Mean, Sd) UCL 0.763 99% Chebyshev(Mean, Sd) UCL 1.01
95% Hall's Bootstrap UCL 0.456 95% Percentile Bootstrap UCL 0.458
95% BCA Bootstrap UCL 0.459
95% CLT UCL 0.455 95% Jackknife UCL 0.459
95% Standard Bootstrap UCL 0.452 95% Bootstrap-t UCL 0.475
Nonparametric Distribution Free UCL Statistics
Data appear to follow a Discernible Distribution at 5% Significance Level
Nonparametric Distribution Free UCLs
95% Chebyshev (MVUE) UCL 1.072 97.5% Chebyshev (MVUE) UCL 1.348
99% Chebyshev (MVUE) UCL 1.891
Assuming Lognormal Distribution
95% H-UCL 1.088 90% Chebyshev (MVUE) UCL 0.873
Maximum of Logged Data -0.0101 SD of logged Data 1.46
Lognormal Statistics
Minimum of Logged Data -4.605 Mean of logged Data -1.833
5% Lilliefors Critical Value 0.161 Data appear Lognormal at 5% Significance Level
Data appear Approximate Lognormal at 5% Significance Level
5% Shapiro Wilk Critical Value 0.926 Data Not Lognormal at 5% Significance Level
Lilliefors Test Statistic 0.143 Lilliefors Lognormal GOF Test
Lognormal GOF Test
Shapiro Wilk Test Statistic 0.912 Shapiro Wilk Lognormal GOF Test
Assuming Gamma Distribution
95% Approximate Gamma UCL (use when n>=50) 0.517 95% Adjusted Gamma UCL (use when n<50) 0.53
Adjusted Level of Significance 0.0407 Adjusted Chi Square Value 27.11
MLE Mean (bias corrected) 0.346 MLE Sd (bias corrected) 0.408
Approximate Chi Square Value (0.05) 27.78
Theta hat (MLE) 0.447 Theta star (bias corrected MLE) 0.482
nu hat (MLE) 44.87 nu star (bias corrected) 41.56
Gamma Statistics
k hat (MLE) 0.774 k star (bias corrected MLE) 0.717
Coffey Appendix H - Data Statistics
RAAF Base Tindal PFAS Ecological Risk Assessment
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43
44
A B C D E F G H I J K L
If possible, compute and collect Data Quality Objectives (DQO) based sample size and analytical results.
Warning: This data set only has 0 observations!
Data set is too small to compute reliable and meaningful statistics and estimates!
The data set for variable Perfluoro-n-octanoic acid (PFOA) (offsite tindal) was not processed!
It is suggested to collect at least 8 to 10 observations before using these statistical methods!
Maximum N/A Median N/A
Number of Missing Observations 11
Minimum N/A Mean N/A
General Statistics
Total Number of Observations 0 Number of Distinct Observations 0
If possible, compute and collect Data Quality Objectives (DQO) based sample size and analytical results.
Perfluoro-n-octanoic acid (PFOA) (offsite tindal)
Warning: This data set only has 0 observations!
Data set is too small to compute reliable and meaningful statistics and estimates!
The data set for variable Perfluoro-n-octanoic acid (PFOA) (background) was not processed!
It is suggested to collect at least 8 to 10 observations before using these statistical methods!
Maximum N/A Median N/A
Number of Missing Observations 7
Minimum N/A Mean N/A
General Statistics
Total Number of Observations 0 Number of Distinct Observations 0
Number of Bootstrap Operations 2000
Perfluoro-n-octanoic acid (PFOA) (background)
From File Tindal_Terrestrial Invertebrates_20180605_a.xls
Full Precision OFF
Confidence Coefficient 95%
UCL Statistics for Uncensored Full Data Sets
User Selected Options
Date/Time of Computation ProUCL 5.16/6/2018 9:01:28 AM
Coffey Appendix H - Data Statistics
RAAF Base Tindal PFAS Ecological Risk Assessment
45
46
47
48
49
50
51
52
53
54
55
56
57
58
59
60
61
62
63
64
65
66
67
68
69
70
71
72
73
74
75
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77
78
79
80
81
82
83
84
85
86
87
88
89
90
91
92
93
A B C D E F G H I J K L
Note: Sample size is small (e.g., <10), if data are collected using ISM approach, you should use
guidance provided in ITRC Tech Reg Guide on ISM (ITRC, 2012) to compute statistics of interest.
For example, you may want to use Chebyshev UCL to estimate EPC (ITRC, 2012).
Chebyshev UCL can be computed using the Nonparametric and All UCL Options of ProUCL 5.1
Coefficient of Variation 0.514 Skewness -0.059
Maximum 5.5 Median 3.5
SD 1.61 Std. Error of Mean 0.537
Number of Missing Observations 2
Minimum 0.7 Mean 3.133
General Statistics
Total Number of Observations 9 Number of Distinct Observations 9
If possible, compute and collect Data Quality Objectives (DQO) based sample size and analytical results.
Perfluoro-n-octane sulfonic acid (PFOS) (offsite tindal)
Warning: This data set only has 1 observations!
Data set is too small to compute reliable and meaningful statistics and estimates!
The data set for variable Perfluoro-n-octane sulfonic acid (PFOS) (background) was not processed!
It is suggested to collect at least 8 to 10 observations before using these statistical methods!
Maximum 0.6 Median 0.6
Number of Missing Observations 6
Minimum 0.6 Mean 0.6
General Statistics
Total Number of Observations 1 Number of Distinct Observations 1
If possible, compute and collect Data Quality Objectives (DQO) based sample size and analytical results.
Perfluoro-n-octane sulfonic acid (PFOS) (background)
Warning: This data set only has 2 observations!
Data set is too small to compute reliable and meaningful statistics and estimates!
The data set for variable Perfluoro-n-octanoic acid (PFOA) (source area) was not processed!
It is suggested to collect at least 8 to 10 observations before using these statistical methods!
Maximum 0.6 Median 0.55
Number of Missing Observations 5
Minimum 0.5 Mean 0.55
General Statistics
Total Number of Observations 2 Number of Distinct Observations 2
Perfluoro-n-octanoic acid (PFOA) (source area)
Coffey Appendix H - Data Statistics
RAAF Base Tindal PFAS Ecological Risk Assessment
94
95
96
97
98
99
100
101
102
103
104
105
106
107
108
109
110
111
112
113
114
115
116
117
118
119
120
121
122
123
124
125
126
127
128
129
130
131
132
133
134
135
136
137
138
139
140
141
142
A B C D E F G H I J K L
Nonparametric Distribution Free UCL Statistics
Data appear to follow a Discernible Distribution at 5% Significance Level
95% Chebyshev (MVUE) UCL 6.428 97.5% Chebyshev (MVUE) UCL 7.81
99% Chebyshev (MVUE) UCL 10.53
Assuming Lognormal Distribution
95% H-UCL 6.072 90% Chebyshev (MVUE) UCL 5.432
Maximum of Logged Data 1.705 SD of logged Data 0.665
Lognormal Statistics
Minimum of Logged Data -0.357 Mean of logged Data 0.98
5% Lilliefors Critical Value 0.274 Data appear Lognormal at 5% Significance Level
Data appear Lognormal at 5% Significance Level
5% Shapiro Wilk Critical Value 0.829 Data appear Lognormal at 5% Significance Level
Lilliefors Test Statistic 0.214 Lilliefors Lognormal GOF Test
Lognormal GOF Test
Shapiro Wilk Test Statistic 0.91 Shapiro Wilk Lognormal GOF Test
Assuming Gamma Distribution
95% Approximate Gamma UCL (use when n>=50)) 4.72 95% Adjusted Gamma UCL (use when n<50) 5.165
Adjusted Level of Significance 0.0231 Adjusted Chi Square Value 24.45
MLE Mean (bias corrected) 3.133 MLE Sd (bias corrected) 2.094
Approximate Chi Square Value (0.05) 26.76
Theta hat (MLE) 0.965 Theta star (bias corrected MLE) 1.399
nu hat (MLE) 58.45 nu star (bias corrected) 40.3
Gamma Statistics
k hat (MLE) 3.247 k star (bias corrected MLE) 2.239
5% K-S Critical Value 0.281 Detected data appear Gamma Distributed at 5% Significance Level
Detected data appear Gamma Distributed at 5% Significance Level
5% A-D Critical Value 0.726 Detected data appear Gamma Distributed at 5% Significance Level
K-S Test Statistic 0.206 Kolmogorov-Smirnov Gamma GOF Test
Gamma GOF Test
A-D Test Statistic 0.291 Anderson-Darling Gamma GOF Test
95% Student's-t UCL 4.131 95% Adjusted-CLT UCL (Chen-1995) 4.005
95% Modified-t UCL (Johnson-1978) 4.13
Data appear Normal at 5% Significance Level
Assuming Normal Distribution
95% Normal UCL 95% UCLs (Adjusted for Skewness)
Lilliefors Test Statistic 0.146 Lilliefors GOF Test
5% Lilliefors Critical Value 0.274 Data appear Normal at 5% Significance Level
Normal GOF Test
Shapiro Wilk Test Statistic 0.967 Shapiro Wilk GOF Test
5% Shapiro Wilk Critical Value 0.829 Data appear Normal at 5% Significance Level
Coffey Appendix H - Data Statistics
RAAF Base Tindal PFAS Ecological Risk Assessment
143
144
145
146
147
148
149
150
151
152
153
154
155
156
157
158
159
160
161
162
163
164
165
166
167
168
169
170
171
172
173
174
175
176
177
178
179
180
181
182
183
184
185
186
187
188
189
190
191
192
193
194
195
A B C D E F G H I J K L
5% K-S Critical Value 0.319 Detected data appear Gamma Distributed at 5% Significance Level
Detected data appear Gamma Distributed at 5% Significance Level
5% A-D Critical Value 0.726 Detected data appear Gamma Distributed at 5% Significance Level
K-S Test Statistic 0.253 Kolmogorov-Smirnov Gamma GOF Test
Gamma GOF Test
A-D Test Statistic 0.508 Anderson-Darling Gamma GOF Test
95% Student's-t UCL 131.3 95% Adjusted-CLT UCL (Chen-1995) 122.1
95% Modified-t UCL (Johnson-1978) 130.9
Data appear Normal at 5% Significance Level
Assuming Normal Distribution
95% Normal UCL 95% UCLs (Adjusted for Skewness)
Lilliefors Test Statistic 0.158 Lilliefors GOF Test
5% Lilliefors Critical Value 0.304 Data appear Normal at 5% Significance Level
Normal GOF Test
Shapiro Wilk Test Statistic 0.936 Shapiro Wilk GOF Test
5% Shapiro Wilk Critical Value 0.803 Data appear Normal at 5% Significance Level
Note: Sample size is small (e.g., <10), if data are collected using ISM approach, you should use
guidance provided in ITRC Tech Reg Guide on ISM (ITRC, 2012) to compute statistics of interest.
For example, you may want to use Chebyshev UCL to estimate EPC (ITRC, 2012).
Chebyshev UCL can be computed using the Nonparametric and All UCL Options of ProUCL 5.1
Coefficient of Variation 0.701 Skewness -0.247
Maximum 160 Median 100
SD 60.72 Std. Error of Mean 22.95
Number of Missing Observations 0
Minimum 2.7 Mean 86.67
Perfluoro-n-octane sulfonic acid (PFOS) (source area)
General Statistics
Total Number of Observations 7 Number of Distinct Observations 7
Note: For highly negatively-skewed data, confidence limits (e.g., Chen, Johnson, Lognormal, and Gamma) may not be
reliable. Chen's and Johnson's methods provide adjustments for positvely skewed data sets.
Note: Suggestions regarding the selection of a 95% UCL are provided to help the user to select the most appropriate 95% UCL.
Recommendations are based upon data size, data distribution, and skewness.
These recommendations are based upon the results of the simulation studies summarized in Singh, Maichle, and Lee (2006).
However, simulations results will not cover all Real World data sets; for additional insight the user may want to consult a statistician.
Suggested UCL to Use
95% Student's-t UCL 4.131
90% Chebyshev(Mean, Sd) UCL 4.743 95% Chebyshev(Mean, Sd) UCL 5.473
97.5% Chebyshev(Mean, Sd) UCL 6.485 99% Chebyshev(Mean, Sd) UCL 8.474
95% Hall's Bootstrap UCL 3.923 95% Percentile Bootstrap UCL 3.944
95% BCA Bootstrap UCL 3.967
95% CLT UCL 4.016 95% Jackknife UCL 4.131
95% Standard Bootstrap UCL 3.975 95% Bootstrap-t UCL 4.112
Nonparametric Distribution Free UCLs
Coffey Appendix H - Data Statistics
RAAF Base Tindal PFAS Ecological Risk Assessment
196
197
198
199
200
201
202
203
204
205
206
207
208
209
210
211
212
213
214
215
216
217
218
219
220
221
222
223
224
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231
232
233
234
235
236
237
238
239
240
241
242
243
244
245
A B C D E F G H I J K L
Note: For highly negatively-skewed data, confidence limits (e.g., Chen, Johnson, Lognormal, and Gamma) may not be
reliable. Chen's and Johnson's methods provide adjustments for positvely skewed data sets.
Note: Suggestions regarding the selection of a 95% UCL are provided to help the user to select the most appropriate 95% UCL.
Recommendations are based upon data size, data distribution, and skewness.
These recommendations are based upon the results of the simulation studies summarized in Singh, Maichle, and Lee (2006).
However, simulations results will not cover all Real World data sets; for additional insight the user may want to consult a statistician.
Suggested UCL to Use
95% Student's-t UCL 131.3
90% Chebyshev(Mean, Sd) UCL 155.5 95% Chebyshev(Mean, Sd) UCL 186.7
97.5% Chebyshev(Mean, Sd) UCL 230 99% Chebyshev(Mean, Sd) UCL 315
95% Hall's Bootstrap UCL 120.8 95% Percentile Bootstrap UCL 122
95% BCA Bootstrap UCL 119.1
95% CLT UCL 124.4 95% Jackknife UCL 131.3
95% Standard Bootstrap UCL 121.7 95% Bootstrap-t UCL 127.7
Nonparametric Distribution Free UCL Statistics
Data appear to follow a Discernible Distribution at 5% Significance Level
Nonparametric Distribution Free UCLs
95% Chebyshev (MVUE) UCL 402.6 97.5% Chebyshev (MVUE) UCL 525.2
99% Chebyshev (MVUE) UCL 766.1
Assuming Lognormal Distribution
95% H-UCL 3310 90% Chebyshev (MVUE) UCL 314.2
Maximum of Logged Data 5.075 SD of logged Data 1.476
Lognormal Statistics
Minimum of Logged Data 0.993 Mean of logged Data 3.934
5% Lilliefors Critical Value 0.304 Data appear Lognormal at 5% Significance Level
Data appear Approximate Lognormal at 5% Significance Level
5% Shapiro Wilk Critical Value 0.803 Data Not Lognormal at 5% Significance Level
Lilliefors Test Statistic 0.275 Lilliefors Lognormal GOF Test
Lognormal GOF Test
Shapiro Wilk Test Statistic 0.798 Shapiro Wilk Lognormal GOF Test
Assuming Gamma Distribution
95% Approximate Gamma UCL (use when n>=50)) 219.9 95% Adjusted Gamma UCL (use when n<50) 300.9
Adjusted Level of Significance 0.0158 Adjusted Chi Square Value 2.881
MLE Mean (bias corrected) 86.67 MLE Sd (bias corrected) 102.6
Approximate Chi Square Value (0.05) 3.942
Theta hat (MLE) 80 Theta star (bias corrected MLE) 121.3
nu hat (MLE) 15.17 nu star (bias corrected) 10
Gamma Statistics
k hat (MLE) 1.083 k star (bias corrected MLE) 0.714
Coffey Appendix H - Data Statistics
RAAF Base Tindal PFAS Ecological Risk Assessment
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
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18
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31
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39
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44
A B C D E F G H I J K L
If possible, compute and collect Data Quality Objectives (DQO) based sample size and analytical results.
Warning: This data set only has 0 observations!
Data set is too small to compute reliable and meaningful statistics and estimates!
The data set for variable Perfluoro-n-octanoic acid (PFOA) (katherine river us) was not processed!
It is suggested to collect at least 8 to 10 observations before using these statistical methods!
Maximum N/A Median N/A
Number of Missing Observations 6
Minimum N/A Mean N/A
General Statistics
Total Number of Observations 0 Number of Distinct Observations 0
If possible, compute and collect Data Quality Objectives (DQO) based sample size and analytical results.
Perfluoro-n-octanoic acid (PFOA) (katherine river us)
Warning: This data set only has 0 observations!
Data set is too small to compute reliable and meaningful statistics and estimates!
The data set for variable Perfluoro-n-octanoic acid (PFOA) (background) was not processed!
It is suggested to collect at least 8 to 10 observations before using these statistical methods!
