← All validation
Descriptive Statistics validation
Free descriptive statistics for environmental data: mean, median, percentiles, and 95% UCL with full non-detect handling (Kaplan-Meier, ROS, substitution).
- Scenarios
- 107
- Values agreeing
- 1542
- Values differing
- 8
- Validated against
- USEPA ProUCL, R EnvStats / nortest, R NADA
Every descriptive statistic and every UCL method is compared against USEPA ProUCL and R EnvStats. The two censored-data estimators are compared against their own references: Kaplan-Meier against ProUCL, robust ROS against NADA. The recommended UCL is the one ProUCL 5.2 prints under "Suggested UCL to Use", following the decision logic in Appendix C of the ProUCL 5.2 Technical Guide, and it is compared against that printed suggestion for both uncensored and censored data. For uncensored data ProUCL 5.2 suggests only Student's t, Land's H and the two gamma UCLs; it no longer suggests a Chebyshev or bootstrap UCL. In a sweep of 1,015 uncensored datasets run through ProUCL 5.2, the toolkit names the same method on all but one, where the two Shapiro-Wilk statistics fall either side of the critical value. ProUCL applies a separate decision tree to censored data: it fits the distribution to the detected results only and recommends only Kaplan-Meier methods; the toolkit matches it on all 60 censored datasets measured. A January 2023 review of ProUCL 5.2 prepared for the Florida Department of Environmental Protection noted that, according to the simulations in the Technical Guide, the 5.2 suggestion can give coverage of about 80% rather than 95% for skewed data with small samples, and recommended continued use of ProUCL 5.1. The toolkit follows ProUCL 5.2 and shows every candidate UCL, including the Chebyshev limits, so a reviewer can choose another with reasons.
Scenarios
- Drawn from a gamma distribution, shape 0.2, n = 10: ProUCL 5.2 finds gamma and suggests adjusted gammaBoundary case
- Drawn from a gamma distribution, shape 0.2, n = 8: not normal and under ten results, so ProUCL 5.2 makes no suggestionBoundary case
- Drawn from a gamma distribution, shape 0.35, n = 10: ProUCL 5.2 finds normal and suggests Student's tBoundary case
- Drawn from a lognormal distribution near a branch threshold, n = 10: ProUCL 5.2 finds gamma and suggests adjusted gammaBoundary case
- n = 37, sitting on a Shapiro-Wilk critical value that does not follow the trend of its neighboursBoundary case
- Ten uncensored results from a roughly normal populationTypical use
- Three non-detects fitted by robust ROSSpecial case
- Three non-detects handled by Kaplan-MeierSpecial case
- Approximately lognormal, widely spread logs, fifteen results - Student's t rather than Land's HBoundary case
- Detected results below the reporting limit - Kaplan-Meier stops matching substitutionBoundary case
- Detects that pass one normality test and both gamma testsBoundary case
- Drawn from a gamma distribution near a branch threshold, n = 10: ProUCL 5.2 finds gamma and suggests adjusted gammaBoundary case
- Drawn from a gamma distribution near a branch threshold, n = 10: ProUCL 5.2 finds normal and suggests Student's tBoundary case
- Drawn from a gamma distribution near a branch threshold, n = 50: ProUCL 5.2 finds gamma and suggests adjusted gammaBoundary case
- Drawn from a gamma distribution near a branch threshold, n = 50: ProUCL 5.2 finds gamma and suggests approximate gammaBoundary case
- Drawn from a gamma distribution near a branch threshold, n = 50: ProUCL 5.2 finds lognormal and suggests Land's HBoundary case
- Drawn from a gamma distribution near a branch threshold, n = 50: ProUCL 5.2 finds normal and suggests Student's tBoundary case
- Drawn from a gamma distribution near a branch threshold, n = 51: ProUCL 5.2 finds gamma and suggests adjusted gammaBoundary case
- Drawn from a gamma distribution near a branch threshold, n = 51: ProUCL 5.2 finds gamma and suggests approximate gammaBoundary case
- Drawn from a gamma distribution near a branch threshold, n = 51: ProUCL 5.2 finds no discernible distribution and suggests Student's tBoundary case
- Drawn from a gamma distribution near a branch threshold, n = 55: ProUCL 5.2 finds lognormal and suggests Land's HBoundary case
- Drawn from a gamma distribution near a branch threshold, n = 9: not normal and under ten results, so ProUCL 5.2 makes no suggestionBoundary case
- Drawn from a gamma distribution near a branch threshold, n = 9: ProUCL 5.2 finds normal and suggests Student's tBoundary case
- Drawn from a gamma distribution, shape 0.2, n = 120: ProUCL 5.2 finds gamma and suggests adjusted gammaBoundary case
- Drawn from a gamma distribution, shape 0.2, n = 30: ProUCL 5.2 finds gamma and suggests adjusted gammaBoundary case
- Drawn from a gamma distribution, shape 0.2, n = 49: ProUCL 5.2 finds gamma and suggests adjusted gammaBoundary case
- Drawn from a gamma distribution, shape 0.2, n = 50: ProUCL 5.2 finds gamma and suggests adjusted gammaBoundary case
- Drawn from a gamma distribution, shape 0.35, n = 8: ProUCL 5.2 finds normal and suggests Student's tBoundary case
- Drawn from a gamma distribution, shape 0.5, n = 120: ProUCL 5.2 finds gamma and suggests approximate gammaBoundary case
- Drawn from a gamma distribution, shape 0.5, n = 50: ProUCL 5.2 finds gamma and suggests approximate gammaBoundary case
- Drawn from a gamma distribution, shape 0.8, n = 49: ProUCL 5.2 finds normal and suggests Student's tBoundary case
- Drawn from a gamma distribution, shape 1.0, n = 30: ProUCL 5.2 finds normal and suggests Student's tBoundary case
- Drawn from a gamma distribution, shape 3.0, n = 50: ProUCL 5.2 finds normal and suggests Student's tBoundary case
- Drawn from a gamma distribution, shape 3.0, n = 70: ProUCL 5.2 finds normal and suggests Student's tBoundary case
- Drawn from a gamma distribution, shape 8.0, n = 120: ProUCL 5.2 finds normal and suggests Student's tBoundary case
- Drawn from a lognormal distribution near a branch threshold, n = 10: ProUCL 5.2 finds lognormal and suggests Land's HBoundary case
- Drawn from a lognormal distribution near a branch threshold, n = 10: ProUCL 5.2 finds normal and suggests Student's tBoundary case
- Drawn from a lognormal distribution near a branch threshold, n = 12: ProUCL 5.2 finds gamma and suggests adjusted gammaBoundary case
- Drawn from a lognormal distribution near a branch threshold, n = 12: ProUCL 5.2 finds lognormal and suggests Land's HBoundary case
- Drawn from a lognormal distribution near a branch threshold, n = 12: ProUCL 5.2 finds lognormal and suggests Student's tBoundary case
- Drawn from a lognormal distribution near a branch threshold, n = 27: ProUCL 5.2 finds gamma and suggests adjusted gammaBoundary case
- Drawn from a lognormal distribution near a branch threshold, n = 27: ProUCL 5.2 finds lognormal and suggests Land's HBoundary case
- Drawn from a lognormal distribution near a branch threshold, n = 27: ProUCL 5.2 finds lognormal and suggests Student's tBoundary case
- Drawn from a lognormal distribution near a branch threshold, n = 28: ProUCL 5.2 finds gamma and suggests adjusted gammaBoundary case
- Drawn from a lognormal distribution near a branch threshold, n = 28: ProUCL 5.2 finds lognormal and suggests Land's HBoundary case
- Drawn from a lognormal distribution near a branch threshold, n = 28: ProUCL 5.2 finds no discernible distribution and suggests Student's tBoundary case
- Drawn from a lognormal distribution near a branch threshold, n = 29: ProUCL 5.2 finds gamma and suggests adjusted gammaBoundary case
- Drawn from a lognormal distribution near a branch threshold, n = 29: ProUCL 5.2 finds lognormal and suggests Land's HBoundary case
- Drawn from a lognormal distribution near a branch threshold, n = 29: ProUCL 5.2 finds normal and suggests Student's tBoundary case
- Drawn from a lognormal distribution near a branch threshold, n = 9: not normal and under ten results, so ProUCL 5.2 makes no suggestionBoundary case
- Drawn from a lognormal distribution near a branch threshold, n = 9: ProUCL 5.2 finds normal and suggests Student's tBoundary case
- Drawn from a lognormal distribution, sd of logs 0.3, n = 10: ProUCL 5.2 finds normal and suggests Student's tBoundary case
- Drawn from a lognormal distribution, sd of logs 0.3, n = 100: ProUCL 5.2 finds normal and suggests Student's tBoundary case
- Drawn from a lognormal distribution, sd of logs 0.3, n = 28: ProUCL 5.2 finds no discernible distribution and suggests Student's tBoundary case
- Drawn from a lognormal distribution, sd of logs 0.3, n = 8: ProUCL 5.2 finds normal and suggests Student's tBoundary case
- Drawn from a lognormal distribution, sd of logs 0.6, n = 100: ProUCL 5.2 finds gamma and suggests approximate gammaBoundary case
- Drawn from a lognormal distribution, sd of logs 0.6, n = 15: ProUCL 5.2 finds gamma and suggests adjusted gammaBoundary case
- Drawn from a lognormal distribution, sd of logs 0.6, n = 40: ProUCL 5.2 finds gamma and suggests adjusted gammaBoundary case
- Drawn from a lognormal distribution, sd of logs 0.9, n = 15: ProUCL 5.2 finds lognormal and suggests Land's HBoundary case
- Drawn from a lognormal distribution, sd of logs 0.9, n = 8: not normal and under ten results, so ProUCL 5.2 makes no suggestionBoundary case
- Drawn from a lognormal distribution, sd of logs 1.2, n = 100: ProUCL 5.2 finds lognormal and suggests Land's HBoundary case
- Drawn from a lognormal distribution, sd of logs 1.2, n = 28: ProUCL 5.2 finds lognormal and suggests Land's HBoundary case
- Drawn from a normal distribution, CV 0.1, n = 10: ProUCL 5.2 finds normal and suggests Student's tBoundary case
- Drawn from a normal distribution, CV 0.1, n = 100: ProUCL 5.2 finds normal and suggests Student's tBoundary case
- Drawn from a normal distribution, CV 0.1, n = 30: ProUCL 5.2 finds normal and suggests Student's tBoundary case
- Drawn from a normal distribution, CV 0.1, n = 5: ProUCL 5.2 finds normal and suggests Student's tBoundary case
- Drawn from a very widely spread lognormal distribution, n = 100: ProUCL 5.2 finds lognormal and suggests Land's HBoundary case
- Drawn from a very widely spread lognormal distribution, n = 150: ProUCL 5.2 finds no discernible distribution and suggests Student's tBoundary case
- Drawn from a very widely spread lognormal distribution, n = 200: ProUCL 5.2 finds lognormal and suggests Land's HBoundary case
- Eight results, six of them non-detects, no distribution identifiedBoundary case
- Fifty results, where the approximate gamma limit takes overBoundary case
- Gamma data with a comfortable shape - the approximate gamma UCLBoundary case
- Gamma data with a low shape - the adjusted gamma UCLBoundary case
- Gamma detects at forty-nine results, still the adjusted limitBoundary case
- Gamma-distributed detects, shape at or below one, fourteen resultsBoundary case
- Land's H off a tabulated sample size - where ProUCL's own interpolation goes the wrong wayBoundary case
- Nine results - one below the size at which ProUCL will recommend a UCLBoundary case
- No discernible distribution (bimodal), n = 10: ProUCL 5.2 finds no discernible distribution and suggests Student's tBoundary case
- No discernible distribution (bimodal), n = 150: ProUCL 5.2 finds no discernible distribution and suggests Student's tBoundary case
- No discernible distribution (bimodal), n = 30: ProUCL 5.2 finds no discernible distribution and suggests Student's tBoundary case
- No discernible distribution (bimodal), n = 8: ProUCL 5.2 finds normal and suggests Student's tBoundary case
- No discernible distribution (cluster outliers), n = 8: not normal and under ten results, so ProUCL 5.2 makes no suggestionBoundary case
- No discernible distribution, n = 10: ProUCL 5.2 finds no discernible distribution and suggests Student's tBoundary case
- No discernible distribution, n = 200: ProUCL 5.2 finds no discernible distribution and suggests Student's tBoundary case
- No discernible distribution, n = 9: not normal and under ten results, so ProUCL 5.2 makes no suggestionBoundary case
- Normal data - ProUCL recommends Student's tBoundary case
- Normal data with one mild outlier, n = 10: ProUCL 5.2 finds normal and suggests Student's tBoundary case
- Normal data with one mild outlier, n = 30: ProUCL 5.2 finds normal and suggests Student's tBoundary case
- Normal data with one mild outlier, n = 5: ProUCL 5.2 finds normal and suggests Student's tBoundary case
- Not normal and fewer than ten results - no recommendation at allBoundary case
- Packed lead soil results (synthetic), n = 15: ProUCL 5.2 finds no discernible distribution and suggests Student's tBoundary case
- Robust ROS at seventy-five per cent censoring, two reporting limitsBoundary case
- Robust ROS with detected results below the reporting limitBoundary case
- Seven results, two detected, below the recommendation floorBoundary case
- Seventy-five per cent non-detects across two reporting limitsBoundary case
- Strongly right-skewed lognormal data - Land's HBoundary case
- Ten identical results - zero varianceBoundary case
- The same shape, one result later, where the gamma limit is usedBoundary case
- The same spread at twenty-eight results, where Land’s H returnsBoundary case
- Three results - the documented minimumBoundary case
- Widely spread lognormal detects at twenty-seven resultsBoundary case
- Widely spread small sample that ProUCL 5.2 reads as gamma - the adjusted gamma UCL, not a Chebyshev limitBoundary case
- Benzo(a)pyrene, five-analyte SME cross-check (was Land's H mismatch before the KM H-UCL fix)regression
- Copper, five-analyte SME cross-check (matches ProUCL)regression
- Lead, five-analyte SME cross-check (was Land's H mismatch before the KM H-UCL fix)regression
- Mercury, five-analyte SME cross-check (matches ProUCL)regression
- TRH fraction, five-analyte SME cross-check (matches ProUCL)regression
Drawn from a gamma distribution, shape 0.2, n = 10: ProUCL 5.2 finds gamma and suggests adjusted gamma
Boundary caseInput
10 values
| value |
|---|
| 0.001 |
| 18.79 |
| 6.591 |
| 27.75 |
| 6.395 |
| 0.001 |
| 0.02915 |
| 378 |
| 32.49 |
| 21.22 |
Against USEPA ProUCL (ProUCL 5.2.0)
| Value | USEPA ProUCL | EnviroAutomate | Difference | Agreement band | Verdict |
|---|---|---|---|---|---|
| Sample size (n) n | 10 | 10 | 0 | exact match | Agree |
| Mean mean | 49.12671500000001 | 49.126715000000004 | 7.11e-15 | within 0.000001 relative | Agree |
| Standard deviation sd | 116.17181336796433 | 116.17181336796433 | 0 | within 0.000001 relative | Agree |
| Skewness skewness | 3.1001278446851446 | 3.1001278446851437 | 8.88e-16 | within 0.000001 relative | Agree |
| 95% UCL - Student's t ucl.studentT | 116.46933252324158 | 116.46933205646774 | 4.67e-7 | within 0.000001 relative | Agree |
| 95% UCL - Modified t (Johnson) ucl.modifiedT | 122.4717904130681 | 122.47178994629428 | 4.67e-7 | within 0.000001 relative | Agree |
| 95% UCL - Central limit theorem ucl.clt | 109.55329647611816 | 109.55329643992678 | 3.62e-8 | within 0.000001 relative | Agree |
| 95% UCL - Land's H ucl.landsH | 4159140930837.528 | 4159140930837.557 | 0.0293 | within 0.02 relative | Agree |
| 95% UCL - approximateGamma ucl.approximateGamma | 247.49959136443374 | 250.15220151884333 | 2.65 | within 0.005 relative | Differs |
| Why these differ: A small sample with a low fitted shape: n = 10 and k star = 0.217, so the approximate gamma UCL rests on a chi-square quantile with about 4.3 degrees of freedom. The toolkit's value is +1.1% against ProUCL's here. ProUCL's chi-square quantile was measured to lose accuracy as the degrees of freedom fall (3.3e-3 relative at about 7); whether that accounts for all of this difference has not been confirmed. Gamma UCLs on larger samples or higher shapes agree within the published band in this corpus. | |||||
| 95% UCL - adjustedGamma ucl.adjustedGamma | 338.60310359852053 | 346.2387762993754 | 7.64 | within 0.005 relative | Differs |
| Why these differ: A small sample with a low fitted shape: n = 10 and k star = 0.217, so the adjusted gamma UCL rests on a chi-square quantile with about 4.3 degrees of freedom. The toolkit's value is +2.3% against ProUCL's here. ProUCL's chi-square quantile was measured to lose accuracy as the degrees of freedom fall (3.3e-3 relative at about 7); whether that accounts for all of this difference has not been confirmed. Gamma UCLs on larger samples or higher shapes agree within the published band in this corpus. | |||||
| Distribution used distributionUsed | gamma | gamma | - | exact match | Agree |
| Recommended method recommendedMethod | adjustedGamma | adjustedGamma | - | exact match | Agree |
| 95% UCL - Chebyshev, 95% ucl.chebyshev95 | 209.25850890827462 | 209.25850890827462 | 0 | within 0.000001 relative | Agree |
| 95% UCL - Chebyshev, 97.5% ucl.chebyshev975 | 278.5476640493063 | 278.54766404930626 | 5.68e-14 | within 0.000001 relative | Agree |
| 95% UCL - Chebyshev, 99% ucl.chebyshev99 | 414.6527923048774 | 414.6527923048773 | 5.68e-14 | within 0.000001 relative | Agree |
Drawn from a gamma distribution, shape 0.2, n = 8: not normal and under ten results, so ProUCL 5.2 makes no suggestion
Boundary caseInput
8 values
| value |
|---|
| 0.1028 |
| 3.273 |
| 0.001 |
| 0.004025 |
| 0.001 |
| 80.42 |
| 0.04484 |
| 1.286 |
Against USEPA ProUCL (ProUCL 5.2.0)
| Value | USEPA ProUCL | EnviroAutomate | Difference | Agreement band | Verdict |
|---|---|---|---|---|---|
| Sample size (n) n | 8 | 8 | 0 | exact match | Agree |
| Mean mean | 10.641583125 | 10.641583125 | 0 | within 0.000001 relative | Agree |
| Standard deviation sd | 28.21805144233524 | 28.21805144233524 | 0 | within 0.000001 relative | Agree |
| Skewness skewness | 2.819228145957364 | 2.8192281459573625 | 1.33e-15 | within 0.000001 relative | Agree |
| 95% UCL - Student's t ucl.studentT | 29.543012662502385 | 29.543012853289326 | 1.91e-7 | within 0.000001 relative | Agree |
| 95% UCL - Modified t (Johnson) ucl.modifiedT | 31.20036943021706 | 31.200369621004 | 1.91e-7 | within 0.000001 relative | Agree |
| 95% UCL - Central limit theorem ucl.clt | 27.051609702012307 | 27.051609692183828 | 9.83e-9 | within 0.000001 relative | Agree |
| 95% UCL - Land's H ucl.landsH | 57081584267.94018 | 57081584267.93997 | 0.000206 | within 0.02 relative | Agree |
| 95% UCL - approximateGamma ucl.approximateGamma | 88.03716014127272 | 93.68378511196534 | 5.65 | within 0.005 relative | Differs |
| Why these differ: A small sample with a low fitted shape: n = 8 and k star = 0.184, so the approximate gamma UCL rests on a chi-square quantile with about 2.9 degrees of freedom. The toolkit's value is +6.4% against ProUCL's here. ProUCL's chi-square quantile was measured to lose accuracy as the degrees of freedom fall (3.3e-3 relative at about 7); whether that accounts for all of this difference has not been confirmed. Gamma UCLs on larger samples or higher shapes agree within the published band in this corpus. | |||||
| 95% UCL - adjustedGamma ucl.adjustedGamma | 153.33009403331678 | 183.80631625681255 | 30.5 | within 0.005 relative | Differs |
| Why these differ: A small sample with a low fitted shape: n = 8 and k star = 0.184, so the adjusted gamma UCL rests on a chi-square quantile with about 2.9 degrees of freedom. The toolkit's value is +19.9% against ProUCL's here. ProUCL's chi-square quantile was measured to lose accuracy as the degrees of freedom fall (3.3e-3 relative at about 7); whether that accounts for all of this difference has not been confirmed. Gamma UCLs on larger samples or higher shapes agree within the published band in this corpus. | |||||
| 95% UCL - Chebyshev, 95% ucl.chebyshev95 | 54.128520986907546 | 54.128520986907546 | 0 | within 0.000001 relative | Agree |
| 95% UCL - Chebyshev, 97.5% ucl.chebyshev975 | 72.94535373811057 | 72.94535373811058 | 1.42e-14 | within 0.000001 relative | Agree |
| 95% UCL - Chebyshev, 99% ucl.chebyshev99 | 109.90737802247806 | 109.90737802247806 | 0 | within 0.000001 relative | Agree |
Drawn from a gamma distribution, shape 0.35, n = 10: ProUCL 5.2 finds normal and suggests Student's t
Boundary caseInput
10 values
| value |
|---|
| 94.53 |
| 70.61 |
| 5.972 |
| 0.001 |
| 1.86 |
| 47.95 |
| 50.68 |
| 114.6 |
| 0.04749 |
| 310.3 |
Against USEPA ProUCL (ProUCL 5.2.0)
| Value | USEPA ProUCL | EnviroAutomate | Difference | Agreement band | Verdict |
|---|---|---|---|---|---|
| Sample size (n) n | 10 | 10 | 0 | exact match | Agree |
| Mean mean | 69.65504899999999 | 69.65504899999999 | 0 | within 0.000001 relative | Agree |
| Standard deviation sd | 94.12136138953562 | 94.12136138953562 | 0 | within 0.000001 relative | Agree |
| Skewness skewness | 2.128761992319787 | 2.128761992319787 | 0 | within 0.000001 relative | Agree |
| 95% UCL - Student's t ucl.studentT | 124.21543380475482 | 124.21543342657884 | 3.78e-7 | within 0.000001 relative | Agree |
| 95% UCL - Modified t (Johnson) ucl.modifiedT | 127.55480008461211 | 127.55479970643614 | 3.78e-7 | within 0.000001 relative | Agree |
| 95% UCL - Central limit theorem ucl.clt | 118.6121234207416 | 118.61212339141969 | 2.93e-8 | within 0.000001 relative | Agree |
| 95% UCL - Land's H ucl.landsH | 33974749050.910393 | 33974749050.910393 | 0 | within 0.02 relative | Agree |
| 95% UCL - approximateGamma ucl.approximateGamma | 273.48382290134475 | 274.5200075049311 | 1.04 | within 0.005 relative | Agree |
| 95% UCL - adjustedGamma ucl.adjustedGamma | 356.3219656783506 | 359.09002798301935 | 2.77 | within 0.005 relative | Differs |
| Why these differ: A small sample with a low fitted shape: n = 10 and k star = 0.277, so the adjusted gamma UCL rests on a chi-square quantile with about 5.5 degrees of freedom. The toolkit's value is +0.8% against ProUCL's here. ProUCL's chi-square quantile was measured to lose accuracy as the degrees of freedom fall (3.3e-3 relative at about 7); whether that accounts for all of this difference has not been confirmed. Gamma UCLs on larger samples or higher shapes agree within the published band in this corpus. | |||||
| Distribution used distributionUsed | normal | normal | - | exact match | Agree |
| Recommended method recommendedMethod | studentT | studentT | - | exact match | Agree |
| 95% UCL - Chebyshev, 95% ucl.chebyshev95 | 199.39239240064603 | 199.39239240064603 | 0 | within 0.000001 relative | Agree |
| 95% UCL - Chebyshev, 97.5% ucl.chebyshev975 | 255.52984452724806 | 255.52984452724806 | 0 | within 0.000001 relative | Agree |
| 95% UCL - Chebyshev, 99% ucl.chebyshev99 | 365.8009988814962 | 365.8009988814962 | 0 | within 0.000001 relative | Agree |
Drawn from a lognormal distribution near a branch threshold, n = 10: ProUCL 5.2 finds gamma and suggests adjusted gamma
Boundary caseInput
10 values
| value |
|---|
| 46.69 |
| 1721 |
| 8.722 |
| 101.5 |
| 3.232 |
| 6.688 |
| 1.681 |
| 12.96 |
| 33.05 |
| 336.2 |
Against USEPA ProUCL (ProUCL 5.2.0)
| Value | USEPA ProUCL | EnviroAutomate | Difference | Agreement band | Verdict |
|---|---|---|---|---|---|
| Sample size (n) n | 10 | 10 | 0 | exact match | Agree |
| Mean mean | 227.1723 | 227.1723 | 0 | within 0.000001 relative | Agree |
| Standard deviation sd | 534.6520618890695 | 534.6520618890695 | 0 | within 0.000001 relative | Agree |
| Skewness skewness | 2.9680020409952688 | 2.968002040995269 | 4.44e-16 | within 0.000001 relative | Agree |
| 95% UCL - Student's t ucl.studentT | 537.100055003408 | 537.1000528551967 | 2.15e-6 | within 0.000001 relative | Agree |
| 95% UCL - Modified t (Johnson) ucl.modifiedT | 563.5475285185594 | 563.5475263703481 | 2.15e-6 | within 0.000001 relative | Agree |
| 95% UCL - Central limit theorem ucl.clt | 505.27070823250415 | 505.27070806594224 | 1.67e-7 | within 0.000001 relative | Agree |
| 95% UCL - Land's H ucl.landsH | 18089.087890501345 | 18089.087890501345 | 0 | within 0.02 relative | Agree |
| 95% UCL - approximateGamma ucl.approximateGamma | 840.032352100945 | 842.4520482394895 | 2.42 | within 0.005 relative | Agree |
| 95% UCL - adjustedGamma ucl.adjustedGamma | 1081.2127016406 | 1087.5601420056937 | 6.35 | within 0.005 relative | Differs |
| Why these differ: A small sample with a low fitted shape: n = 10 and k star = 0.296, so the adjusted gamma UCL rests on a chi-square quantile with about 5.9 degrees of freedom. The toolkit's value is +0.6% against ProUCL's here. ProUCL's chi-square quantile was measured to lose accuracy as the degrees of freedom fall (3.3e-3 relative at about 7); whether that accounts for all of this difference has not been confirmed. Gamma UCLs on larger samples or higher shapes agree within the published band in this corpus. | |||||
| Distribution used distributionUsed | gamma | gamma | - | exact match | Agree |
| Recommended method recommendedMethod | adjustedGamma | adjustedGamma | - | exact match | Agree |
| 95% UCL - Chebyshev, 95% ucl.chebyshev95 | 964.1393086484488 | 964.1393086484488 | 0 | within 0.000001 relative | Agree |
| 95% UCL - Chebyshev, 97.5% ucl.chebyshev975 | 1283.0255219966512 | 1283.025521996651 | 2.27e-13 | within 0.000001 relative | Agree |
| 95% UCL - Chebyshev, 99% ucl.chebyshev99 | 1909.415739605014 | 1909.4157396050139 | 2.27e-13 | within 0.000001 relative | Agree |
n = 37, sitting on a Shapiro-Wilk critical value that does not follow the trend of its neighbours
Boundary caseInput
37 values
| value |
|---|
| 1 |
| 8.876556 |
| 31.836986 |
| 78.793242 |
| 159.131264 |
| 282.602786 |
| 459.260216 |
| 699.412611 |
| 1013.593705 |
| 1412.537545 |
| 1907.159248 |
| 2508.539391 |
| 3227.911059 |
| 4076.648926 |
| 5066.259907 |
| 6208.375056 |
| 7514.742477 |
| 8997.221059 |
| 10667.774898 |
| 12538.468301 |
| 14621.461277 |
| 16929.005442 |
| 19473.440299 |
| 22267.189822 |
| 25322.759323 |
| 28652.732556 |
| 32269.76904 |
| 36186.601575 |
| 40416.033921 |
| 44970.938645 |
| 49864.255087 |
| 55108.98747 |
| 60718.203112 |
| 66705.030746 |
| 73082.658933 |
| 79864.334561 |
| 87063.361427 |
Against USEPA ProUCL (ProUCL 5.2.0)
| Value | USEPA ProUCL | EnviroAutomate | Difference | Agreement band | Verdict |
|---|---|---|---|---|---|
| Sample size (n) n | 37 | 37 | 0 | exact match | Agree |
| Mean mean | 22172.348877540546 | 22172.348877540542 | 3.64e-12 | within 0.000001 relative | Agree |
| Standard deviation sd | 25888.21086778352 | 25888.21086778352 | 0 | within 0.000001 relative | Agree |
| Skewness skewness | 1.1381451446070394 | 1.138145144607039 | 4.44e-16 | within 0.000001 relative | Agree |
| 95% UCL - Student's t ucl.studentT | 29357.73622749272 | 29357.73660440753 | 0.000377 | within 0.000001 relative | Agree |
| 95% UCL - Modified t (Johnson) ucl.modifiedT | 29490.45938741043 | 29490.459764325242 | 0.000377 | within 0.000001 relative | Agree |
| 95% UCL - Central limit theorem ucl.clt | 29172.838762614923 | 29172.838758422113 | 4.19e-6 | within 0.000001 relative | Agree |
| 95% UCL - Land's H ucl.landsH | 1783478.5496222111 | 1783478.5496222111 | 0 | within 0.02 relative | Agree |
| 95% UCL - approximateGamma ucl.approximateGamma | 35981.06423843859 | 35981.33602630633 | 0.272 | within 0.005 relative | Agree |
| 95% UCL - adjustedGamma ucl.adjustedGamma | 36763.13362973485 | 36763.464307847076 | 0.331 | within 0.005 relative | Agree |
| Distribution used distributionUsed | gamma | normal | - | exact match | Differs |
| Why these differ: This dataset sits on the 1% Shapiro-Wilk critical value of 0.814. The toolkit's W (Royston's AS R94, the algorithm R implements) is 0.8198, a pass; ProUCL's W, which is not AS R94, falls just below the cutoff, a fail. Lilliefors fails in both. ProUCL 5.2 takes the normal branch when either test passes, so the toolkit calls the sample approximately normal and suggests Student's t, where ProUCL goes on to gamma and the adjusted gamma UCL. The decision rules agree; the Shapiro-Wilk statistics do not, and this is the one dataset in the 1,015-dataset sweep where that changes the answer. | |||||
| Recommended method recommendedMethod | adjustedGamma | studentT | - | exact match | Differs |
| Why these differ: This dataset sits on the 1% Shapiro-Wilk critical value of 0.814. The toolkit's W (Royston's AS R94, the algorithm R implements) is 0.8198, a pass; ProUCL's W, which is not AS R94, falls just below the cutoff, a fail. Lilliefors fails in both. ProUCL 5.2 takes the normal branch when either test passes, so the toolkit calls the sample approximately normal and suggests Student's t, where ProUCL goes on to gamma and the adjusted gamma UCL. The decision rules agree; the Shapiro-Wilk statistics do not, and this is the one dataset in the 1,015-dataset sweep where that changes the answer. | |||||
| 95% UCL - Chebyshev, 95% ucl.chebyshev95 | 40723.80381921608 | 40723.80381921608 | 0 | within 0.000001 relative | Agree |
| 95% UCL - Chebyshev, 97.5% ucl.chebyshev975 | 48751.03319180349 | 48751.03319180349 | 0 | within 0.000001 relative | Agree |
| 95% UCL - Chebyshev, 99% ucl.chebyshev99 | 64518.97091696579 | 64518.97091696579 | 0 | within 0.000001 relative | Agree |
Ten uncensored results from a roughly normal population
Typical useInput
10 values
| value |
|---|
| 4.2 |
| 5.1 |
| 6.3 |
| 7.8 |
| 9.1 |
| 11.4 |
| 3.3 |
| 8.8 |
| 12.1 |
| 6.6 |
Against R EnvStats / nortest (EnvStats 3.1.0, nortest 1.0-4, R 4.6.1)
| Value | R EnvStats / nortest | EnviroAutomate | Difference | Agreement band | Verdict |
|---|---|---|---|---|---|
| Sample size (n) n | 10 | 10 | 0 | exact match | Agree |
| Mean mean | 7.47 | 7.469999999999999 | 8.88e-16 | within 0.000001 relative | Agree |
| Standard deviation sd | 2.929561969532874 | 2.9295619695328745 | 4.44e-16 | within 0.000001 relative | Agree |
| Median median | 7.199999999999999 | 7.199999999999999 | 0 | within 0.000001 relative | Agree |
| Minimum min | 3.3 | 3.3 | 0 | within 0.000001 relative | Agree |
| Maximum max | 12.1 | 12.1 | 0 | within 0.000001 relative | Agree |
| Coefficient of variation cv | 0.39217697048632855 | 0.39217697048632866 | 1.11e-16 | within 0.000001 relative | Agree |
| Skewness skewness | 0.2409653823674704 | 0.2409653823674715 | 1.11e-15 | within 0.000001 relative | Agree |
| 95% UCL - Student's t ucl.studentT | 9.168212020092708 | 9.168212020092707 | 1.78e-15 | within 0.000001 relative | Agree |
| 95% UCL - Land's H ucl.landsH | 10.20653096003897 | 10.206358905136355 | 0.000172 | within 0.02 relative | Agree |
Against USEPA ProUCL (ProUCL 5.2.0)
| Value | USEPA ProUCL | EnviroAutomate | Difference | Agreement band | Verdict |
|---|---|---|---|---|---|
| Sample size (n) n | 10 | 10 | 0 | exact match | Agree |
| Mean mean | 7.469999999999998 | 7.469999999999999 | 8.88e-16 | within 0.000001 relative | Agree |
| Standard deviation sd | 2.9295619695328745 | 2.9295619695328745 | 0 | within 0.000001 relative | Agree |
| Skewness skewness | 0.2409653823674716 | 0.2409653823674715 | 8.33e-17 | within 0.000001 relative | Agree |
| 95% UCL - Student's t ucl.studentT | 9.168212031863574 | 9.168212020092707 | 1.18e-8 | within 0.000001 relative | Agree |
| 95% UCL - Modified t (Johnson) ucl.modifiedT | 9.179977415532868 | 9.179977403762003 | 1.18e-8 | within 0.000001 relative | Agree |
| 95% UCL - Central limit theorem ucl.clt | 8.993806936546722 | 8.993806935634066 | 9.13e-10 | within 0.000001 relative | Agree |
| 95% UCL - Land's H ucl.landsH | 10.206358905136355 | 10.206358905136355 | 0 | within 0.02 relative | Agree |
| 95% UCL - approximateGamma ucl.approximateGamma | 9.64113803717746 | 9.641139646958198 | 1.61e-6 | within 0.005 relative | Agree |
| 95% UCL - adjustedGamma ucl.adjustedGamma | 10.088791848337234 | 10.088794997554814 | 3.15e-6 | within 0.005 relative | Agree |
| Distribution used distributionUsed | normal | normal | - | exact match | Agree |
| Recommended method recommendedMethod | studentT | studentT | - | exact match | Agree |
| 95% UCL - Chebyshev, 95% ucl.chebyshev95 | 11.508122501031059 | 11.508122501031057 | 1.78e-15 | within 0.000001 relative | Agree |
| 95% UCL - Chebyshev, 97.5% ucl.chebyshev975 | 13.255421332971348 | 13.255421332971348 | 0 | within 0.000001 relative | Agree |
| 95% UCL - Chebyshev, 99% ucl.chebyshev99 | 16.68765154472656 | 16.68765154472656 | 0 | within 0.000001 relative | Agree |
Three non-detects fitted by robust ROS
Special caseInput
10 values
| value | non-detect | reporting limit |
|---|---|---|
| 1 | no | |
| 2.4 | no | |
| 0.5 | yes | 0.5 |
| 3.1 | no | |
| 0.5 | yes | 0.5 |
| 4.7 | no | |
| 0.5 | yes | 0.5 |
| 2.2 | no | |
| 5.9 | no | |
| 3.3 | no |
Settings: nonDetectMethod = robustRos
Against R NADA (NADA 1.6.1.2, R 4.6.1)
| Value | R NADA | EnviroAutomate | Difference | Agreement band | Verdict |
|---|---|---|---|---|---|
| Sample size (n) n | 10 | 10 | 0 | exact match | Agree |
| Detected results nDetected | 7 | 7 | 0 | exact match | Agree |
| Non-detects nCensored | 3 | 3 | 0 | exact match | Agree |
| Mean mean | 2.468967432995583 | 2.468967432995583 | 0 | within 0.000001 relative | Agree |
| Standard deviation sd | 1.813286650968749 | 1.813286650968749 | 0 | within 0.000001 relative | Agree |
| Median median | 2.3 | 2.3 | 0 | within 0.000001 relative | Agree |
| Minimum min | 0.47774283475044715 | 0.4777428347504473 | 1.67e-16 | within 0.000001 relative | Agree |
| Maximum max | 5.9 | 5.9 | 0 | within 0.000001 relative | Agree |
| Coefficient of variation cv | 0.734431174237361 | 0.734431174237361 | 0 | within 0.000001 relative | Agree |
| Standard error of the mean standardError | 0.5734115867840012 | 0.5734115867840012 | 0 | within 0.000001 relative | Agree |
| Fitted non-detect, result 3 ros.fitted.2 | 0.47774283475044715 | 0.4777428347504473 | 1.67e-16 | within 0.000001 relative | Agree |
| Fitted non-detect, result 5 ros.fitted.4 | 0.6994801373348627 | 0.6994801373348628 | 1.11e-16 | within 0.000001 relative | Agree |
| Fitted non-detect, result 7 ros.fitted.6 | 0.912451357870521 | 0.9124513578705212 | 2.22e-16 | within 0.000001 relative | Agree |
Three non-detects handled by Kaplan-Meier
Special caseInput
10 values
| value | non-detect | reporting limit |
|---|---|---|
| 1 | no | |
| 2.4 | no | |
| 0.5 | yes | 0.5 |
| 3.1 | no | |
| 0.5 | yes | 0.5 |
| 4.7 | no | |
| 0.5 | yes | 0.5 |
| 2.2 | no | |
| 5.9 | no | |
| 3.3 | no |
Settings: nonDetectMethod = kaplanMeier
Against USEPA ProUCL (ProUCL 5.2.0)
| Value | USEPA ProUCL | EnviroAutomate | Difference | Agreement band | Verdict |
|---|---|---|---|---|---|
| Sample size (n) n | 10 | 10 | 0 | exact match | Agree |
| Mean mean | 2.4099999999999997 | 2.41 | 4.44e-16 | within 0.000001 relative | Agree |
| Standard deviation sd | 1.7795786018043716 | 1.7795786018043713 | 2.22e-16 | within 0.000001 relative | Agree |
| Standard error of the mean standardError | 0.607841810561487 | 0.607841810561487 | 0 | within 0.000001 relative | Agree |
| 95% UCL - Chebyshev, 95% ucl.chebyshev95 | 5.059521025896315 | 5.059521025896315 | 0 | within 0.000001 relative | Agree |
| Distribution used distributionUsed | normal | normal | - | exact match | Agree |
| Recommended method recommendedMethod | studentT | studentT | - | exact match | Agree |
| 95% UCL - Student's t ucl.studentT | 3.524242691672626 | 3.524242683949444 | 7.72e-9 | within 0.000001 relative | Agree |
Approximately lognormal, widely spread logs, fifteen results - Student's t rather than Land's H
Boundary caseInput
15 values
| value |
|---|
| 0.5 |
| 0.6 |
| 0.8 |
| 1.1 |
| 1.4 |
| 2 |
| 3.5 |
| 9 |
| 28 |
| 140 |
| 0.55 |
| 0.7 |
| 1.2 |
| 2.6 |
| 55 |
Against USEPA ProUCL (ProUCL 5.2.0)
| Value | USEPA ProUCL | EnviroAutomate | Difference | Agreement band | Verdict |
|---|---|---|---|---|---|
| Sample size (n) n | 15 | 15 | 0 | exact match | Agree |
| Mean mean | 16.46333333333333 | 16.46333333333333 | 0 | within 0.000001 relative | Agree |
| Standard deviation sd | 37.27699628968182 | 37.27699628968182 | 0 | within 0.000001 relative | Agree |
| Skewness skewness | 3.031620414087312 | 3.0316204140873118 | 4.44e-16 | within 0.000001 relative | Agree |
| 95% UCL - Student's t ucl.studentT | 33.415730618268356 | 33.41573036869691 | 2.50e-7 | within 0.000001 relative | Agree |
| 95% UCL - Modified t (Johnson) ucl.modifiedT | 34.67139398413121 | 34.67139373455976 | 2.50e-7 | within 0.000001 relative | Agree |
| 95% UCL - Central limit theorem ucl.clt | 32.29485056557386 | 32.29485055609187 | 9.48e-9 | within 0.000001 relative | Agree |
| 95% UCL - Land's H ucl.landsH | 100.35081128104522 | 100.35081128104522 | 0 | within 0.02 relative | Agree |
| 95% UCL - approximateGamma ucl.approximateGamma | 40.854265828588574 | 40.867397665755874 | 0.0131 | within 0.005 relative | Agree |
| 95% UCL - adjustedGamma ucl.adjustedGamma | 46.055002359736285 | 46.079192151367565 | 0.0242 | within 0.005 relative | Agree |
| Distribution used distributionUsed | lognormal | lognormal | - | exact match | Agree |
| Recommended method recommendedMethod | studentT | studentT | - | exact match | Agree |
| 95% UCL - Chebyshev, 95% ucl.chebyshev95 | 58.41720847833677 | 58.41720847833677 | 0 | within 0.000001 relative | Agree |
| 95% UCL - Chebyshev, 97.5% ucl.chebyshev975 | 76.57068376729 | 76.57068376729 | 0 | within 0.000001 relative | Agree |
| 95% UCL - Chebyshev, 99% ucl.chebyshev99 | 112.2296707683333 | 112.2296707683333 | 0 | within 0.000001 relative | Agree |
Against R EnvStats / nortest (EnvStats 3.1.0, nortest 1.0-4, R 4.6.1)
| Value | R EnvStats / nortest | EnviroAutomate | Difference | Agreement band | Verdict |
|---|---|---|---|---|---|
| Sample size (n) n | 15 | 15 | 0 | exact match | Agree |
| Mean mean | 16.46333333333333 | 16.46333333333333 | 0 | within 0.000001 relative | Agree |
| Standard deviation sd | 37.27699628968182 | 37.27699628968182 | 0 | within 0.000001 relative | Agree |
| Median median | 1.4 | 1.4 | 0 | within 0.000001 relative | Agree |
| Minimum min | 0.5 | 0.5 | 0 | within 0.000001 relative | Agree |
| Maximum max | 140 | 140 | 0 | within 0.000001 relative | Agree |
| Coefficient of variation cv | 2.264243548674741 | 2.264243548674741 | 0 | within 0.000001 relative | Agree |
| Skewness skewness | 3.031620414087312 | 3.0316204140873118 | 4.44e-16 | within 0.000001 relative | Agree |
| 95% UCL - Student's t ucl.studentT | 33.415730368697034 | 33.41573036869691 | 1.21e-13 | within 0.000001 relative | Agree |
| 95% UCL - Land's H ucl.landsH | 100.3635909918477 | 100.35081128104522 | 0.0128 | within 0.02 relative | Agree |
Detected results below the reporting limit - Kaplan-Meier stops matching substitution
Boundary caseInput
12 values
| value | non-detect | reporting limit |
|---|---|---|
| 0.3 | no | |
| 2.4 | no | |
| 1 | yes | 1 |
| 3.1 | no | |
| 1 | yes | 1 |
| 4.7 | no | |
| 1 | yes | 1 |
| 0.7 | no | |
| 5.9 | no | |
| 3.3 | no | |
| 1 | yes | 1 |
| 2 | no |
Settings: nonDetectMethod = kaplanMeier
Against USEPA ProUCL (ProUCL 5.2.0)
| Value | USEPA ProUCL | EnviroAutomate | Difference | Agreement band | Verdict |
|---|---|---|---|---|---|
| Sample size (n) n | 12 | 12 | 0 | exact match | Agree |
| Mean mean | 2.0333333333333337 | 2.0333333333333337 | 0 | within 0.000001 relative | Agree |
| Standard deviation sd | 1.8093890927296121 | 1.8093890927296123 | 2.22e-16 | within 0.000001 relative | Agree |
| Standard error of the mean standardError | 0.5617904107480525 | 0.5617904107480526 | 1.11e-16 | within 0.000001 relative | Agree |
| 95% UCL - Chebyshev, 95% ucl.chebyshev95 | 4.482120961234299 | 4.482120961234299 | 0 | within 0.000001 relative | Agree |
| Distribution used distributionUsed | normal | normal | - | exact match | Agree |
| Recommended method recommendedMethod | studentT | studentT | - | exact match | Agree |
| 95% UCL - Student's t ucl.studentT | 3.042244200835333 | 3.0422442032892656 | 2.45e-9 | within 0.000001 relative | Agree |
Detects that pass one normality test and both gamma tests
Boundary caseInput
45 values
| value | non-detect | reporting limit |
|---|---|---|
| 6.034 | yes | 6.034 |
| 6.034 | yes | 6.034 |
| 6.034 | yes | 6.034 |
| 6.034 | yes | 6.034 |
| 6.034 | yes | 6.034 |
| 6.034 | yes | 6.034 |
| 6.034 | yes | 6.034 |
| 6.034 | yes | 6.034 |
| 6.034 | yes | 6.034 |
| 6.034 | yes | 6.034 |
| 6.034 | yes | 6.034 |
| 6.034 | yes | 6.034 |
| 6.034 | yes | 6.034 |
| 6.034 | yes | 6.034 |
| 6.034 | yes | 6.034 |
| 6.034 | yes | 6.034 |
| 6.034 | yes | 6.034 |
| 6.034 | yes | 6.034 |
| 6.034 | yes | 6.034 |
| 6.034 | yes | 6.034 |
| 6.034 | yes | 6.034 |
| 6.034 | yes | 6.034 |
| 6.034 | yes | 6.034 |
| 6.034 | yes | 6.034 |
| 6.034 | yes | 6.034 |
| 6.034 | yes | 6.034 |
| 6.034 | yes | 6.034 |