Maximum N/A Median N/A
Number of Missing Observations 4
Minimum N/A Mean N/A
General Statistics
Total Number of Observations 0 Number of Distinct Observations 0
Number of Bootstrap Operations 2000
Perfluoro-n-octanoic acid (PFOA) (background)
From File Data_Tindal_Terrestrial Vertebrates_20180606_j.xls
Full Precision OFF
Confidence Coefficient 95%
UCL Statistics for Uncensored Full Data Sets
User Selected Options
Date/Time of Computation ProUCL 5.16/6/2018 10:44:04 AM
Coffey Appendix H - Data Statistics
RAAF Base Tindal PFAS Ecological Risk Assessment
45
46
47
48
49
50
51
52
53
54
55
56
57
58
59
60
61
62
63
64
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77
78
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81
82
83
84
85
86
87
88
89
90
91
92
93
94
95
96
97
A B C D E F G H I J K L
Adjusted Level of Significance 0.0278 Adjusted Chi Square Value 7.673
MLE Mean (bias corrected) 3.045 MLE Sd (bias corrected) 3.472
Approximate Chi Square Value (0.05) 8.621
Theta hat (MLE) 3.125 Theta star (bias corrected MLE) 3.958
nu hat (MLE) 21.44 nu star (bias corrected) 16.93
Gamma Statistics
k hat (MLE) 0.975 k star (bias corrected MLE) 0.769
5% K-S Critical Value 0.263 Data Not Gamma Distributed at 5% Significance Level
Data Not Gamma Distributed at 5% Significance Level
5% A-D Critical Value 0.753 Data Not Gamma Distributed at 5% Significance Level
K-S Test Statistic 0.328 Kolmogorov-Smirnov Gamma GOF Test
Gamma GOF Test
A-D Test Statistic 0.935 Anderson-Darling Gamma GOF Test
95% Student's-t UCL 5.18 95% Adjusted-CLT UCL (Chen-1995) 5.751
95% Modified-t UCL (Johnson-1978) 5.3
Data Not Normal at 5% Significance Level
Assuming Normal Distribution
95% Normal UCL 95% UCLs (Adjusted for Skewness)
Lilliefors Test Statistic 0.327 Lilliefors GOF Test
5% Lilliefors Critical Value 0.251 Data Not Normal at 5% Significance Level
Normal GOF Test
Shapiro Wilk Test Statistic 0.693 Shapiro Wilk GOF Test
5% Shapiro Wilk Critical Value 0.85 Data Not Normal at 5% Significance Level
Coefficient of Variation 1.283 Skewness 2.026
Maximum 13 Median 1.1
SD 3.906 Std. Error of Mean 1.178
Number of Missing Observations 8
Minimum 0.6 Mean 3.045
General Statistics
Total Number of Observations 11 Number of Distinct Observations 9
If possible, compute and collect Data Quality Objectives (DQO) based sample size and analytical results.
Perfluoro-n-octanoic acid (PFOA) (source area)
Warning: This data set only has 0 observations!
Data set is too small to compute reliable and meaningful statistics and estimates!
The data set for variable Perfluoro-n-octanoic acid (PFOA) (offsite tindal) was not processed!
It is suggested to collect at least 8 to 10 observations before using these statistical methods!
Maximum N/A Median N/A
Number of Missing Observations 20
Minimum N/A Mean N/A
General Statistics
Total Number of Observations 0 Number of Distinct Observations 0
Perfluoro-n-octanoic acid (PFOA) (offsite tindal)
Coffey Appendix H - Data Statistics
RAAF Base Tindal PFAS Ecological Risk Assessment
98
99
100
101
102
103
104
105
106
107
108
109
110
111
112
113
114
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141
142
143
144
145
146
147
148
149
150
151
A B C D E F G H I J K L
It is suggested to collect at least 8 to 10 observations before using these statistical methods!
If possible, compute and collect Data Quality Objectives (DQO) based sample size and analytical results.
Warning: This data set only has 2 observations!
Data set is too small to compute reliable and meaningful statistics and estimates!
The data set for variable Perfluoro-n-octane sulfonic acid (PFOS) (background) was not processed!
Minimum 2.9 Mean 6
Maximum 9.1 Median 6
Total Number of Observations 2 Number of Distinct Observations 2
Number of Missing Observations 2
Perfluoro-n-octane sulfonic acid (PFOS) (background)
General Statistics
Note: Suggestions regarding the selection of a 95% UCL are provided to help the user to select the most appropriate 95% UCL.
Recommendations are based upon data size, data distribution, and skewness.
These recommendations are based upon the results of the simulation studies summarized in Singh, Maichle, and Lee (2006).
However, simulations results will not cover all Real World data sets; for additional insight the user may want to consult a statistician.
Suggested UCL to Use
95% Chebyshev (Mean, Sd) UCL 8.179
90% Chebyshev(Mean, Sd) UCL 6.579 95% Chebyshev(Mean, Sd) UCL 8.179
97.5% Chebyshev(Mean, Sd) UCL 10.4 99% Chebyshev(Mean, Sd) UCL 14.76
95% Hall's Bootstrap UCL 12.86 95% Percentile Bootstrap UCL 5.127
95% BCA Bootstrap UCL 5.7
95% CLT UCL 4.983 95% Jackknife UCL 5.18
95% Standard Bootstrap UCL 4.878 95% Bootstrap-t UCL 8.628
Nonparametric Distribution Free UCL Statistics
Data appear to follow a Discernible Distribution at 5% Significance Level
Nonparametric Distribution Free UCLs
95% Chebyshev (MVUE) UCL 7.002 97.5% Chebyshev (MVUE) UCL 8.824
99% Chebyshev (MVUE) UCL 12.4
Assuming Lognormal Distribution
95% H-UCL 8.797 90% Chebyshev (MVUE) UCL 5.69
Maximum of Logged Data 2.565 SD of logged Data 1.078
Lognormal Statistics
Minimum of Logged Data -0.511 Mean of logged Data 0.52
5% Lilliefors Critical Value 0.251 Data Not Lognormal at 5% Significance Level
Data appear Approximate Lognormal at 5% Significance Level
5% Shapiro Wilk Critical Value 0.85 Data appear Lognormal at 5% Significance Level
Lilliefors Test Statistic 0.289 Lilliefors Lognormal GOF Test
Lognormal GOF Test
Shapiro Wilk Test Statistic 0.857 Shapiro Wilk Lognormal GOF Test
Assuming Gamma Distribution
95% Approximate Gamma UCL (use when n>=50)) 5.98 95% Adjusted Gamma UCL (use when n<50) 6.719
Coffey Appendix H - Data Statistics
RAAF Base Tindal PFAS Ecological Risk Assessment
152
153
154
155
156
157
158
159
160
161
162
163
164
165
166
167
168
169
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A B C D E F G H I J K L
Maximum of Logged Data 3.97 SD of logged Data 0.686
Lognormal Statistics
Minimum of Logged Data 2.282 Mean of logged Data 2.939
5% Lilliefors Critical Value 0.325 Data appear Lognormal at 5% Significance Level
Data appear Lognormal at 5% Significance Level
5% Shapiro Wilk Critical Value 0.788 Data appear Lognormal at 5% Significance Level
Lilliefors Test Statistic 0.228 Lilliefors Lognormal GOF Test
Lognormal GOF Test
Shapiro Wilk Test Statistic 0.883 Shapiro Wilk Lognormal GOF Test
Assuming Gamma Distribution
95% Approximate Gamma UCL (use when n>=50)) 46.16 95% Adjusted Gamma UCL (use when n<50) 60.58
Adjusted Level of Significance 0.0122 Adjusted Chi Square Value 6.371
MLE Mean (bias corrected) 23.3 MLE Sd (bias corrected) 19.83
Approximate Chi Square Value (0.05) 8.36
Theta hat (MLE) 9.18 Theta star (bias corrected MLE) 16.88
nu hat (MLE) 30.46 nu star (bias corrected) 16.56
Gamma Statistics
k hat (MLE) 2.538 k star (bias corrected MLE) 1.38
5% K-S Critical Value 0.335 Detected data appear Gamma Distributed at 5% Significance Level
Detected data appear Gamma Distributed at 5% Significance Level
5% A-D Critical Value 0.703 Detected data appear Gamma Distributed at 5% Significance Level
K-S Test Statistic 0.27 Kolmogorov-Smirnov Gamma GOF Test
Gamma GOF Test
A-D Test Statistic 0.501 Anderson-Darling Gamma GOF Test
95% Student's-t UCL 37.66 95% Adjusted-CLT UCL (Chen-1995) 38.98
95% Modified-t UCL (Johnson-1978) 38.27
Data appear Normal at 5% Significance Level
Assuming Normal Distribution
95% Normal UCL 95% UCLs (Adjusted for Skewness)
Lilliefors Test Statistic 0.308 Lilliefors GOF Test
5% Lilliefors Critical Value 0.325 Data appear Normal at 5% Significance Level
Normal GOF Test
Shapiro Wilk Test Statistic 0.811 Shapiro Wilk GOF Test
5% Shapiro Wilk Critical Value 0.788 Data appear Normal at 5% Significance Level
Note: Sample size is small (e.g., <10), if data are collected using ISM approach, you should use
guidance provided in ITRC Tech Reg Guide on ISM (ITRC, 2012) to compute statistics of interest.
For example, you may want to use Chebyshev UCL to estimate EPC (ITRC, 2012).
Chebyshev UCL can be computed using the Nonparametric and All UCL Options of ProUCL 5.1
Coefficient of Variation 0.749 Skewness 1.275
Maximum 53 Median 15
SD 17.45 Std. Error of Mean 7.124
Number of Missing Observations 0
Minimum 9.8 Mean 23.3
Perfluoro-n-octane sulfonic acid (PFOS) (katherine river us)
General Statistics
Total Number of Observations 6 Number of Distinct Observations 6
Coffey Appendix H - Data Statistics
RAAF Base Tindal PFAS Ecological Risk Assessment
210
211
212
213
214
215
216
217
218
219
220
221
222
223
224
225
226
227
228
229
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244
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246
247
248
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250
251
252
253
254
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256
257
A B C D E F G H I J K L
95% Modified-t UCL (Johnson-1978) 28.86
Assuming Normal Distribution
95% Normal UCL 95% UCLs (Adjusted for Skewness)
95% Student's-t UCL 28.58 95% Adjusted-CLT UCL (Chen-1995) 29.97
5% Lilliefors Critical Value 0.192 Data Not Normal at 5% Significance Level
Data Not Normal at 5% Significance Level
5% Shapiro Wilk Critical Value 0.905 Data Not Normal at 5% Significance Level
Lilliefors Test Statistic 0.246 Lilliefors GOF Test
Normal GOF Test
Shapiro Wilk Test Statistic 0.752 Shapiro Wilk GOF Test
SD 22.81 Std. Error of Mean 5.101
Coefficient of Variation 1.155 Skewness 1.495
Minimum 0.9 Mean 19.76
Maximum 73 Median 11.5
Total Number of Observations 20 Number of Distinct Observations 19
Number of Missing Observations 0
Perfluoro-n-octane sulfonic acid (PFOS) (offsite tindal)
General Statistics
Note: Suggestions regarding the selection of a 95% UCL are provided to help the user to select the most appropriate 95% UCL.
Recommendations are based upon data size, data distribution, and skewness.
These recommendations are based upon the results of the simulation studies summarized in Singh, Maichle, and Lee (2006).
However, simulations results will not cover all Real World data sets; for additional insight the user may want to consult a statistician.
Suggested UCL to Use
95% Student's-t UCL 37.66
90% Chebyshev(Mean, Sd) UCL 44.67 95% Chebyshev(Mean, Sd) UCL 54.35
97.5% Chebyshev(Mean, Sd) UCL 67.79 99% Chebyshev(Mean, Sd) UCL 94.19
95% Hall's Bootstrap UCL 108.4 95% Percentile Bootstrap UCL 34.33
95% BCA Bootstrap UCL 35.97
95% CLT UCL 35.02 95% Jackknife UCL 37.66
95% Standard Bootstrap UCL 34.34 95% Bootstrap-t UCL 93.36
Nonparametric Distribution Free UCL Statistics
Data appear to follow a Discernible Distribution at 5% Significance Level
Nonparametric Distribution Free UCLs
95% Chebyshev (MVUE) UCL 50.66 97.5% Chebyshev (MVUE) UCL 62.69
99% Chebyshev (MVUE) UCL 86.32
Assuming Lognormal Distribution
95% H-UCL 62.49 90% Chebyshev (MVUE) UCL 42
Coffey Appendix H - Data Statistics
RAAF Base Tindal PFAS Ecological Risk Assessment
258
259
260
261
262
263
264
265
266
267
268
269
270
271
272
273
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275
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304
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311
A B C D E F G H I J K L
Note: Suggestions regarding the selection of a 95% UCL are provided to help the user to select the most appropriate 95% UCL.
Recommendations are based upon data size, data distribution, and skewness.
These recommendations are based upon the results of the simulation studies summarized in Singh, Maichle, and Lee (2006).
However, simulations results will not cover all Real World data sets; for additional insight the user may want to consult a statistician.
Suggested UCL to Use
95% Adjusted Gamma UCL 32.99
90% Chebyshev(Mean, Sd) UCL 35.06 95% Chebyshev(Mean, Sd) UCL 41.99
97.5% Chebyshev(Mean, Sd) UCL 51.61 99% Chebyshev(Mean, Sd) UCL 70.51
95% Hall's Bootstrap UCL 27.99 95% Percentile Bootstrap UCL 28.2
95% BCA Bootstrap UCL 30.06
95% CLT UCL 28.15 95% Jackknife UCL 28.58
95% Standard Bootstrap UCL 28.03 95% Bootstrap-t UCL 32.47
Nonparametric Distribution Free UCL Statistics
Data appear to follow a Discernible Distribution at 5% Significance Level
Nonparametric Distribution Free UCLs
95% Chebyshev (MVUE) UCL 52.12 97.5% Chebyshev (MVUE) UCL 65.46
99% Chebyshev (MVUE) UCL 91.66
Assuming Lognormal Distribution
95% H-UCL 55.64 90% Chebyshev (MVUE) UCL 42.51
Maximum of Logged Data 4.29 SD of logged Data 1.275
Lognormal Statistics
Minimum of Logged Data -0.105 Mean of logged Data 2.313
5% Lilliefors Critical Value 0.192 Data appear Lognormal at 5% Significance Level
Data appear Lognormal at 5% Significance Level
5% Shapiro Wilk Critical Value 0.905 Data appear Lognormal at 5% Significance Level
Lilliefors Test Statistic 0.104 Lilliefors Lognormal GOF Test
Lognormal GOF Test
Shapiro Wilk Test Statistic 0.955 Shapiro Wilk Lognormal GOF Test
Assuming Gamma Distribution
95% Approximate Gamma UCL (use when n>=50) 31.74 95% Adjusted Gamma UCL (use when n<50) 32.99
Adjusted Level of Significance 0.038 Adjusted Chi Square Value 18.61
MLE Mean (bias corrected) 19.76 MLE Sd (bias corrected) 22.41
Approximate Chi Square Value (0.05) 19.34
Theta hat (MLE) 22.59 Theta star (bias corrected MLE) 25.43
nu hat (MLE) 34.98 nu star (bias corrected) 31.07
Detected data appear Gamma Distributed at 5% Significance Level
Gamma Statistics
k hat (MLE) 0.875 k star (bias corrected MLE) 0.777
K-S Test Statistic 0.148 Kolmogorov-Smirnov Gamma GOF Test
5% K-S Critical Value 0.2 Detected data appear Gamma Distributed at 5% Significance Level
Gamma GOF Test
A-D Test Statistic 0.523 Anderson-Darling Gamma GOF Test
5% A-D Critical Value 0.774 Detected data appear Gamma Distributed at 5% Significance Level
Coffey Appendix H - Data Statistics
RAAF Base Tindal PFAS Ecological Risk Assessment
312
313
314
315
316
317
318
319
320
321
322
323
324
325
326
327
328
329
330
331
332
333
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335
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339
340
341
342
343
344
345
346
347
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351
352
353
354
355
356
357
358
359
360
361
362
363
364
365
366
A B C D E F G H I J K L
95% Chebyshev (MVUE) UCL 13824 97.5% Chebyshev (MVUE) UCL 18307
99% Chebyshev (MVUE) UCL 27114
Assuming Lognormal Distribution
95% H-UCL 118144 90% Chebyshev (MVUE) UCL 10594
Maximum of Logged Data 8.594 SD of logged Data 2.447
Lognormal Statistics
Minimum of Logged Data -0.916 Mean of logged Data 5.639
5% Lilliefors Critical Value 0.202 Data appear Lognormal at 5% Significance Level
Data appear Lognormal at 5% Significance Level
5% Shapiro Wilk Critical Value 0.897 Data appear Lognormal at 5% Significance Level
Lilliefors Test Statistic 0.15 Lilliefors Lognormal GOF Test
Lognormal GOF Test
Shapiro Wilk Test Statistic 0.905 Shapiro Wilk Lognormal GOF Test
Assuming Gamma Distribution
95% Approximate Gamma UCL (use when n>=50) 2508 95% Adjusted Gamma UCL (use when n<50) 2701
Adjusted Level of Significance 0.0357 Adjusted Chi Square Value 6.541
MLE Mean (bias corrected) 1203 MLE Sd (bias corrected) 1883
Approximate Chi Square Value (0.05) 7.045
Theta hat (MLE) 2702 Theta star (bias corrected MLE) 2948
nu hat (MLE) 16.03 nu star (bias corrected) 14.69
Detected data appear Gamma Distributed at 5% Significance Level
Gamma Statistics
k hat (MLE) 0.445 k star (bias corrected MLE) 0.408
K-S Test Statistic 0.103 Kolmogorov-Smirnov Gamma GOF Test
5% K-S Critical Value 0.217 Detected data appear Gamma Distributed at 5% Significance Level
Gamma GOF Test
A-D Test Statistic 0.185 Anderson-Darling Gamma GOF Test
5% A-D Critical Value 0.812 Detected data appear Gamma Distributed at 5% Significance Level
95% Modified-t UCL (Johnson-1978) 1880
Assuming Normal Distribution
95% Normal UCL 95% UCLs (Adjusted for Skewness)
95% Student's-t UCL 1856 95% Adjusted-CLT UCL (Chen-1995) 1969
5% Lilliefors Critical Value 0.202 Data Not Normal at 5% Significance Level
Data Not Normal at 5% Significance Level
5% Shapiro Wilk Critical Value 0.897 Data Not Normal at 5% Significance Level
Lilliefors Test Statistic 0.279 Lilliefors GOF Test
Normal GOF Test
Shapiro Wilk Test Statistic 0.77 Shapiro Wilk GOF Test
SD 1594 Std. Error of Mean 375.7
Coefficient of Variation 1.325 Skewness 1.57
Minimum 0.4 Mean 1203
Maximum 5400 Median 455
Total Number of Observations 18 Number of Distinct Observations 17
Number of Missing Observations 1
Perfluoro-n-octane sulfonic acid (PFOS) (source area)
General Statistics
Coffey Appendix H - Data Statistics
RAAF Base Tindal PFAS Ecological Risk Assessment
367
368
369
370
371
372
373
374
375
376
377
378
379
380
381
382
383
384
385
386
A B C D E F G H I J K L
Note: Suggestions regarding the selection of a 95% UCL are provided to help the user to select the most appropriate 95% UCL.
Recommendations are based upon data size, data distribution, and skewness.
These recommendations are based upon the results of the simulation studies summarized in Singh, Maichle, and Lee (2006).
However, simulations results will not cover all Real World data sets; for additional insight the user may want to consult a statistician.
Suggested UCL to Use
95% Adjusted Gamma UCL 2701
90% Chebyshev(Mean, Sd) UCL 2330 95% Chebyshev(Mean, Sd) UCL 2840
97.5% Chebyshev(Mean, Sd) UCL 3549 99% Chebyshev(Mean, Sd) UCL 4941
95% Hall's Bootstrap UCL 2014 95% Percentile Bootstrap UCL 1828
95% BCA Bootstrap UCL 1982
95% CLT UCL 1821 95% Jackknife UCL 1856
95% Standard Bootstrap UCL 1814 95% Bootstrap-t UCL 2134
Nonparametric Distribution Free UCL Statistics
Data appear to follow a Discernible Distribution at 5% Significance Level
Nonparametric Distribution Free UCLs
Coffey Appendix H - Data Statistics
RAAF Base Tindal PFAS Ecological Risk Assessment
1
2
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4
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6
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A B C D E F G H I J K L
5% K-S Critical Value 0.263 Data Not Gamma Distributed at 5% Significance Level
Data Not Gamma Distributed at 5% Significance Level
5% A-D Critical Value 0.753 Data Not Gamma Distributed at 5% Significance Level
K-S Test Statistic 0.328 Kolmogorov-Smirnov Gamma GOF Test
Gamma GOF Test
A-D Test Statistic 0.935 Anderson-Darling Gamma GOF Test
95% Student's-t UCL 5.18 95% Adjusted-CLT UCL (Chen-1995) 5.751
95% Modified-t UCL (Johnson-1978) 5.3
Data Not Normal at 5% Significance Level
Assuming Normal Distribution
95% Normal UCL 95% UCLs (Adjusted for Skewness)
Lilliefors Test Statistic 0.327 Lilliefors GOF Test
5% Lilliefors Critical Value 0.251 Data Not Normal at 5% Significance Level
Normal GOF Test
Shapiro Wilk Test Statistic 0.693 Shapiro Wilk GOF Test
5% Shapiro Wilk Critical Value 0.85 Data Not Normal at 5% Significance Level
Coefficient of Variation 1.283 Skewness 2.026
Maximum 13 Median 1.1
SD 3.906 Std. Error of Mean 1.178
Number of Missing Observations 12
Minimum 0.6 Mean 3.045
General Statistics
Total Number of Observations 11 Number of Distinct Observations 9
If possible, compute and collect Data Quality Objectives (DQO) based sample size and analytical results.
Perfluoro-n-octanoic acid (PFOA) (on-base)
Warning: This data set only has 0 observations!
Data set is too small to compute reliable and meaningful statistics and estimates!
The data set for variable Perfluoro-n-octanoic acid (PFOA) (off-base) was not processed!
It is suggested to collect at least 8 to 10 observations before using these statistical methods!
Maximum N/A Median N/A
Minimum N/A Mean N/A
General Statistics
Total Number of Observations 0 Number of Distinct Observations 0
Perfluoro-n-octanoic acid (PFOA) (off-base)
From File Data_Tindal_Terrestrial Vertebrates_20180709_j.xls
Full Precision OFF
Confidence Coefficient 95%
Number of Missing Observations 35
UCL Statistics for Uncensored Full Data Sets
User Selected Options
Date/Time of Computation ProUCL 5.17/9/2018 10:15:37 AM
Number of Bootstrap Operations 2000
Coffey Appendix H - Data Statistics
RAAF Base Tindal PFAS Ecological Risk Assessment
57
58
59
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61
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63
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65
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71
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A B C D E F G H I J K L
Note: Suggestions regarding the selection of a 95% UCL are provided to help the user to select the most appropriate 95% UCL.
Recommendations are based upon data size, data distribution, and skewness.
These recommendations are based upon the results of the simulation studies summarized in Singh, Maichle, and Lee (2006).
However, simulations results will not cover all Real World data sets; for additional insight the user may want to consult a statistician.
Suggested UCL to Use
95% Chebyshev (Mean, Sd) UCL 8.179
90% Chebyshev(Mean, Sd) UCL 6.579 95% Chebyshev(Mean, Sd) UCL 8.179
97.5% Chebyshev(Mean, Sd) UCL 10.4 99% Chebyshev(Mean, Sd) UCL 14.76
95% Hall's Bootstrap UCL 12.86 95% Percentile Bootstrap UCL 4.973
95% BCA Bootstrap UCL 5.6
95% CLT UCL 4.983 95% Jackknife UCL 5.18
95% Standard Bootstrap UCL 4.871 95% Bootstrap-t UCL 8.542
Nonparametric Distribution Free UCL Statistics
Data appear to follow a Discernible Distribution at 5% Significance Level
Nonparametric Distribution Free UCLs
95% Chebyshev (MVUE) UCL 7.002 97.5% Chebyshev (MVUE) UCL 8.824
99% Chebyshev (MVUE) UCL 12.4
Assuming Lognormal Distribution
95% H-UCL 8.797 90% Chebyshev (MVUE) UCL 5.69
Maximum of Logged Data 2.565 SD of logged Data 1.078
Lognormal Statistics
Minimum of Logged Data -0.511 Mean of logged Data 0.52
5% Lilliefors Critical Value 0.251 Data Not Lognormal at 5% Significance Level
Data appear Approximate Lognormal at 5% Significance Level
5% Shapiro Wilk Critical Value 0.85 Data appear Lognormal at 5% Significance Level
Lilliefors Test Statistic 0.289 Lilliefors Lognormal GOF Test
Lognormal GOF Test
Shapiro Wilk Test Statistic 0.857 Shapiro Wilk Lognormal GOF Test
Assuming Gamma Distribution
95% Approximate Gamma UCL (use when n>=50)) 5.98 95% Adjusted Gamma UCL (use when n<50) 6.719
Adjusted Level of Significance 0.0278 Adjusted Chi Square Value 7.673
MLE Mean (bias corrected) 3.045 MLE Sd (bias corrected) 3.472
Approximate Chi Square Value (0.05) 8.621
Theta hat (MLE) 3.125 Theta star (bias corrected MLE) 3.958
nu hat (MLE) 21.44 nu star (bias corrected) 16.93
Gamma Statistics
k hat (MLE) 0.975 k star (bias corrected MLE) 0.769Coffey Appendix H - Data Statistics
RAAF Base Tindal PFAS Ecological Risk Assessment
104
105
106
107
108
109
110
111
112
113
114
115
116
117
118
119
120
121
122
123
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A B C D E F G H I J K L
95% Chebyshev (MVUE) UCL 45.1 97.5% Chebyshev (MVUE) UCL 55.12
99% Chebyshev (MVUE) UCL 74.81
Assuming Lognormal Distribution
95% H-UCL 39.24 90% Chebyshev (MVUE) UCL 37.88
Maximum of Logged Data 4.942 SD of logged Data 1.188
Lognormal Statistics
Minimum of Logged Data -0.105 Mean of logged Data 2.415
5% Lilliefors Critical Value 0.148 Data appear Lognormal at 5% Significance Level
Data appear Lognormal at 5% Significance Level
5% Shapiro Wilk Critical Value 0.934 Data appear Lognormal at 5% Significance Level
Lilliefors Test Statistic 0.0839 Lilliefors Lognormal GOF Test
Lognormal GOF Test
Shapiro Wilk Test Statistic 0.981 Shapiro Wilk Lognormal GOF Test
Assuming Gamma Distribution
95% Approximate Gamma UCL (use when n>=50) 29.85 95% Adjusted Gamma UCL (use when n<50) 30.33
Adjusted Level of Significance 0.0425 Adjusted Chi Square Value 41.63
MLE Mean (bias corrected) 21.42 MLE Sd (bias corrected) 22.34
Approximate Chi Square Value (0.05) 42.3
Theta hat (MLE) 23.79 Theta star (bias corrected MLE) 25.43
nu hat (MLE) 63.02 nu star (bias corrected) 58.95
Detected data appear Gamma Distributed at 5% Significance Level
Gamma Statistics
k hat (MLE) 0.9 k star (bias corrected MLE) 0.842
K-S Test Statistic 0.156 Kolmogorov-Smirnov Gamma GOF Test
5% K-S Critical Value 0.154 Detected data appear Gamma Distributed at 5% Significance Level
Gamma GOF Test
A-D Test Statistic 0.76 Anderson-Darling Gamma GOF Test
5% A-D Critical Value 0.78 Detected data appear Gamma Distributed at 5% Significance Level
95% Modified-t UCL (Johnson-1978) 29.84
Assuming Normal Distribution
95% Normal UCL 95% UCLs (Adjusted for Skewness)
95% Student's-t UCL 29.48 95% Adjusted-CLT UCL (Chen-1995) 31.57
5% Lilliefors Critical Value 0.148 Data Not Normal at 5% Significance Level
Data Not Normal at 5% Significance Level
5% Shapiro Wilk Critical Value 0.934 Data Not Normal at 5% Significance Level
Lilliefors Test Statistic 0.292 Lilliefors GOF Test
Normal GOF Test
Shapiro Wilk Test Statistic 0.678 Shapiro Wilk GOF Test
SD 28.2 Std. Error of Mean 4.766
Coefficient of Variation 1.316 Skewness 2.682
Minimum 0.9 Mean 21.42
Maximum 140 Median 12
Total Number of Observations 35 Number of Distinct Observations 31
Number of Missing Observations 0
Perfluoro-n-octane sulfonic acid (PFOS) (off-base)
General Statistics
Coffey Appendix H - Data Statistics
RAAF Base Tindal PFAS Ecological Risk Assessment
160
161
162
163
164
165
166
167
168
169
170
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172
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174
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176
177
178
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A B C D E F G H I J K L
Adjusted Level of Significance 0.038 Adjusted Chi Square Value 6.329
MLE Mean (bias corrected) 1083 MLE Sd (bias corrected) 1816
Approximate Chi Square Value (0.05) 6.734
Theta hat (MLE) 2854 Theta star (bias corrected MLE) 3044
nu hat (MLE) 15.18 nu star (bias corrected) 14.24
Detected data appear Gamma Distributed at 5% Significance Level
Gamma Statistics
k hat (MLE) 0.38 k star (bias corrected MLE) 0.356
K-S Test Statistic 0.126 Kolmogorov-Smirnov Gamma GOF Test
5% K-S Critical Value 0.208 Detected data appear Gamma Distributed at 5% Significance Level
Gamma GOF Test
A-D Test Statistic 0.221 Anderson-Darling Gamma GOF Test
5% A-D Critical Value 0.828 Detected data appear Gamma Distributed at 5% Significance Level
95% Modified-t UCL (Johnson-1978) 1705
Assuming Normal Distribution
95% Normal UCL 95% UCLs (Adjusted for Skewness)
95% Student's-t UCL 1683 95% Adjusted-CLT UCL (Chen-1995) 1796
5% Lilliefors Critical Value 0.192 Data Not Normal at 5% Significance Level
Data Not Normal at 5% Significance Level
5% Shapiro Wilk Critical Value 0.905 Data Not Normal at 5% Significance Level
Lilliefors Test Statistic 0.294 Lilliefors GOF Test
Normal GOF Test
Shapiro Wilk Test Statistic 0.738 Shapiro Wilk GOF Test
SD 1552 Std. Error of Mean 347
Coefficient of Variation 1.433 Skewness 1.707
Minimum 0.4 Mean 1083
Maximum 5400 Median 360
Total Number of Observations 20 Number of Distinct Observations 19
Number of Missing Observations 3
Perfluoro-n-octane sulfonic acid (PFOS) (on-base)
General Statistics
Note: Suggestions regarding the selection of a 95% UCL are provided to help the user to select the most appropriate 95% UCL.
Recommendations are based upon data size, data distribution, and skewness.
These recommendations are based upon the results of the simulation studies summarized in Singh, Maichle, and Lee (2006).
However, simulations results will not cover all Real World data sets; for additional insight the user may want to consult a statistician.
Suggested UCL to Use
95% Adjusted Gamma UCL 30.33
90% Chebyshev(Mean, Sd) UCL 35.72 95% Chebyshev(Mean, Sd) UCL 42.2
97.5% Chebyshev(Mean, Sd) UCL 51.19 99% Chebyshev(Mean, Sd) UCL 68.84
95% Hall's Bootstrap UCL 34.58 95% Percentile Bootstrap UCL 30.03
95% BCA Bootstrap UCL 31.69
95% CLT UCL 29.26 95% Jackknife UCL 29.48
95% Standard Bootstrap UCL 29.11 95% Bootstrap-t UCL 33.94
Nonparametric Distribution Free UCL Statistics
Data appear to follow a Discernible Distribution at 5% Significance Level
Nonparametric Distribution Free UCLs
Coffey Appendix H - Data Statistics
RAAF Base Tindal PFAS Ecological Risk Assessment
216
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251
252
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A B C D E F G H I J K L
Note: Suggestions regarding the selection of a 95% UCL are provided to help the user to select the most appropriate 95% UCL.
Recommendations are based upon data size, data distribution, and skewness.
These recommendations are based upon the results of the simulation studies summarized in Singh, Maichle, and Lee (2006).
However, simulations results will not cover all Real World data sets; for additional insight the user may want to consult a statistician.
Suggested UCL to Use
95% Adjusted Gamma UCL 2437
90% Chebyshev(Mean, Sd) UCL 2124 95% Chebyshev(Mean, Sd) UCL 2596
97.5% Chebyshev(Mean, Sd) UCL 3250 99% Chebyshev(Mean, Sd) UCL 4536
95% Hall's Bootstrap UCL 1813 95% Percentile Bootstrap UCL 1658
95% BCA Bootstrap UCL 1759
95% CLT UCL 1654 95% Jackknife UCL 1683
95% Standard Bootstrap UCL 1638 95% Bootstrap-t UCL 1935
Nonparametric Distribution Free UCL Statistics
Data appear to follow a Discernible Distribution at 5% Significance Level
Nonparametric Distribution Free UCLs
95% Chebyshev (MVUE) UCL 14125 97.5% Chebyshev (MVUE) UCL 18754
99% Chebyshev (MVUE) UCL 27846
Assuming Lognormal Distribution
95% H-UCL 160594 90% Chebyshev (MVUE) UCL 10790
Maximum of Logged Data 8.594 SD of logged Data 2.628
Lognormal Statistics
Minimum of Logged Data -0.916 Mean of logged Data 5.239
5% Lilliefors Critical Value 0.192 Data appear Lognormal at 5% Significance Level
Data appear Lognormal at 5% Significance Level
5% Shapiro Wilk Critical Value 0.905 Data appear Lognormal at 5% Significance Level
Lilliefors Test Statistic 0.143 Lilliefors Lognormal GOF Test
Lognormal GOF Test
Shapiro Wilk Test Statistic 0.933 Shapiro Wilk Lognormal GOF Test
Assuming Gamma Distribution
95% Approximate Gamma UCL (use when n>=50) 2290 95% Adjusted Gamma UCL (use when n<50) 2437
Coffey Appendix H - Data Statistics
RAAF Base Tindal PFAS Ecological Risk Assessment
1
2
3
4
5
6
7
8
9
10
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58
A B C D E F G H I J K L
If possible, compute and collect Data Quality Objectives (DQO) based sample size and analytical results.