| 6.034 | yes | 6.034 |
| 6.034 | yes | 6.034 |
| 6.034 | yes | 6.034 |
| 6.034 | yes | 6.034 |
| 6.562 | no | |
| 7.324 | no | |
| 8.935 | no | |
| 10.559 | no | |
| 14.409 | no | |
| 16.007 | no | |
| 19.919 | no | |
| 24.231 | no | |
| 27.334 | no | |
| 29.945 | no | |
| 46.548 | no | |
| 48.718 | no | |
| 58.982 | no | |
| 149.359 | no |
Settings: nonDetectMethod = kaplanMeier
Against USEPA ProUCL (ProUCL 5.2.0)
| Value | USEPA ProUCL | EnviroAutomate | Difference | Agreement band | Verdict |
|---|---|---|---|---|---|
| Sample size (n) n | 45 | 45 | 0 | exact match | Agree |
| Mean mean | 14.575244444444454 | 14.575244444444454 | 0 | within 0.000001 relative | Agree |
| Standard deviation sd | 23.699864720809952 | 23.699864720809952 | 0 | within 0.000001 relative | Agree |
| Standard error of the mean standardError | 3.666333371561908 | 3.6663333715619086 | 4.44e-16 | within 0.000001 relative | Agree |
| 95% UCL - Chebyshev, 95% ucl.chebyshev95 | 30.556421104413563 | 30.556421104413566 | 3.55e-15 | within 0.000001 relative | Agree |
| Distribution used distributionUsed | normal | normal | - | exact match | Agree |
| Recommended method recommendedMethod | studentT | studentT | - | exact match | Agree |
| 95% UCL - Student's t ucl.studentT | 20.73552780591255 | 20.735527679450723 | 1.26e-7 | within 0.000001 relative | Agree |
Drawn from a gamma distribution near a branch threshold, n = 10: ProUCL 5.2 finds gamma and suggests adjusted gamma
Boundary caseInput
10 values
| value |
|---|
| 6.107 |
| 0.005058 |
| 296.7 |
| 40.51 |
| 506.4 |
| 5.669 |
| 40.74 |
| 94.97 |
| 14.02 |
| 88.34 |
Against USEPA ProUCL (ProUCL 5.2.0)
| Value | USEPA ProUCL | EnviroAutomate | Difference | Agreement band | Verdict |
|---|---|---|---|---|---|
| Sample size (n) n | 10 | 10 | 0 | exact match | Agree |
| Mean mean | 109.34610579999998 | 109.34610579999999 | 1.42e-14 | within 0.000001 relative | Agree |
| Standard deviation sd | 165.09128757526693 | 165.09128757526693 | 0 | within 0.000001 relative | Agree |
| Skewness skewness | 1.9792904746684692 | 1.9792904746684685 | 6.66e-16 | within 0.000001 relative | Agree |
| 95% UCL - Student's t ucl.studentT | 205.04642340102063 | 205.04642273769025 | 6.63e-7 | within 0.000001 relative | Agree |
| 95% UCL - Modified t (Johnson) ucl.modifiedT | 210.49248361682862 | 210.49248295349824 | 6.63e-7 | within 0.000001 relative | Agree |
| 95% UCL - Central limit theorem ucl.clt | 195.21807293600654 | 195.21807288457512 | 5.14e-8 | within 0.000001 relative | Agree |
| 95% UCL - Land's H ucl.landsH | 36018082.80694275 | 36018082.80694275 | 0 | within 0.02 relative | Agree |
| 95% UCL - approximateGamma ucl.approximateGamma | 369.5747360513123 | 370.2651335527028 | 0.69 | within 0.005 relative | Agree |
| 95% UCL - adjustedGamma ucl.adjustedGamma | 467.0071607615869 | 468.76955931352165 | 1.76 | within 0.005 relative | Agree |
| Distribution used distributionUsed | gamma | gamma | - | exact match | Agree |
| Recommended method recommendedMethod | adjustedGamma | adjustedGamma | - | exact match | Agree |
| 95% UCL - Chebyshev, 95% ucl.chebyshev95 | 336.90874144828246 | 336.90874144828246 | 0 | within 0.000001 relative | Agree |
| 95% UCL - Chebyshev, 97.5% ucl.chebyshev975 | 435.3752756755065 | 435.3752756755065 | 0 | within 0.000001 relative | Agree |
| 95% UCL - Chebyshev, 99% ucl.chebyshev99 | 628.7937152942287 | 628.7937152942287 | 0 | within 0.000001 relative | Agree |
Drawn from a gamma distribution near a branch threshold, n = 10: ProUCL 5.2 finds normal and suggests Student's t
Boundary caseInput
10 values
| value |
|---|
| 29.32 |
| 15 |
| 38.86 |
| 33.3 |
| 50.25 |
| 65.26 |
| 15.55 |
| 2.52 |
| 6.565 |
| 37.11 |
Against USEPA ProUCL (ProUCL 5.2.0)
| Value | USEPA ProUCL | EnviroAutomate | Difference | Agreement band | Verdict |
|---|---|---|---|---|---|
| Sample size (n) n | 10 | 10 | 0 | exact match | Agree |
| Mean mean | 29.373500000000007 | 29.373500000000007 | 0 | within 0.000001 relative | Agree |
| Standard deviation sd | 19.79888128854198 | 19.79888128854198 | 0 | within 0.000001 relative | Agree |
| Skewness skewness | 0.35524470192751756 | 0.3552447019275175 | 5.55e-17 | within 0.000001 relative | Agree |
| 95% UCL - Student's t ucl.studentT | 40.85053949304128 | 40.85053941349015 | 7.96e-8 | within 0.000001 relative | Agree |
| 95% UCL - Modified t (Johnson) ucl.modifiedT | 40.96776362107206 | 40.96776354152092 | 7.96e-8 | within 0.000001 relative | Agree |
| 95% UCL - Central limit theorem ucl.clt | 39.67185619014266 | 39.671856183974654 | 6.17e-9 | within 0.000001 relative | Agree |
| 95% UCL - Land's H ucl.landsH | 99.90525949977621 | 99.90525949977621 | 0 | within 0.02 relative | Agree |
| 95% UCL - approximateGamma ucl.approximateGamma | 50.46369924181273 | 50.46443824153183 | 0.000739 | within 0.005 relative | Agree |
| 95% UCL - adjustedGamma ucl.adjustedGamma | 55.69547972205567 | 55.69703230225066 | 0.00155 | within 0.005 relative | Agree |
| Distribution used distributionUsed | normal | normal | - | exact match | Agree |
| Recommended method recommendedMethod | studentT | studentT | - | exact match | Agree |
| 95% UCL - Chebyshev, 95% ucl.chebyshev95 | 56.664374491810946 | 56.664374491810946 | 0 | within 0.000001 relative | Agree |
| 95% UCL - Chebyshev, 97.5% ucl.chebyshev975 | 68.47315768498916 | 68.47315768498916 | 0 | within 0.000001 relative | Agree |
| 95% UCL - Chebyshev, 99% ucl.chebyshev99 | 91.66922563787983 | 91.66922563787983 | 0 | within 0.000001 relative | Agree |
Drawn from a gamma distribution near a branch threshold, n = 50: ProUCL 5.2 finds gamma and suggests adjusted gamma
Boundary caseInput
50 values
| value |
|---|
| 58.74 |
| 33.15 |
| 0.01844 |
| 86.6 |
| 0.06581 |
| 3.188 |
| 424.3 |
| 0.08352 |
| 4.947 |
| 81.32 |
| 108.9 |
| 13.86 |
| 18.55 |
| 20.21 |
| 94.42 |
| 2.552 |
| 33.07 |
| 202.7 |
| 28.87 |
| 35.6 |
| 38.98 |
| 52.54 |
| 2.653 |
| 2.595 |
| 0.9881 |
| 106.8 |
| 8.705 |
| 43.87 |
| 8.174 |
| 16.09 |
| 2.324 |
| 9.838 |
| 1.587 |
| 6.38 |
| 10.34 |
| 31.98 |
| 39.57 |
| 14.91 |
| 0.2011 |
| 1.626 |
| 10.73 |
| 86.75 |
| 8.342 |
| 62.36 |
| 83.97 |
| 94.91 |
| 0.3398 |
| 37.29 |
| 45.19 |
| 0.7468 |
Against USEPA ProUCL (ProUCL 5.2.0)
| Value | USEPA ProUCL | EnviroAutomate | Difference | Agreement band | Verdict |
|---|---|---|---|---|---|
| Sample size (n) n | 50 | 50 | 0 | exact match | Agree |
| Mean mean | 41.638491399999985 | 41.638491399999985 | 0 | within 0.000001 relative | Agree |
| Standard deviation sd | 68.54613313514741 | 68.54613313514741 | 0 | within 0.000001 relative | Agree |
| Skewness skewness | 3.9689290653050033 | 3.9689290653050033 | 0 | within 0.000001 relative | Agree |
| 95% UCL - Student's t ucl.studentT | 57.89078544016254 | 57.89078649189286 | 1.05e-6 | within 0.000001 relative | Agree |
| 95% UCL - Modified t (Johnson) ucl.modifiedT | 58.79763457387705 | 58.79763562560737 | 1.05e-6 | within 0.000001 relative | Agree |
| 95% UCL - Central limit theorem ucl.clt | 57.583516786290154 | 57.583516776740176 | 9.55e-9 | within 0.000001 relative | Agree |
| 95% UCL - Land's H ucl.landsH | 397.2096149613544 | 397.209614961354 | 3.98e-13 | within 0.02 relative | Agree |
| 95% UCL - approximateGamma ucl.approximateGamma | 60.7438530196248 | 60.74395770617043 | 0.000105 | within 0.005 relative | Agree |
| 95% UCL - adjustedGamma ucl.adjustedGamma | 61.43798166364458 | 61.43810102430037 | 0.000119 | within 0.005 relative | Agree |
| Distribution used distributionUsed | gamma | gamma | - | exact match | Agree |
| Recommended method recommendedMethod | adjustedGamma | adjustedGamma | - | exact match | Agree |
| 95% UCL - Chebyshev, 95% ucl.chebyshev95 | 83.89316569476783 | 83.89316569476782 | 1.42e-14 | within 0.000001 relative | Agree |
| 95% UCL - Chebyshev, 97.5% ucl.chebyshev975 | 102.1767970161093 | 102.1767970161093 | 0 | within 0.000001 relative | Agree |
| 95% UCL - Chebyshev, 99% ucl.chebyshev99 | 138.09145033961508 | 138.09145033961508 | 0 | within 0.000001 relative | Agree |
Drawn from a gamma distribution near a branch threshold, n = 50: ProUCL 5.2 finds gamma and suggests approximate gamma
Boundary caseInput
50 values
| value |
|---|
| 23.04 |
| 3.5 |
| 1.613 |
| 9.083 |
| 30.02 |
| 57.84 |
| 65.66 |
| 7.262 |
| 28.1 |
| 0.1291 |
| 199.9 |
| 0.207 |
| 93.93 |
| 1.222 |
| 29.51 |
| 32.28 |
| 17.49 |
| 54.36 |
| 1.861 |
| 1.545 |
| 15.33 |
| 0.5503 |
| 10.56 |
| 92.2 |
| 8.491 |
| 18.47 |
| 98.38 |
| 8.266 |
| 40.96 |
| 1.613 |
| 7.45 |
| 24.17 |
| 85.43 |
| 29.02 |
| 308.8 |
| 102.4 |
| 47.71 |
| 8.298 |
| 39.31 |
| 47.43 |
| 57.51 |
| 28.62 |
| 4.606 |
| 89.39 |
| 72.35 |
| 5.602 |
| 5.972 |
| 13.39 |
| 0.06922 |
| 61.06 |
Against USEPA ProUCL (ProUCL 5.2.0)
| Value | USEPA ProUCL | EnviroAutomate | Difference | Agreement band | Verdict |
|---|---|---|---|---|---|
| Sample size (n) n | 50 | 50 | 0 | exact match | Agree |
| Mean mean | 39.83919240000001 | 39.83919240000001 | 0 | within 0.000001 relative | Agree |
| Standard deviation sd | 54.85293225081222 | 54.85293225081222 | 0 | within 0.000001 relative | Agree |
| Skewness skewness | 3.041370163581544 | 3.0413701635815436 | 4.44e-16 | within 0.000001 relative | Agree |
| 95% UCL - Student's t ucl.studentT | 52.844827337096135 | 52.84482817872629 | 8.42e-7 | within 0.000001 relative | Agree |
| 95% UCL - Modified t (Johnson) ucl.modifiedT | 53.4009209088714 | 53.40092175050155 | 8.42e-7 | within 0.000001 relative | Agree |
| 95% UCL - Central limit theorem ucl.clt | 52.59894057612554 | 52.59894056848333 | 7.64e-9 | within 0.000001 relative | Agree |
| 95% UCL - Land's H ucl.landsH | 198.62311692945698 | 198.62311692945715 | 1.71e-13 | within 0.02 relative | Agree |
| 95% UCL - approximateGamma ucl.approximateGamma | 55.80925382574574 | 55.809302744936986 | 4.89e-5 | within 0.005 relative | Agree |
| 95% UCL - adjustedGamma ucl.adjustedGamma | 56.37670995938386 | 56.376765651275605 | 5.57e-5 | within 0.005 relative | Agree |
| Distribution used distributionUsed | gamma | gamma | - | exact match | Agree |
| Recommended method recommendedMethod | approximateGamma | approximateGamma | - | exact match | Agree |
| 95% UCL - Chebyshev, 95% ucl.chebyshev95 | 73.65281076708153 | 73.65281076708153 | 0 | within 0.000001 relative | Agree |
| 95% UCL - Chebyshev, 97.5% ucl.chebyshev975 | 88.2839904456056 | 88.2839904456056 | 0 | within 0.000001 relative | Agree |
| 95% UCL - Chebyshev, 99% ucl.chebyshev99 | 117.02410977052094 | 117.02410977052094 | 0 | within 0.000001 relative | Agree |
Drawn from a gamma distribution near a branch threshold, n = 50: ProUCL 5.2 finds lognormal and suggests Land's H
Boundary caseInput
50 values
| value |
|---|
| 5.453 |
| 209.2 |
| 10.72 |
| 5.244 |
| 20.35 |
| 4.319 |
| 116.6 |
| 4.694 |
| 0.9773 |
| 99.27 |
| 141.3 |
| 178 |
| 2.728 |
| 21.4 |
| 20.52 |
| 30.9 |
| 4.47 |
| 18.41 |
| 0.2865 |
| 102.9 |
| 0.622 |
| 80.79 |
| 10.31 |
| 9.807 |
| 51.6 |
| 25 |
| 32.97 |
| 74.81 |
| 6.603 |
| 497.5 |
| 25.73 |
| 186.9 |
| 30.22 |
| 2.026 |
| 32.79 |
| 0.6704 |
| 220.8 |
| 5.014 |
| 7.016 |
| 73.28 |
| 25.32 |
| 3.184 |
| 10.89 |
| 2.854 |
| 3.828 |
| 27.69 |
| 1.217 |
| 20.41 |
| 4.521 |
| 349.9 |
Against USEPA ProUCL (ProUCL 5.2.0)
| Value | USEPA ProUCL | EnviroAutomate | Difference | Agreement band | Verdict |
|---|---|---|---|---|---|
| Sample size (n) n | 50 | 50 | 0 | exact match | Agree |
| Mean mean | 56.44028400000001 | 56.44028400000002 | 7.11e-15 | within 0.000001 relative | Agree |
| Standard deviation sd | 96.2000520721641 | 96.2000520721641 | 0 | within 0.000001 relative | Agree |
| Skewness skewness | 2.877053156621127 | 2.8770531566211273 | 4.44e-16 | within 0.000001 relative | Agree |
| 95% UCL - Student's t ucl.studentT | 79.24932458983426 | 79.24932606586957 | 1.48e-6 | within 0.000001 relative | Agree |
| 95% UCL - Modified t (Johnson) ucl.modifiedT | 80.17190013477205 | 80.17190161080735 | 1.48e-6 | within 0.000001 relative | Agree |
| 95% UCL - Central limit theorem ucl.clt | 78.81809296303501 | 78.81809294963224 | 1.34e-8 | within 0.000001 relative | Agree |
| 95% UCL - Land's H ucl.landsH | 173.6675532526276 | 173.6675532526276 | 0 | within 0.02 relative | Agree |
| 95% UCL - approximateGamma ucl.approximateGamma | 81.66071923973148 | 81.66084263959212 | 0.000123 | within 0.005 relative | Agree |
| 95% UCL - adjustedGamma ucl.adjustedGamma | 82.57288819720142 | 82.57302885056778 | 0.000141 | within 0.005 relative | Agree |
| Distribution used distributionUsed | lognormal | lognormal | - | exact match | Agree |
| Recommended method recommendedMethod | landsH | landsH | - | exact match | Agree |
| 95% UCL - Chebyshev, 95% ucl.chebyshev95 | 115.7419788079993 | 115.74197880799929 | 1.42e-14 | within 0.000001 relative | Agree |
| 95% UCL - Chebyshev, 97.5% ucl.chebyshev975 | 141.40186952296398 | 141.40186952296398 | 0 | within 0.000001 relative | Agree |
| 95% UCL - Chebyshev, 99% ucl.chebyshev99 | 191.80575610053387 | 191.80575610053387 | 0 | within 0.000001 relative | Agree |
Drawn from a gamma distribution near a branch threshold, n = 50: ProUCL 5.2 finds normal and suggests Student's t
Boundary caseInput
50 values
| value |
|---|
| 1.723 |
| 47.98 |
| 54.86 |
| 70.66 |
| 14.79 |
| 14.13 |
| 1.555 |
| 1.999 |
| 4.413 |
| 27.17 |
| 43.96 |
| 11.75 |
| 4.313 |
| 1.883 |
| 1.162 |
| 25.8 |
| 11.45 |
| 3.608 |
| 42.19 |
| 25.9 |
| 56.28 |
| 11.59 |
| 1.788 |
| 35.6 |
| 22.76 |
| 76.99 |
| 99.42 |
| 1.923 |
| 40.62 |
| 74.85 |
| 101.9 |
| 25.43 |
| 1.338 |
| 50.31 |
| 8.764 |
| 46.26 |
| 7.191 |
| 89.08 |
| 31.16 |
| 43.65 |
| 64.27 |
| 104.9 |
| 45.13 |
| 48.31 |
| 23.58 |
| 22.98 |
| 10.15 |
| 41.47 |
| 29.85 |
| 63.41 |
Against USEPA ProUCL (ProUCL 5.2.0)
| Value | USEPA ProUCL | EnviroAutomate | Difference | Agreement band | Verdict |
|---|---|---|---|---|---|
| Sample size (n) n | 50 | 50 | 0 | exact match | Agree |
| Mean mean | 33.845000000000006 | 33.845000000000006 | 0 | within 0.000001 relative | Agree |
| Standard deviation sd | 29.17082006990925 | 29.17082006990925 | 0 | within 0.000001 relative | Agree |
| Skewness skewness | 0.8293562864683917 | 0.8293562864683915 | 1.11e-16 | within 0.000001 relative | Agree |
| 95% UCL - Student's t ucl.studentT | 40.761403938266035 | 40.76140438584541 | 4.48e-7 | within 0.000001 relative | Agree |
| 95% UCL - Modified t (Johnson) ucl.modifiedT | 40.84204728162075 | 40.84204772920013 | 4.48e-7 | within 0.000001 relative | Agree |
| 95% UCL - Central limit theorem ucl.clt | 40.63064122116917 | 40.63064121710504 | 4.06e-9 | within 0.000001 relative | Agree |
| 95% UCL - Land's H ucl.landsH | 77.27698109269389 | 77.27698109269389 | 0 | within 0.02 relative | Agree |
| 95% UCL - approximateGamma ucl.approximateGamma | 43.951287294637126 | 43.95129574288904 | 8.45e-6 | within 0.005 relative | Agree |
| 95% UCL - adjustedGamma ucl.adjustedGamma | 44.295685452007206 | 44.295695043480016 | 9.59e-6 | within 0.005 relative | Agree |
| Distribution used distributionUsed | normal | normal | - | exact match | Agree |
| Recommended method recommendedMethod | studentT | studentT | - | exact match | Agree |
| 95% UCL - Chebyshev, 95% ucl.chebyshev95 | 51.8271011717037 | 51.8271011717037 | 0 | within 0.000001 relative | Agree |
| 95% UCL - Chebyshev, 97.5% ucl.chebyshev975 | 59.60797071321154 | 59.60797071321154 | 0 | within 0.000001 relative | Agree |
| 95% UCL - Chebyshev, 99% ucl.chebyshev99 | 74.89198225486278 | 74.89198225486277 | 1.42e-14 | within 0.000001 relative | Agree |
Drawn from a gamma distribution near a branch threshold, n = 51: ProUCL 5.2 finds gamma and suggests adjusted gamma
Boundary caseInput
51 values
| value |
|---|
| 10.68 |
| 3.718 |
| 5.896 |
| 0.7645 |
| 43.8 |
| 86.59 |
| 69.18 |
| 11.86 |
| 212.7 |
| 8.258 |
| 122.9 |
| 37.69 |
| 0.1234 |
| 1.732 |
| 110.6 |
| 67.57 |
| 1.247 |
| 1.4 |
| 0.09506 |
| 1.941 |
| 1.577 |
| 24.56 |
| 65.49 |
| 0.2527 |
| 48.68 |
| 8.086 |
| 9.299 |
| 77.69 |
| 9.554 |
| 5.154 |
| 49.96 |
| 441.6 |
| 213.5 |
| 125.8 |
| 2.451 |
| 177.7 |
| 33.34 |
| 0.1424 |
| 41.29 |
| 8.661 |
| 50.42 |
| 0.1226 |
| 101.1 |
| 10.97 |
| 6.04 |
| 0.8382 |
| 53.25 |
| 35.87 |
| 52.09 |
| 9.05 |
| 37.48 |
Against USEPA ProUCL (ProUCL 5.2.0)
| Value | USEPA ProUCL | EnviroAutomate | Difference | Agreement band | Verdict |
|---|---|---|---|---|---|
| Sample size (n) n | 51 | 51 | 0 | exact match | Agree |
| Mean mean | 49.03456588235296 | 49.03456588235296 | 0 | within 0.000001 relative | Agree |
| Standard deviation sd | 77.2951801152507 | 77.2951801152507 | 0 | within 0.000001 relative | Agree |
| Skewness skewness | 3.1745423604345366 | 3.1745423604345357 | 8.88e-16 | within 0.000001 relative | Agree |
| 95% UCL - Student's t ucl.studentT | 67.17370863279871 | 67.1737073821449 | 1.25e-6 | within 0.000001 relative | Agree |
| 95% UCL - Modified t (Johnson) ucl.modifiedT | 67.97559367702512 | 67.97559242637132 | 1.25e-6 | within 0.000001 relative | Agree |
| 95% UCL - Central limit theorem ucl.clt | 66.83762289072892 | 66.8376228800661 | 1.07e-8 | within 0.000001 relative | Agree |
| 95% UCL - Land's H ucl.landsH | 394.534317695227 | 394.534317695227 | 0 | within 0.02 relative | Agree |
| 95% UCL - approximateGamma ucl.approximateGamma | 71.99543144993368 | 71.99556865263267 | 0.000137 | within 0.005 relative | Agree |
| 95% UCL - adjustedGamma ucl.adjustedGamma | 72.8153667867859 | 72.81552285018496 | 0.000156 | within 0.005 relative | Agree |
| Distribution used distributionUsed | gamma | gamma | - | exact match | Agree |
| Recommended method recommendedMethod | adjustedGamma | adjustedGamma | - | exact match | Agree |
| 95% UCL - Chebyshev, 95% ucl.chebyshev95 | 96.21306557837222 | 96.21306557837222 | 0 | within 0.000001 relative | Agree |
| 95% UCL - Chebyshev, 97.5% ucl.chebyshev975 | 116.62724008409901 | 116.62724008409901 | 0 | within 0.000001 relative | Agree |
| 95% UCL - Chebyshev, 99% ucl.chebyshev99 | 156.72693293903748 | 156.72693293903748 | 0 | within 0.000001 relative | Agree |
Drawn from a gamma distribution near a branch threshold, n = 51: ProUCL 5.2 finds gamma and suggests approximate gamma
Boundary caseInput
51 values
| value |
|---|
| 88.41 |
| 11.73 |
| 15.84 |
| 99.64 |
| 70.18 |
| 1.793 |
| 3.581 |
| 178.9 |
| 19.32 |
| 2.445 |
| 27.03 |
| 9.123 |
| 91.51 |
| 67.43 |
| 10.62 |
| 9.757 |
| 3.013 |
| 0.3937 |
| 1.26 |
| 132.3 |
| 3.002 |
| 113.5 |
| 9.872 |
| 0.524 |
| 96.33 |
| 18.47 |
| 52.3 |
| 4.105 |
| 6.68 |
| 8.309 |
| 67.08 |
| 34.21 |
| 6.092 |
| 119 |
| 14.83 |
| 0.1039 |
| 8.394 |
| 0.085 |
| 36.84 |
| 19.89 |
| 0.5136 |
| 0.1733 |
| 26.84 |
| 40.21 |
| 9.114 |
| 37.41 |
| 21.52 |
| 17 |
| 78.91 |
| 6.879 |
| 6.377 |
Against USEPA ProUCL (ProUCL 5.2.0)
| Value | USEPA ProUCL | EnviroAutomate | Difference | Agreement band | Verdict |
|---|---|---|---|---|---|
| Sample size (n) n | 51 | 51 | 0 | exact match | Agree |
| Mean mean | 33.506656862745096 | 33.506656862745096 | 0 | within 0.000001 relative | Agree |
| Standard deviation sd | 41.93608524784952 | 41.93608524784952 | 0 | within 0.000001 relative | Agree |
| Skewness skewness | 1.5972643323941347 | 1.5972643323941345 | 2.22e-16 | within 0.000001 relative | Agree |
| 95% UCL - Student's t ucl.studentT | 43.34795143727598 | 43.347950758740474 | 6.79e-7 | within 0.000001 relative | Agree |
| 95% UCL - Modified t (Johnson) ucl.modifiedT | 43.56685017324536 | 43.56684949470985 | 6.79e-7 | within 0.000001 relative | Agree |
| 95% UCL - Central limit theorem ucl.clt | 43.16560992116838 | 43.16560991538333 | 5.79e-9 | within 0.000001 relative | Agree |
| 95% UCL - Land's H ucl.landsH | 165.95405541916145 | 165.95405541916145 | 0 | within 0.02 relative | Agree |
| 95% UCL - approximateGamma ucl.approximateGamma | 47.1296400105398 | 47.129684380626195 | 4.44e-5 | within 0.005 relative | Agree |
| 95% UCL - adjustedGamma ucl.adjustedGamma | 47.60481539707166 | 47.604865787201675 | 5.04e-5 | within 0.005 relative | Agree |
| Distribution used distributionUsed | gamma | gamma | - | exact match | Agree |
| Recommended method recommendedMethod | approximateGamma | approximateGamma | - | exact match | Agree |
| 95% UCL - Chebyshev, 95% ucl.chebyshev95 | 59.103098738783146 | 59.103098738783146 | 0 | within 0.000001 relative | Agree |