Warning: This data set only has 0 observations!
Data set is too small to compute reliable and meaningful statistics and estimates!
The data set for variable Perfluoro-n-octanoic acid (PFOA) (offsite tindal) was not processed!
It is suggested to collect at least 8 to 10 observations before using these statistical methods!
Maximum N/A Median N/A
Number of Missing Observations 7
Minimum N/A Mean N/A
General Statistics
Total Number of Observations 0 Number of Distinct Observations 0
If possible, compute and collect Data Quality Objectives (DQO) based sample size and analytical results.
Perfluoro-n-octanoic acid (PFOA) (offsite tindal)
Warning: This data set only has 0 observations!
Data set is too small to compute reliable and meaningful statistics and estimates!
The data set for variable Perfluoro-n-octanoic acid (PFOA) (katherine river us) was not processed!
It is suggested to collect at least 8 to 10 observations before using these statistical methods!
Maximum N/A Median N/A
Number of Missing Observations 6
Minimum N/A Mean N/A
General Statistics
Total Number of Observations 0 Number of Distinct Observations 0
If possible, compute and collect Data Quality Objectives (DQO) based sample size and analytical results.
Perfluoro-n-octanoic acid (PFOA) (katherine river us)
Warning: This data set only has 0 observations!
Data set is too small to compute reliable and meaningful statistics and estimates!
The data set for variable Perfluoro-n-octanoic acid (PFOA) (background) was not processed!
It is suggested to collect at least 8 to 10 observations before using these statistical methods!
Maximum N/A Median N/A
Number of Missing Observations 1
Minimum N/A Mean N/A
General Statistics
Total Number of Observations 0 Number of Distinct Observations 0
Number of Bootstrap Operations 2000
Perfluoro-n-octanoic acid (PFOA) (background)
From File Data_Tindal_Terrestrial Vertebrates_20180606_h.xls
Full Precision OFF
Confidence Coefficient 95%
UCL Statistics for Uncensored Full Data Sets
User Selected Options
Date/Time of Computation ProUCL 5.16/6/2018 10:40:23 AM
Coffey Appendix H - Data Statistics
RAAF Base Tindal PFAS Ecological Risk Assessment
59
60
61
62
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68
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A B C D E F G H I J K L
Maximum of Logged Data 2.565 SD of logged Data 1.152
Lognormal Statistics
Minimum of Logged Data -0.511 Mean of logged Data 0.468
5% Lilliefors Critical Value 0.274 Data Not Lognormal at 5% Significance Level
Data Not Lognormal at 5% Significance Level
5% Shapiro Wilk Critical Value 0.829 Data Not Lognormal at 5% Significance Level
Lilliefors Test Statistic 0.293 Lilliefors Lognormal GOF Test
Lognormal GOF Test
Shapiro Wilk Test Statistic 0.82 Shapiro Wilk Lognormal GOF Test
Assuming Gamma Distribution
95% Approximate Gamma UCL (use when n>=50)) 7.304 95% Adjusted Gamma UCL (use when n<50) 8.857
Adjusted Level of Significance 0.0231 Adjusted Chi Square Value 4.165
MLE Mean (bias corrected) 3.144 MLE Sd (bias corrected) 3.895
Approximate Chi Square Value (0.05) 5.051
Theta hat (MLE) 3.629 Theta star (bias corrected MLE) 4.825
nu hat (MLE) 15.6 nu star (bias corrected) 11.73
Gamma Statistics
k hat (MLE) 0.867 k star (bias corrected MLE) 0.652
5% K-S Critical Value 0.288 Data Not Gamma Distributed at 5% Significance Level
Data Not Gamma Distributed at 5% Significance Level
5% A-D Critical Value 0.748 Data Not Gamma Distributed at 5% Significance Level
K-S Test Statistic 0.341 Kolmogorov-Smirnov Gamma GOF Test
Gamma GOF Test
A-D Test Statistic 0.976 Anderson-Darling Gamma GOF Test
95% Student's-t UCL 5.807 95% Adjusted-CLT UCL (Chen-1995) 6.482
95% Modified-t UCL (Johnson-1978) 5.96
Data Not Normal at 5% Significance Level
Assuming Normal Distribution
95% Normal UCL 95% UCLs (Adjusted for Skewness)
Lilliefors Test Statistic 0.35 Lilliefors GOF Test
5% Lilliefors Critical Value 0.274 Data Not Normal at 5% Significance Level
Normal GOF Test
Shapiro Wilk Test Statistic 0.677 Shapiro Wilk GOF Test
5% Shapiro Wilk Critical Value 0.829 Data Not Normal at 5% Significance Level
Note: Sample size is small (e.g., <10), if data are collected using ISM approach, you should use
guidance provided in ITRC Tech Reg Guide on ISM (ITRC, 2012) to compute statistics of interest.
For example, you may want to use Chebyshev UCL to estimate EPC (ITRC, 2012).
Chebyshev UCL can be computed using the Nonparametric and All UCL Options of ProUCL 5.1
Coefficient of Variation 1.366 Skewness 1.927
Maximum 13 Median 1
SD 4.295 Std. Error of Mean 1.432
Number of Missing Observations 3
Minimum 0.6 Mean 3.144
General Statistics
Total Number of Observations 9 Number of Distinct Observations 8
Perfluoro-n-octanoic acid (PFOA) (source area)
Coffey Appendix H - Data Statistics
RAAF Base Tindal PFAS Ecological Risk Assessment
117
118
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120
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125
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A B C D E F G H I J K L
Note: Sample size is small (e.g., <10), if data are collected using ISM approach, you should use
guidance provided in ITRC Tech Reg Guide on ISM (ITRC, 2012) to compute statistics of interest.
For example, you may want to use Chebyshev UCL to estimate EPC (ITRC, 2012).
Chebyshev UCL can be computed using the Nonparametric and All UCL Options of ProUCL 5.1
Coefficient of Variation 0.749 Skewness 1.275
Maximum 53 Median 15
SD 17.45 Std. Error of Mean 7.124
Number of Missing Observations 0
Minimum 9.8 Mean 23.3
General Statistics
Total Number of Observations 6 Number of Distinct Observations 6
If possible, compute and collect Data Quality Objectives (DQO) based sample size and analytical results.
Perfluoro-n-octane sulfonic acid (PFOS) (katherine river us)
Warning: This data set only has 1 observations!
Data set is too small to compute reliable and meaningful statistics and estimates!
The data set for variable Perfluoro-n-octane sulfonic acid (PFOS) (background) was not processed!
It is suggested to collect at least 8 to 10 observations before using these statistical methods!
Maximum 2.9 Median 2.9
Number of Missing Observations 0
Minimum 2.9 Mean 2.9
Perfluoro-n-octane sulfonic acid (PFOS) (background)
General Statistics
Total Number of Observations 1 Number of Distinct Observations 1
Note: Suggestions regarding the selection of a 95% UCL are provided to help the user to select the most appropriate 95% UCL.
Recommendations are based upon data size, data distribution, and skewness.
These recommendations are based upon the results of the simulation studies summarized in Singh, Maichle, and Lee (2006).
However, simulations results will not cover all Real World data sets; for additional insight the user may want to consult a statistician.
Recommended UCL exceeds the maximum observation
In Case Bootstrap t and/or Hall's Bootstrap yields an unreasonably large UCL value, use 97.5% or 99% Chebyshev (Mean, Sd) UCL
Suggested UCL to Use
95% Hall's Bootstrap UCL 17.06
90% Chebyshev(Mean, Sd) UCL 7.44 95% Chebyshev(Mean, Sd) UCL 9.385
97.5% Chebyshev(Mean, Sd) UCL 12.09 99% Chebyshev(Mean, Sd) UCL 17.39
95% Hall's Bootstrap UCL 17.06 95% Percentile Bootstrap UCL 5.689
95% BCA Bootstrap UCL 6.467
95% CLT UCL 5.5 95% Jackknife UCL 5.807
95% Standard Bootstrap UCL 5.323 95% Bootstrap-t UCL 13.96
Nonparametric Distribution Free UCL Statistics
Data do not follow a Discernible Distribution (0.05)
Nonparametric Distribution Free UCLs
95% Chebyshev (MVUE) UCL 7.648 97.5% Chebyshev (MVUE) UCL 9.749
99% Chebyshev (MVUE) UCL 13.88
Assuming Lognormal Distribution
95% H-UCL 13.37 90% Chebyshev (MVUE) UCL 6.134Coffey Appendix H - Data Statistics
RAAF Base Tindal PFAS Ecological Risk Assessment
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A B C D E F G H I J K L
Note: Suggestions regarding the selection of a 95% UCL are provided to help the user to select the most appropriate 95% UCL.
Recommendations are based upon data size, data distribution, and skewness.
These recommendations are based upon the results of the simulation studies summarized in Singh, Maichle, and Lee (2006).
However, simulations results will not cover all Real World data sets; for additional insight the user may want to consult a statistician.
Suggested UCL to Use
95% Student's-t UCL 37.66
90% Chebyshev(Mean, Sd) UCL 44.67 95% Chebyshev(Mean, Sd) UCL 54.35
97.5% Chebyshev(Mean, Sd) UCL 67.79 99% Chebyshev(Mean, Sd) UCL 94.19
95% Hall's Bootstrap UCL 111.2 95% Percentile Bootstrap UCL 33.8
95% BCA Bootstrap UCL 36.3
95% CLT UCL 35.02 95% Jackknife UCL 37.66
95% Standard Bootstrap UCL 33.82 95% Bootstrap-t UCL 82.38
Nonparametric Distribution Free UCL Statistics
Data appear to follow a Discernible Distribution at 5% Significance Level
Nonparametric Distribution Free UCLs
95% Chebyshev (MVUE) UCL 50.66 97.5% Chebyshev (MVUE) UCL 62.69
99% Chebyshev (MVUE) UCL 86.32
Assuming Lognormal Distribution
95% H-UCL 62.49 90% Chebyshev (MVUE) UCL 42
Maximum of Logged Data 3.97 SD of logged Data 0.686
Lognormal Statistics
Minimum of Logged Data 2.282 Mean of logged Data 2.939
5% Lilliefors Critical Value 0.325 Data appear Lognormal at 5% Significance Level
Data appear Lognormal at 5% Significance Level
5% Shapiro Wilk Critical Value 0.788 Data appear Lognormal at 5% Significance Level
Lilliefors Test Statistic 0.228 Lilliefors Lognormal GOF Test
Lognormal GOF Test
Shapiro Wilk Test Statistic 0.883 Shapiro Wilk Lognormal GOF Test
Assuming Gamma Distribution
95% Approximate Gamma UCL (use when n>=50)) 46.16 95% Adjusted Gamma UCL (use when n<50) 60.58
Adjusted Level of Significance 0.0122 Adjusted Chi Square Value 6.371
MLE Mean (bias corrected) 23.3 MLE Sd (bias corrected) 19.83
Approximate Chi Square Value (0.05) 8.36
Theta hat (MLE) 9.18 Theta star (bias corrected MLE) 16.88
nu hat (MLE) 30.46 nu star (bias corrected) 16.56
Gamma Statistics
k hat (MLE) 2.538 k star (bias corrected MLE) 1.38
5% K-S Critical Value 0.335 Detected data appear Gamma Distributed at 5% Significance Level
Detected data appear Gamma Distributed at 5% Significance Level
5% A-D Critical Value 0.703 Detected data appear Gamma Distributed at 5% Significance Level
K-S Test Statistic 0.27 Kolmogorov-Smirnov Gamma GOF Test
Gamma GOF Test
A-D Test Statistic 0.501 Anderson-Darling Gamma GOF Test
95% Student's-t UCL 37.66 95% Adjusted-CLT UCL (Chen-1995) 38.98
95% Modified-t UCL (Johnson-1978) 38.27
Data appear Normal at 5% Significance Level
Assuming Normal Distribution
95% Normal UCL 95% UCLs (Adjusted for Skewness)
Lilliefors Test Statistic 0.308 Lilliefors GOF Test
5% Lilliefors Critical Value 0.325 Data appear Normal at 5% Significance Level
Normal GOF Test
Shapiro Wilk Test Statistic 0.811 Shapiro Wilk GOF Test
5% Shapiro Wilk Critical Value 0.788 Data appear Normal at 5% Significance Level
Coffey Appendix H - Data Statistics
RAAF Base Tindal PFAS Ecological Risk Assessment
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A B C D E F G H I J K L
Nonparametric Distribution Free UCL Statistics
Data appear to follow a Discernible Distribution at 5% Significance Level
95% Chebyshev (MVUE) UCL 90 97.5% Chebyshev (MVUE) UCL 110.2
99% Chebyshev (MVUE) UCL 149.8
Assuming Lognormal Distribution
95% H-UCL 93.64 90% Chebyshev (MVUE) UCL 75.48
Maximum of Logged Data 4.29 SD of logged Data 0.648
Lognormal Statistics
Minimum of Logged Data 2.89 Mean of logged Data 3.594
5% Lilliefors Critical Value 0.304 Data appear Lognormal at 5% Significance Level
Data appear Lognormal at 5% Significance Level
5% Shapiro Wilk Critical Value 0.803 Data appear Lognormal at 5% Significance Level
Lilliefors Test Statistic 0.251 Lilliefors Lognormal GOF Test
Lognormal GOF Test
Shapiro Wilk Test Statistic 0.807 Shapiro Wilk Lognormal GOF Test
Assuming Gamma Distribution
95% Approximate Gamma UCL (use when n>=50)) 72.21 95% Adjusted Gamma UCL (use when n<50) 85.37
Adjusted Level of Significance 0.0158 Adjusted Chi Square Value 13.39
MLE Mean (bias corrected) 43 MLE Sd (bias corrected) 31.21
Approximate Chi Square Value (0.05) 15.83
Theta hat (MLE) 13.62 Theta star (bias corrected MLE) 22.65
nu hat (MLE) 44.18 nu star (bias corrected) 26.58
Detected data appear Gamma Distributed at 5% Significance Level
Gamma Statistics
k hat (MLE) 3.156 k star (bias corrected MLE) 1.899
K-S Test Statistic 0.272 Kolmogorov-Smirnov Gamma GOF Test
5% K-S Critical Value 0.314 Detected data appear Gamma Distributed at 5% Significance Level
Gamma GOF Test
A-D Test Statistic 0.682 Anderson-Darling Gamma GOF Test
5% A-D Critical Value 0.712 Detected data appear Gamma Distributed at 5% Significance Level
95% Modified-t UCL (Johnson-1978) 61.03
Assuming Normal Distribution
95% Normal UCL 95% UCLs (Adjusted for Skewness)
95% Student's-t UCL 61 95% Adjusted-CLT UCL (Chen-1995) 58.44
5% Lilliefors Critical Value 0.304 Data appear Normal at 5% Significance Level
Data appear Normal at 5% Significance Level
5% Shapiro Wilk Critical Value 0.803 Data appear Normal at 5% Significance Level
Lilliefors Test Statistic 0.255 Lilliefors GOF Test
Normal GOF Test
Shapiro Wilk Test Statistic 0.83 Shapiro Wilk GOF Test
Note: Sample size is small (e.g., <10), if data are collected using ISM approach, you should use
guidance provided in ITRC Tech Reg Guide on ISM (ITRC, 2012) to compute statistics of interest.
For example, you may want to use Chebyshev UCL to estimate EPC (ITRC, 2012).
Chebyshev UCL can be computed using the Nonparametric and All UCL Options of ProUCL 5.1
SD 24.51 Std. Error of Mean 9.263
Coefficient of Variation 0.57 Skewness 0.0553
Minimum 18 Mean 43
Maximum 73 Median 43
Total Number of Observations 7 Number of Distinct Observations 6
Number of Missing Observations 0
Perfluoro-n-octane sulfonic acid (PFOS) (offsite tindal)
General Statistics
Coffey Appendix H - Data Statistics
RAAF Base Tindal PFAS Ecological Risk Assessment
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A B C D E F G H I J K L
5% Lilliefors Critical Value 0.243 Data appear Lognormal at 5% Significance Level
Data appear Lognormal at 5% Significance Level
5% Shapiro Wilk Critical Value 0.859 Data appear Lognormal at 5% Significance Level
Lilliefors Test Statistic 0.135 Lilliefors Lognormal GOF Test
Lognormal GOF Test
Shapiro Wilk Test Statistic 0.911 Shapiro Wilk Lognormal GOF Test
Assuming Gamma Distribution
95% Approximate Gamma UCL (use when n>=50) 3508 95% Adjusted Gamma UCL (use when n<50) 4028
Adjusted Level of Significance 0.029 Adjusted Chi Square Value 4.374
MLE Mean (bias corrected) 1507 MLE Sd (bias corrected) 2160
Approximate Chi Square Value (0.05) 5.022
Theta hat (MLE) 2620 Theta star (bias corrected MLE) 3095
nu hat (MLE) 13.81 nu star (bias corrected) 11.69
Detected data appear Gamma Distributed at 5% Significance Level
Gamma Statistics
k hat (MLE) 0.575 k star (bias corrected MLE) 0.487
K-S Test Statistic 0.175 Kolmogorov-Smirnov Gamma GOF Test
5% K-S Critical Value 0.258 Detected data appear Gamma Distributed at 5% Significance Level
Gamma GOF Test
A-D Test Statistic 0.307 Anderson-Darling Gamma GOF Test
5% A-D Critical Value 0.779 Detected data appear Gamma Distributed at 5% Significance Level
95% Modified-t UCL (Johnson-1978) 2485
Assuming Normal Distribution
95% Normal UCL 95% UCLs (Adjusted for Skewness)
95% Student's-t UCL 2454 95% Adjusted-CLT UCL (Chen-1995) 2572
5% Lilliefors Critical Value 0.243 Data Not Normal at 5% Significance Level
Data Not Normal at 5% Significance Level
5% Shapiro Wilk Critical Value 0.859 Data Not Normal at 5% Significance Level
Lilliefors Test Statistic 0.291 Lilliefors GOF Test
Normal GOF Test
Shapiro Wilk Test Statistic 0.799 Shapiro Wilk GOF Test
SD 1826 Std. Error of Mean 527.2
Coefficient of Variation 1.212 Skewness 1.212
Minimum 19 Mean 1507
Maximum 5400 Median 490
Total Number of Observations 12 Number of Distinct Observations 11
Number of Missing Observations 0
Perfluoro-n-octane sulfonic acid (PFOS) (source area)
General Statistics
Note: Suggestions regarding the selection of a 95% UCL are provided to help the user to select the most appropriate 95% UCL.