| 95% UCL - Chebyshev, 97.5% ucl.chebyshev975 | 70.1786995855651 | 70.1786995855651 | 0 | within 0.000001 relative | Agree |
| 95% UCL - Chebyshev, 99% ucl.chebyshev99 | 91.93457279098233 | 91.93457279098234 | 1.42e-14 | within 0.000001 relative | Agree |
Drawn from a gamma distribution near a branch threshold, n = 51: ProUCL 5.2 finds no discernible distribution and suggests Student's t
Boundary caseInput
51 values
| value |
|---|
| 0.05451 |
| 71.11 |
| 4.056 |
| 0.5023 |
| 729.6 |
| 3.238 |
| 1.895 |
| 0.6008 |
| 51.8 |
| 9.621 |
| 8.647 |
| 5.347 |
| 120.9 |
| 0.2639 |
| 5.463 |
| 52.36 |
| 21.53 |
| 0.1143 |
| 15.83 |
| 5.238 |
| 1.927 |
| 0.9039 |
| 0.71 |
| 94.24 |
| 57.69 |
| 0.8354 |
| 0.0132 |
| 153.3 |
| 4.145 |
| 2.869 |
| 15.56 |
| 21.54 |
| 3.482 |
| 1.828 |
| 94.46 |
| 1.534 |
| 3.182 |
| 1.654 |
| 4.395 |
| 22.36 |
| 28.88 |
| 88.23 |
| 3.746 |
| 0.0001 |
| 0.6791 |
| 65.42 |
| 0.01104 |
| 15.83 |
| 8.874 |
| 13.87 |
| 2.242 |
Against USEPA ProUCL (ProUCL 5.2.0)
| Value | USEPA ProUCL | EnviroAutomate | Difference | Agreement band | Verdict |
|---|---|---|---|---|---|
| Sample size (n) n | 51 | 51 | 0 | exact match | Agree |
| Mean mean | 35.7368931372549 | 35.7368931372549 | 0 | within 0.000001 relative | Agree |
| Standard deviation sd | 105.13222715580594 | 105.13222715580594 | 0 | within 0.000001 relative | Agree |
| Skewness skewness | 6.014226981351441 | 6.014226981351437 | 3.55e-15 | within 0.000001 relative | Agree |
| 95% UCL - Student's t ucl.studentT | 60.40865757596913 | 60.40865587490549 | 1.70e-6 | within 0.000001 relative | Agree |
| 95% UCL - Modified t (Johnson) ucl.modifiedT | 62.47496174972736 | 62.47496004866372 | 1.70e-6 | within 0.000001 relative | Agree |
| 95% UCL - Central limit theorem ucl.clt | 59.95153408487403 | 59.95153407037111 | 1.45e-8 | within 0.000001 relative | Agree |
| 95% UCL - Land's H ucl.landsH | 1127.288349694845 | 1127.288349694845 | 0 | within 0.02 relative | Agree |
| 95% UCL - approximateGamma ucl.approximateGamma | 57.04708237257521 | 57.04743320214735 | 0.000351 | within 0.005 relative | Agree |
| 95% UCL - adjustedGamma ucl.adjustedGamma | 57.84348551059975 | 57.84388582907591 | 0.0004 | within 0.005 relative | Agree |
| Distribution used distributionUsed | nonparametric | nonparametric | - | exact match | Agree |
| Recommended method recommendedMethod | studentT | studentT | - | exact match | Agree |
| 95% UCL - Chebyshev, 95% ucl.chebyshev95 | 99.90623383245037 | 99.90623383245034 | 2.84e-14 | within 0.000001 relative | Agree |
| 95% UCL - Chebyshev, 97.5% ucl.chebyshev975 | 127.67235881119115 | 127.67235881119112 | 2.84e-14 | within 0.000001 relative | Agree |
| 95% UCL - Chebyshev, 99% ucl.chebyshev99 | 182.21353475278974 | 182.2135347527897 | 2.84e-14 | within 0.000001 relative | Agree |
Drawn from a gamma distribution near a branch threshold, n = 55: ProUCL 5.2 finds lognormal and suggests Land's H
Boundary caseInput
55 values
| value |
|---|
| 9.537 |
| 49.64 |
| 83 |
| 6.337 |
| 228.9 |
| 23.66 |
| 8.748 |
| 1.269 |
| 11.93 |
| 8.03 |
| 20.68 |
| 8.519 |
| 2.564 |
| 8.013 |
| 61.96 |
| 246.4 |
| 0.2848 |
| 62.68 |
| 1.525 |
| 1.624 |
| 8.761 |
| 30.58 |
| 11.33 |
| 24.94 |
| 0.01802 |
| 150.7 |
| 149.9 |
| 0.9834 |
| 1.494 |
| 4.657 |
| 0.2857 |
| 53.63 |
| 199.9 |
| 1.316 |
| 4.797 |
| 1.066 |
| 30.72 |
| 100.3 |
| 4.132 |
| 1.448 |
| 5.743 |
| 3.112 |
| 38.16 |
| 0.737 |
| 0.0007173 |
| 0.2293 |
| 12.02 |
| 11.48 |
| 2.833 |
| 0.9658 |
| 1.822 |
| 6.118 |
| 9.25 |
| 913.3 |
| 22.76 |
Against USEPA ProUCL (ProUCL 5.2.0)
| Value | USEPA ProUCL | EnviroAutomate | Difference | Agreement band | Verdict |
|---|---|---|---|---|---|
| Sample size (n) n | 55 | 55 | 0 | exact match | Agree |
| Mean mean | 48.268904314545466 | 48.268904314545466 | 0 | within 0.000001 relative | Agree |
| Standard deviation sd | 132.0098144375724 | 132.0098144375724 | 0 | within 0.000001 relative | Agree |
| Skewness skewness | 5.543400576807638 | 5.54340057680764 | 1.78e-15 | within 0.000001 relative | Agree |
| 95% UCL - Student's t ucl.studentT | 78.05869193468833 | 78.05869393804176 | 2.00e-6 | within 0.000001 relative | Agree |
| 95% UCL - Modified t (Johnson) ucl.modifiedT | 80.27621703013531 | 80.27621903348876 | 2.00e-6 | within 0.000001 relative | Agree |
| 95% UCL - Central limit theorem ucl.clt | 77.54762744725346 | 77.54762742971752 | 1.75e-8 | within 0.000001 relative | Agree |
| 95% UCL - Land's H ucl.landsH | 519.6221208679337 | 519.6221208679337 | 0 | within 0.02 relative | Agree |
| 95% UCL - approximateGamma ucl.approximateGamma | 73.97304143810909 | 73.97330586150133 | 0.000264 | within 0.005 relative | Agree |
| 95% UCL - adjustedGamma ucl.adjustedGamma | 74.84117726631743 | 74.84147563323478 | 0.000298 | within 0.005 relative | Agree |
| Distribution used distributionUsed | lognormal | lognormal | - | exact match | Agree |
| Recommended method recommendedMethod | landsH | landsH | - | exact match | Agree |
| 95% UCL - Chebyshev, 95% ucl.chebyshev95 | 125.85817618883154 | 125.85817618883154 | 0 | within 0.000001 relative | Agree |
| 95% UCL - Chebyshev, 97.5% ucl.chebyshev975 | 159.43111610891125 | 159.43111610891125 | 0 | within 0.000001 relative | Agree |
| 95% UCL - Chebyshev, 99% ucl.chebyshev99 | 225.37865558227242 | 225.37865558227242 | 0 | within 0.000001 relative | Agree |
Drawn from a gamma distribution near a branch threshold, n = 9: not normal and under ten results, so ProUCL 5.2 makes no suggestion
Boundary caseInput
9 values
| value |
|---|
| 69.63 |
| 14.05 |
| 0.3392 |
| 3.425 |
| 4.936 |
| 14.72 |
| 0.4296 |
| 112.3 |
| 3.245 |
Against USEPA ProUCL (ProUCL 5.2.0)
| Value | USEPA ProUCL | EnviroAutomate | Difference | Agreement band | Verdict |
|---|---|---|---|---|---|
| Sample size (n) n | 9 | 9 | 0 | exact match | Agree |
| Mean mean | 24.786088888888887 | 24.786088888888887 | 0 | within 0.000001 relative | Agree |
| Standard deviation sd | 39.35651206777744 | 39.35651206777744 | 0 | within 0.000001 relative | Agree |
| Skewness skewness | 1.8495125022823238 | 1.8495125022823233 | 4.44e-16 | within 0.000001 relative | Agree |
| 95% UCL - Student's t ucl.studentT | 49.18119704995063 | 49.18119714878784 | 9.88e-8 | within 0.000001 relative | Agree |
| 95% UCL - Modified t (Johnson) ucl.modifiedT | 50.529166700239145 | 50.52916679907635 | 9.88e-8 | within 0.000001 relative | Agree |
| 95% UCL - Central limit theorem ucl.clt | 46.364656108094 | 46.36465609516992 | 1.29e-8 | within 0.000001 relative | Agree |
| 95% UCL - Land's H ucl.landsH | 2607.243588546278 | 2607.24358854628 | 2.27e-12 | within 0.02 relative | Agree |
| 95% UCL - approximateGamma ucl.approximateGamma | 81.00334170848289 | 81.13106012743992 | 0.128 | within 0.005 relative | Agree |
| 95% UCL - adjustedGamma ucl.adjustedGamma | 106.97264751864573 | 107.36126111367915 | 0.389 | within 0.005 relative | Agree |
| 95% UCL - Chebyshev, 95% ucl.chebyshev95 | 81.9697751801158 | 81.9697751801158 | 0 | within 0.000001 relative | Agree |
| 95% UCL - Chebyshev, 97.5% ucl.chebyshev975 | 106.71320191795968 | 106.71320191795968 | 0 | within 0.000001 relative | Agree |
| 95% UCL - Chebyshev, 99% ucl.chebyshev99 | 155.31687247480093 | 155.31687247480093 | 0 | within 0.000001 relative | Agree |
Drawn from a gamma distribution near a branch threshold, n = 9: ProUCL 5.2 finds normal and suggests Student's t
Boundary caseInput
9 values
| value |
|---|
| 20.82 |
| 91.9 |
| 34.68 |
| 32.25 |
| 3.135 |
| 13.58 |
| 17.7 |
| 56.38 |
| 34.53 |
Against USEPA ProUCL (ProUCL 5.2.0)
| Value | USEPA ProUCL | EnviroAutomate | Difference | Agreement band | Verdict |
|---|---|---|---|---|---|
| Sample size (n) n | 9 | 9 | 0 | exact match | Agree |
| Mean mean | 33.88611111111111 | 33.88611111111111 | 0 | within 0.000001 relative | Agree |
| Standard deviation sd | 26.61294442768615 | 26.61294442768615 | 0 | within 0.000001 relative | Agree |
| Skewness skewness | 1.3873322957697782 | 1.387332295769778 | 2.22e-16 | within 0.000001 relative | Agree |
| 95% UCL - Student's t ucl.studentT | 50.38212723875147 | 50.38212730558537 | 6.68e-8 | within 0.000001 relative | Agree |
| 95% UCL - Modified t (Johnson) ucl.modifiedT | 51.06584941078954 | 51.06584947762343 | 6.68e-8 | within 0.000001 relative | Agree |
| 95% UCL - Central limit theorem ucl.clt | 48.47757717509624 | 48.47757716635696 | 8.74e-9 | within 0.000001 relative | Agree |
| 95% UCL - Land's H ucl.landsH | 114.90658049349064 | 114.90658049349054 | 9.95e-14 | within 0.02 relative | Agree |
| 95% UCL - approximateGamma ucl.approximateGamma | 60.87572470926476 | 60.87715343843205 | 0.00143 | within 0.005 relative | Agree |
| 95% UCL - adjustedGamma ucl.adjustedGamma | 69.39120831408204 | 69.39472077768315 | 0.00351 | within 0.005 relative | Agree |
| 95% UCL - Chebyshev, 95% ucl.chebyshev95 | 72.55382289456037 | 72.55382289456037 | 0 | within 0.000001 relative | Agree |
| 95% UCL - Chebyshev, 97.5% ucl.chebyshev975 | 89.28537267190703 | 89.28537267190703 | 0 | within 0.000001 relative | Agree |
| 95% UCL - Chebyshev, 99% ucl.chebyshev99 | 122.15126234432554 | 122.15126234432554 | 0 | within 0.000001 relative | Agree |
Drawn from a gamma distribution, shape 0.2, n = 120: ProUCL 5.2 finds gamma and suggests adjusted gamma
Boundary caseInput
120 values
| value |
|---|
| 30.41 |
| 52.88 |
| 111.7 |
| 548.1 |
| 28.35 |
| 0.003838 |
| 30.87 |
| 73.17 |
| 662.8 |
| 8.971 |
| 0.2075 |
| 0.0193 |
| 2.817 |
| 8.552 |
| 23.2 |
| 111.6 |
| 43.47 |
| 0.01161 |
| 236.5 |
| 0.001 |
| 9.647 |
| 0.007327 |
| 7.479 |
| 2.267 |
| 103.4 |
| 61.51 |
| 95.74 |
| 0.004029 |
| 2.746 |
| 0.001 |
| 194.4 |
| 6.227 |
| 57.75 |
| 0.01935 |
| 0.02963 |
| 0.001 |
| 0.001 |
| 0.2975 |
| 8.17 |
| 0.02285 |
| 0.001 |
| 1.696 |
| 0.001 |
| 0.7632 |
| 158 |
| 0.002882 |
| 131.2 |
| 81.94 |
| 143.7 |
| 0.398 |
| 33.65 |
| 1.391 |
| 9.027 |
| 25.75 |
| 0.5002 |
| 46.44 |
| 14.43 |
| 11.85 |
| 4.378 |
| 0.3889 |
| 0.03745 |
| 94.63 |
| 17.09 |
| 1.767 |
| 0.9668 |
| 0.006427 |
| 35.21 |
| 26.04 |
| 3.634 |
| 41.29 |
| 41.86 |
| 0.007337 |
| 73.68 |
| 0.1853 |
| 38.13 |
| 0.001 |
| 31.15 |
| 18.2 |
| 532.1 |
| 6.111 |
| 0.03862 |
| 0.4896 |
| 1.701 |
| 334.8 |
| 38.85 |
| 1123 |
| 430.7 |
| 0.04491 |
| 0.005863 |
| 65.22 |
| 0.1004 |
| 0.003681 |
| 18.33 |
| 0.001 |
| 93.82 |
| 0.001 |
| 0.001 |
| 1.021 |
| 0.001231 |
| 486.3 |
| 1.187 |
| 0.3687 |
| 36.99 |
| 0.642 |
| 0.003463 |
| 4.009 |
| 0.8516 |
| 21.29 |
| 2.622 |
| 0.3825 |
| 0.001 |
| 140.5 |
| 0.03831 |
| 11.12 |
| 13.55 |
| 1.878 |
| 20.86 |
| 0.001 |
| 3.195 |
| 2.501 |
Against USEPA ProUCL (ProUCL 5.2.0)
| Value | USEPA ProUCL | EnviroAutomate | Difference | Agreement band | Verdict |
|---|---|---|---|---|---|
| Sample size (n) n | 120 | 120 | 0 | exact match | Agree |
| Mean mean | 58.39480256666668 | 58.394802566666684 | 7.11e-15 | within 0.000001 relative | Agree |
| Standard deviation sd | 150.6916262479509 | 150.69162624795086 | 2.84e-14 | within 0.000001 relative | Agree |
| Skewness skewness | 4.4947882967777755 | 4.494788296777777 | 1.78e-15 | within 0.000001 relative | Agree |
| 95% UCL - Student's t ucl.studentT | 81.19926938248892 | 81.19927164984614 | 2.27e-6 | within 0.000001 relative | Agree |
| 95% UCL - Modified t (Johnson) ucl.modifiedT | 82.14000126871352 | 82.14000353607072 | 2.27e-6 | within 0.000001 relative | Agree |
| 95% UCL - Central limit theorem ucl.clt | 81.02173884464482 | 81.02173883109285 | 1.36e-8 | within 0.000001 relative | Agree |
| 95% UCL - Land's H ucl.landsH | 68388.42599720192 | 68388.42599720192 | 0 | within 0.02 relative | Agree |
| 95% UCL - approximateGamma ucl.approximateGamma | 84.21694763614754 | 84.21706843599503 | 0.000121 | within 0.005 relative | Agree |
| 95% UCL - adjustedGamma ucl.adjustedGamma | 84.59466767968092 | 84.59479518029549 | 0.000128 | within 0.005 relative | Agree |
| Distribution used distributionUsed | gamma | gamma | - | exact match | Agree |
| Recommended method recommendedMethod | adjustedGamma | adjustedGamma | - | exact match | Agree |
| 95% UCL - Chebyshev, 95% ucl.chebyshev95 | 118.35669033741301 | 118.35669033741303 | 1.42e-14 | within 0.000001 relative | Agree |
| 95% UCL - Chebyshev, 97.5% ucl.chebyshev975 | 144.30224707473553 | 144.30224707473553 | 0 | within 0.000001 relative | Agree |
| 95% UCL - Chebyshev, 99% ucl.chebyshev99 | 195.26726923740722 | 195.26726923740722 | 0 | within 0.000001 relative | Agree |
Drawn from a gamma distribution, shape 0.2, n = 30: ProUCL 5.2 finds gamma and suggests adjusted gamma
Boundary caseInput
30 values
| value |
|---|
| 0.001 |
| 183.8 |
| 3.176 |
| 12.52 |
| 29.1 |
| 2.458 |
| 0.07329 |
| 1.608 |
| 37.23 |
| 0.001 |
| 81.23 |
| 5.55 |
| 82.7 |
| 0.08322 |
| 1.135 |
| 4.391 |
| 3.671 |
| 0.00278 |
| 13.29 |
| 19.67 |
| 15.59 |
| 0.001 |
| 18.23 |
| 1.283 |
| 1.286 |
| 4.297 |
| 60.8 |
| 12.89 |
| 59.37 |
| 1.327 |
Against USEPA ProUCL (ProUCL 5.2.0)
| Value | USEPA ProUCL | EnviroAutomate | Difference | Agreement band | Verdict |
|---|---|---|---|---|---|
| Sample size (n) n | 30 | 30 | 0 | exact match | Agree |
| Mean mean | 21.892142999999994 | 21.892142999999994 | 0 | within 0.000001 relative | Agree |
| Standard deviation sd | 38.89211471704392 | 38.89211471704392 | 0 | within 0.000001 relative | Agree |
| Skewness skewness | 2.92017937974936 | 2.92017937974936 | 0 | within 0.000001 relative | Agree |
| 95% UCL - Student's t ucl.studentT | 33.95712728236807 | 33.957127786415555 | 5.04e-7 | within 0.000001 relative | Agree |
| 95% UCL - Modified t (Johnson) ucl.modifiedT | 34.588082568098955 | 34.58808307214644 | 5.04e-7 | within 0.000001 relative | Agree |
| 95% UCL - Central limit theorem ucl.clt | 33.571748872331405 | 33.57174886533612 | 7.00e-9 | within 0.000001 relative | Agree |
| 95% UCL - Land's H ucl.landsH | 60533.13931826727 | 60533.13931826749 | 2.18e-10 | within 0.02 relative | Agree |
| 95% UCL - approximateGamma ucl.approximateGamma | 42.47641144041128 | 42.478489617352956 | 0.00208 | within 0.005 relative | Agree |
| 95% UCL - adjustedGamma ucl.adjustedGamma | 44.19605041149936 | 44.19878028290657 | 0.00273 | within 0.005 relative | Agree |
| Distribution used distributionUsed | gamma | gamma | - | exact match | Agree |
| Recommended method recommendedMethod | adjustedGamma | adjustedGamma | - | exact match | Agree |
| 95% UCL - Chebyshev, 95% ucl.chebyshev95 | 52.84336007682933 | 52.84336007682933 | 0 | within 0.000001 relative | Agree |
| 95% UCL - Chebyshev, 97.5% ucl.chebyshev975 | 66.23597643050996 | 66.23597643050996 | 0 | within 0.000001 relative | Agree |
| 95% UCL - Chebyshev, 99% ucl.chebyshev99 | 92.54317793679493 | 92.54317793679493 | 0 | within 0.000001 relative | Agree |
Drawn from a gamma distribution, shape 0.2, n = 49: ProUCL 5.2 finds gamma and suggests adjusted gamma
Boundary caseInput
49 values
| value |
|---|
| 17.15 |
| 158.2 |
| 22.06 |
| 0.001 |
| 166.4 |
| 0.001249 |
| 0.003595 |
| 1.432 |
| 17.19 |
| 0.1113 |
| 0.001 |
| 0.001 |
| 2.67 |
| 0.002296 |
| 23.03 |
| 12.95 |
| 1.11 |
| 13.17 |
| 18.61 |
| 0.0317 |
| 0.001 |
| 0.006713 |
| 1.37 |
| 172.9 |
| 0.03611 |
| 19.7 |
| 0.04942 |
| 23.48 |
| 0.6143 |
| 0.2734 |
| 0.1891 |
| 116.8 |
| 300 |
| 12.89 |
| 0.04766 |
| 347.2 |
| 0.2577 |
| 1.006 |
| 11.56 |
| 36.29 |
| 64.22 |
| 0.3096 |
| 0.001447 |
| 55.13 |
| 64.4 |
| 19.35 |
| 13.45 |
| 0.02295 |
| 0.09305 |
Against USEPA ProUCL (ProUCL 5.2.0)
| Value | USEPA ProUCL | EnviroAutomate | Difference | Agreement band | Verdict |
|---|---|---|---|---|---|
| Sample size (n) n | 49 | 49 | 0 | exact match | Agree |
| Mean mean | 35.01578755102042 | 35.01578755102042 | 0 | within 0.000001 relative | Agree |
| Standard deviation sd | 74.08497274322086 | 74.08497274322086 | 0 | within 0.000001 relative | Agree |
| Skewness skewness | 2.9501182769897505 | 2.9501182769897514 | 8.88e-16 | within 0.000001 relative | Agree |
| 95% UCL - Student's t ucl.studentT | 52.76680277880875 | 52.76680310160424 | 3.23e-7 | within 0.000001 relative | Agree |
| 95% UCL - Modified t (Johnson) ucl.modifiedT | 53.51020220785658 | 53.51020253065208 | 3.23e-7 | within 0.000001 relative | Agree |
| 95% UCL - Central limit theorem ucl.clt | 52.42420700705941 | 52.42420699663297 | 1.04e-8 | within 0.000001 relative | Agree |
| 95% UCL - Land's H ucl.landsH | 171837.70356024985 | 171837.70356024953 | 3.20e-10 | within 0.02 relative | Agree |
| 95% UCL - approximateGamma ucl.approximateGamma | 64.07311137757785 | 64.07491875979025 | 0.00181 | within 0.005 relative | Agree |
| 95% UCL - adjustedGamma ucl.adjustedGamma | 65.2919352518522 | 65.29402064554787 | 0.00209 | within 0.005 relative | Agree |
| Distribution used distributionUsed | gamma | gamma | - | exact match | Agree |
| Recommended method recommendedMethod | adjustedGamma | adjustedGamma | - | exact match | Agree |
| 95% UCL - Chebyshev, 95% ucl.chebyshev95 | 81.14848889711539 | 81.1484888971154 | 1.42e-14 | within 0.000001 relative | Agree |
| 95% UCL - Chebyshev, 97.5% ucl.chebyshev975 | 101.1101456214224 | 101.11014562142242 | 1.42e-14 | within 0.000001 relative | Agree |
| 95% UCL - Chebyshev, 99% ucl.chebyshev99 | 140.32095491943625 | 140.32095491943628 | 2.84e-14 | within 0.000001 relative | Agree |
Drawn from a gamma distribution, shape 0.2, n = 50: ProUCL 5.2 finds gamma and suggests adjusted gamma
Boundary caseInput
50 values
| value |
|---|
| 4.539 |
| 678.6 |
| 0.001 |
| 0.006873 |
| 18.41 |
| 49.71 |
| 65.16 |
| 0.001 |
| 38.17 |
| 47.44 |
| 0.001392 |
| 14.23 |
| 3.094 |
| 17.87 |
| 0.01548 |
| 10.38 |
| 35.2 |
| 1.015 |
| 0.002502 |
| 13.48 |
| 0.001 |
| 49.42 |
| 0.001 |
| 0.03505 |
| 0.08968 |
| 1.712 |
| 26.47 |
| 19.8 |
| 2.2 |
| 133.5 |
| 0.001 |
| 73.77 |
| 103 |
| 0.001 |
| 0.4918 |
| 251.1 |
| 32.49 |
| 7.619 |
| 0.1097 |
| 48 |
| 0.3836 |
| 71.13 |
| 0.1448 |
| 4.385 |
| 14.79 |
| 86.12 |
| 9.726 |
| 0.006241 |
| 19.93 |
| 4.252 |
Against USEPA ProUCL (ProUCL 5.2.0)
| Value | USEPA ProUCL | EnviroAutomate | Difference | Agreement band | Verdict |
|---|---|---|---|---|---|
| Sample size (n) n | 50 | 50 | 0 | exact match | Agree |
| Mean mean | 39.16010236 | 39.16010236 | 0 | within 0.000001 relative | Agree |
| Standard deviation sd | 102.39743447619917 | 102.39743447619917 | 0 | within 0.000001 relative | Agree |
| Skewness skewness | 5.361159833296691 | 5.361159833296689 | 1.78e-15 | within 0.000001 relative | Agree |
| 95% UCL - Student's t ucl.studentT | 63.4385428488938 | 63.43854442001796 | 1.57e-6 | within 0.000001 relative | Agree |
| 95% UCL - Modified t (Johnson) ucl.modifiedT | 65.26843955804856 | 65.26844112917273 | 1.57e-6 | within 0.000001 relative | Agree |
| 95% UCL - Central limit theorem ucl.clt | 62.979530496009446 | 62.97953048174324 | 1.43e-8 | within 0.000001 relative | Agree |
| 95% UCL - Land's H ucl.landsH | 410365.2317707935 | 410365.23177079356 | 5.82e-11 | within 0.02 relative | Agree |
| 95% UCL - approximateGamma ucl.approximateGamma | 69.44948455369027 | 69.45091250977681 | 0.00143 | within 0.005 relative | Agree |
| 95% UCL - adjustedGamma ucl.adjustedGamma | 70.67261924123858 | 70.67425992713983 | 0.00164 | within 0.005 relative | Agree |
| Distribution used distributionUsed | gamma | gamma | - | exact match | Agree |
| Recommended method recommendedMethod | adjustedGamma | adjustedGamma | - | exact match | Agree |
| 95% UCL - Chebyshev, 95% ucl.chebyshev95 | 102.282120255318 | 102.282120255318 | 0 | within 0.000001 relative | Agree |
| 95% UCL - Chebyshev, 97.5% ucl.chebyshev975 | 129.59506782192653 | 129.59506782192653 | 0 | within 0.000001 relative | Agree |
| 95% UCL - Chebyshev, 99% ucl.chebyshev99 | 183.24606448979543 | 183.2460644897954 | 2.84e-14 | within 0.000001 relative | Agree |
Drawn from a gamma distribution, shape 0.35, n = 8: ProUCL 5.2 finds normal and suggests Student's t
Boundary caseInput
8 values
| value |
|---|
| 0.976 |
| 11.77 |
| 2.058 |
| 0.9828 |
| 10.76 |
| 11.56 |
| 4.385 |
| 11.47 |
Against USEPA ProUCL (ProUCL 5.2.0)
| Value | USEPA ProUCL | EnviroAutomate | Difference | Agreement band | Verdict |
|---|---|---|---|---|---|
| Sample size (n) n | 8 | 8 | 0 | exact match | Agree |
| Mean mean | 6.745225 | 6.745225 | 0 | within 0.000001 relative | Agree |