Recommendations are based upon data size, data distribution, and skewness.
These recommendations are based upon the results of the simulation studies summarized in Singh, Maichle, and Lee (2006).
However, simulations results will not cover all Real World data sets; for additional insight the user may want to consult a statistician.
Suggested UCL to Use
95% Student's-t UCL 61
90% Chebyshev(Mean, Sd) UCL 70.79 95% Chebyshev(Mean, Sd) UCL 83.38
97.5% Chebyshev(Mean, Sd) UCL 100.8 99% Chebyshev(Mean, Sd) UCL 135.2
95% Hall's Bootstrap UCL 54.23 95% Percentile Bootstrap UCL 56.43
95% BCA Bootstrap UCL 57.43
95% CLT UCL 58.24 95% Jackknife UCL 61
95% Standard Bootstrap UCL 57.06 95% Bootstrap-t UCL 62.31
Nonparametric Distribution Free UCLs
Coffey Appendix H - Data Statistics
RAAF Base Tindal PFAS Ecological Risk Assessment
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A B C D E F G H I J K L
Note: Suggestions regarding the selection of a 95% UCL are provided to help the user to select the most appropriate 95% UCL.
Recommendations are based upon data size, data distribution, and skewness.
These recommendations are based upon the results of the simulation studies summarized in Singh, Maichle, and Lee (2006).
However, simulations results will not cover all Real World data sets; for additional insight the user may want to consult a statistician.
Suggested UCL to Use
95% Adjusted Gamma UCL 4028
90% Chebyshev(Mean, Sd) UCL 3089 95% Chebyshev(Mean, Sd) UCL 3805
97.5% Chebyshev(Mean, Sd) UCL 4800 99% Chebyshev(Mean, Sd) UCL 6753
95% Hall's Bootstrap UCL 2369 95% Percentile Bootstrap UCL 2371
95% BCA Bootstrap UCL 2490
95% CLT UCL 2374 95% Jackknife UCL 2454
95% Standard Bootstrap UCL 2335 95% Bootstrap-t UCL 2805
Nonparametric Distribution Free UCL Statistics
Data appear to follow a Discernible Distribution at 5% Significance Level
Nonparametric Distribution Free UCLs
95% Chebyshev (MVUE) UCL 8113 97.5% Chebyshev (MVUE) UCL 10648
99% Chebyshev (MVUE) UCL 15626
Assuming Lognormal Distribution
95% H-UCL 46260 90% Chebyshev (MVUE) UCL 6287
Maximum of Logged Data 8.594 SD of logged Data 1.896
Lognormal Statistics
Minimum of Logged Data 2.944 Mean of logged Data 6.237Coffey Appendix H - Data Statistics
RAAF Base Tindal PFAS Ecological Risk Assessment
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A B C D E F G H I J K L
If possible, compute and collect Data Quality Objectives (DQO) based sample size and analytical results.
Warning: This data set only has 2 observations!
Data set is too small to compute reliable and meaningful statistics and estimates!
The data set for variable Perfluoro-n-octanoic acid (PFOA) (source area) was not processed!
It is suggested to collect at least 8 to 10 observations before using these statistical methods!
Maximum 4.1 Median 2.6
Number of Missing Observations 5
Minimum 1.1 Mean 2.6
General Statistics
Total Number of Observations 2 Number of Distinct Observations 2
If possible, compute and collect Data Quality Objectives (DQO) based sample size and analytical results.
Perfluoro-n-octanoic acid (PFOA) (source area)
Warning: This data set only has 0 observations!
Data set is too small to compute reliable and meaningful statistics and estimates!
The data set for variable Perfluoro-n-octanoic acid (PFOA) (offsite tindal) was not processed!
It is suggested to collect at least 8 to 10 observations before using these statistical methods!
Maximum N/A Median N/A
Number of Missing Observations 13
Minimum N/A Mean N/A
General Statistics
Total Number of Observations 0 Number of Distinct Observations 0
If possible, compute and collect Data Quality Objectives (DQO) based sample size and analytical results.
Perfluoro-n-octanoic acid (PFOA) (offsite tindal)
Warning: This data set only has 0 observations!
Data set is too small to compute reliable and meaningful statistics and estimates!
The data set for variable Perfluoro-n-octanoic acid (PFOA) (background) was not processed!
It is suggested to collect at least 8 to 10 observations before using these statistical methods!
Maximum N/A Median N/A
Number of Missing Observations 3
Minimum N/A Mean N/A
General Statistics
Total Number of Observations 0 Number of Distinct Observations 0
Number of Bootstrap Operations 2000
Perfluoro-n-octanoic acid (PFOA) (background)
From File Data_Tindal_Terrestrial Vertebrates_20180606_i.xls
Full Precision OFF
Confidence Coefficient 95%
UCL Statistics for Uncensored Full Data Sets
User Selected Options
Date/Time of Computation ProUCL 5.16/6/2018 10:42:36 AM
Coffey Appendix H - Data Statistics
RAAF Base Tindal PFAS Ecological Risk Assessment
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A B C D E F G H I J K L
Adjusted Level of Significance 0.0301 Adjusted Chi Square Value 18.93
MLE Mean (bias corrected) 7.238 MLE Sd (bias corrected) 6.499
Approximate Chi Square Value (0.05) 20.27
Theta hat (MLE) 4.683 Theta star (bias corrected MLE) 5.836
nu hat (MLE) 40.19 nu star (bias corrected) 32.25
Gamma Statistics
k hat (MLE) 1.546 k star (bias corrected MLE) 1.24
5% K-S Critical Value 0.241 Detected data appear Gamma Distributed at 5% Significance Level
Detected data appear Gamma Distributed at 5% Significance Level
5% A-D Critical Value 0.75 Detected data appear Gamma Distributed at 5% Significance Level
K-S Test Statistic 0.169 Kolmogorov-Smirnov Gamma GOF Test
Gamma GOF Test
A-D Test Statistic 0.353 Anderson-Darling Gamma GOF Test
95% Student's-t UCL 10.31 95% Adjusted-CLT UCL (Chen-1995) 10.85
95% Modified-t UCL (Johnson-1978) 10.44
Data Not Normal at 5% Significance Level
Assuming Normal Distribution
95% Normal UCL 95% UCLs (Adjusted for Skewness)
Lilliefors Test Statistic 0.252 Lilliefors GOF Test
5% Lilliefors Critical Value 0.234 Data Not Normal at 5% Significance Level
Normal GOF Test
Shapiro Wilk Test Statistic 0.84 Shapiro Wilk GOF Test
5% Shapiro Wilk Critical Value 0.866 Data Not Normal at 5% Significance Level
Coefficient of Variation 0.86 Skewness 1.517
Maximum 23 Median 5
SD 6.224 Std. Error of Mean 1.726
Number of Missing Observations 0
Minimum 0.9 Mean 7.238
General Statistics
Total Number of Observations 13 Number of Distinct Observations 13
If possible, compute and collect Data Quality Objectives (DQO) based sample size and analytical results.
Perfluoro-n-octane sulfonic acid (PFOS) (offsite tindal)
Warning: This data set only has 1 observations!
Data set is too small to compute reliable and meaningful statistics and estimates!
The data set for variable Perfluoro-n-octane sulfonic acid (PFOS) (background) was not processed!
It is suggested to collect at least 8 to 10 observations before using these statistical methods!
Maximum 9.1 Median 9.1
Number of Missing Observations 2
Minimum 9.1 Mean 9.1
General Statistics
Total Number of Observations 1 Number of Distinct Observations 1
Perfluoro-n-octane sulfonic acid (PFOS) (background)
Coffey Appendix H - Data Statistics
RAAF Base Tindal PFAS Ecological Risk Assessment
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A B C D E F G H I J K L
5% Lilliefors Critical Value 0.325 Data appear Normal at 5% Significance Level
Data appear Approximate Normal at 5% Significance Level
5% Shapiro Wilk Critical Value 0.788 Data Not Normal at 5% Significance Level
Lilliefors Test Statistic 0.32 Lilliefors GOF Test
Normal GOF Test
Shapiro Wilk Test Statistic 0.772 Shapiro Wilk GOF Test
Note: Sample size is small (e.g., <10), if data are collected using ISM approach, you should use
guidance provided in ITRC Tech Reg Guide on ISM (ITRC, 2012) to compute statistics of interest.
For example, you may want to use Chebyshev UCL to estimate EPC (ITRC, 2012).
Chebyshev UCL can be computed using the Nonparametric and All UCL Options of ProUCL 5.1
SD 795.5 Std. Error of Mean 324.8
Coefficient of Variation 1.339 Skewness 1.012
Minimum 0.4 Mean 594.2
Maximum 1800 Median 172
Total Number of Observations 6 Number of Distinct Observations 6
Number of Missing Observations 1
Perfluoro-n-octane sulfonic acid (PFOS) (source area)
General Statistics
Note: Suggestions regarding the selection of a 95% UCL are provided to help the user to select the most appropriate 95% UCL.
Recommendations are based upon data size, data distribution, and skewness.
These recommendations are based upon the results of the simulation studies summarized in Singh, Maichle, and Lee (2006).
However, simulations results will not cover all Real World data sets; for additional insight the user may want to consult a statistician.
Suggested UCL to Use
95% Adjusted Gamma UCL 12.33
90% Chebyshev(Mean, Sd) UCL 12.42 95% Chebyshev(Mean, Sd) UCL 14.76
97.5% Chebyshev(Mean, Sd) UCL 18.02 99% Chebyshev(Mean, Sd) UCL 24.41
95% Hall's Bootstrap UCL 12.15 95% Percentile Bootstrap UCL 10.32
95% BCA Bootstrap UCL 10.9
95% CLT UCL 10.08 95% Jackknife UCL 10.31
95% Standard Bootstrap UCL 9.976 95% Bootstrap-t UCL 12.12
Nonparametric Distribution Free UCL Statistics
Data appear to follow a Discernible Distribution at 5% Significance Level
Nonparametric Distribution Free UCLs
95% Chebyshev (MVUE) UCL 16.78 97.5% Chebyshev (MVUE) UCL 20.78
99% Chebyshev (MVUE) UCL 28.62
Assuming Lognormal Distribution
95% H-UCL 16.71 90% Chebyshev (MVUE) UCL 13.9
Maximum of Logged Data 3.135 SD of logged Data 0.943
Lognormal Statistics
Minimum of Logged Data -0.105 Mean of logged Data 1.622
5% Lilliefors Critical Value 0.234 Data appear Lognormal at 5% Significance Level
Data appear Lognormal at 5% Significance Level
5% Shapiro Wilk Critical Value 0.866 Data appear Lognormal at 5% Significance Level
Lilliefors Test Statistic 0.181 Lilliefors Lognormal GOF Test
Lognormal GOF Test
Shapiro Wilk Test Statistic 0.937 Shapiro Wilk Lognormal GOF Test
Assuming Gamma Distribution
95% Approximate Gamma UCL (use when n>=50) 11.52 95% Adjusted Gamma UCL (use when n<50) 12.33Coffey Appendix H - Data Statistics
RAAF Base Tindal PFAS Ecological Risk Assessment
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A B C D E F G H I J K L
Recommendations are based upon data size, data distribution, and skewness.
These recommendations are based upon the results of the simulation studies summarized in Singh, Maichle, and Lee (2006).
However, simulations results will not cover all Real World data sets; for additional insight the user may want to consult a statistician.
When a data set follows an approximate (e.g., normal) distribution passing one of the GOF test
When applicable, it is suggested to use a UCL based upon a distribution (e.g., gamma) passing both GOF tests in ProUCL
Note: Suggestions regarding the selection of a 95% UCL are provided to help the user to select the most appropriate 95% UCL.
Suggested UCL to Use
95% Student's-t UCL 1249
90% Chebyshev(Mean, Sd) UCL 1569 95% Chebyshev(Mean, Sd) UCL 2010
97.5% Chebyshev(Mean, Sd) UCL 2622 99% Chebyshev(Mean, Sd) UCL 3826
95% Hall's Bootstrap UCL 7532 95% Percentile Bootstrap UCL 1113
95% BCA Bootstrap UCL 1155
95% CLT UCL 1128 95% Jackknife UCL 1249
95% Standard Bootstrap UCL 1081 95% Bootstrap-t UCL 3725
Nonparametric Distribution Free UCL Statistics
Data appear to follow a Discernible Distribution at 5% Significance Level
Nonparametric Distribution Free UCLs
95% Chebyshev (MVUE) UCL 7863 97.5% Chebyshev (MVUE) UCL 10574
99% Chebyshev (MVUE) UCL 15900
Assuming Lognormal Distribution
95% H-UCL 2.240E+11 90% Chebyshev (MVUE) UCL 5909
Maximum of Logged Data 7.496 SD of logged Data 3.141
Lognormal Statistics
Minimum of Logged Data -0.916 Mean of logged Data 4.444
5% Lilliefors Critical Value 0.325 Data appear Lognormal at 5% Significance Level
Data appear Lognormal at 5% Significance Level
5% Shapiro Wilk Critical Value 0.788 Data appear Lognormal at 5% Significance Level
Lilliefors Test Statistic 0.166 Lilliefors Lognormal GOF Test
Lognormal GOF Test
Shapiro Wilk Test Statistic 0.914 Shapiro Wilk Lognormal GOF Test
Assuming Gamma Distribution
95% Approximate Gamma UCL (use when n>=50)) 4020 95% Adjusted Gamma UCL (use when n<50) 8742
Adjusted Level of Significance 0.0122 Adjusted Chi Square Value 0.232
MLE Mean (bias corrected) 594.2 MLE Sd (bias corrected) 1114
Approximate Chi Square Value (0.05) 0.504
Theta hat (MLE) 1715 Theta star (bias corrected MLE) 2090
nu hat (MLE) 4.158 nu star (bias corrected) 3.412
Detected data appear Gamma Distributed at 5% Significance Level
Gamma Statistics
k hat (MLE) 0.347 k star (bias corrected MLE) 0.284
K-S Test Statistic 0.202 Kolmogorov-Smirnov Gamma GOF Test
5% K-S Critical Value 0.355 Detected data appear Gamma Distributed at 5% Significance Level
Gamma GOF Test
A-D Test Statistic 0.24 Anderson-Darling Gamma GOF Test
5% A-D Critical Value 0.76 Detected data appear Gamma Distributed at 5% Significance Level
95% Modified-t UCL (Johnson-1978) 1271
Assuming Normal Distribution
95% Normal UCL 95% UCLs (Adjusted for Skewness)
95% Student's-t UCL 1249 95% Adjusted-CLT UCL (Chen-1995) 1272
Coffey Appendix H - Data Statistics
RAAF Base Tindal PFAS Ecological Risk Assessment
1
2
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A B C D E F G H I J K L
Warning: This data set only has 0 observations!
Data set is too small to compute reliable and meaningful statistics and estimates!
The data set for variable Perfluoro-n-octanoate acid (PFOA) (offsite tindal) was not processed!
It is suggested to collect at least 8 to 10 observations before using these statistical methods!
Maximum N/A Median N/A
Number of Missing Observations 3
Minimum N/A Mean N/A
General Statistics
Total Number of Observations 0 Number of Distinct Observations 0
If possible, compute and collect Data Quality Objectives (DQO) based sample size and analytical results.
Perfluoro-n-octanoate acid (PFOA) (offsite tindal)
Warning: This data set only has 0 observations!
Data set is too small to compute reliable and meaningful statistics and estimates!
The data set for variable Perfluoro-n-octanoate acid (PFOA) (katherine river us) was not processed!
It is suggested to collect at least 8 to 10 observations before using these statistical methods!
Maximum N/A Median N/A
Number of Missing Observations 3
Minimum N/A Mean N/A
General Statistics
Total Number of Observations 0 Number of Distinct Observations 0
If possible, compute and collect Data Quality Objectives (DQO) based sample size and analytical results.