| Standard deviation sd | 5.083623264042516 | 5.083623264042516 | 0 | within 0.000001 relative | Agree |
| Skewness skewness | -0.13168148249572884 | -0.13168148249572867 | 1.67e-16 | within 0.000001 relative | Agree |
| 95% UCL - Student's t ucl.studentT | 10.15041217661518 | 10.150412210986403 | 3.44e-8 | within 0.000001 relative | Agree |
| 95% UCL - Modified t (Johnson) ucl.modifiedT | 10.136465946451455 | 10.136465980822678 | 3.44e-8 | within 0.000001 relative | Agree |
| 95% UCL - Central limit theorem ucl.clt | 9.701573458040516 | 9.701573456269866 | 1.77e-9 | within 0.000001 relative | Agree |
| 95% UCL - Land's H ucl.landsH | 39.44362411140034 | 39.44362411140034 | 0 | within 0.02 relative | Agree |
| 95% UCL - approximateGamma ucl.approximateGamma | 14.112006281695837 | 14.113317315377412 | 0.00131 | within 0.005 relative | Agree |
| 95% UCL - adjustedGamma ucl.adjustedGamma | 17.27721329946848 | 17.281241414963482 | 0.00403 | within 0.005 relative | Agree |
| 95% UCL - Chebyshev, 95% ucl.chebyshev95 | 14.57961460867063 | 14.57961460867063 | 0 | within 0.000001 relative | Agree |
| 95% UCL - Chebyshev, 97.5% ucl.chebyshev975 | 17.969561250631127 | 17.969561250631127 | 0 | within 0.000001 relative | Agree |
| 95% UCL - Chebyshev, 99% ucl.chebyshev99 | 24.628455006002525 | 24.628455006002525 | 0 | within 0.000001 relative | Agree |
Drawn from a gamma distribution, shape 0.5, n = 120: ProUCL 5.2 finds gamma and suggests approximate gamma
Boundary caseInput
120 values
| value |
|---|
| 6.815 |
| 20.48 |
| 33.71 |
| 1.419 |
| 187.2 |
| 14.26 |
| 127.2 |
| 45.53 |
| 712.2 |
| 13.23 |
| 88.98 |
| 4.5 |
| 112.4 |
| 1.228 |
| 2.144 |
| 10.54 |
| 1.12 |
| 17.26 |
| 7.103 |
| 164.1 |
| 26.64 |
| 469.7 |
| 20.21 |
| 49.41 |
| 174.4 |
| 3.941 |
| 23.18 |
| 57.68 |
| 21.38 |
| 5.176 |
| 128.3 |
| 14.44 |
| 5.038 |
| 152.7 |
| 27.66 |
| 11.97 |
| 51.71 |
| 0.2522 |
| 1.181 |
| 222.6 |
| 1.85 |
| 23.25 |
| 34.37 |
| 0.02659 |
| 8.919 |
| 185 |
| 45.56 |
| 1.696 |
| 28.36 |
| 37.83 |
| 161.5 |
| 9.657 |
| 35.8 |
| 122.5 |
| 39.91 |
| 40.37 |
| 45.22 |
| 68.33 |
| 126.1 |
| 22.85 |
| 66.14 |
| 2.52 |
| 47.34 |
| 101.8 |
| 39.18 |
| 103.5 |
| 9.908 |
| 12.81 |
| 214.7 |
| 168.8 |
| 19.82 |
| 19 |
| 8.556 |
| 61.69 |
| 4.927 |
| 190.1 |
| 38.95 |
| 1.37 |
| 89.75 |
| 22.46 |
| 2.053 |
| 0.001 |
| 0.267 |
| 16.42 |
| 181.1 |
| 222.1 |
| 8.555 |
| 209.7 |
| 0.1841 |
| 10.3 |
| 91.04 |
| 121.7 |
| 11.99 |
| 19.83 |
| 43.62 |
| 70.14 |
| 18.39 |
| 69.14 |
| 0.9221 |
| 2.969 |
| 6.211 |
| 194.1 |
| 14.19 |
| 0.05172 |
| 10.52 |
| 35.97 |
| 11.62 |
| 0.6175 |
| 90.67 |
| 83.19 |
| 11.14 |
| 62.21 |
| 61.39 |
| 211 |
| 28.67 |
| 5.374 |
| 22.77 |
| 2.299 |
| 5.681 |
| 8.2 |
Against USEPA ProUCL (ProUCL 5.2.0)
| Value | USEPA ProUCL | EnviroAutomate | Difference | Agreement band | Verdict |
|---|---|---|---|---|---|
| Sample size (n) n | 120 | 120 | 0 | exact match | Agree |
| Mean mean | 60.56418508333335 | 60.56418508333335 | 0 | within 0.000001 relative | Agree |
| Standard deviation sd | 94.24777766380275 | 94.24777766380275 | 0 | within 0.000001 relative | Agree |
| Skewness skewness | 3.80253406165778 | 3.802534061657779 | 8.88e-16 | within 0.000001 relative | Agree |
| 95% UCL - Student's t ucl.studentT | 74.82689079375373 | 74.8268922118377 | 1.42e-6 | within 0.000001 relative | Agree |
| 95% UCL - Modified t (Johnson) ucl.modifiedT | 75.32464132820118 | 75.32464274628514 | 1.42e-6 | within 0.000001 relative | Agree |
| 95% UCL - Central limit theorem ucl.clt | 74.71585702846849 | 74.71585701999261 | 8.48e-9 | within 0.000001 relative | Agree |
| 95% UCL - Land's H ucl.landsH | 297.06743187153995 | 297.06743187153995 | 0 | within 0.02 relative | Agree |
| 95% UCL - approximateGamma ucl.approximateGamma | 75.63042147395605 | 75.63042699532723 | 5.52e-6 | within 0.005 relative | Agree |
| 95% UCL - adjustedGamma ucl.adjustedGamma | 75.834317564487 | 75.8343233795538 | 5.82e-6 | within 0.005 relative | Agree |
| Distribution used distributionUsed | gamma | gamma | - | exact match | Agree |
| Recommended method recommendedMethod | approximateGamma | approximateGamma | - | exact match | Agree |
| 95% UCL - Chebyshev, 95% ucl.chebyshev95 | 98.06643260450934 | 98.06643260450934 | 0 | within 0.000001 relative | Agree |
| 95% UCL - Chebyshev, 97.5% ucl.chebyshev975 | 114.293685064571 | 114.293685064571 | 0 | within 0.000001 relative | Agree |
| 95% UCL - Chebyshev, 99% ucl.chebyshev99 | 146.16898030834753 | 146.16898030834753 | 0 | within 0.000001 relative | Agree |
Drawn from a gamma distribution, shape 0.5, n = 50: ProUCL 5.2 finds gamma and suggests approximate gamma
Boundary caseInput
50 values
| value |
|---|
| 89.59 |
| 451.6 |
| 107.7 |
| 17.06 |
| 8.477 |
| 10.29 |
| 0.3903 |
| 58.21 |
| 152.4 |
| 0.522 |
| 3.998 |
| 4.47 |
| 383.9 |
| 93.89 |
| 28.32 |
| 14.42 |
| 22.36 |
| 3.536 |
| 2.926 |
| 10.42 |
| 47.76 |
| 10.44 |
| 87.57 |
| 17.73 |
| 0.007144 |
| 123.2 |
| 53.41 |
| 22.25 |
| 110.3 |
| 2.639 |
| 6.048 |
| 156.8 |
| 0.5311 |
| 27.68 |
| 22.62 |
| 8.542 |
| 7.243 |
| 80.2 |
| 39.66 |
| 47.23 |
| 75.97 |
| 25.4 |
| 77.74 |
| 23.7 |
| 0.02441 |
| 20.31 |
| 29.7 |
| 57.35 |
| 43.36 |
| 8.982 |
Against USEPA ProUCL (ProUCL 5.2.0)
| Value | USEPA ProUCL | EnviroAutomate | Difference | Agreement band | Verdict |
|---|---|---|---|---|---|
| Sample size (n) n | 50 | 50 | 0 | exact match | Agree |
| Mean mean | 53.97751907999998 | 53.97751907999997 | 7.11e-15 | within 0.000001 relative | Agree |
| Standard deviation sd | 85.6836936594976 | 85.68369365949759 | 1.42e-14 | within 0.000001 relative | Agree |
| Skewness skewness | 3.349589173775364 | 3.3495891737753642 | 4.44e-16 | within 0.000001 relative | Agree |
| 95% UCL - Student's t ucl.studentT | 74.29313018902876 | 74.29313150370741 | 1.31e-6 | within 0.000001 relative | Agree |
| 95% UCL - Modified t (Johnson) ucl.modifiedT | 75.24981409786521 | 75.24981541254388 | 1.31e-6 | within 0.000001 relative | Agree |
| 95% UCL - Central limit theorem ucl.clt | 73.90903976692341 | 73.9090397549858 | 1.19e-8 | within 0.000001 relative | Agree |
| 95% UCL - Land's H ucl.landsH | 519.6268187601287 | 519.6268187601287 | 0 | within 0.02 relative | Agree |
| 95% UCL - approximateGamma ucl.approximateGamma | 77.3019533144047 | 77.30205213498115 | 9.88e-5 | within 0.005 relative | Agree |
| 95% UCL - adjustedGamma ucl.adjustedGamma | 78.14082764660581 | 78.14094024086447 | 0.000113 | within 0.005 relative | Agree |
| Distribution used distributionUsed | gamma | gamma | - | exact match | Agree |
| Recommended method recommendedMethod | approximateGamma | approximateGamma | - | exact match | Agree |
| 95% UCL - Chebyshev, 95% ucl.chebyshev95 | 106.79649518207106 | 106.79649518207106 | 0 | within 0.000001 relative | Agree |
| 95% UCL - Chebyshev, 97.5% ucl.chebyshev975 | 129.65130833443737 | 129.65130833443737 | 0 | within 0.000001 relative | Agree |
| 95% UCL - Chebyshev, 99% ucl.chebyshev99 | 174.545163210117 | 174.54516321011704 | 2.84e-14 | within 0.000001 relative | Agree |
Drawn from a gamma distribution, shape 0.8, n = 49: ProUCL 5.2 finds normal and suggests Student's t
Boundary caseInput
49 values
| value |
|---|
| 25.79 |
| 42.81 |
| 206.8 |
| 70.05 |
| 102.3 |
| 112 |
| 33.98 |
| 8.362 |
| 51.03 |
| 0.07625 |
| 53.72 |
| 18.85 |
| 13.14 |
| 100.5 |
| 2.568 |
| 13.51 |
| 51.17 |
| 23.27 |
| 12.84 |
| 117.7 |
| 53.39 |
| 62.99 |
| 101 |
| 56.29 |
| 66.52 |
| 10.95 |
| 80.24 |
| 58.34 |
| 1.712 |
| 52.01 |
| 37.38 |
| 11.72 |
| 1.705 |
| 25.67 |
| 37.92 |
| 53.73 |
| 52.39 |
| 27.69 |
| 12.93 |
| 17.42 |
| 41.87 |
| 8.241 |
| 5.391 |
| 0.4309 |
| 58.9 |
| 23.66 |
| 114.7 |
| 48.85 |
| 92.16 |
Against USEPA ProUCL (ProUCL 5.2.0)
| Value | USEPA ProUCL | EnviroAutomate | Difference | Agreement band | Verdict |
|---|---|---|---|---|---|
| Sample size (n) n | 49 | 49 | 0 | exact match | Agree |
| Mean mean | 46.46257448979593 | 46.46257448979593 | 0 | within 0.000001 relative | Agree |
| Standard deviation sd | 40.77671902801396 | 40.77671902801396 | 0 | within 0.000001 relative | Agree |
| Skewness skewness | 1.5274408711133418 | 1.5274408711133418 | 0 | within 0.000001 relative | Agree |
| 95% UCL - Student's t ucl.studentT | 56.23281713960179 | 56.23281731726996 | 1.78e-7 | within 0.000001 relative | Agree |
| 95% UCL - Modified t (Johnson) ucl.modifiedT | 56.444667572368104 | 56.44466775003626 | 1.78e-7 | within 0.000001 relative | Agree |
| 95% UCL - Central limit theorem ucl.clt | 56.04425080816468 | 56.04425080242591 | 5.74e-9 | within 0.000001 relative | Agree |
| 95% UCL - Land's H ucl.landsH | 148.29441889443385 | 148.29441889443385 | 0 | within 0.02 relative | Agree |
| 95% UCL - approximateGamma ucl.approximateGamma | 60.50930578124682 | 60.509318191983716 | 1.24e-5 | within 0.005 relative | Agree |
| 95% UCL - adjustedGamma ucl.adjustedGamma | 60.99899895739934 | 60.99901308615809 | 1.41e-5 | within 0.005 relative | Agree |
| Distribution used distributionUsed | normal | normal | - | exact match | Agree |
| Recommended method recommendedMethod | studentT | studentT | - | exact match | Agree |
| 95% UCL - Chebyshev, 95% ucl.chebyshev95 | 71.85423127440518 | 71.85423127440518 | 0 | within 0.000001 relative | Agree |
| 95% UCL - Chebyshev, 97.5% ucl.chebyshev975 | 82.84122144853892 | 82.84122144853892 | 0 | within 0.000001 relative | Agree |
| 95% UCL - Chebyshev, 99% ucl.chebyshev99 | 104.42303614593926 | 104.42303614593926 | 0 | within 0.000001 relative | Agree |
Drawn from a gamma distribution, shape 1.0, n = 30: ProUCL 5.2 finds normal and suggests Student's t
Boundary caseInput
30 values
| value |
|---|
| 47.32 |
| 34.27 |
| 44.16 |
| 72.48 |
| 26.9 |
| 135.8 |
| 74.62 |
| 103.6 |
| 15.84 |
| 44.81 |
| 73.97 |
| 19.35 |
| 58.95 |
| 23.4 |
| 1.757 |
| 34.28 |
| 20.71 |
| 39.96 |
| 7.769 |
| 10.92 |
| 112.9 |
| 137.4 |
| 22.02 |
| 71.39 |
| 60.2 |
| 1.213 |
| 48.26 |
| 7.923 |
| 5.909 |
| 98.03 |
Against USEPA ProUCL (ProUCL 5.2.0)
| Value | USEPA ProUCL | EnviroAutomate | Difference | Agreement band | Verdict |
|---|---|---|---|---|---|
| Sample size (n) n | 30 | 30 | 0 | exact match | Agree |
| Mean mean | 48.53703333333334 | 48.53703333333335 | 7.11e-15 | within 0.000001 relative | Agree |
| Standard deviation sd | 38.857747927078435 | 38.85774792707843 | 7.11e-15 | within 0.000001 relative | Agree |
| Skewness skewness | 0.8672191525077892 | 0.8672191525077892 | 0 | within 0.000001 relative | Agree |
| 95% UCL - Student's t ucl.studentT | 60.59135646282286 | 60.59135696642495 | 5.04e-7 | within 0.000001 relative | Agree |
| 95% UCL - Modified t (Johnson) ucl.modifiedT | 60.77856859185442 | 60.77856909545651 | 5.04e-7 | within 0.000001 relative | Agree |
| 95% UCL - Central limit theorem ucl.clt | 60.20631859016687 | 60.206318583177776 | 6.99e-9 | within 0.000001 relative | Agree |
| 95% UCL - Land's H ucl.landsH | 112.1486297037247 | 112.1486297037248 | 9.95e-14 | within 0.02 relative | Agree |
| 95% UCL - approximateGamma ucl.approximateGamma | 66.14064675355216 | 66.1406815960569 | 3.48e-5 | within 0.005 relative | Agree |
| 95% UCL - adjustedGamma ucl.adjustedGamma | 67.34755407332499 | 67.34759858312896 | 4.45e-5 | within 0.005 relative | Agree |
| Distribution used distributionUsed | normal | normal | - | exact match | Agree |
| Recommended method recommendedMethod | studentT | studentT | - | exact match | Agree |
| 95% UCL - Chebyshev, 95% ucl.chebyshev95 | 79.46090054800696 | 79.46090054800696 | 0 | within 0.000001 relative | Agree |
| 95% UCL - Chebyshev, 97.5% ucl.chebyshev975 | 92.84168259448512 | 92.84168259448512 | 0 | within 0.000001 relative | Agree |
| 95% UCL - Chebyshev, 99% ucl.chebyshev99 | 119.12563789584338 | 119.12563789584337 | 1.42e-14 | within 0.000001 relative | Agree |
Drawn from a gamma distribution, shape 3.0, n = 50: ProUCL 5.2 finds normal and suggests Student's t
Boundary caseInput
50 values
| value |
|---|
| 50.47 |
| 18.88 |
| 34.37 |
| 83.92 |
| 48.37 |
| 31.52 |
| 26.64 |
| 85.85 |
| 47.96 |
| 30.44 |
| 86.39 |
| 62.35 |
| 77.66 |
| 72.67 |
| 76.49 |
| 45.16 |
| 19.32 |
| 19.32 |
| 59.14 |
| 28.26 |
| 64.55 |
| 75.41 |
| 36.83 |
| 8.379 |
| 47.79 |
| 49.53 |
| 57.75 |
| 39.6 |
| 40.56 |
| 77.75 |
| 70.33 |
| 69.41 |
| 61.89 |
| 11.04 |
| 56.12 |
| 44.31 |
| 31.21 |
| 43.6 |
| 132.1 |
| 42.38 |
| 16.58 |
| 78.64 |
| 21.54 |
| 47.25 |
| 51.68 |
| 30.98 |
| 49.27 |
| 52.62 |
| 34.33 |
| 37.07 |
Against USEPA ProUCL (ProUCL 5.2.0)
| Value | USEPA ProUCL | EnviroAutomate | Difference | Agreement band | Verdict |
|---|---|---|---|---|---|
| Sample size (n) n | 50 | 50 | 0 | exact match | Agree |
| Mean mean | 49.713579999999986 | 49.713579999999986 | 0 | within 0.000001 relative | Agree |
| Standard deviation sd | 23.856515227064985 | 23.856515227064985 | 0 | within 0.000001 relative | Agree |
| Skewness skewness | 0.7862785715560294 | 0.7862785715560291 | 3.33e-16 | within 0.000001 relative | Agree |
| 95% UCL - Student's t ucl.studentT | 55.36996180463702 | 55.36996217067693 | 3.66e-7 | within 0.000001 relative | Agree |
| 95% UCL - Modified t (Johnson) ucl.modifiedT | 55.43248802702049 | 55.432488393060396 | 3.66e-7 | within 0.000001 relative | Agree |
| 95% UCL - Central limit theorem ucl.clt | 55.26302128174197 | 55.263021278418236 | 3.32e-9 | within 0.000001 relative | Agree |
| 95% UCL - Land's H ucl.landsH | 59.158912787500675 | 59.158912787500675 | 0 | within 0.02 relative | Agree |
| 95% UCL - approximateGamma ucl.approximateGamma | 56.25421336572479 | 56.254213492009946 | 1.26e-7 | within 0.005 relative | Agree |
| 95% UCL - adjustedGamma ucl.adjustedGamma | 56.46066100928023 | 56.46066115135847 | 1.42e-7 | within 0.005 relative | Agree |
| Distribution used distributionUsed | normal | normal | - | exact match | Agree |
| Recommended method recommendedMethod | studentT | studentT | - | exact match | Agree |
| 95% UCL - Chebyshev, 95% ucl.chebyshev95 | 64.41972365277618 | 64.41972365277618 | 0 | within 0.000001 relative | Agree |
| 95% UCL - Chebyshev, 97.5% ucl.chebyshev975 | 70.78308375893468 | 70.78308375893467 | 1.42e-14 | within 0.000001 relative | Agree |
| 95% UCL - Chebyshev, 99% ucl.chebyshev99 | 83.28267249864794 | 83.28267249864794 | 0 | within 0.000001 relative | Agree |
Drawn from a gamma distribution, shape 3.0, n = 70: ProUCL 5.2 finds normal and suggests Student's t
Boundary caseInput
70 values
| value |
|---|
| 33.75 |
| 63.39 |
| 36.52 |
| 104.2 |
| 50.09 |
| 45.42 |
| 32.09 |
| 48.11 |
| 47.95 |
| 24.37 |
| 48.14 |
| 75.73 |
| 57.63 |
| 34.72 |
| 54.52 |
| 81.18 |
| 65.5 |
| 46.74 |
| 11.96 |
| 21.97 |
| 51.05 |
| 29.72 |
| 54.34 |
| 29.4 |
| 17.49 |
| 42.75 |
| 73.3 |
| 36.01 |
| 10.02 |
| 41.06 |
| 67.06 |
| 135 |
| 46.85 |
| 20.53 |
| 64.89 |
| 18.12 |
| 21.85 |
| 45.46 |
| 3.907 |
| 14.45 |
| 20.96 |
| 63.86 |
| 31.99 |
| 53.2 |
| 80.74 |
| 22.81 |
| 48.97 |
| 61.11 |
| 27.71 |
| 62.98 |
| 14.06 |
| 58.33 |
| 69.23 |
| 33.63 |
| 68.78 |
| 50.22 |
| 39.16 |
| 120.4 |
| 21.25 |
| 55.56 |
| 30.99 |
| 102.6 |
| 64.34 |
| 53.71 |
| 120.9 |
| 71.08 |
| 37.8 |
| 29.67 |
| 67.42 |
| 11.91 |
Against USEPA ProUCL (ProUCL 5.2.0)
| Value | USEPA ProUCL | EnviroAutomate | Difference | Agreement band | Verdict |
|---|---|---|---|---|---|
| Sample size (n) n | 70 | 70 | 0 | exact match | Agree |
| Mean mean | 48.60867142857142 | 48.60867142857142 | 0 | within 0.000001 relative | Agree |
| Standard deviation sd | 27.011772791770706 | 27.011772791770706 | 0 | within 0.000001 relative | Agree |
| Skewness skewness | 0.9951818647366577 | 0.9951818647366577 | 0 | within 0.000001 relative | Agree |
| 95% UCL - Student's t ucl.studentT | 53.991391366403334 | 53.99139170180677 | 3.35e-7 | within 0.000001 relative | Agree |
| 95% UCL - Modified t (Johnson) ucl.modifiedT | 54.05539523882418 | 54.05539557422762 | 3.35e-7 | within 0.000001 relative | Agree |
| 95% UCL - Central limit theorem ucl.clt | 53.91912143986216 | 53.919121436681564 | 3.18e-9 | within 0.000001 relative | Agree |
| 95% UCL - Land's H ucl.landsH | 58.578984126628974 | 58.578984126628974 | 0 | within 0.02 relative | Agree |
| 95% UCL - approximateGamma ucl.approximateGamma | 54.73583044196439 | 54.73583053723577 | 9.53e-8 | within 0.005 relative | Agree |
| 95% UCL - adjustedGamma ucl.adjustedGamma | 54.871888053718294 | 54.871888157144554 | 1.03e-7 | within 0.005 relative | Agree |
| Distribution used distributionUsed | normal | normal | - | exact match | Agree |
| Recommended method recommendedMethod | studentT | studentT | - | exact match | Agree |
| 95% UCL - Chebyshev, 95% ucl.chebyshev95 | 62.6814828634577 | 62.6814828634577 | 0 | within 0.000001 relative | Agree |
| 95% UCL - Chebyshev, 97.5% ucl.chebyshev975 | 68.77079961301504 | 68.77079961301504 | 0 | within 0.000001 relative | Agree |
| 95% UCL - Chebyshev, 99% ucl.chebyshev99 | 80.73208324391484 | 80.73208324391483 | 1.42e-14 | within 0.000001 relative | Agree |
Drawn from a gamma distribution, shape 8.0, n = 120: ProUCL 5.2 finds normal and suggests Student's t
Boundary caseInput
120 values
| value |
|---|
| 47.91 |
| 61.32 |
| 72.69 |
| 41.25 |
| 103.7 |
| 32.93 |
| 70.35 |
| 65.21 |
| 38.8 |
| 50.37 |
| 63.42 |
| 65.63 |
| 32.5 |
| 45.44 |
| 48.67 |
| 66.36 |
| 41.78 |
| 29.32 |
| 63.41 |
| 47.72 |
| 37.22 |
| 37.11 |
| 41.32 |
| 63.89 |
| 78.97 |
| 82.65 |
| 55.37 |
| 43.19 |
| 60.2 |
| 60.79 |
| 44.42 |
| 57.11 |
| 45.49 |
| 73.19 |
| 13.18 |
| 39.82 |
| 72.17 |
| 44.77 |
| 46.67 |
| 28.22 |
| 44.96 |
| 32.42 |
| 31.47 |
| 72.06 |
| 43.81 |
| 70.34 |
| 45.98 |
| 42.52 |
| 74.7 |
| 61.98 |
| 38.29 |
| 38.29 |
| 35.27 |
| 33.88 |
| 62.88 |
| 69.32 |
| 67.45 |
| 27.64 |
| 49.26 |
| 31.06 |
| 20.27 |
| 63.17 |
| 49.38 |
| 47.41 |
| 49.86 |
| 43.12 |
| 61.21 |
| 83.18 |
| 44.77 |
| 69.59 |
| 61.65 |
| 64.86 |
| 62.15 |
| 59.48 |
| 37.74 |
| 39.97 |
| 70.76 |
| 38.73 |
| 71 |
| 28.73 |
| 51.77 |
| 98.46 |
| 32 |
| 20.42 |
| 47.38 |
| 102.4 |
| 49 |
| 41.6 |
| 62.86 |
| 43.53 |
| 23.66 |
| 25.44 |
| 47.71 |
| 68.85 |
| 42.09 |
| 47.65 |
| 48.43 |
| 61.19 |
| 49.92 |
| 71.07 |
| 83.74 |
| 37.34 |
| 27.72 |
| 60.28 |
| 30.63 |
| 70.78 |
| 26.36 |
| 11.42 |
| 58.34 |
| 41.01 |
| 48.97 |
| 31.78 |
| 39.44 |
| 51.14 |
| 53.59 |
| 80.24 |
| 69.95 |
| 84.99 |
| 71.4 |
| 42.26 |
Against USEPA ProUCL (ProUCL 5.2.0)
| Value | USEPA ProUCL | EnviroAutomate | Difference | Agreement band | Verdict |
|---|---|---|---|---|---|
| Sample size (n) n | 120 | 120 | 0 | exact match | Agree |
| Mean mean | 51.766249999999985 | 51.766249999999985 | 0 | within 0.000001 relative | Agree |
| Standard deviation sd | 18.13555429306771 | 18.13555429306771 | 0 | within 0.000001 relative | Agree |
| Skewness skewness | 0.3942568987274183 | 0.3942568987274184 | 1.11e-16 | within 0.000001 relative | Agree |
| 95% UCL - Student's t ucl.studentT | 54.51073989874397 | 54.51074017161766 | 2.73e-7 | within 0.000001 relative | Agree |
| 95% UCL - Modified t (Johnson) ucl.modifiedT | 54.520670547899925 | 54.52067082077362 | 2.73e-7 | within 0.000001 relative | Agree |
| 95% UCL - Central limit theorem ucl.clt | 54.489374314020296 | 54.48937431238933 | 1.63e-9 | within 0.000001 relative | Agree |
| 95% UCL - Land's H ucl.landsH | 55.529469921304305 | 55.529469921304305 | 0 | within 0.02 relative | Agree |
| 95% UCL - approximateGamma ucl.approximateGamma | 54.75465059132675 | 54.75465059370337 | 2.38e-9 | within 0.005 relative | Agree |
| 95% UCL - adjustedGamma ucl.adjustedGamma | 54.7915827298184 | 54.79158273208176 | 2.26e-9 | within 0.005 relative | Agree |
| Distribution used distributionUsed | normal | normal | - | exact match | Agree |
| Recommended method recommendedMethod | studentT | studentT | - | exact match | Agree |
| 95% UCL - Chebyshev, 95% ucl.chebyshev95 | 58.98259040495324 | 58.98259040495324 | 0 | within 0.000001 relative | Agree |
| 95% UCL - Chebyshev, 97.5% ucl.chebyshev975 | 62.10510666275347 | 62.10510666275347 | 0 | within 0.000001 relative | Agree |
| 95% UCL - Chebyshev, 99% ucl.chebyshev99 | 68.2386852131482 | 68.2386852131482 | 0 | within 0.000001 relative | Agree |
Drawn from a lognormal distribution near a branch threshold, n = 10: ProUCL 5.2 finds lognormal and suggests Land's H
Boundary caseInput
10 values
| value |
|---|
| 5.931 |
| 19.31 |
| 5.693 |
| 2.528 |
| 33.77 |
| 5.71 |
| 8.219 |
| 389.3 |
| 17.96 |
| 23.16 |
Against USEPA ProUCL (ProUCL 5.2.0)
| Value | USEPA ProUCL | EnviroAutomate | Difference | Agreement band | Verdict |
|---|---|---|---|---|---|
| Sample size (n) n | 10 | 10 | 0 | exact match | Agree |
| Mean mean | 51.158100000000005 | 51.158100000000005 | 0 | within 0.000001 relative | Agree |
| Standard deviation sd | 119.22404124583637 | 119.22404124583636 | 1.42e-14 | within 0.000001 relative | Agree |
| Skewness skewness | 3.121873810746447 | 3.1218738107464463 | 8.88e-16 | within 0.000001 relative | Agree |
| 95% UCL - Student's t ucl.studentT | 120.27003667746934 | 120.27003619843175 | 4.79e-7 | within 0.000001 relative | Agree |
| 95% UCL - Modified t (Johnson) ucl.modifiedT | 126.47341021041485 | 126.47340973137727 | 4.79e-7 | within 0.000001 relative | Agree |
| 95% UCL - Central limit theorem ucl.clt | 113.172292887173 | 113.17229285003074 | 3.71e-8 | within 0.000001 relative | Agree |
| 95% UCL - Land's H ucl.landsH | 253.89641418679108 | 253.89641418679108 | 0 | within 0.02 relative | Agree |
| 95% UCL - approximateGamma ucl.approximateGamma | 144.82310003756305 | 144.92785343355794 | 0.105 | within 0.005 relative | Agree |
| 95% UCL - adjustedGamma ucl.adjustedGamma | 176.47382333985277 | 176.72737584675812 | 0.254 | within 0.005 relative | Agree |
| Distribution used distributionUsed | lognormal | lognormal | - | exact match | Agree |
| Recommended method recommendedMethod | landsH | landsH | - | exact match | Agree |
| 95% UCL - Chebyshev, 95% ucl.chebyshev95 | 215.4970996953823 | 215.4970996953823 | 0 | within 0.000001 relative | Agree |
| 95% UCL - Chebyshev, 97.5% ucl.chebyshev975 | 286.60671614130723 | 286.6067161413072 | 5.68e-14 | within 0.000001 relative | Agree |
| 95% UCL - Chebyshev, 99% ucl.chebyshev99 | 426.2877881197087 | 426.28778811970864 | 5.68e-14 | within 0.000001 relative | Agree |
Drawn from a lognormal distribution near a branch threshold, n = 10: ProUCL 5.2 finds normal and suggests Student's t
Boundary caseInput
10 values
| value |
|---|
| 47.31 |
| 16.93 |
| 84.23 |
| 45.21 |
| 16.27 |
| 22.74 |
| 16.62 |
| 15.57 |
| 27.8 |
| 85.91 |
Against USEPA ProUCL (ProUCL 5.2.0)
| Value | USEPA ProUCL | EnviroAutomate | Difference | Agreement band | Verdict |
|---|---|---|---|---|---|
| Sample size (n) n | 10 | 10 | 0 | exact match | Agree |
| Mean mean | 37.859 | 37.859 | 0 | within 0.000001 relative | Agree |
| Standard deviation sd | 27.455614867960577 | 27.455614867960577 | 0 | within 0.000001 relative | Agree |
| Skewness skewness | 1.1243199751891273 | 1.1243199751891275 | 2.22e-16 | within 0.000001 relative | Agree |
| 95% UCL - Student's t ucl.studentT | 53.774504091015224 | 53.774503980699635 | 1.10e-7 | within 0.000001 relative | Agree |
| 95% UCL - Modified t (Johnson) ucl.modifiedT | 54.28898569480102 | 54.28898558448543 | 1.10e-7 | within 0.000001 relative | Agree |
| 95% UCL - Central limit theorem ucl.clt | 52.139993820255214 | 52.139993811701885 | 8.55e-9 | within 0.000001 relative | Agree |
| 95% UCL - Land's H ucl.landsH | 67.15883855396537 | 67.15883855396537 | 0 | within 0.02 relative | Agree |
| 95% UCL - approximateGamma ucl.approximateGamma | 58.61689224589658 | 58.61713351121523 | 0.000241 | within 0.005 relative | Agree |
| 95% UCL - adjustedGamma ucl.adjustedGamma | 63.433596316726 | 63.43408957851769 | 0.000493 | within 0.005 relative | Agree |
| Distribution used distributionUsed | normal | normal | - | exact match | Agree |
| Recommended method recommendedMethod | studentT | studentT | - | exact match | Agree |
| 95% UCL - Chebyshev, 95% ucl.chebyshev95 | 75.70395338585814 | 75.70395338585814 | 0 | within 0.000001 relative | Agree |
| 95% UCL - Chebyshev, 97.5% ucl.chebyshev975 | 92.07949494732901 | 92.07949494732901 | 0 | within 0.000001 relative | Agree |
| 95% UCL - Chebyshev, 99% ucl.chebyshev99 | 124.24607541640702 | 124.24607541640702 | 0 | within 0.000001 relative | Agree |
Drawn from a lognormal distribution near a branch threshold, n = 12: ProUCL 5.2 finds gamma and suggests adjusted gamma
Boundary caseInput
12 values
| value |
|---|
| 68.05 |
| 73.24 |
| 1.665 |
| 5.765 |
| 13.43 |
| 4.886 |
| 4.946 |
| 146.3 |
| 58.36 |
| 3.923 |
| 15.84 |
| 4.049 |
Against USEPA ProUCL (ProUCL 5.2.0)
| Value | USEPA ProUCL | EnviroAutomate | Difference | Agreement band | Verdict |
|---|---|---|---|---|---|
| Sample size (n) n | 12 | 12 | 0 | exact match | Agree |
| Mean mean | 33.37116666666666 | 33.37116666666666 | 0 | within 0.000001 relative | Agree |
| Standard deviation sd | 44.70942621342097 | 44.70942621342097 | 0 | within 0.000001 relative | Agree |
| Skewness skewness | 1.7062203916864322 | 1.7062203916864327 | 4.44e-16 | within 0.000001 relative | Agree |
| 95% UCL - Student's t ucl.studentT | 56.54975335808643 | 56.54975341446274 | 5.64e-8 | within 0.000001 relative | Agree |
| 95% UCL - Modified t (Johnson) ucl.modifiedT | 57.60925522900223 | 57.60925528537856 | 5.64e-8 | within 0.000001 relative | Agree |
| 95% UCL - Central limit theorem ucl.clt | 54.600469406732486 | 54.600469394017594 | 1.27e-8 | within 0.000001 relative | Agree |
| 95% UCL - Land's H ucl.landsH | 208.25376162990995 | 208.25376162990995 | 0 | within 0.02 relative | Agree |
| 95% UCL - approximateGamma ucl.approximateGamma | 72.7354341353768 | 72.74475569784911 | 0.00932 | within 0.005 relative | Agree |
| 95% UCL - adjustedGamma ucl.adjustedGamma | 82.56569760764891 | 82.58476826078791 | 0.0191 | within 0.005 relative | Agree |
| Distribution used distributionUsed | gamma | gamma | - | exact match | Agree |
| Recommended method recommendedMethod | adjustedGamma | adjustedGamma | - | exact match | Agree |
| 95% UCL - Chebyshev, 95% ucl.chebyshev95 | 89.62929426788035 | 89.62929426788037 | 1.42e-14 | within 0.000001 relative | Agree |
| 95% UCL - Chebyshev, 97.5% ucl.chebyshev975 | 113.97223102119818 | 113.97223102119818 | 0 | within 0.000001 relative | Agree |
| 95% UCL - Chebyshev, 99% ucl.chebyshev99 | 161.78921655354975 | 161.78921655354975 | 0 | within 0.000001 relative | Agree |
Drawn from a lognormal distribution near a branch threshold, n = 12: ProUCL 5.2 finds lognormal and suggests Land's H
Boundary caseInput
12 values
| value |
|---|
| 4.642 |
| 172.7 |
| 7.127 |
| 11.71 |
| 6.31 |
| 26.16 |
| 16.17 |
| 9.939 |
| 198.8 |
| 36.19 |
| 33.56 |
| 31.67 |
Against USEPA ProUCL (ProUCL 5.2.0)
| Value | USEPA ProUCL | EnviroAutomate | Difference | Agreement band | Verdict |
|---|---|---|---|---|---|
| Sample size (n) n | 12 | 12 | 0 | exact match | Agree |
| Mean mean | 46.24816666666666 | 46.24816666666666 | 0 | within 0.000001 relative | Agree |
| Standard deviation sd | 66.3413173558918 | 66.3413173558918 | 0 | within 0.000001 relative | Agree |
| Skewness skewness | 1.9600471800698591 | 1.9600471800698585 | 6.66e-16 | within 0.000001 relative | Agree |
| 95% UCL - Student's t ucl.studentT | 80.64131607136511 | 80.64131615501816 | 8.37e-8 | within 0.000001 relative | Agree |
| 95% UCL - Modified t (Johnson) ucl.modifiedT | 82.44731762699755 | 82.4473177106506 | 8.37e-8 | within 0.000001 relative | Agree |
| 95% UCL - Central limit theorem ucl.clt | 77.74890442161106 | 77.74890440274429 | 1.89e-8 | within 0.000001 relative | Agree |
| 95% UCL - Land's H ucl.landsH | 152.88927721566307 | 152.88927721566307 | 0 | within 0.02 relative | Agree |
| 95% UCL - approximateGamma ucl.approximateGamma | 93.44714875380222 | 93.45365939374751 | 0.00651 | within 0.005 relative | Agree |
| 95% UCL - adjustedGamma ucl.adjustedGamma | 104.70266252367387 | 104.71573849015219 | 0.0131 | within 0.005 relative | Agree |
| Distribution used distributionUsed | lognormal | lognormal | - | exact match | Agree |
| Recommended method recommendedMethod | landsH | landsH | - | exact match | Agree |
| 95% UCL - Chebyshev, 95% ucl.chebyshev95 | 129.7258270424561 | 129.7258270424561 | 0 | within 0.000001 relative | Agree |
| 95% UCL - Chebyshev, 97.5% ucl.chebyshev975 | 165.84667737091513 | 165.84667737091513 | 0 | within 0.000001 relative | Agree |
| 95% UCL - Chebyshev, 99% ucl.chebyshev99 | 236.79909346905714 | 236.79909346905714 | 0 | within 0.000001 relative | Agree |
Drawn from a lognormal distribution near a branch threshold, n = 12: ProUCL 5.2 finds lognormal and suggests Student's t
Boundary caseInput
12 values
| value |
|---|
| 18.33 |
| 204.6 |
| 41.65 |
| 15.29 |
| 1454 |
| 88.58 |
| 25.43 |
| 5.122 |
| 3.272 |
| 14.49 |
| 60.13 |
| 38.01 |
Against USEPA ProUCL (ProUCL 5.2.0)
| Value | USEPA ProUCL | EnviroAutomate | Difference | Agreement band | Verdict |
|---|---|---|---|---|---|
| Sample size (n) n | 12 | 12 | 0 | exact match | Agree |
| Mean mean | 164.07533333333333 | 164.07533333333333 | 0 | within 0.000001 relative | Agree |
| Standard deviation sd | 409.9926224022116 | 409.9926224022116 | 0 | within 0.000001 relative | Agree |
| Skewness skewness | 3.356453617110366 | 3.356453617110367 | 8.88e-16 | within 0.000001 relative | Agree |
| 95% UCL - Student's t ucl.studentT | 376.6266976883414 | 376.6266982053213 | 5.17e-7 | within 0.000001 relative | Agree |
| 95% UCL - Modified t (Johnson) ucl.modifiedT | 395.7394924168201 | 395.7394929338001 | 5.17e-7 | within 0.000001 relative | Agree |
| 95% UCL - Central limit theorem ucl.clt | 358.75145063848686 | 358.75145052188924 | 1.17e-7 | within 0.000001 relative | Agree |
| 95% UCL - Land's H ucl.landsH | 1076.2501303960003 | 1076.2501303960003 | 0 | within 0.02 relative | Agree |
| 95% UCL - approximateGamma ucl.approximateGamma | 443.1272216269584 | 443.37000576431166 | 0.243 | within 0.005 relative | Agree |
| 95% UCL - adjustedGamma ucl.adjustedGamma | 522.2894077866057 | 522.8136357107246 | 0.524 | within 0.005 relative | Agree |
| Distribution used distributionUsed | lognormal | lognormal | - | exact match | Agree |
| Recommended method recommendedMethod | studentT | studentT | - | exact match | Agree |
| 95% UCL - Chebyshev, 95% ucl.chebyshev95 | 679.9714031365289 | 679.9714031365289 | 0 | within 0.000001 relative | Agree |
| 95% UCL - Chebyshev, 97.5% ucl.chebyshev975 | 903.200044649893 | 903.200044649893 | 0 | within 0.000001 relative | Agree |
| 95% UCL - Chebyshev, 99% ucl.chebyshev99 | 1341.6894853372905 | 1341.6894853372905 | 0 | within 0.000001 relative | Agree |
Drawn from a lognormal distribution near a branch threshold, n = 27: ProUCL 5.2 finds gamma and suggests adjusted gamma
Boundary caseInput
27 values
| value |
|---|
| 1.019 |
| 6.983 |
| 5.989 |
| 0.9029 |
| 26.48 |
| 563.9 |
| 29.01 |
| 2.236 |
| 18.79 |
| 19.93 |
| 24.02 |
| 32.25 |
| 133.7 |
| 2.406 |
| 128.6 |
| 14.76 |
| 77.86 |
| 80.9 |
| 29.2 |
| 11.55 |
| 251.5 |
| 177 |
| 40.85 |
| 367.3 |
| 41.74 |
| 10.09 |
| 40.09 |
Against USEPA ProUCL (ProUCL 5.2.0)
| Value | USEPA ProUCL | EnviroAutomate | Difference | Agreement band | Verdict |
|---|---|---|---|---|---|
| Sample size (n) n | 27 | 27 | 0 | exact match | Agree |
| Mean mean | 79.22429259259259 | 79.22429259259259 | 0 | within 0.000001 relative | Agree |
| Standard deviation sd | 129.4010463098078 | 129.4010463098078 | 0 | within 0.000001 relative | Agree |
| Skewness skewness | 2.670026581753762 | 2.670026581753762 | 0 | within 0.000001 relative | Agree |
| 95% UCL - Student's t ucl.studentT | 121.69971167482905 | 121.69971006824693 | 1.61e-6 | within 0.000001 relative | Agree |
| 95% UCL - Modified t (Johnson) ucl.modifiedT | 123.83245385602618 | 123.83245224944406 | 1.61e-6 | within 0.000001 relative | Agree |
| 95% UCL - Central limit theorem ucl.clt | 120.1864821448793 | 120.18648212034574 | 2.45e-8 | within 0.000001 relative | Agree |
| 95% UCL - Land's H ucl.landsH | 337.0071447964719 | 337.0071447964719 | 0 | within 0.02 relative | Agree |
| 95% UCL - approximateGamma ucl.approximateGamma | 130.7530275332469 | 130.75423845439724 | 0.00121 | within 0.005 relative | Agree |
| 95% UCL - adjustedGamma ucl.adjustedGamma | 135.12969377154985 | 135.13130661712484 | 0.00161 | within 0.005 relative | Agree |
| Distribution used distributionUsed | gamma | gamma | - | exact match | Agree |
| Recommended method recommendedMethod | adjustedGamma | adjustedGamma | - | exact match | Agree |
| 95% UCL - Chebyshev, 95% ucl.chebyshev95 | 187.77501208035386 | 187.77501208035386 | 0 | within 0.000001 relative | Agree |
| 95% UCL - Chebyshev, 97.5% ucl.chebyshev975 | 234.74499511549328 | 234.74499511549328 | 0 | within 0.000001 relative | Agree |
| 95% UCL - Chebyshev, 99% ucl.chebyshev99 | 327.008431610679 | 327.008431610679 | 0 | within 0.000001 relative | Agree |
Drawn from a lognormal distribution near a branch threshold, n = 27: ProUCL 5.2 finds lognormal and suggests Land's H
Boundary caseInput
27 values
| value |
|---|
| 96.39 |
| 111.2 |
| 72.4 |
| 6.786 |
| 185.9 |
| 35.87 |
| 36.88 |
| 154.8 |
| 13.39 |
| 17.45 |
| 6.869 |
| 5.283 |
| 46.13 |
| 9.426 |
| 47.74 |
| 51.38 |
| 1177 |
| 10.87 |
| 52.18 |
| 13.19 |
| 82.09 |
| 20.58 |
| 18.42 |
| 8.322 |
| 90.9 |
| 47.84 |
| 12.17 |
Against USEPA ProUCL (ProUCL 5.2.0)
| Value | USEPA ProUCL | EnviroAutomate | Difference | Agreement band | Verdict |
|---|---|---|---|---|---|
| Sample size (n) n | 27 | 27 | 0 | exact match | Agree |
| Mean mean | 90.05392592592595 | 90.05392592592595 | 0 | within 0.000001 relative | Agree |
| Standard deviation sd | 222.1797450947743 | 222.17974509477432 | 2.84e-14 | within 0.000001 relative | Agree |
| Skewness skewness | 4.843587989546231 | 4.843587989546231 | 0 | within 0.000001 relative | Agree |
| 95% UCL - Student's t ucl.studentT | 162.9836127685719 | 162.98361001009337 | 2.76e-6 | within 0.000001 relative | Agree |
| 95% UCL - Modified t (Johnson) ucl.modifiedT | 169.626496378828 | 169.6264936203495 | 2.76e-6 | within 0.000001 relative | Agree |
| 95% UCL - Central limit theorem ucl.clt | 160.38541931633983 | 160.38541927421608 | 4.21e-8 | within 0.000001 relative | Agree |
| 95% UCL - Land's H ucl.landsH | 150.01627600053303 | 150.01627600053303 | 0 | within 0.02 relative | Agree |
| 95% UCL - approximateGamma ucl.approximateGamma | 144.11820417069387 | 144.11911939033314 | 0.000915 | within 0.005 relative | Agree |
| 95% UCL - adjustedGamma ucl.adjustedGamma | 148.6311334647566 | 148.6323491454564 | 0.00122 | within 0.005 relative | Agree |
| Distribution used distributionUsed | lognormal | lognormal | - | exact match | Agree |
| Recommended method recommendedMethod | landsH | landsH | - | exact match | Agree |
| 95% UCL - Chebyshev, 95% ucl.chebyshev95 | 276.43395818550414 | 276.43395818550414 | 0 | within 0.000001 relative | Agree |
| 95% UCL - Chebyshev, 97.5% ucl.chebyshev975 | 357.08074702883505 | 357.08074702883505 | 0 | within 0.000001 relative | Agree |
| 95% UCL - Chebyshev, 99% ucl.chebyshev99 | 515.4957474221862 | 515.4957474221862 | 0 | within 0.000001 relative | Agree |
Drawn from a lognormal distribution near a branch threshold, n = 27: ProUCL 5.2 finds lognormal and suggests Student's t
Boundary caseInput
27 values
| value |
|---|
| 2.942 |
| 23.45 |
| 490.1 |
| 10.7 |
| 1.218 |
| 30.27 |
| 11.12 |
| 45.03 |
| 49.91 |
| 2.529 |
| 10.01 |
| 44.86 |
| 30.93 |
| 1.616 |
| 21.98 |
| 20.73 |
| 475.8 |
| 5.055 |
| 3.182 |
| 12.09 |
| 66.6 |
| 48.38 |
| 41.93 |
| 55.31 |
| 55.83 |
| 107.8 |
| 22.65 |
Against USEPA ProUCL (ProUCL 5.2.0)
| Value | USEPA ProUCL | EnviroAutomate | Difference | Agreement band | Verdict |
|---|---|---|---|---|---|
| Sample size (n) n | 27 | 27 | 0 | exact match | Agree |
| Mean mean | 62.66748148148148 | 62.66748148148148 | 0 | within 0.000001 relative | Agree |
| Standard deviation sd | 123.69307681993499 | 123.69307681993497 | 1.42e-14 | within 0.000001 relative | Agree |
| Skewness skewness | 3.215399968058202 | 3.215399968058203 | 8.88e-16 | within 0.000001 relative | Agree |
| 95% UCL - Student's t ucl.studentT | 103.2692805034094 | 103.26927896769473 | 1.54e-6 | within 0.000001 relative | Agree |
| 95% UCL - Modified t (Johnson) ucl.modifiedT | 105.72435899264298 | 105.72435745692832 | 1.54e-6 | within 0.000001 relative | Agree |
| 95% UCL - Central limit theorem ucl.clt | 101.82280057274382 | 101.82280054929245 | 2.35e-8 | within 0.000001 relative | Agree |
| 95% UCL - Land's H ucl.landsH | 175.13325287319637 | 175.1332528731964 | 2.84e-14 | within 0.02 relative | Agree |
| 95% UCL - approximateGamma ucl.approximateGamma | 102.56006662262973 | 102.5609253731874 | 0.000859 | within 0.005 relative | Agree |
| 95% UCL - adjustedGamma ucl.adjustedGamma | 105.9323631797733 | 105.93350610848496 | 0.00114 | within 0.005 relative | Agree |
| Distribution used distributionUsed | lognormal | lognormal | - | exact match | Agree |
| Recommended method recommendedMethod | studentT | studentT | - | exact match | Agree |
| 95% UCL - Chebyshev, 95% ucl.chebyshev95 | 166.4299537903409 | 166.4299537903409 | 0 | within 0.000001 relative | Agree |
| 95% UCL - Chebyshev, 97.5% ucl.chebyshev975 | 211.32805844620864 | 211.32805844620864 | 0 | within 0.000001 relative | Agree |
| 95% UCL - Chebyshev, 99% ucl.chebyshev99 | 299.5216910598672 | 299.5216910598672 | 0 | within 0.000001 relative | Agree |
Drawn from a lognormal distribution near a branch threshold, n = 28: ProUCL 5.2 finds gamma and suggests adjusted gamma
Boundary caseInput
28 values
| value |
|---|
| 132.1 |
| 1.58 |
| 38.28 |
| 4.544 |
| 13.99 |
| 21.53 |
| 1.215 |
| 409.3 |
| 31.37 |
| 291.9 |
| 21.28 |
| 56.47 |
| 56.69 |
| 2.804 |
| 56.73 |
| 32.21 |
| 3.61 |
| 37.96 |
| 97.25 |
| 26.58 |
| 1.488 |
| 22.2 |
| 10.27 |
| 9.293 |
| 265.1 |
| 2.78 |
| 166.7 |
| 1.019 |
Against USEPA ProUCL (ProUCL 5.2.0)
| Value | USEPA ProUCL | EnviroAutomate | Difference | Agreement band | Verdict |
|---|---|---|---|---|---|
| Sample size (n) n | 28 | 28 | 0 | exact match | Agree |
| Mean mean | 64.86582142857144 | 64.86582142857144 | 0 | within 0.000001 relative | Agree |
| Standard deviation sd | 101.2886293611273 | 101.2886293611273 | 0 | within 0.000001 relative | Agree |
| Skewness skewness | 2.270587906041764 | 2.2705879060417655 | 1.33e-15 | within 0.000001 relative | Agree |
| 95% UCL - Student's t ucl.studentT | 97.46974645351426 | 97.46974594565216 | 5.08e-7 | within 0.000001 relative | Agree |
| 95% UCL - Modified t (Johnson) ucl.modifiedT | 98.83870322046025 | 98.83870271259815 | 5.08e-7 | within 0.000001 relative | Agree |
| 95% UCL - Central limit theorem ucl.clt | 96.35120117243339 | 96.35120115357581 | 1.89e-8 | within 0.000001 relative | Agree |
| 95% UCL - Land's H ucl.landsH | 294.14245143755016 | 294.14245143755016 | 0 | within 0.02 relative | Agree |
| 95% UCL - approximateGamma ucl.approximateGamma | 107.31257945002282 | 107.31360190461295 | 0.00102 | within 0.005 relative | Agree |
| 95% UCL - adjustedGamma ucl.adjustedGamma | 110.8007497168195 | 110.80209951714184 | 0.00135 | within 0.005 relative | Agree |
| Distribution used distributionUsed | gamma | gamma | - | exact match | Agree |
| Recommended method recommendedMethod | adjustedGamma | adjustedGamma | - | exact match | Agree |
| 95% UCL - Chebyshev, 95% ucl.chebyshev95 | 148.30278273111503 | 148.30278273111503 | 0 | within 0.000001 relative | Agree |
| 95% UCL - Chebyshev, 97.5% ucl.chebyshev975 | 184.40602253806918 | 184.40602253806918 | 0 | within 0.000001 relative | Agree |
| 95% UCL - Chebyshev, 99% ucl.chebyshev99 | 255.32384617678252 | 255.32384617678252 | 0 | within 0.000001 relative | Agree |
Drawn from a lognormal distribution near a branch threshold, n = 28: ProUCL 5.2 finds lognormal and suggests Land's H
Boundary caseInput
28 values
| value |
|---|
| 104.6 |
| 16.28 |
| 423 |
| 111.3 |
| 111.2 |
| 23.39 |
| 2.97 |
| 10.12 |
| 11.73 |
| 6.555 |
| 61.82 |
| 50.5 |
| 534.4 |
| 348.2 |
| 7.844 |
| 28.48 |
| 6.184 |
| 24.36 |
| 8.565 |
| 14.94 |
| 73.46 |
| 79.78 |
| 10.47 |
| 1.47 |
| 23.28 |
| 10.8 |
| 2.312 |
| 30.24 |
Against USEPA ProUCL (ProUCL 5.2.0)
| Value | USEPA ProUCL | EnviroAutomate | Difference | Agreement band | Verdict |
|---|---|---|---|---|---|
| Sample size (n) n | 28 | 28 | 0 | exact match | Agree |
| Mean mean | 76.36607142857143 | 76.36607142857143 | 0 | within 0.000001 relative | Agree |
| Standard deviation sd | 133.45664895441837 | 133.45664895441837 | 0 | within 0.000001 relative | Agree |
| Skewness skewness | 2.5699339040172906 | 2.56993390401729 | 4.44e-16 | within 0.000001 relative | Agree |