Perfluoro-n-octanoate acid (PFOA) (katherine river us)
Warning: This data set only has 0 observations!
Data set is too small to compute reliable and meaningful statistics and estimates!
The data set for variable Perfluoro-n-octanoate acid (PFOA) (katherine river ds) was not processed!
It is suggested to collect at least 8 to 10 observations before using these statistical methods!
Maximum N/A Median N/A
Number of Missing Observations 15
Minimum N/A Mean N/A
General Statistics
Total Number of Observations 0 Number of Distinct Observations 0
Number of Bootstrap Operations 2000
Perfluoro-n-octanoate acid (PFOA) (katherine river ds)
From File Tindal_Aquatic Invertebrates_20180605_b.xls
Full Precision OFF
Confidence Coefficient 95%
UCL Statistics for Uncensored Full Data Sets
User Selected Options
Date/Time of Computation ProUCL 5.16/6/2018 8:46:25 AM
Coffey Appendix H - Data Statistics
RAAF Base Tindal PFAS Ecological Risk Assessment
58
59
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61
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66
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A B C D E F G H I J K L
5% Lilliefors Critical Value 0.22 Data appear Lognormal at 5% Significance Level
Data appear Lognormal at 5% Significance Level
5% Shapiro Wilk Critical Value 0.881 Data appear Lognormal at 5% Significance Level
Lilliefors Test Statistic 0.194 Lilliefors Lognormal GOF Test
Lognormal GOF Test
Shapiro Wilk Test Statistic 0.916 Shapiro Wilk Lognormal GOF Test
Assuming Gamma Distribution
95% Approximate Gamma UCL (use when n>=50)) 30.16 95% Adjusted Gamma UCL (use when n<50) 32.2
Adjusted Level of Significance 0.029 Adjusted Chi Square Value 15.27
MLE Mean (bias corrected) 18.08 MLE Sd (bias corrected) 18.99
Approximate Chi Square Value (0.05) 16.31
Theta hat (MLE) 16.78 Theta star (bias corrected MLE) 19.94
nu hat (MLE) 32.33 nu star (bias corrected) 27.2
Gamma Statistics
k hat (MLE) 1.078 k star (bias corrected MLE) 0.907
5% K-S Critical Value 0.228 Data Not Gamma Distributed at 5% Significance Level
Data Not Gamma Distributed at 5% Significance Level
5% A-D Critical Value 0.762 Data Not Gamma Distributed at 5% Significance Level
K-S Test Statistic 0.2 Kolmogorov-Smirnov Gamma GOF Test
Gamma GOF Test
A-D Test Statistic 0.688 Anderson-Darling Gamma GOF Test
95% Student's-t UCL 25.85 95% Adjusted-CLT UCL (Chen-1995) 26.33
95% Modified-t UCL (Johnson-1978) 26
Data Not Normal at 5% Significance Level
Assuming Normal Distribution
95% Normal UCL 95% UCLs (Adjusted for Skewness)
Lilliefors Test Statistic 0.227 Lilliefors GOF Test
5% Lilliefors Critical Value 0.22 Data Not Normal at 5% Significance Level
Normal GOF Test
Shapiro Wilk Test Statistic 0.844 Shapiro Wilk GOF Test
5% Shapiro Wilk Critical Value 0.881 Data Not Normal at 5% Significance Level
Coefficient of Variation 0.945 Skewness 1.282
Maximum 53 Median 9.1
SD 17.08 Std. Error of Mean 4.409
Number of Missing Observations 0
Minimum 1.7 Mean 18.08
General Statistics
Total Number of Observations 15 Number of Distinct Observations 15
If possible, compute and collect Data Quality Objectives (DQO) based sample size and analytical results.
Perfluoro-n-octane sulfonic acid (PFOS) (katherine river ds)
Coffey Appendix H - Data Statistics
RAAF Base Tindal PFAS Ecological Risk Assessment
109
110
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A B C D E F G H I J K L
37.3
95% Modified-t UCL (Johnson-1978) 0.758
Assuming Normal Distribution
95% Normal UCL 95% UCLs (Adjusted for Skewness)
95% Student's-t UCL 0.764 95% Adjusted-CLT UCL (Chen-1995) 0.686
5% Lilliefors Critical Value 0.425 Data appear Normal at 5% Significance Level
Data appear Approximate Normal at 5% Significance Level
5% Shapiro Wilk Critical Value 0.767 Data Not Normal at 5% Significance Level
Lilliefors Test Statistic 0.385 Lilliefors GOF Test
Normal GOF Test
Shapiro Wilk Test Statistic 0.75 Shapiro Wilk GOF Test
Note: Sample size is small (e.g., <10), if data are collected using ISM approach, you should use
guidance provided in ITRC Tech Reg Guide on ISM (ITRC, 2012) to compute statistics of interest.
For example, you may want to use Chebyshev UCL to estimate EPC (ITRC, 2012).
Chebyshev UCL can be computed using the Nonparametric and All UCL Options of ProUCL 5.1
SD 0.0577 Std. Error of Mean 0.0333
Coefficient of Variation 0.0866 Skewness -1.732
Minimum 0.6 Mean 0.667
Maximum 0.7 Median 0.7
Total Number of Observations 3 Number of Distinct Observations 2
Number of Missing Observations 0
Perfluoro-n-octane sulfonic acid (PFOS) (katherine river us)
General Statistics
Note: Suggestions regarding the selection of a 95% UCL are provided to help the user to select the most appropriate 95% UCL.
Recommendations are based upon data size, data distribution, and skewness.
These recommendations are based upon the results of the simulation studies summarized in Singh, Maichle, and Lee (2006).
However, simulations results will not cover all Real World data sets; for additional insight the user may want to consult a statistician.
Suggested UCL to Use
95% Adjusted Gamma UCL 32.2
90% Chebyshev(Mean, Sd) UCL 31.31 95% Chebyshev(Mean, Sd) UCL
97.5% Chebyshev(Mean, Sd) UCL 45.62 99% Chebyshev(Mean, Sd) UCL 61.95
95% Hall's Bootstrap UCL 26.05 95% Percentile Bootstrap UCL 24.97
95% BCA Bootstrap UCL 26.1
95% CLT UCL 25.33 95% Jackknife UCL 25.85
95% Standard Bootstrap UCL 25.01 95% Bootstrap-t UCL 26.7
Nonparametric Distribution Free UCL Statistics
Data appear to follow a Discernible Distribution at 5% Significance Level
Nonparametric Distribution Free UCLs
95% Chebyshev (MVUE) UCL 46.11 97.5% Chebyshev (MVUE) UCL 57.81
99% Chebyshev (MVUE) UCL 80.81
Assuming Lognormal Distribution
95% H-UCL 50.11 90% Chebyshev (MVUE) UCL 37.67
Maximum of Logged Data 3.97 SD of logged Data 1.138
Lognormal Statistics
Minimum of Logged Data 0.531 Mean of logged Data 2.364Coffey Appendix H - Data Statistics
RAAF Base Tindal PFAS Ecological Risk Assessment
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A B C D E F G H I J K L
Note: For highly negatively-skewed data, confidence limits (e.g., Chen, Johnson, Lognormal, and Gamma) may not be
reliable. Chen's and Johnson's methods provide adjustments for positvely skewed data sets.
Note: Suggestions regarding the selection of a 95% UCL are provided to help the user to select the most appropriate 95% UCL.
Recommendations are based upon data size, data distribution, and skewness.
These recommendations are based upon the results of the simulation studies summarized in Singh, Maichle, and Lee (2006).
However, simulations results will not cover all Real World data sets; for additional insight the user may want to consult a statistician.
Recommended UCL exceeds the maximum observation
When a data set follows an approximate (e.g., normal) distribution passing one of the GOF test
When applicable, it is suggested to use a UCL based upon a distribution (e.g., gamma) passing both GOF tests in ProUCL
Suggested UCL to Use
95% Student's-t UCL 0.764
90% Chebyshev(Mean, Sd) UCL 0.767 95% Chebyshev(Mean, Sd) UCL 0.812
97.5% Chebyshev(Mean, Sd) UCL 0.875 99% Chebyshev(Mean, Sd) UCL 0.998
95% Hall's Bootstrap UCL N/A 95% Percentile Bootstrap UCL N/A
95% BCA Bootstrap UCL N/A
95% CLT UCL 0.721 95% Jackknife UCL N/A
95% Standard Bootstrap UCL N/A 95% Bootstrap-t UCL N/A
Nonparametric Distribution Free UCL Statistics
Data appear to follow a Discernible Distribution at 5% Significance Level
Nonparametric Distribution Free UCLs
95% Chebyshev (MVUE) UCL 0.816 97.5% Chebyshev (MVUE) UCL 0.88
99% Chebyshev (MVUE) UCL 1.007
Assuming Lognormal Distribution
95% H-UCL N/A 90% Chebyshev (MVUE) UCL 0.769
Maximum of Logged Data -0.357 SD of logged Data 0.089
Lognormal Statistics
Minimum of Logged Data -0.511 Mean of logged Data -0.408
5% Lilliefors Critical Value 0.425 Data appear Lognormal at 5% Significance Level
Data appear Approximate Lognormal at 5% Significance Level
5% Shapiro Wilk Critical Value 0.767 Data Not Lognormal at 5% Significance Level
Lilliefors Test Statistic 0.385 Lilliefors Lognormal GOF Test
Lognormal GOF Test
Shapiro Wilk Test Statistic 0.75 Shapiro Wilk Lognormal GOF Test
Assuming Gamma Distribution
95% Approximate Gamma UCL (use when n>=50)) N/A 95% Adjusted Gamma UCL (use when n<50) N/A
Adjusted Level of Significance N/A Adjusted Chi Square Value N/A
MLE Mean (bias corrected) N/A MLE Sd (bias corrected) N/A
Approximate Chi Square Value (0.05) N/A
Theta hat (MLE) 0.00345 Theta star (bias corrected MLE) N/A
nu hat (MLE) 1158 nu star (bias corrected) N/A
Gamma GOF Test
Not Enough Data to Perform GOF Test
Gamma Statistics
k hat (MLE) 193 k star (bias corrected MLE) N/A
Coffey Appendix H - Data Statistics
RAAF Base Tindal PFAS Ecological Risk Assessment
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222
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A B C D E F G H I J K L
Maximum of Logged Data 3.784 SD of logged Data 0.303
Lognormal Statistics
Minimum of Logged Data 3.178 Mean of logged Data 3.486
5% Lilliefors Critical Value 0.425 Data appear Lognormal at 5% Significance Level
Data appear Lognormal at 5% Significance Level
5% Shapiro Wilk Critical Value 0.767 Data appear Lognormal at 5% Significance Level
Lilliefors Test Statistic 0.18 Lilliefors Lognormal GOF Test
Lognormal GOF Test
Shapiro Wilk Test Statistic 0.999 Shapiro Wilk Lognormal GOF Test
Assuming Gamma Distribution
95% Approximate Gamma UCL (use when n>=50)) N/A 95% Adjusted Gamma UCL (use when n<50) N/A
Approximate Chi Square Value (0.05) N/A
Adjusted Level of Significance N/A Adjusted Chi Square Value N/A
nu hat (MLE) 100.1 nu star (bias corrected) N/A
MLE Mean (bias corrected) N/A MLE Sd (bias corrected) N/A
k hat (MLE) 16.69 k star (bias corrected MLE) N/A
Theta hat (MLE) 2.017 Theta star (bias corrected MLE) N/A
Gamma GOF Test
Not Enough Data to Perform GOF Test
Gamma Statistics
95% Student's-t UCL 50.55 95% Adjusted-CLT UCL (Chen-1995) 44.24
95% Modified-t UCL (Johnson-1978) 50.72
Data appear Normal at 5% Significance Level
Assuming Normal Distribution
95% Normal UCL 95% UCLs (Adjusted for Skewness)
Lilliefors Test Statistic 0.193 Lilliefors GOF Test
5% Lilliefors Critical Value 0.425 Data appear Normal at 5% Significance Level
Normal GOF Test
Shapiro Wilk Test Statistic 0.997 Shapiro Wilk GOF Test
5% Shapiro Wilk Critical Value 0.767 Data appear Normal at 5% Significance Level
Note: Sample size is small (e.g., <10), if data are collected using ISM approach, you should use
guidance provided in ITRC Tech Reg Guide on ISM (ITRC, 2012) to compute statistics of interest.
For example, you may want to use Chebyshev UCL to estimate EPC (ITRC, 2012).
Chebyshev UCL can be computed using the Nonparametric and All UCL Options of ProUCL 5.1
Coefficient of Variation 0.298 Skewness 0.298
Maximum 44 Median 33
SD 10.02 Std. Error of Mean 5.783
Number of Missing Observations 0
Minimum 24 Mean 33.67
Perfluoro-n-octane sulfonic acid (PFOS) (offsite tindal)
General Statistics
Total Number of Observations 3 Number of Distinct Observations 3
Coffey Appendix H - Data Statistics
RAAF Base Tindal PFAS Ecological Risk Assessment
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A B C D E F G H I J K L
These recommendations are based upon the results of the simulation studies summarized in Singh, Maichle, and Lee (2006).
However, simulations results will not cover all Real World data sets; for additional insight the user may want to consult a statistician.
Recommended UCL exceeds the maximum observation
Note: Suggestions regarding the selection of a 95% UCL are provided to help the user to select the most appropriate 95% UCL.
Recommendations are based upon data size, data distribution, and skewness.
Suggested UCL to Use
95% Student's-t UCL 50.55
90% Chebyshev(Mean, Sd) UCL 51.02 95% Chebyshev(Mean, Sd) UCL 58.87
97.5% Chebyshev(Mean, Sd) UCL 69.78 99% Chebyshev(Mean, Sd) UCL 91.21
95% Hall's Bootstrap UCL N/A 95% Percentile Bootstrap UCL N/A
95% BCA Bootstrap UCL N/A
95% CLT UCL 43.18 95% Jackknife UCL 50.55
95% Standard Bootstrap UCL N/A 95% Bootstrap-t UCL N/A
Nonparametric Distribution Free UCL Statistics
Data appear to follow a Discernible Distribution at 5% Significance Level
Nonparametric Distribution Free UCLs
95% Chebyshev (MVUE) UCL 59.07 97.5% Chebyshev (MVUE) UCL 70.07
99% Chebyshev (MVUE) UCL 91.66
Assuming Lognormal Distribution
95% H-UCL 83.08 90% Chebyshev (MVUE) UCL 51.15Coffey Appendix H - Data Statistics
RAAF Base Tindal PFAS Ecological Risk Assessment
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A B C D E F G H I J K L
If possible, compute and collect Data Quality Objectives (DQO) based sample size and analytical results.
Warning: This data set only has 1 observations!
Data set is too small to compute reliable and meaningful statistics and estimates!
The data set for variable Perfluoro-n-octanoate acid (PFOA) (tindal creek) was not processed!
It is suggested to collect at least 8 to 10 observations before using these statistical methods!
Maximum 0.39 Median 0.39
Number of Missing Observations 10
Minimum 0.39 Mean 0.39
General Statistics
Total Number of Observations 1 Number of Distinct Observations 1
If possible, compute and collect Data Quality Objectives (DQO) based sample size and analytical results.
Perfluoro-n-octanoate acid (PFOA) (tindal creek)
Warning: This data set only has 0 observations!
Data set is too small to compute reliable and meaningful statistics and estimates!
The data set for variable Perfluoro-n-octanoate acid (PFOA) (katherine river us) was not processed!
It is suggested to collect at least 8 to 10 observations before using these statistical methods!
Maximum N/A Median N/A
Number of Missing Observations 17
Minimum N/A Mean N/A
General Statistics
Total Number of Observations 0 Number of Distinct Observations 0
If possible, compute and collect Data Quality Objectives (DQO) based sample size and analytical results.
Perfluoro-n-octanoate acid (PFOA) (katherine river us)
Warning: This data set only has 0 observations!
Data set is too small to compute reliable and meaningful statistics and estimates!
The data set for variable Perfluoro-n-octanoate acid (PFOA) (katherine river ds) was not processed!
It is suggested to collect at least 8 to 10 observations before using these statistical methods!