| 95% UCL - Student's t ucl.studentT | 119.32460096969568 | 119.32460030054284 | 6.69e-7 | within 0.000001 relative | Agree |
| 95% UCL - Modified t (Johnson) ucl.modifiedT | 121.3661174391272 | 121.36611676997435 | 6.69e-7 | within 0.000001 relative | Agree |
| 95% UCL - Central limit theorem ucl.clt | 117.85081950124862 | 117.85081947640211 | 2.48e-8 | within 0.000001 relative | Agree |
| 95% UCL - Land's H ucl.landsH | 202.85786296153438 | 202.85786296153438 | 0 | within 0.02 relative | Agree |
| 95% UCL - approximateGamma ucl.approximateGamma | 124.41214763340362 | 124.41313349414229 | 0.000986 | within 0.005 relative | Agree |
| 95% UCL - adjustedGamma ucl.adjustedGamma | 128.32651357027956 | 128.32781334896848 | 0.0013 | within 0.005 relative | Agree |
| Distribution used distributionUsed | lognormal | lognormal | - | exact match | Agree |
| Recommended method recommendedMethod | landsH | landsH | - | exact match | Agree |
| 95% UCL - Chebyshev, 95% ucl.chebyshev95 | 186.30158269584544 | 186.3015826958454 | 2.84e-14 | within 0.000001 relative | Agree |
| 95% UCL - Chebyshev, 97.5% ucl.chebyshev975 | 233.87076624018323 | 233.87076624018317 | 5.68e-14 | within 0.000001 relative | Agree |
| 95% UCL - Chebyshev, 99% ucl.chebyshev99 | 327.3112161076528 | 327.31121610765274 | 5.68e-14 | within 0.000001 relative | Agree |
Drawn from a lognormal distribution near a branch threshold, n = 28: ProUCL 5.2 finds no discernible distribution and suggests Student's t
Boundary caseInput
28 values
| value |
|---|
| 0.5769 |
| 16.94 |
| 11.6 |
| 2003 |
| 48.12 |
| 163.6 |
| 35.7 |
| 18.31 |
| 133.6 |
| 54.65 |
| 759.6 |
| 76.74 |
| 9.709 |
| 20.99 |
| 31.3 |
| 12.04 |
| 16.33 |
| 21.51 |
| 12.66 |
| 6.065 |
| 12.32 |
| 19.04 |
| 0.9568 |
| 158.3 |
| 21.98 |
| 23.6 |
| 18.45 |
| 4.883 |
Against USEPA ProUCL (ProUCL 5.2.0)
| Value | USEPA ProUCL | EnviroAutomate | Difference | Agreement band | Verdict |
|---|---|---|---|---|---|
| Sample size (n) n | 28 | 28 | 0 | exact match | Agree |
| Mean mean | 132.59181071428569 | 132.59181071428569 | 0 | within 0.000001 relative | Agree |
| Standard deviation sd | 393.66020959786033 | 393.66020959786033 | 0 | within 0.000001 relative | Agree |
| Skewness skewness | 4.417405354570524 | 4.417405354570524 | 0 | within 0.000001 relative | Agree |
| 95% UCL - Student's t ucl.studentT | 259.3075935221603 | 259.3075915483445 | 1.97e-6 | within 0.000001 relative | Agree |
| 95% UCL - Modified t (Johnson) ucl.modifiedT | 269.65852636596355 | 269.6585243921477 | 1.97e-6 | within 0.000001 relative | Agree |
| 95% UCL - Central limit theorem ucl.clt | 254.9603457355891 | 254.96034566229872 | 7.33e-8 | within 0.000001 relative | Agree |
| 95% UCL - Land's H ucl.landsH | 310.16571817219204 | 310.16571817219204 | 0 | within 0.02 relative | Agree |
| 95% UCL - approximateGamma ucl.approximateGamma | 239.54520684398665 | 239.55115839650796 | 0.00595 | within 0.005 relative | Agree |
| 95% UCL - adjustedGamma ucl.adjustedGamma | 248.77728884366496 | 248.7852064789427 | 0.00792 | within 0.005 relative | Agree |
| Distribution used distributionUsed | nonparametric | nonparametric | - | exact match | Agree |
| Recommended method recommendedMethod | studentT | studentT | - | exact match | Agree |
| 95% UCL - Chebyshev, 95% ucl.chebyshev95 | 456.8711684441818 | 456.8711684441819 | 5.68e-14 | within 0.000001 relative | Agree |
| 95% UCL - Chebyshev, 97.5% ucl.chebyshev975 | 597.1871055756388 | 597.1871055756388 | 0 | within 0.000001 relative | Agree |
| 95% UCL - Chebyshev, 99% ucl.chebyshev99 | 872.8105935616874 | 872.8105935616874 | 0 | within 0.000001 relative | Agree |
Drawn from a lognormal distribution near a branch threshold, n = 29: ProUCL 5.2 finds gamma and suggests adjusted gamma
Boundary caseInput
29 values
| value |
|---|
| 22.48 |
| 217 |
| 36.69 |
| 17.33 |
| 17.17 |
| 78.2 |
| 3.007 |
| 72.31 |
| 58.93 |
| 26.67 |
| 5.892 |
| 15.04 |
| 11.75 |
| 75.79 |
| 14.2 |
| 39.23 |
| 4.616 |
| 6.662 |
| 9.733 |
| 17.19 |
| 6.976 |
| 45 |
| 14.89 |
| 6.336 |
| 81.46 |
| 12.82 |
| 2.974 |
| 24.63 |
| 10.96 |
Against USEPA ProUCL (ProUCL 5.2.0)
| Value | USEPA ProUCL | EnviroAutomate | Difference | Agreement band | Verdict |
|---|---|---|---|---|---|
| Sample size (n) n | 29 | 29 | 0 | exact match | Agree |
| Mean mean | 32.96331034482759 | 32.96331034482759 | 0 | within 0.000001 relative | Agree |
| Standard deviation sd | 43.00030889100304 | 43.00030889100304 | 0 | within 0.000001 relative | Agree |
| Skewness skewness | 3.0756556905363337 | 3.0756556905363333 | 4.44e-16 | within 0.000001 relative | Agree |
| 95% UCL - Student's t ucl.studentT | 46.54676762496818 | 46.54676753829462 | 8.67e-8 | within 0.000001 relative | Agree |
| 95% UCL - Modified t (Johnson) ucl.modifiedT | 47.30684891655114 | 47.306848829877566 | 8.67e-8 | within 0.000001 relative | Agree |
| 95% UCL - Central limit theorem ucl.clt | 46.09739567273747 | 46.09739566487106 | 7.87e-9 | within 0.000001 relative | Agree |
| 95% UCL - Land's H ucl.landsH | 55.260389652005045 | 55.260389652004996 | 4.97e-14 | within 0.02 relative | Agree |
| 95% UCL - approximateGamma ucl.approximateGamma | 46.64854533208655 | 46.648594128066 | 4.88e-5 | within 0.005 relative | Agree |
| 95% UCL - adjustedGamma ucl.adjustedGamma | 47.64246143558416 | 47.64252448008197 | 6.30e-5 | within 0.005 relative | Agree |
| Distribution used distributionUsed | gamma | gamma | - | exact match | Agree |
| Recommended method recommendedMethod | adjustedGamma | adjustedGamma | - | exact match | Agree |
| 95% UCL - Chebyshev, 95% ucl.chebyshev95 | 67.76893054582771 | 67.76893054582773 | 1.42e-14 | within 0.000001 relative | Agree |
| 95% UCL - Chebyshev, 97.5% ucl.chebyshev975 | 82.82935021032199 | 82.829350210322 | 1.42e-14 | within 0.000001 relative | Agree |
| 95% UCL - Chebyshev, 99% ucl.chebyshev99 | 112.41262837046898 | 112.412628370469 | 1.42e-14 | within 0.000001 relative | Agree |
Drawn from a lognormal distribution near a branch threshold, n = 29: ProUCL 5.2 finds lognormal and suggests Land's H
Boundary caseInput
29 values
| value |
|---|
| 486.5 |
| 8.609 |
| 26.57 |
| 22.15 |
| 3.946 |
| 8.249 |
| 9.191 |
| 91.37 |
| 174.1 |
| 14.04 |
| 53.45 |
| 245.4 |
| 379.7 |
| 11.08 |
| 17.12 |
| 70.27 |
| 2.86 |
| 3.673 |
| 47.02 |
| 29.33 |
| 1.179 |
| 10.65 |
| 12.53 |
| 7.374 |
| 11.84 |
| 14.34 |
| 0.5691 |
| 23.67 |
| 2.6 |
Against USEPA ProUCL (ProUCL 5.2.0)
| Value | USEPA ProUCL | EnviroAutomate | Difference | Agreement band | Verdict |
|---|---|---|---|---|---|
| Sample size (n) n | 29 | 29 | 0 | exact match | Agree |
| Mean mean | 61.702762068965505 | 61.702762068965505 | 0 | within 0.000001 relative | Agree |
| Standard deviation sd | 117.03232260157998 | 117.03232260157999 | 1.42e-14 | within 0.000001 relative | Agree |
| Skewness skewness | 2.718432175889089 | 2.718432175889089 | 0 | within 0.000001 relative | Agree |
| 95% UCL - Student's t ucl.studentT | 98.67234660110844 | 98.67234636521223 | 2.36e-7 | within 0.000001 relative | Agree |
| 95% UCL - Modified t (Johnson) ucl.modifiedT | 100.50076287340251 | 100.50076263750631 | 2.36e-7 | within 0.000001 relative | Agree |
| 95% UCL - Central limit theorem ucl.clt | 97.44930786864552 | 97.44930784723579 | 2.14e-8 | within 0.000001 relative | Agree |
| 95% UCL - Land's H ucl.landsH | 181.87760907012645 | 181.87760907012645 | 0 | within 0.02 relative | Agree |
| 95% UCL - approximateGamma ucl.approximateGamma | 102.59104566745954 | 102.59208226367338 | 0.00104 | within 0.005 relative | Agree |
| 95% UCL - adjustedGamma ucl.adjustedGamma | 105.84360671332902 | 105.84496341255593 | 0.00136 | within 0.005 relative | Agree |
| Distribution used distributionUsed | lognormal | lognormal | - | exact match | Agree |
| Recommended method recommendedMethod | landsH | landsH | - | exact match | Agree |
| 95% UCL - Chebyshev, 95% ucl.chebyshev95 | 156.43190883013662 | 156.4319088301366 | 2.84e-14 | within 0.000001 relative | Agree |
| 95% UCL - Chebyshev, 97.5% ucl.chebyshev975 | 197.42128630549362 | 197.42128630549362 | 0 | within 0.000001 relative | Agree |
| 95% UCL - Chebyshev, 99% ucl.chebyshev99 | 277.9369812514663 | 277.9369812514663 | 0 | within 0.000001 relative | Agree |
Drawn from a lognormal distribution near a branch threshold, n = 29: ProUCL 5.2 finds normal and suggests Student's t
Boundary caseInput
29 values
| value |
|---|
| 83.35 |
| 70.09 |
| 2.477 |
| 196.3 |
| 38.32 |
| 2.518 |
| 66.27 |
| 4.939 |
| 9.78 |
| 83.8 |
| 16.13 |
| 10.11 |
| 53.64 |
| 34.89 |
| 14.36 |
| 53.12 |
| 101.4 |
| 55.28 |
| 4.215 |
| 29.57 |
| 108 |
| 78.74 |
| 6.374 |
| 22.83 |
| 103.2 |
| 2.848 |
| 81.79 |
| 5.229 |
| 68.51 |
Against USEPA ProUCL (ProUCL 5.2.0)
| Value | USEPA ProUCL | EnviroAutomate | Difference | Agreement band | Verdict |
|---|---|---|---|---|---|
| Sample size (n) n | 29 | 29 | 0 | exact match | Agree |
| Mean mean | 48.554482758620686 | 48.554482758620686 | 0 | within 0.000001 relative | Agree |
| Standard deviation sd | 45.217586708697986 | 45.217586708697986 | 0 | within 0.000001 relative | Agree |
| Skewness skewness | 1.2804140503902877 | 1.2804140503902877 | 0 | within 0.000001 relative | Agree |
| 95% UCL - Student's t ucl.studentT | 62.838360554139584 | 62.83836046299676 | 9.11e-8 | within 0.000001 relative | Agree |
| 95% UCL - Modified t (Johnson) ucl.modifiedT | 63.1711032745221 | 63.17110318337928 | 9.11e-8 | within 0.000001 relative | Agree |
| 95% UCL - Central limit theorem ucl.clt | 62.36581708320883 | 62.36581707493679 | 8.27e-9 | within 0.000001 relative | Agree |
| 95% UCL - Land's H ucl.landsH | 128.2206681941133 | 128.2206681941133 | 0 | within 0.02 relative | Agree |
| 95% UCL - approximateGamma ucl.approximateGamma | 69.78084083000749 | 69.78093536943467 | 9.45e-5 | within 0.005 relative | Agree |
| 95% UCL - adjustedGamma ucl.adjustedGamma | 71.33603629593335 | 71.33615858720442 | 0.000122 | within 0.005 relative | Agree |
| Distribution used distributionUsed | normal | normal | - | exact match | Agree |
| Recommended method recommendedMethod | studentT | studentT | - | exact match | Agree |
| 95% UCL - Chebyshev, 95% ucl.chebyshev95 | 85.15482796493211 | 85.15482796493211 | 0 | within 0.000001 relative | Agree |
| 95% UCL - Chebyshev, 97.5% ucl.chebyshev975 | 100.99182657289175 | 100.99182657289177 | 1.42e-14 | within 0.000001 relative | Agree |
| 95% UCL - Chebyshev, 99% ucl.chebyshev99 | 132.10054369222067 | 132.1005436922207 | 2.84e-14 | within 0.000001 relative | Agree |
Drawn from a lognormal distribution near a branch threshold, n = 9: not normal and under ten results, so ProUCL 5.2 makes no suggestion
Boundary caseInput
9 values
| value |
|---|
| 18.86 |
| 20.4 |
| 3.49 |
| 1.067 |
| 1.654 |
| 35.13 |
| 315.4 |
| 5.766 |
| 21.7 |
Against USEPA ProUCL (ProUCL 5.2.0)
| Value | USEPA ProUCL | EnviroAutomate | Difference | Agreement band | Verdict |
|---|---|---|---|---|---|
| Sample size (n) n | 9 | 9 | 0 | exact match | Agree |
| Mean mean | 47.05188888888889 | 47.05188888888889 | 0 | within 0.000001 relative | Agree |
| Standard deviation sd | 101.29067413198074 | 101.29067413198074 | 0 | within 0.000001 relative | Agree |
| Skewness skewness | 2.9260712927254584 | 2.926071292725458 | 4.44e-16 | within 0.000001 relative | Agree |
| 95% UCL - Student's t ucl.studentT | 109.83684673528354 | 109.83684698965789 | 2.54e-7 | within 0.000001 relative | Agree |
| 95% UCL - Modified t (Johnson) ucl.modifiedT | 115.32543439821686 | 115.32543465259118 | 2.54e-7 | within 0.000001 relative | Agree |
| 95% UCL - Central limit theorem ucl.clt | 102.58799982960062 | 102.5879997963383 | 3.33e-8 | within 0.000001 relative | Agree |
| 95% UCL - Land's H ucl.landsH | 1211.7949970441891 | 1211.7949970441891 | 0 | within 0.02 relative | Agree |
| 95% UCL - approximateGamma ucl.approximateGamma | 155.31039397951477 | 155.56801409009861 | 0.258 | within 0.005 relative | Agree |
| 95% UCL - adjustedGamma ucl.adjustedGamma | 205.61830483115585 | 206.40508595490482 | 0.787 | within 0.005 relative | Agree |
| 95% UCL - Chebyshev, 95% ucl.chebyshev95 | 194.22382637702665 | 194.22382637702663 | 2.84e-14 | within 0.000001 relative | Agree |
| 95% UCL - Chebyshev, 97.5% ucl.chebyshev975 | 257.90524129243687 | 257.9052412924368 | 5.68e-14 | within 0.000001 relative | Agree |
| 95% UCL - Chebyshev, 99% ucl.chebyshev99 | 382.99504974682645 | 382.99504974682645 | 0 | within 0.000001 relative | Agree |
Drawn from a lognormal distribution near a branch threshold, n = 9: ProUCL 5.2 finds normal and suggests Student's t
Boundary caseInput
9 values
| value |
|---|
| 1.988 |
| 0.736 |
| 54.04 |
| 39.15 |
| 21.6 |
| 7.207 |
| 13.27 |
| 10.36 |
| 30.3 |
Against USEPA ProUCL (ProUCL 5.2.0)
| Value | USEPA ProUCL | EnviroAutomate | Difference | Agreement band | Verdict |
|---|---|---|---|---|---|
| Sample size (n) n | 9 | 9 | 0 | exact match | Agree |
| Mean mean | 19.85011111111111 | 19.85011111111111 | 0 | within 0.000001 relative | Agree |
| Standard deviation sd | 18.135976293299215 | 18.135976293299215 | 0 | within 0.000001 relative | Agree |
| Skewness skewness | 0.8745068952289224 | 0.8745068952289218 | 6.66e-16 | within 0.000001 relative | Agree |
| 95% UCL - Student's t ucl.studentT | 31.09168410720287 | 31.091684152748293 | 4.55e-8 | within 0.000001 relative | Agree |
| 95% UCL - Modified t (Johnson) ucl.modifiedT | 31.385388483502837 | 31.385388529048264 | 4.55e-8 | within 0.000001 relative | Agree |
| 95% UCL - Central limit theorem ucl.clt | 29.793786578513068 | 29.79378657255749 | 5.96e-9 | within 0.000001 relative | Agree |
| 95% UCL - Land's H ucl.landsH | 246.53963712723487 | 246.5396371272353 | 4.26e-13 | within 0.02 relative | Agree |
| 95% UCL - approximateGamma ucl.approximateGamma | 44.14765517176354 | 44.15424560713556 | 0.00659 | within 0.005 relative | Agree |
| 95% UCL - adjustedGamma ucl.adjustedGamma | 52.967803234513454 | 52.98523854557751 | 0.0174 | within 0.005 relative | Agree |
| 95% UCL - Chebyshev, 95% ucl.chebyshev95 | 46.20107374609131 | 46.20107374609131 | 0 | within 0.000001 relative | Agree |
| 95% UCL - Chebyshev, 97.5% ucl.chebyshev975 | 57.6031563279959 | 57.6031563279959 | 0 | within 0.000001 relative | Agree |
| 95% UCL - Chebyshev, 99% ucl.chebyshev99 | 80.0003396827651 | 80.0003396827651 | 0 | within 0.000001 relative | Agree |
Drawn from a lognormal distribution, sd of logs 0.3, n = 10: ProUCL 5.2 finds normal and suggests Student's t
Boundary caseInput
10 values
| value |
|---|
| 18.36 |
| 18.68 |
| 24.51 |
| 10.19 |
| 33.88 |
| 12.58 |
| 24.63 |
| 25.74 |
| 23.49 |
| 33.87 |
Against USEPA ProUCL (ProUCL 5.2.0)
| Value | USEPA ProUCL | EnviroAutomate | Difference | Agreement band | Verdict |
|---|---|---|---|---|---|
| Sample size (n) n | 10 | 10 | 0 | exact match | Agree |
| Mean mean | 22.593000000000004 | 22.593000000000004 | 0 | within 0.000001 relative | Agree |
| Standard deviation sd | 7.891092094535739 | 7.891092094535739 | 0 | within 0.000001 relative | Agree |
| Skewness skewness | -0.036254132577482 | -0.03625413257748207 | 5.55e-17 | within 0.000001 relative | Agree |
| 95% UCL - Student's t ucl.studentT | 27.167317825958435 | 27.167317794252334 | 3.17e-8 | within 0.000001 relative | Agree |
| 95% UCL - Modified t (Johnson) ucl.modifiedT | 27.16254974764216 | 27.16254971593606 | 3.17e-8 | within 0.000001 relative | Agree |
| 95% UCL - Central limit theorem ucl.clt | 26.69753883400866 | 26.697538831550325 | 2.46e-9 | within 0.000001 relative | Agree |
| 95% UCL - Land's H ucl.landsH | 30.02036674093878 | 30.02036674093878 | 0 | within 0.02 relative | Agree |
| 95% UCL - approximateGamma ucl.approximateGamma | 28.49624944016502 | 28.49625215615935 | 2.72e-6 | within 0.005 relative | Agree |
| 95% UCL - adjustedGamma ucl.adjustedGamma | 29.695242024064267 | 29.6952473079855 | 5.28e-6 | within 0.005 relative | Agree |
| Distribution used distributionUsed | normal | normal | - | exact match | Agree |
| Recommended method recommendedMethod | studentT | studentT | - | exact match | Agree |
| 95% UCL - Chebyshev, 95% ucl.chebyshev95 | 33.47011981383143 | 33.47011981383143 | 0 | within 0.000001 relative | Agree |
| 95% UCL - Chebyshev, 97.5% ucl.chebyshev975 | 38.17665824616714 | 38.17665824616714 | 0 | within 0.000001 relative | Agree |
| 95% UCL - Chebyshev, 99% ucl.chebyshev99 | 47.42174163142384 | 47.42174163142384 | 0 | within 0.000001 relative | Agree |
Drawn from a lognormal distribution, sd of logs 0.3, n = 100: ProUCL 5.2 finds normal and suggests Student's t
Boundary caseInput
100 values
| value |
|---|
| 18.57 |
| 27.15 |
| 14.25 |
| 22.03 |
| 17.72 |
| 30.28 |
| 12.93 |
| 14.7 |
| 13.58 |
| 16.36 |
| 27.83 |
| 14.78 |
| 17.46 |
| 19.83 |
| 17.44 |
| 20.38 |
| 18.83 |
| 14.84 |
| 7.971 |
| 26.64 |
| 21.8 |
| 15.35 |
| 12.9 |
| 21.64 |
| 21.05 |
| 14.02 |
| 21.02 |
| 21.09 |
| 17.06 |
| 20.49 |
| 15.94 |
| 16.74 |
| 24.56 |
| 19.67 |
| 22.71 |
| 21.75 |
| 18.97 |
| 27.87 |
| 28.25 |
| 18.35 |
| 20.87 |
| 17.36 |
| 15.52 |
| 26.72 |
| 13.94 |
| 12.83 |
| 17.66 |
| 20.63 |
| 21.97 |
| 26.52 |
| 27.37 |
| 23.87 |
| 17.02 |
| 11 |
| 24.29 |
| 23.53 |
| 15.67 |
| 22.81 |
| 15.07 |
| 20.07 |
| 25 |
| 16.22 |
| 9.939 |
| 23.44 |
| 23.31 |
| 19.88 |
| 14.05 |
| 20.54 |
| 23.22 |
| 18.47 |
| 16.67 |
| 17.59 |
| 13.63 |
| 21.06 |
| 34.84 |
| 23.27 |
| 11.93 |
| 11.01 |
| 21.9 |
| 15.55 |
| 23.85 |
| 19.77 |
| 17.23 |
| 12.06 |
| 18.09 |
| 23.56 |
| 24.96 |
| 25.52 |
| 25.25 |
| 11.41 |
| 30.27 |
| 15.87 |
| 23.71 |
| 25.38 |
| 24.96 |
| 23.69 |
| 17.96 |
| 14.76 |
| 20.13 |
| 23.72 |
Against USEPA ProUCL (ProUCL 5.2.0)
| Value | USEPA ProUCL | EnviroAutomate | Difference | Agreement band | Verdict |
|---|---|---|---|---|---|
| Sample size (n) n | 100 | 100 | 0 | exact match | Agree |
| Mean mean | 19.731900000000003 | 19.731900000000003 | 0 | within 0.000001 relative | Agree |
| Standard deviation sd | 5.120214642951894 | 5.120214642951894 | 0 | within 0.000001 relative | Agree |
| Skewness skewness | 0.18622187983483005 | 0.18622187983482996 | 8.33e-17 | within 0.000001 relative | Agree |
| 95% UCL - Student's t ucl.studentT | 20.582055819708568 | 20.582055911006787 | 9.13e-8 | within 0.000001 relative | Agree |
| 95% UCL - Modified t (Johnson) ucl.modifiedT | 20.583644979701848 | 20.583645071000067 | 9.13e-8 | within 0.000001 relative | Agree |
| 95% UCL - Central limit theorem ucl.clt | 20.574100363127368 | 20.57410036262295 | 5.04e-10 | within 0.000001 relative | Agree |
| 95% UCL - Land's H ucl.landsH | 20.73962890883413 | 20.73962890883413 | 0 | within 0.02 relative | Agree |
| 95% UCL - approximateGamma ucl.approximateGamma | 20.635460319917 | 20.635460319498893 | 4.18e-10 | within 0.005 relative | Agree |
| 95% UCL - adjustedGamma ucl.adjustedGamma | 20.64882209826513 | 20.648822097783782 | 4.81e-10 | within 0.005 relative | Agree |
| Distribution used distributionUsed | normal | normal | - | exact match | Agree |
| Recommended method recommendedMethod | studentT | studentT | - | exact match | Agree |
| 95% UCL - Chebyshev, 95% ucl.chebyshev95 | 21.96374981978645 | 21.96374981978645 | 0 | within 0.000001 relative | Agree |
| 95% UCL - Chebyshev, 97.5% ucl.chebyshev975 | 22.929473019660477 | 22.929473019660477 | 0 | within 0.000001 relative | Agree |
| 95% UCL - Chebyshev, 99% ucl.chebyshev99 | 24.82644924502649 | 24.826449245026495 | 3.55e-15 | within 0.000001 relative | Agree |
Drawn from a lognormal distribution, sd of logs 0.3, n = 28: ProUCL 5.2 finds no discernible distribution and suggests Student's t
Boundary caseInput
28 values
| value |
|---|
| 16.53 |
| 25.02 |
| 18.53 |
| 19.38 |
| 16.28 |
| 18.49 |
| 30.58 |
| 24.44 |
| 15.78 |
| 16.47 |
| 12.75 |
| 26.38 |
| 39.98 |
| 14.88 |
| 21.73 |
| 15.18 |
| 14.4 |
| 17.89 |
| 31.5 |
| 17.16 |
| 18.37 |
| 16.52 |
| 12.49 |
| 12.56 |
| 23.35 |
| 17.94 |
| 13.58 |
| 17.51 |
Against USEPA ProUCL (ProUCL 5.2.0)
| Value | USEPA ProUCL | EnviroAutomate | Difference | Agreement band | Verdict |
|---|---|---|---|---|---|
| Sample size (n) n | 28 | 28 | 0 | exact match | Agree |
| Mean mean | 19.48821428571429 | 19.48821428571429 | 0 | within 0.000001 relative | Agree |