Maximum N/A Median N/A
Number of Missing Observations 195
Minimum N/A Mean N/A
General Statistics
Total Number of Observations 0 Number of Distinct Observations 0
Number of Bootstrap Operations 2000
Perfluoro-n-octanoate acid (PFOA) (katherine river ds)
From File Tindal_Fish_20180605_b.xls
Full Precision OFF
Confidence Coefficient 95%
UCL Statistics for Uncensored Full Data Sets
User Selected Options
Date/Time of Computation ProUCL 5.16/6/2018 8:38:49 AM
Coffey Appendix H - Data Statistics
RAAF Base Tindal PFAS Ecological Risk Assessment
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A B C D E F G H I J K L
Nonparametric Distribution Free UCL Statistics
95% Chebyshev (MVUE) UCL 111.6 97.5% Chebyshev (MVUE) UCL 128.1
99% Chebyshev (MVUE) UCL 160.4
Assuming Lognormal Distribution
95% H-UCL 92.19 90% Chebyshev (MVUE) UCL 99.74
Maximum of Logged Data 5.94 SD of logged Data 1.26
Lognormal Statistics
Minimum of Logged Data -1.204 Mean of logged Data 3.511
5% Lilliefors Critical Value 0.0639 Data appear Lognormal at 5% Significance Level
Data appear Lognormal at 5% Significance Level
5% Shapiro Wilk P Value 0.0609 Data appear Lognormal at 5% Significance Level
Lilliefors Test Statistic 0.0603 Lilliefors Lognormal GOF Test
Lognormal GOF Test
Shapiro Wilk Test Statistic 0.973 Shapiro Wilk Lognormal GOF Test
Assuming Gamma Distribution
95% Approximate Gamma UCL (use when n>=50)) 73.2 95% Adjusted Gamma UCL (use when n<50) 73.27
Adjusted Level of Significance 0.0488 Adjusted Chi Square Value 303.2
MLE Mean (bias corrected) 64.29 MLE Sd (bias corrected) 68.29
Approximate Chi Square Value (0.05) 303.5
Theta hat (MLE) 71.71 Theta star (bias corrected MLE) 72.55
nu hat (MLE) 349.6 nu star (bias corrected) 345.6
Gamma Statistics
k hat (MLE) 0.897 k star (bias corrected MLE) 0.886
5% K-S Critical Value 0.0671 Data Not Gamma Distributed at 5% Significance Level
Data Not Gamma Distributed at 5% Significance Level
5% A-D Critical Value 0.789 Data Not Gamma Distributed at 5% Significance Level
K-S Test Statistic 0.0686 Kolmogorov-Smirnov Gamma GOF Test
Gamma GOF Test
A-D Test Statistic 1.217 Anderson-Darling Gamma GOF Test
95% Student's-t UCL 73.1 95% Adjusted-CLT UCL (Chen-1995) 73.91
95% Modified-t UCL (Johnson-1978) 73.23
Data Not Normal at 5% Significance Level
Assuming Normal Distribution
95% Normal UCL 95% UCLs (Adjusted for Skewness)
Lilliefors Test Statistic 0.196 Lilliefors GOF Test
5% Lilliefors Critical Value 0.0639 Data Not Normal at 5% Significance Level
Normal GOF Test
Shapiro Wilk Test Statistic 0.746 Shapiro Wilk GOF Test
5% Shapiro Wilk P Value 0 Data Not Normal at 5% Significance Level
Coefficient of Variation 1.158 Skewness 2.095
Maximum 380 Median 37
SD 74.46 Std. Error of Mean 5.332
Number of Missing Observations 0
Minimum 0.3 Mean 64.29
General Statistics
Total Number of Observations 195 Number of Distinct Observations 109
Perfluoro-n-octane sulfonic acid (PFOS) (katherine river ds)
Coffey Appendix H - Data Statistics
RAAF Base Tindal PFAS Ecological Risk Assessment
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A B C D E F G H I J K L
Detected data appear Gamma Distributed at 5% Significance Level
K-S Test Statistic 0.162 Kolmogorov-Smirnov Gamma GOF Test
5% K-S Critical Value 0.248 Detected data appear Gamma Distributed at 5% Significance Level
Gamma GOF Test
A-D Test Statistic 0.316 Anderson-Darling Gamma GOF Test
5% A-D Critical Value 0.78 Detected data appear Gamma Distributed at 5% Significance Level
95% Modified-t UCL (Johnson-1978) 35.18
Assuming Normal Distribution
95% Normal UCL 95% UCLs (Adjusted for Skewness)
95% Student's-t UCL 34.83 95% Adjusted-CLT UCL (Chen-1995) 36.1
5% Lilliefors Critical Value 0.234 Data appear Normal at 5% Significance Level
Data appear Approximate Normal at 5% Significance Level
5% Shapiro Wilk Critical Value 0.866 Data Not Normal at 5% Significance Level
Lilliefors Test Statistic 0.191 Lilliefors GOF Test
Normal GOF Test
Shapiro Wilk Test Statistic 0.852 Shapiro Wilk GOF Test
SD 24.64 Std. Error of Mean 6.834
Coefficient of Variation 1.088 Skewness 1.09
Minimum 0.4 Mean 22.65
Maximum 75 Median 13
Total Number of Observations 13 Number of Distinct Observations 13
Number of Missing Observations 4
Perfluoro-n-octane sulfonic acid (PFOS) (katherine river us)
General Statistics
ProUCL computes and outputs H-statistic based UCLs for historical reasons only.
H-statistic often results in unstable (both high and low) values of UCL95 as shown in examples in the Technical Guide.
It is therefore recommended to avoid the use of H-statistic based 95% UCLs.
Use of nonparametric methods are preferred to compute UCL95 for skewed data sets which do not follow a gamma distribution.
Note: Suggestions regarding the selection of a 95% UCL are provided to help the user to select the most appropriate 95% UCL.
Recommendations are based upon data size, data distribution, and skewness.
These recommendations are based upon the results of the simulation studies summarized in Singh, Maichle, and Lee (2006).
However, simulations results will not cover all Real World data sets; for additional insight the user may want to consult a statistician.
Suggested UCL to Use
95% H-UCL 92.19
90% Chebyshev(Mean, Sd) UCL 80.28 95% Chebyshev(Mean, Sd) UCL 87.53
97.5% Chebyshev(Mean, Sd) UCL 97.58 99% Chebyshev(Mean, Sd) UCL 117.3
95% Hall's Bootstrap UCL 74.02 95% Percentile Bootstrap UCL 72.99
95% BCA Bootstrap UCL 73.67
95% CLT UCL 73.06 95% Jackknife UCL 73.1
95% Standard Bootstrap UCL 73.07 95% Bootstrap-t UCL 73.98
Data appear to follow a Discernible Distribution at 5% Significance Level
Nonparametric Distribution Free UCLs
Coffey Appendix H - Data Statistics
RAAF Base Tindal PFAS Ecological Risk Assessment
172
173
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A B C D E F G H I J K L
Coefficient of Variation 1.048 Skewness 2.39
Maximum 1600 Median 240
SD 433.2 Std. Error of Mean 130.6
Number of Missing Observations 0
Minimum 35 Mean 413.2
Perfluoro-n-octane sulfonic acid (PFOS) (tindal creek)
General Statistics
Total Number of Observations 11 Number of Distinct Observations 10
Recommendations are based upon data size, data distribution, and skewness.
These recommendations are based upon the results of the simulation studies summarized in Singh, Maichle, and Lee (2006).
However, simulations results will not cover all Real World data sets; for additional insight the user may want to consult a statistician.
When a data set follows an approximate (e.g., normal) distribution passing one of the GOF test
When applicable, it is suggested to use a UCL based upon a distribution (e.g., gamma) passing both GOF tests in ProUCL
Note: Suggestions regarding the selection of a 95% UCL are provided to help the user to select the most appropriate 95% UCL.
Suggested UCL to Use
95% Student's-t UCL 34.83
90% Chebyshev(Mean, Sd) UCL 43.16 95% Chebyshev(Mean, Sd) UCL 52.44
97.5% Chebyshev(Mean, Sd) UCL 65.33 99% Chebyshev(Mean, Sd) UCL 90.65
95% Hall's Bootstrap UCL 35.49 95% Percentile Bootstrap UCL 33.63
95% BCA Bootstrap UCL 35.77
95% CLT UCL 33.89 95% Jackknife UCL 34.83
95% Standard Bootstrap UCL 33.26 95% Bootstrap-t UCL 39.24
Nonparametric Distribution Free UCL Statistics
Data appear to follow a Discernible Distribution at 5% Significance Level
Nonparametric Distribution Free UCLs
95% Chebyshev (MVUE) UCL 118.7 97.5% Chebyshev (MVUE) UCL 155.3
99% Chebyshev (MVUE) UCL 227
Assuming Lognormal Distribution
95% H-UCL 454.9 90% Chebyshev (MVUE) UCL 92.41
Maximum of Logged Data 4.317 SD of logged Data 1.828
Lognormal Statistics
Minimum of Logged Data -0.916 Mean of logged Data 2.13
5% Lilliefors Critical Value 0.234 Data appear Lognormal at 5% Significance Level
Data appear Lognormal at 5% Significance Level
5% Shapiro Wilk Critical Value 0.866 Data appear Lognormal at 5% Significance Level
Lilliefors Test Statistic 0.174 Lilliefors Lognormal GOF Test
Lognormal GOF Test
Shapiro Wilk Test Statistic 0.9 Shapiro Wilk Lognormal GOF Test
Assuming Gamma Distribution
95% Approximate Gamma UCL (use when n>=50)) 48.68 95% Adjusted Gamma UCL (use when n<50) 54.65
Adjusted Level of Significance 0.0301 Adjusted Chi Square Value 5.697
MLE Mean (bias corrected) 22.65 MLE Sd (bias corrected) 31.16
Approximate Chi Square Value (0.05) 6.397
Theta hat (MLE) 36.51 Theta star (bias corrected MLE) 42.85
nu hat (MLE) 16.13 nu star (bias corrected) 13.74
Gamma Statistics
k hat (MLE) 0.621 k star (bias corrected MLE) 0.529Coffey Appendix H - Data Statistics
RAAF Base Tindal PFAS Ecological Risk Assessment
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A B C D E F G H I J K L
Nonparametric Distribution Free UCL Statistics
Data appear to follow a Discernible Distribution at 5% Significance Level
95% Chebyshev (MVUE) UCL 986.8 97.5% Chebyshev (MVUE) UCL 1232
99% Chebyshev (MVUE) UCL 1714
Assuming Lognormal Distribution
95% H-UCL 1099 90% Chebyshev (MVUE) UCL 809.9
Maximum of Logged Data 7.378 SD of logged Data 0.972
Lognormal Statistics
Minimum of Logged Data 3.555 Mean of logged Data 5.624
5% Lilliefors Critical Value 0.251 Data appear Lognormal at 5% Significance Level
Data appear Lognormal at 5% Significance Level
5% Shapiro Wilk Critical Value 0.85 Data appear Lognormal at 5% Significance Level
Lilliefors Test Statistic 0.167 Lilliefors Lognormal GOF Test
Lognormal GOF Test
Shapiro Wilk Test Statistic 0.955 Shapiro Wilk Lognormal GOF Test
Assuming Gamma Distribution
95% Approximate Gamma UCL (use when n>=50)) 719.7 95% Adjusted Gamma UCL (use when n<50) 791.3
Adjusted Level of Significance 0.0278 Adjusted Chi Square Value 12.33
MLE Mean (bias corrected) 413.2 MLE Sd (bias corrected) 398.7
Approximate Chi Square Value (0.05) 13.56
Theta hat (MLE) 296.6 Theta star (bias corrected MLE) 384.8
nu hat (MLE) 30.65 nu star (bias corrected) 23.62
Gamma Statistics
k hat (MLE) 1.393 k star (bias corrected MLE) 1.074
5% K-S Critical Value 0.26 Detected data appear Gamma Distributed at 5% Significance Level
Detected data appear Gamma Distributed at 5% Significance Level
5% A-D Critical Value 0.744 Detected data appear Gamma Distributed at 5% Significance Level
K-S Test Statistic 0.163 Kolmogorov-Smirnov Gamma GOF Test
Gamma GOF Test
A-D Test Statistic 0.4 Anderson-Darling Gamma GOF Test
95% Student's-t UCL 649.9 95% Adjusted-CLT UCL (Chen-1995) 728.6
95% Modified-t UCL (Johnson-1978) 665.6
Data appear Approximate Normal at 5% Significance Level
Assuming Normal Distribution
95% Normal UCL 95% UCLs (Adjusted for Skewness)
Lilliefors Test Statistic 0.249 Lilliefors GOF Test
5% Lilliefors Critical Value 0.251 Data appear Normal at 5% Significance Level
Normal GOF Test
Shapiro Wilk Test Statistic 0.717 Shapiro Wilk GOF Test
5% Shapiro Wilk Critical Value 0.85 Data Not Normal at 5% Significance Level
Coffey Appendix H - Data Statistics
RAAF Base Tindal PFAS Ecological Risk Assessment
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A B C D E F G H I J K L
Recommendations are based upon data size, data distribution, and skewness.
These recommendations are based upon the results of the simulation studies summarized in Singh, Maichle, and Lee (2006).
However, simulations results will not cover all Real World data sets; for additional insight the user may want to consult a statistician.
When a data set follows an approximate (e.g., normal) distribution passing one of the GOF test
When applicable, it is suggested to use a UCL based upon a distribution (e.g., gamma) passing both GOF tests in ProUCL
Note: Suggestions regarding the selection of a 95% UCL are provided to help the user to select the most appropriate 95% UCL.
Suggested UCL to Use
95% Student's-t UCL 649.9
90% Chebyshev(Mean, Sd) UCL 805 95% Chebyshev(Mean, Sd) UCL 982.5
97.5% Chebyshev(Mean, Sd) UCL 1229 99% Chebyshev(Mean, Sd) UCL 1713
95% Hall's Bootstrap UCL 1618 95% Percentile Bootstrap UCL 640
95% BCA Bootstrap UCL 733.6
95% CLT UCL 628 95% Jackknife UCL 649.9
95% Standard Bootstrap UCL 619.8 95% Bootstrap-t UCL 1003
Nonparametric Distribution Free UCLs
Coffey Appendix H - Data Statistics
RAAF Base Tindal PFAS Ecological Risk Assessment
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A B C D E F G H I J K L
If possible, compute and collect Data Quality Objectives (DQO) based sample size and analytical results.
Warning: This data set only has 0 observations!
Data set is too small to compute reliable and meaningful statistics and estimates!
The data set for variable Perfluoro-n-octanoate acid (PFOA) (katherine river us - wet) was not processed!
It is suggested to collect at least 8 to 10 observations before using these statistical methods!
Maximum N/A Median N/A
Number of Missing Observations 17
Minimum N/A Mean N/A
General Statistics
Total Number of Observations 0 Number of Distinct Observations 0
If possible, compute and collect Data Quality Objectives (DQO) based sample size and analytical results.
Perfluoro-n-octanoate acid (PFOA) (katherine river us - wet)
Warning: This data set only has 0 observations!
Data set is too small to compute reliable and meaningful statistics and estimates!
The data set for variable Perfluoro-n-octanoate acid (PFOA) (katherine river ds - wet) was not processed!
It is suggested to collect at least 8 to 10 observations before using these statistical methods!
Maximum N/A Median N/A
Number of Missing Observations 80
Minimum N/A Mean N/A
General Statistics
Total Number of Observations 0 Number of Distinct Observations 0
If possible, compute and collect Data Quality Objectives (DQO) based sample size and analytical results.
Perfluoro-n-octanoate acid (PFOA) (katherine river ds - wet)
Warning: This data set only has 0 observations!
Data set is too small to compute reliable and meaningful statistics and estimates!
The data set for variable Perfluoro-n-octanoate acid (PFOA) (katherine river ds - dry) was not processed!
It is suggested to collect at least 8 to 10 observations before using these statistical methods!
Maximum N/A Median N/A
Number of Missing Observations 115
Minimum N/A Mean N/A
General Statistics
Total Number of Observations 0 Number of Distinct Observations 0
Number of Bootstrap Operations 2000
Perfluoro-n-octanoate acid (PFOA) (katherine river ds - dry)
From File Data_Tindal_Fish_20180708_b.xls
Full Precision OFF
Confidence Coefficient 95%
UCL Statistics for Uncensored Full Data Sets
User Selected Options
Date/Time of Computation ProUCL 5.17/8/2018 8:50:49 AM
Coffey Appendix H - Data Statistics
RAAF Base Tindal PFAS Ecological Risk Assessment
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A B C D E F G H I J K L
Assuming Gamma Distribution
95% Approximate Gamma UCL (use when n>=50) 96.72 95% Adjusted Gamma UCL (use when n<50) 96.89
Adjusted Level of Significance 0.0479 Adjusted Chi Square Value 240.5
MLE Mean (bias corrected) 83.64 MLE Sd (bias corrected) 76
Approximate Chi Square Value (0.05) 241
Theta hat (MLE) 67.57 Theta star (bias corrected MLE) 69.05
nu hat (MLE) 284.7 nu star (bias corrected) 278.6
Gamma Statistics
k hat (MLE) 1.238 k star (bias corrected MLE) 1.211
5% K-S Critical Value 0.0877 Detected data appear Gamma Distributed at 5% Significance Level
Detected data appear Gamma Distributed at 5% Significance Level
5% A-D Critical Value 0.777 Detected data appear Gamma Distributed at 5% Significance Level
K-S Test Statistic 0.0577 Kolmogorov-Smirnov Gamma GOF Test
Gamma GOF Test
A-D Test Statistic 0.643 Anderson-Darling Gamma GOF Test
95% Student's-t UCL 95.76 95% Adjusted-CLT UCL (Chen-1995) 96.97
95% Modified-t UCL (Johnson-1978) 95.97
Data Not Normal at 5% Significance Level
Assuming Normal Distribution
95% Normal UCL 95% UCLs (Adjusted for Skewness)
Lilliefors Test Statistic 0.153 Lilliefors GOF Test
5% Lilliefors Critical Value 0.0829 Data Not Normal at 5% Significance Level
Normal GOF Test
Shapiro Wilk Test Statistic 0.807 Shapiro Wilk GOF Test
5% Shapiro Wilk P Value 0 Data Not Normal at 5% Significance Level
Coefficient of Variation 0.937 Skewness 1.794
Maximum 380 Median 59
SD 78.38 Std. Error of Mean 7.309
Number of Missing Observations 0
Minimum 0.3 Mean 83.64
General Statistics
Total Number of Observations 115 Number of Distinct Observations 70
If possible, compute and collect Data Quality Objectives (DQO) based sample size and analytical results.
Perfluoro-n-octane sulfonic acid (PFOS) (katherine river ds - dry)
Warning: This data set only has 1 observations!
Data set is too small to compute reliable and meaningful statistics and estimates!
The data set for variable Perfluoro-n-octanoate acid (PFOA) (tindal creek - wet) was not processed!
It is suggested to collect at least 8 to 10 observations before using these statistical methods!
Maximum 0.39 Median 0.39
Number of Missing Observations 10
Minimum 0.39 Mean 0.39
General Statistics
Total Number of Observations 1 Number of Distinct Observations 1
Perfluoro-n-octanoate acid (PFOA) (tindal creek - wet)
Coffey Appendix H - Data Statistics
RAAF Base Tindal PFAS Ecological Risk Assessment
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A B C D E F G H I J K L
Data Not Gamma Distributed at 5% Significance Level
K-S Test Statistic 0.122 Kolmogorov-Smirnov Gamma GOF Test
5% K-S Critical Value 0.104 Data Not Gamma Distributed at 5% Significance Level
Gamma GOF Test
A-D Test Statistic 2.081 Anderson-Darling Gamma GOF Test
5% A-D Critical Value 0.791 Data Not Gamma Distributed at 5% Significance Level
95% Modified-t UCL (Johnson-1978) 47.75
Assuming Normal Distribution
95% Normal UCL 95% UCLs (Adjusted for Skewness)
95% Student's-t UCL 47.34 95% Adjusted-CLT UCL (Chen-1995) 49.85
5% Lilliefors Critical Value 0.0991 Data Not Normal at 5% Significance Level
Data Not Normal at 5% Significance Level
5% Shapiro Wilk P Value 0 Data Not Normal at 5% Significance Level
Lilliefors Test Statistic 0.278 Lilliefors GOF Test
Normal GOF Test
Shapiro Wilk Test Statistic 0.557 Shapiro Wilk GOF Test
SD 58.47 Std. Error of Mean 6.537
Coefficient of Variation 1.604 Skewness 3.382
Minimum 1.8 Mean 36.46
Maximum 310 Median 18
Total Number of Observations 80 Number of Distinct Observations 61
Number of Missing Observations 0
Perfluoro-n-octane sulfonic acid (PFOS) (katherine river ds - wet)
General Statistics
Note: Suggestions regarding the selection of a 95% UCL are provided to help the user to select the most appropriate 95% UCL.
Recommendations are based upon data size, data distribution, and skewness.
These recommendations are based upon the results of the simulation studies summarized in Singh, Maichle, and Lee (2006).
However, simulations results will not cover all Real World data sets; for additional insight the user may want to consult a statistician.
Suggested UCL to Use
95% Approximate Gamma UCL 96.72
90% Chebyshev(Mean, Sd) UCL 105.6 95% Chebyshev(Mean, Sd) UCL 115.5
97.5% Chebyshev(Mean, Sd) UCL 129.3 99% Chebyshev(Mean, Sd) UCL 156.4
95% Hall's Bootstrap UCL 97.13 95% Percentile Bootstrap UCL 95.66
95% BCA Bootstrap UCL 97.16
95% CLT UCL 95.67 95% Jackknife UCL 95.76
95% Standard Bootstrap UCL 95.5 95% Bootstrap-t UCL 97.3
Nonparametric Distribution Free UCL Statistics
Data appear to follow a Discernible Distribution at 5% Significance Level
Nonparametric Distribution Free UCLs
95% Chebyshev (MVUE) UCL 145.6 97.5% Chebyshev (MVUE) UCL 167.8
99% Chebyshev (MVUE) UCL 211.3
Assuming Lognormal Distribution
95% H-UCL 120.2 90% Chebyshev (MVUE) UCL 129.7
Maximum of Logged Data 5.94 SD of logged Data 1.082
Lognormal Statistics
Minimum of Logged Data -1.204 Mean of logged Data 3.971
5% Lilliefors Critical Value 0.0829 Data Not Lognormal at 5% Significance Level
Data Not Lognormal at 5% Significance Level
5% Shapiro Wilk P Value 3.5637E-4 Data Not Lognormal at 5% Significance Level
Lilliefors Test Statistic 0.0914 Lilliefors Lognormal GOF Test
Lognormal GOF Test
Shapiro Wilk Test Statistic 0.946 Shapiro Wilk Lognormal GOF TestCoffey Appendix H - Data Statistics
RAAF Base Tindal PFAS Ecological Risk Assessment
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A B C D E F G H I J K L
SD 24.64 Std. Error of Mean 6.834
Coefficient of Variation 1.088 Skewness 1.09
Minimum 0.4 Mean 22.65
Maximum 75 Median 13
Total Number of Observations 13 Number of Distinct Observations 13
Number of Missing Observations 4
Perfluoro-n-octane sulfonic acid (PFOS) (katherine river us - wet)
General Statistics
ProUCL computes and outputs H-statistic based UCLs for historical reasons only.
H-statistic often results in unstable (both high and low) values of UCL95 as shown in examples in the Technical Guide.
It is therefore recommended to avoid the use of H-statistic based 95% UCLs.
Use of nonparametric methods are preferred to compute UCL95 for skewed data sets which do not follow a gamma distribution.
Note: Suggestions regarding the selection of a 95% UCL are provided to help the user to select the most appropriate 95% UCL.
Recommendations are based upon data size, data distribution, and skewness.
These recommendations are based upon the results of the simulation studies summarized in Singh, Maichle, and Lee (2006).
However, simulations results will not cover all Real World data sets; for additional insight the user may want to consult a statistician.
Suggested UCL to Use
95% H-UCL 50.27
90% Chebyshev(Mean, Sd) UCL 56.07 95% Chebyshev(Mean, Sd) UCL 64.95
97.5% Chebyshev(Mean, Sd) UCL 77.28 99% Chebyshev(Mean, Sd) UCL 101.5
95% Hall's Bootstrap UCL 49.65 95% Percentile Bootstrap UCL 48.06
95% BCA Bootstrap UCL 50.62
95% CLT UCL 47.21 95% Jackknife UCL 47.34
95% Standard Bootstrap UCL 47.1 95% Bootstrap-t UCL 52.43
Nonparametric Distribution Free UCL Statistics
Data appear to follow a Discernible Distribution at 5% Significance Level
Nonparametric Distribution Free UCLs
95% Chebyshev (MVUE) UCL 61.63 97.5% Chebyshev (MVUE) UCL 73.02
99% Chebyshev (MVUE) UCL 95.39
Assuming Lognormal Distribution
95% H-UCL 50.27 90% Chebyshev (MVUE) UCL 53.43
Maximum of Logged Data 5.737 SD of logged Data 1.209
Lognormal Statistics
Minimum of Logged Data 0.588 Mean of logged Data 2.849
5% Lilliefors Critical Value 0.0991 Data appear Lognormal at 5% Significance Level
Data appear Lognormal at 5% Significance Level
5% Shapiro Wilk P Value 0.142 Data appear Lognormal at 5% Significance Level
Lilliefors Test Statistic 0.0685 Lilliefors Lognormal GOF Test
Lognormal GOF Test
Shapiro Wilk Test Statistic 0.967 Shapiro Wilk Lognormal GOF Test
Assuming Gamma Distribution
95% Approximate Gamma UCL (use when n>=50)) 45.54 95% Adjusted Gamma UCL (use when n<50) 45.73
Adjusted Level of Significance 0.047 Adjusted Chi Square Value 98.72
MLE Mean (bias corrected) 36.46 MLE Sd (bias corrected) 41.44
Approximate Chi Square Value (0.05) 99.12
Theta hat (MLE) 45.84 Theta star (bias corrected MLE) 47.11
nu hat (MLE) 127.3 nu star (bias corrected) 123.8
Gamma Statistics
k hat (MLE) 0.795 k star (bias corrected MLE) 0.774Coffey Appendix H - Data Statistics
RAAF Base Tindal PFAS Ecological Risk Assessment
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A B C D E F G H I J K L
Recommendations are based upon data size, data distribution, and skewness.
These recommendations are based upon the results of the simulation studies summarized in Singh, Maichle, and Lee (2006).
However, simulations results will not cover all Real World data sets; for additional insight the user may want to consult a statistician.
When a data set follows an approximate (e.g., normal) distribution passing one of the GOF test
When applicable, it is suggested to use a UCL based upon a distribution (e.g., gamma) passing both GOF tests in ProUCL
Note: Suggestions regarding the selection of a 95% UCL are provided to help the user to select the most appropriate 95% UCL.
Suggested UCL to Use
95% Student's-t UCL 34.83
90% Chebyshev(Mean, Sd) UCL 43.16 95% Chebyshev(Mean, Sd) UCL 52.44
97.5% Chebyshev(Mean, Sd) UCL 65.33 99% Chebyshev(Mean, Sd) UCL 90.65
95% Hall's Bootstrap UCL 37.23 95% Percentile Bootstrap UCL 33.95
95% BCA Bootstrap UCL 35.2
95% CLT UCL 33.89 95% Jackknife UCL 34.83
95% Standard Bootstrap UCL 33.6 95% Bootstrap-t UCL 38.36
Nonparametric Distribution Free UCL Statistics
Data appear to follow a Discernible Distribution at 5% Significance Level
Nonparametric Distribution Free UCLs
95% Chebyshev (MVUE) UCL 118.7 97.5% Chebyshev (MVUE) UCL 155.3
99% Chebyshev (MVUE) UCL 227
Assuming Lognormal Distribution
95% H-UCL 454.9 90% Chebyshev (MVUE) UCL 92.41
Maximum of Logged Data 4.317 SD of logged Data 1.828
Lognormal Statistics
Minimum of Logged Data -0.916 Mean of logged Data 2.13
5% Lilliefors Critical Value 0.234 Data appear Lognormal at 5% Significance Level
Data appear Lognormal at 5% Significance Level
5% Shapiro Wilk Critical Value 0.866 Data appear Lognormal at 5% Significance Level
Lilliefors Test Statistic 0.174 Lilliefors Lognormal GOF Test
Lognormal GOF Test
Shapiro Wilk Test Statistic 0.9 Shapiro Wilk Lognormal GOF Test
Assuming Gamma Distribution
95% Approximate Gamma UCL (use when n>=50)) 48.68 95% Adjusted Gamma UCL (use when n<50) 54.65
Adjusted Level of Significance 0.0301 Adjusted Chi Square Value 5.697
MLE Mean (bias corrected) 22.65 MLE Sd (bias corrected) 31.16
Approximate Chi Square Value (0.05) 6.397
Theta hat (MLE) 36.51 Theta star (bias corrected MLE) 42.85
nu hat (MLE) 16.13 nu star (bias corrected) 13.74
Detected data appear Gamma Distributed at 5% Significance Level
Gamma Statistics
k hat (MLE) 0.621 k star (bias corrected MLE) 0.529
K-S Test Statistic 0.162 Kolmogorov-Smirnov Gamma GOF Test
5% K-S Critical Value 0.248 Detected data appear Gamma Distributed at 5% Significance Level
Gamma GOF Test
A-D Test Statistic 0.316 Anderson-Darling Gamma GOF Test
5% A-D Critical Value 0.78 Detected data appear Gamma Distributed at 5% Significance Level
95% Modified-t UCL (Johnson-1978) 35.18
Assuming Normal Distribution
95% Normal UCL 95% UCLs (Adjusted for Skewness)
95% Student's-t UCL 34.83 95% Adjusted-CLT UCL (Chen-1995) 36.1
5% Lilliefors Critical Value 0.234 Data appear Normal at 5% Significance Level
Data appear Approximate Normal at 5% Significance Level
5% Shapiro Wilk Critical Value 0.866 Data Not Normal at 5% Significance Level
Lilliefors Test Statistic 0.191 Lilliefors GOF Test
Normal GOF Test
Shapiro Wilk Test Statistic 0.852 Shapiro Wilk GOF TestCoffey Appendix H - Data Statistics
RAAF Base Tindal PFAS Ecological Risk Assessment
313
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321
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327
328
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369
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A B C D E F G H I J K L
Nonparametric Distribution Free UCL Statistics
Data appear to follow a Discernible Distribution at 5% Significance Level
95% Chebyshev (MVUE) UCL 986.8 97.5% Chebyshev (MVUE) UCL 1232
99% Chebyshev (MVUE) UCL 1714
Assuming Lognormal Distribution
95% H-UCL 1099 90% Chebyshev (MVUE) UCL 809.9
Maximum of Logged Data 7.378 SD of logged Data 0.972
Lognormal Statistics
Minimum of Logged Data 3.555 Mean of logged Data 5.624
5% Lilliefors Critical Value 0.251 Data appear Lognormal at 5% Significance Level
Data appear Lognormal at 5% Significance Level
5% Shapiro Wilk Critical Value 0.85 Data appear Lognormal at 5% Significance Level
Lilliefors Test Statistic 0.167 Lilliefors Lognormal GOF Test
Lognormal GOF Test
Shapiro Wilk Test Statistic 0.955 Shapiro Wilk Lognormal GOF Test
Assuming Gamma Distribution
95% Approximate Gamma UCL (use when n>=50)) 719.7 95% Adjusted Gamma UCL (use when n<50) 791.3
Adjusted Level of Significance 0.0278 Adjusted Chi Square Value 12.33
MLE Mean (bias corrected) 413.2 MLE Sd (bias corrected) 398.7
Approximate Chi Square Value (0.05) 13.56
Theta hat (MLE) 296.6 Theta star (bias corrected MLE) 384.8
nu hat (MLE) 30.65 nu star (bias corrected) 23.62
Gamma Statistics
k hat (MLE) 1.393 k star (bias corrected MLE) 1.074
5% K-S Critical Value 0.26 Detected data appear Gamma Distributed at 5% Significance Level
Detected data appear Gamma Distributed at 5% Significance Level
5% A-D Critical Value 0.744 Detected data appear Gamma Distributed at 5% Significance Level
K-S Test Statistic 0.163 Kolmogorov-Smirnov Gamma GOF Test
Gamma GOF Test
A-D Test Statistic 0.4 Anderson-Darling Gamma GOF Test
95% Student's-t UCL 649.9 95% Adjusted-CLT UCL (Chen-1995) 728.6
95% Modified-t UCL (Johnson-1978) 665.6
Data appear Approximate Normal at 5% Significance Level
Assuming Normal Distribution
95% Normal UCL 95% UCLs (Adjusted for Skewness)
Lilliefors Test Statistic 0.249 Lilliefors GOF Test
5% Lilliefors Critical Value 0.251 Data appear Normal at 5% Significance Level
Normal GOF Test
Shapiro Wilk Test Statistic 0.717 Shapiro Wilk GOF Test
5% Shapiro Wilk Critical Value 0.85 Data Not Normal at 5% Significance Level
Coefficient of Variation 1.048 Skewness 2.39
Maximum 1600 Median 240
SD 433.2 Std. Error of Mean 130.6
Number of Missing Observations 0
Minimum 35 Mean 413.2
Perfluoro-n-octane sulfonic acid (PFOS) (tindal creek - wet)
General Statistics
Total Number of Observations 11 Number of Distinct Observations 10
Coffey Appendix H - Data Statistics
RAAF Base Tindal PFAS Ecological Risk Assessment
374
375
376
377
378
379
380
381
382
383
384
385
386
387
388
389
390
391
392
A B C D E F G H I J K L
Recommendations are based upon data size, data distribution, and skewness.
These recommendations are based upon the results of the simulation studies summarized in Singh, Maichle, and Lee (2006).
However, simulations results will not cover all Real World data sets; for additional insight the user may want to consult a statistician.
When a data set follows an approximate (e.g., normal) distribution passing one of the GOF test
When applicable, it is suggested to use a UCL based upon a distribution (e.g., gamma) passing both GOF tests in ProUCL
Note: Suggestions regarding the selection of a 95% UCL are provided to help the user to select the most appropriate 95% UCL.
Suggested UCL to Use
95% Student's-t UCL 649.9
90% Chebyshev(Mean, Sd) UCL 805 95% Chebyshev(Mean, Sd) UCL 982.5
97.5% Chebyshev(Mean, Sd) UCL 1229 99% Chebyshev(Mean, Sd) UCL 1713
95% Hall's Bootstrap UCL 1567 95% Percentile Bootstrap UCL 629.1
95% BCA Bootstrap UCL 754.1
95% CLT UCL 628 95% Jackknife UCL 649.9
95% Standard Bootstrap UCL 625.3 95% Bootstrap-t UCL 1000
Nonparametric Distribution Free UCLs
Coffey Appendix H - Data Statistics
RAAF Base Tindal PFAS Ecological Risk Assessment