| Standard deviation sd | 6.443281918270134 | 6.443281918270134 | 0 | within 0.000001 relative | Agree |
| Skewness skewness | 1.5950564170196253 | 1.595056417019625 | 2.22e-16 | within 0.000001 relative | Agree |
| 95% UCL - Student's t ucl.studentT | 21.562250452487344 | 21.56225042018067 | 3.23e-8 | within 0.000001 relative | Agree |
| 95% UCL - Modified t (Johnson) ucl.modifiedT | 21.623425441596886 | 21.623425409290213 | 3.23e-8 | within 0.000001 relative | Agree |
| 95% UCL - Central limit theorem ucl.clt | 21.491096339436226 | 21.491096338236634 | 1.20e-9 | within 0.000001 relative | Agree |
| 95% UCL - Land's H ucl.landsH | 21.512412573304633 | 21.512412573304633 | 0 | within 0.02 relative | Agree |
| 95% UCL - approximateGamma ucl.approximateGamma | 21.5295515900527 | 21.529551602175392 | 1.21e-8 | within 0.005 relative | Agree |
| 95% UCL - adjustedGamma ucl.adjustedGamma | 21.66266977397315 | 21.662669790069206 | 1.61e-8 | within 0.005 relative | Agree |
| Distribution used distributionUsed | nonparametric | nonparametric | - | exact match | Agree |
| Recommended method recommendedMethod | studentT | studentT | - | exact match | Agree |
| 95% UCL - Chebyshev, 95% ucl.chebyshev95 | 24.795896574111488 | 24.795896574111488 | 0 | within 0.000001 relative | Agree |
| 95% UCL - Chebyshev, 97.5% ucl.chebyshev975 | 27.092534940198362 | 27.092534940198362 | 0 | within 0.000001 relative | Agree |
| 95% UCL - Chebyshev, 99% ucl.chebyshev99 | 31.603836293731717 | 31.603836293731717 | 0 | within 0.000001 relative | Agree |
Drawn from a lognormal distribution, sd of logs 0.3, n = 8: ProUCL 5.2 finds normal and suggests Student's t
Boundary caseInput
8 values
| value |
|---|
| 11.97 |
| 26.09 |
| 20.41 |
| 17.08 |
| 14.93 |
| 16.98 |
| 21.86 |
| 22.69 |
Against USEPA ProUCL (ProUCL 5.2.0)
| Value | USEPA ProUCL | EnviroAutomate | Difference | Agreement band | Verdict |
|---|---|---|---|---|---|
| Sample size (n) n | 8 | 8 | 0 | exact match | Agree |
| Mean mean | 19.00125 | 19.00125 | 0 | within 0.000001 relative | Agree |
| Standard deviation sd | 4.595098125798217 | 4.595098125798217 | 0 | within 0.000001 relative | Agree |
| Skewness skewness | 0.004158925464667383 | 0.004158925464667355 | 2.78e-17 | within 0.000001 relative | Agree |
| 95% UCL - Student's t ucl.studentT | 22.079206095592703 | 22.079206126660928 | 3.11e-8 | within 0.000001 relative | Agree |
| 95% UCL - Modified t (Johnson) ucl.modifiedT | 22.079604234563703 | 22.07960426563193 | 3.11e-8 | within 0.000001 relative | Agree |
| 95% UCL - Central limit theorem ucl.clt | 21.673499801600325 | 21.67349979999983 | 1.60e-9 | within 0.000001 relative | Agree |
| 95% UCL - Land's H ucl.landsH | 23.113274561804182 | 23.113274561804186 | 3.55e-15 | within 0.02 relative | Agree |
| 95% UCL - approximateGamma ucl.approximateGamma | 22.711910306359623 | 22.711910752492468 | 4.46e-7 | within 0.005 relative | Agree |
| 95% UCL - adjustedGamma ucl.adjustedGamma | 23.788326939396637 | 23.78832805053679 | 1.11e-6 | within 0.005 relative | Agree |
| 95% UCL - Chebyshev, 95% ucl.chebyshev95 | 26.082771807921752 | 26.082771807921752 | 0 | within 0.000001 relative | Agree |
| 95% UCL - Chebyshev, 97.5% ucl.chebyshev975 | 29.14695195109028 | 29.146951951090276 | 3.55e-15 | within 0.000001 relative | Agree |
| 95% UCL - Chebyshev, 99% ucl.chebyshev99 | 35.165940500384295 | 35.16594050038429 | 7.11e-15 | within 0.000001 relative | Agree |
Drawn from a lognormal distribution, sd of logs 0.6, n = 100: ProUCL 5.2 finds gamma and suggests approximate gamma
Boundary caseInput
100 values
| value |
|---|
| 27.67 |
| 20.19 |
| 52.26 |
| 9.722 |
| 12 |
| 10.12 |
| 23.48 |
| 31.14 |
| 8.274 |
| 11.79 |
| 14.24 |
| 11.86 |
| 51.25 |
| 13.88 |
| 23.19 |
| 35.6 |
| 21.73 |
| 12.23 |
| 12.78 |
| 23.49 |
| 12.87 |
| 49.8 |
| 16.86 |
| 30.84 |
| 15.2 |
| 31.35 |
| 16.44 |
| 50.23 |
| 12.54 |
| 46.9 |
| 7.627 |
| 19.14 |
| 24.29 |
| 21.3 |
| 14.62 |
| 31.19 |
| 41.19 |
| 18.12 |
| 3.249 |
| 12.09 |
| 21.16 |
| 11.11 |
| 33.76 |
| 22.61 |
| 13.12 |
| 35.76 |
| 22.72 |
| 14.3 |
| 13.24 |
| 23.86 |
| 10.73 |
| 14.85 |
| 10.46 |
| 20.28 |
| 29.55 |
| 8.674 |
| 57.58 |
| 16.19 |
| 15.44 |
| 28.03 |
| 24.07 |
| 29.28 |
| 54.76 |
| 9.695 |
| 30.17 |
| 19.08 |
| 23.67 |
| 14.02 |
| 14.06 |
| 43.61 |
| 11.21 |
| 36.54 |
| 84.65 |
| 15.97 |
| 10.56 |
| 12.87 |
| 45.73 |
| 36.05 |
| 42.43 |
| 30.16 |
| 24.2 |
| 80.69 |
| 18.95 |
| 38.31 |
| 36.95 |
| 136.8 |
| 22.92 |
| 7.956 |
| 35.16 |
| 22.02 |
| 24.98 |
| 25.17 |
| 19.07 |
| 15.92 |
| 31.05 |
| 12.98 |
| 37.69 |
| 33.72 |
| 18.35 |
| 16.18 |
Against USEPA ProUCL (ProUCL 5.2.0)
| Value | USEPA ProUCL | EnviroAutomate | Difference | Agreement band | Verdict |
|---|---|---|---|---|---|
| Sample size (n) n | 100 | 100 | 0 | exact match | Agree |
| Mean mean | 25.73817 | 25.73817 | 0 | within 0.000001 relative | Agree |
| Standard deviation sd | 18.546862140907784 | 18.546862140907784 | 0 | within 0.000001 relative | Agree |
| Skewness skewness | 2.8989295646971556 | 2.898929564697155 | 4.44e-16 | within 0.000001 relative | Agree |
| 95% UCL - Student's t ucl.studentT | 28.81767425635571 | 28.81767458706362 | 3.31e-7 | within 0.000001 relative | Agree |
| 95% UCL - Modified t (Johnson) ucl.modifiedT | 28.907284334676778 | 28.907284665384687 | 3.31e-7 | within 0.000001 relative | Agree |
| 95% UCL - Central limit theorem ucl.clt | 28.788857347931263 | 28.788857346104113 | 1.83e-9 | within 0.000001 relative | Agree |
| 95% UCL - Land's H ucl.landsH | 28.701288856840655 | 28.701288856840655 | 0 | within 0.02 relative | Agree |
| 95% UCL - approximateGamma ucl.approximateGamma | 28.498766870016215 | 28.49876688891794 | 1.89e-8 | within 0.005 relative | Agree |
| 95% UCL - adjustedGamma ucl.adjustedGamma | 28.540895414054848 | 28.540895433984435 | 1.99e-8 | within 0.005 relative | Agree |
| Distribution used distributionUsed | gamma | gamma | - | exact match | Agree |
| Recommended method recommendedMethod | approximateGamma | approximateGamma | - | exact match | Agree |
| 95% UCL - Chebyshev, 95% ucl.chebyshev95 | 33.82255977919974 | 33.82255977919974 | 0 | within 0.000001 relative | Agree |
| 95% UCL - Chebyshev, 97.5% ucl.chebyshev975 | 37.32068169465401 | 37.32068169465401 | 0 | within 0.000001 relative | Agree |
| 95% UCL - Chebyshev, 99% ucl.chebyshev99 | 44.192064827951626 | 44.192064827951626 | 0 | within 0.000001 relative | Agree |
Drawn from a lognormal distribution, sd of logs 0.6, n = 15: ProUCL 5.2 finds gamma and suggests adjusted gamma
Boundary caseInput
15 values
| value |
|---|
| 13.52 |
| 63.26 |
| 9.992 |
| 23.35 |
| 27.29 |
| 25.42 |
| 22.47 |
| 7.983 |
| 14.74 |
| 25.29 |
| 16.48 |
| 19.01 |
| 25.01 |
| 60.92 |
| 10.33 |
Against USEPA ProUCL (ProUCL 5.2.0)
| Value | USEPA ProUCL | EnviroAutomate | Difference | Agreement band | Verdict |
|---|---|---|---|---|---|
| Sample size (n) n | 15 | 15 | 0 | exact match | Agree |
| Mean mean | 24.337666666666667 | 24.337666666666667 | 0 | within 0.000001 relative | Agree |
| Standard deviation sd | 16.556564454131465 | 16.556564454131465 | 0 | within 0.000001 relative | Agree |
| Skewness skewness | 1.726649566053839 | 1.726649566053839 | 0 | within 0.000001 relative | Agree |
| 95% UCL - Student's t ucl.studentT | 31.86706780507759 | 31.86706769423052 | 1.11e-7 | within 0.000001 relative | Agree |
| 95% UCL - Modified t (Johnson) ucl.modifiedT | 32.18470541430057 | 32.184705303453505 | 1.11e-7 | within 0.000001 relative | Agree |
| 95% UCL - Central limit theorem ucl.clt | 31.369229334038454 | 31.369229329827032 | 4.21e-9 | within 0.000001 relative | Agree |
| 95% UCL - Land's H ucl.landsH | 34.343785483711336 | 34.343785483711336 | 0 | within 0.02 relative | Agree |
| 95% UCL - approximateGamma ucl.approximateGamma | 32.63487842061709 | 32.63489093124583 | 1.25e-5 | within 0.005 relative | Agree |
| 95% UCL - adjustedGamma ucl.adjustedGamma | 33.86040729338033 | 33.860427864805146 | 2.06e-5 | within 0.005 relative | Agree |
| Distribution used distributionUsed | gamma | gamma | - | exact match | Agree |
| Recommended method recommendedMethod | adjustedGamma | adjustedGamma | - | exact match | Agree |
| 95% UCL - Chebyshev, 95% ucl.chebyshev95 | 42.97146517717328 | 42.97146517717328 | 0 | within 0.000001 relative | Agree |
| 95% UCL - Chebyshev, 97.5% ucl.chebyshev975 | 51.03432467777181 | 51.03432467777181 | 0 | within 0.000001 relative | Agree |
| 95% UCL - Chebyshev, 99% ucl.chebyshev99 | 66.87225089006236 | 66.87225089006236 | 0 | within 0.000001 relative | Agree |
Drawn from a lognormal distribution, sd of logs 0.6, n = 40: ProUCL 5.2 finds gamma and suggests adjusted gamma
Boundary caseInput
40 values
| value |
|---|
| 22.8 |
| 10.61 |
| 127 |
| 16.66 |
| 28.31 |
| 26.94 |
| 19.45 |
| 20.42 |
| 25.82 |
| 46.97 |
| 39.55 |
| 62.36 |
| 8.112 |
| 4.627 |
| 14.95 |
| 27.36 |
| 21.6 |
| 30.38 |
| 16.37 |
| 27.78 |
| 64.42 |
| 8.167 |
| 19.31 |
| 16.11 |
| 16.44 |
| 29.77 |
| 36.22 |
| 16.42 |
| 22.34 |
| 20.89 |
| 11.47 |
| 30.08 |
| 11.63 |
| 23.12 |
| 32.19 |
| 19.85 |
| 18.47 |
| 33.43 |
| 9.72 |
| 20.24 |
Against USEPA ProUCL (ProUCL 5.2.0)
| Value | USEPA ProUCL | EnviroAutomate | Difference | Agreement band | Verdict |
|---|---|---|---|---|---|
| Sample size (n) n | 40 | 40 | 0 | exact match | Agree |
| Mean mean | 26.458900000000007 | 26.458900000000007 | 0 | within 0.000001 relative | Agree |
| Standard deviation sd | 20.751653683625513 | 20.751653683625513 | 0 | within 0.000001 relative | Agree |
| Skewness skewness | 3.2702520063400486 | 3.270252006340048 | 4.44e-16 | within 0.000001 relative | Agree |
| 95% UCL - Student's t ucl.studentT | 31.987184991573024 | 31.987185113340836 | 1.22e-7 | within 0.000001 relative | Agree |
| 95% UCL - Modified t (Johnson) ucl.modifiedT | 32.269948062796985 | 32.26994818456479 | 1.22e-7 | within 0.000001 relative | Agree |
| 95% UCL - Central limit theorem ucl.clt | 31.855869607877263 | 31.855869604644848 | 3.23e-9 | within 0.000001 relative | Agree |
| 95% UCL - Land's H ucl.landsH | 31.88996965848111 | 31.88996965848111 | 0 | within 0.02 relative | Agree |
| 95% UCL - approximateGamma ucl.approximateGamma | 31.397681570316394 | 31.397682052901413 | 4.83e-7 | within 0.005 relative | Agree |
| 95% UCL - adjustedGamma ucl.adjustedGamma | 31.600085272162968 | 31.600085835847175 | 5.64e-7 | within 0.005 relative | Agree |
| Distribution used distributionUsed | gamma | gamma | - | exact match | Agree |
| Recommended method recommendedMethod | adjustedGamma | adjustedGamma | - | exact match | Agree |
| 95% UCL - Chebyshev, 95% ucl.chebyshev95 | 40.76099030307934 | 40.76099030307934 | 0 | within 0.000001 relative | Agree |
| 95% UCL - Chebyshev, 97.5% ucl.chebyshev975 | 46.949516202056984 | 46.949516202056984 | 0 | within 0.000001 relative | Agree |
| 95% UCL - Chebyshev, 99% ucl.chebyshev99 | 59.10567699632373 | 59.10567699632373 | 0 | within 0.000001 relative | Agree |
Drawn from a lognormal distribution, sd of logs 0.9, n = 15: ProUCL 5.2 finds lognormal and suggests Land's H
Boundary caseInput
15 values
| value |
|---|
| 7.757 |
| 7.222 |
| 4.553 |
| 74.31 |
| 14.53 |
| 30.42 |
| 17.41 |
| 18.07 |
| 14.01 |
| 12.01 |
| 23.95 |
| 23.08 |
| 201.2 |
| 7.125 |
| 4.333 |
Against USEPA ProUCL (ProUCL 5.2.0)
| Value | USEPA ProUCL | EnviroAutomate | Difference | Agreement band | Verdict |
|---|---|---|---|---|---|
| Sample size (n) n | 15 | 15 | 0 | exact match | Agree |
| Mean mean | 30.66533333333333 | 30.66533333333333 | 0 | within 0.000001 relative | Agree |
| Standard deviation sd | 50.22343941210073 | 50.223439412100724 | 7.11e-15 | within 0.000001 relative | Agree |
| Skewness skewness | 3.219227121160483 | 3.219227121160484 | 8.88e-16 | within 0.000001 relative | Agree |
| 95% UCL - Student's t ucl.studentT | 53.5053629138675 | 53.50536257761894 | 3.36e-7 | within 0.000001 relative | Agree |
| 95% UCL - Modified t (Johnson) ucl.modifiedT | 55.30181467246078 | 55.30181433621222 | 3.36e-7 | within 0.000001 relative | Agree |
| 95% UCL - Central limit theorem ucl.clt | 51.99519693972981 | 51.99519692695469 | 1.28e-8 | within 0.000001 relative | Agree |
| 95% UCL - Land's H ucl.landsH | 59.05496963574743 | 59.05496963574743 | 0 | within 0.02 relative | Agree |
| 95% UCL - approximateGamma ucl.approximateGamma | 53.527383099767135 | 53.52831425688466 | 0.000931 | within 0.005 relative | Agree |
| 95% UCL - adjustedGamma ucl.adjustedGamma | 57.49241624130523 | 57.49401909020157 | 0.0016 | within 0.005 relative | Agree |
| Distribution used distributionUsed | lognormal | lognormal | - | exact match | Agree |
| Recommended method recommendedMethod | landsH | landsH | - | exact match | Agree |
| 95% UCL - Chebyshev, 95% ucl.chebyshev95 | 87.1899494819566 | 87.1899494819566 | 0 | within 0.000001 relative | Agree |
| 95% UCL - Chebyshev, 97.5% ucl.chebyshev975 | 111.64819604261567 | 111.64819604261567 | 0 | within 0.000001 relative | Agree |
| 95% UCL - Chebyshev, 99% ucl.chebyshev99 | 159.69168536311938 | 159.69168536311938 | 0 | within 0.000001 relative | Agree |
Drawn from a lognormal distribution, sd of logs 0.9, n = 8: not normal and under ten results, so ProUCL 5.2 makes no suggestion
Boundary caseInput
8 values
| value |
|---|
| 7.457 |
| 11.53 |
| 16.16 |
| 10.93 |
| 17.42 |
| 120.2 |
| 17.11 |
| 59.15 |
Against USEPA ProUCL (ProUCL 5.2.0)
| Value | USEPA ProUCL | EnviroAutomate | Difference | Agreement band | Verdict |
|---|---|---|---|---|---|
| Sample size (n) n | 8 | 8 | 0 | exact match | Agree |
| Mean mean | 32.494625 | 32.494625 | 0 | within 0.000001 relative | Agree |
| Standard deviation sd | 39.032814066912245 | 39.032814066912245 | 0 | within 0.000001 relative | Agree |
| Skewness skewness | 2.073035412327791 | 2.07303541232779 | 8.88e-16 | within 0.000001 relative | Agree |
| 95% UCL - Student's t ucl.studentT | 58.64015762984333 | 58.640157893750676 | 2.64e-7 | within 0.000001 relative | Agree |
| 95% UCL - Modified t (Johnson) ucl.modifiedT | 60.32591608408323 | 60.32591634799058 | 2.64e-7 | within 0.000001 relative | Agree |
| 95% UCL - Central limit theorem ucl.clt | 55.193907320133206 | 55.193907306537895 | 1.36e-8 | within 0.000001 relative | Agree |
| 95% UCL - Land's H ucl.landsH | 101.03183740019846 | 101.03183740019844 | 1.42e-14 | within 0.02 relative | Agree |
| 95% UCL - approximateGamma ucl.approximateGamma | 69.97097223910306 | 69.97913876718789 | 0.00817 | within 0.005 relative | Agree |
| 95% UCL - adjustedGamma ucl.adjustedGamma | 86.39440623901669 | 86.41980743734864 | 0.0254 | within 0.005 relative | Agree |
| 95% UCL - Chebyshev, 95% ucl.chebyshev95 | 92.64823140233955 | 92.64823140233953 | 1.42e-14 | within 0.000001 relative | Agree |
| 95% UCL - Chebyshev, 97.5% ucl.chebyshev975 | 118.67674494470162 | 118.67674494470162 | 0 | within 0.000001 relative | Agree |
| 95% UCL - Chebyshev, 99% ucl.chebyshev99 | 169.8047196872771 | 169.80471968727704 | 5.68e-14 | within 0.000001 relative | Agree |
Drawn from a lognormal distribution, sd of logs 1.2, n = 100: ProUCL 5.2 finds lognormal and suggests Land's H
Boundary caseInput
100 values
| value |
|---|
| 10.09 |
| 36.11 |
| 193.3 |
| 20.85 |
| 3.05 |
| 319.7 |
| 25.12 |
| 7.248 |
| 99.57 |
| 3.135 |
| 3.922 |
| 11.63 |
| 4.62 |
| 101 |
| 6.596 |
| 12.08 |
| 9.887 |
| 139.2 |
| 45.17 |
| 8.348 |
| 16.34 |
| 56.43 |
| 13.57 |
| 29.09 |
| 4.316 |
| 1.205 |
| 22.4 |
| 13.97 |
| 10.49 |
| 61.19 |
| 12.79 |
| 22.78 |
| 46.93 |
| 58.47 |
| 25.71 |
| 35.52 |
| 8.473 |
| 3.498 |
| 5.592 |
| 12.38 |
| 56.31 |
| 47.08 |
| 135.1 |
| 50.39 |
| 36.07 |
| 5.416 |
| 8.729 |
| 0.976 |
| 262.1 |
| 18.33 |
| 9.088 |
| 7.3 |
| 52.69 |
| 2.976 |
| 25.06 |
| 1.667 |
| 12.94 |
| 4.977 |
| 23.17 |
| 1.114 |
| 68.68 |
| 15.08 |
| 37.25 |
| 11.4 |
| 4.049 |
| 5.144 |
| 16.56 |
| 69.85 |
| 43.19 |
| 13.05 |
| 6.007 |
| 38.26 |
| 2.652 |
| 41.47 |
| 26.88 |
| 7.884 |
| 17.07 |
| 2.311 |
| 68.53 |
| 16.7 |
| 26.63 |
| 16.03 |
| 11.75 |
| 16.76 |
| 23.45 |
| 6.449 |
| 56.27 |
| 6.916 |
| 31 |
| 69.98 |
| 26.43 |
| 5.625 |
| 2.761 |
| 36.38 |
| 14.86 |
| 318.3 |
| 4.377 |
| 16.9 |
| 9.173 |
| 117.2 |
Against USEPA ProUCL (ProUCL 5.2.0)
| Value | USEPA ProUCL | EnviroAutomate | Difference | Agreement band | Verdict |
|---|---|---|---|---|---|
| Sample size (n) n | 100 | 100 | 0 | exact match | Agree |
| Mean mean | 36.125110000000014 | 36.125110000000014 | 0 | within 0.000001 relative | Agree |
| Standard deviation sd | 57.1963548022472 | 57.1963548022472 | 0 | within 0.000001 relative | Agree |
| Skewness skewness | 3.4558536752078175 | 3.455853675207819 | 1.33e-15 | within 0.000001 relative | Agree |
| 95% UCL - Student's t ucl.studentT | 45.621941147143616 | 45.62194216700816 | 1.02e-6 | within 0.000001 relative | Agree |
| 95% UCL - Modified t (Johnson) ucl.modifiedT | 45.951378202063346 | 45.95137922192788 | 1.02e-6 | within 0.000001 relative | Agree |
| 95% UCL - Central limit theorem ucl.clt | 45.53307317012269 | 45.53307316448797 | 5.63e-9 | within 0.000001 relative | Agree |
| 95% UCL - Land's H ucl.landsH | 50.05201836849272 | 50.05201836849274 | 2.13e-14 | within 0.02 relative | Agree |
| 95% UCL - approximateGamma ucl.approximateGamma | 44.09074824519155 | 44.09074992597659 | 1.68e-6 | within 0.005 relative | Agree |
| 95% UCL - adjustedGamma ucl.adjustedGamma | 44.2189747389078 | 44.218976526855 | 1.79e-6 | within 0.005 relative | Agree |
| Distribution used distributionUsed | lognormal | lognormal | - | exact match | Agree |
| Recommended method recommendedMethod | landsH | landsH | - | exact match | Agree |
| 95% UCL - Chebyshev, 95% ucl.chebyshev95 | 61.05642305218929 | 61.05642305218929 | 0 | within 0.000001 relative | Agree |
| 95% UCL - Chebyshev, 97.5% ucl.chebyshev975 | 71.84422212557183 | 71.84422212557183 | 0 | within 0.000001 relative | Agree |
| 95% UCL - Chebyshev, 99% ucl.chebyshev99 | 93.03476447652885 | 93.03476447652885 | 0 | within 0.000001 relative | Agree |
Drawn from a lognormal distribution, sd of logs 1.2, n = 28: ProUCL 5.2 finds lognormal and suggests Land's H
Boundary caseInput
28 values
| value |
|---|
| 781.3 |
| 23.85 |
| 19.39 |
| 15.39 |
| 5.317 |
| 24.87 |
| 56.31 |
| 7.257 |
| 64.44 |
| 10.21 |
| 6.394 |
| 41.31 |
| 5.868 |
| 45.85 |
| 7.195 |
| 7.272 |
| 12.33 |
| 14.15 |
| 71.33 |
| 30.86 |
| 19.72 |
| 17.66 |
| 12.81 |
| 81.69 |
| 20.37 |
| 2.662 |
| 12.71 |
| 92.73 |
Against USEPA ProUCL (ProUCL 5.2.0)
| Value | USEPA ProUCL | EnviroAutomate | Difference | Agreement band | Verdict |
|---|---|---|---|---|---|
| Sample size (n) n | 28 | 28 | 0 | exact match | Agree |
| Mean mean | 53.97303571428569 | 53.97303571428569 | 0 | within 0.000001 relative | Agree |
| Standard deviation sd | 144.69299211228602 | 144.69299211228602 | 0 | within 0.000001 relative | Agree |
| Skewness skewness | 5.048377241007637 | 5.048377241007636 | 8.88e-16 | within 0.000001 relative | Agree |
| 95% UCL - Student's t ucl.studentT | 100.5484459673356 | 100.54844524184361 | 7.25e-7 | within 0.000001 relative | Agree |
| 95% UCL - Modified t (Johnson) ucl.modifiedT | 104.89645077872227 | 104.8964500532303 | 7.25e-7 | within 0.000001 relative | Agree |
| 95% UCL - Central limit theorem ucl.clt | 98.95057990326204 | 98.95057987632356 | 2.69e-8 | within 0.000001 relative | Agree |
| 95% UCL - Land's H ucl.landsH | 73.17698175645283 | 73.17698175645283 | 0 | within 0.02 relative | Agree |
| 95% UCL - approximateGamma ucl.approximateGamma | 85.21959743388383 | 85.22005266992166 | 0.000455 | within 0.005 relative | Agree |
| 95% UCL - adjustedGamma ucl.adjustedGamma | 87.72076391130565 | 87.72136251075015 | 0.000599 | within 0.005 relative | Agree |
| Distribution used distributionUsed | lognormal | lognormal | - | exact match | Agree |
| Recommended method recommendedMethod | landsH | landsH | - | exact match | Agree |
| 95% UCL - Chebyshev, 95% ucl.chebyshev95 | 173.16453489608182 | 173.1645348960818 | 2.84e-14 | within 0.000001 relative | Agree |
| 95% UCL - Chebyshev, 97.5% ucl.chebyshev975 | 224.7387918049271 | 224.73879180492705 | 5.68e-14 | within 0.000001 relative | Agree |
| 95% UCL - Chebyshev, 99% ucl.chebyshev99 | 326.04643276225397 | 326.0464327622539 | 5.68e-14 | within 0.000001 relative | Agree |
Drawn from a normal distribution, CV 0.1, n = 10: ProUCL 5.2 finds normal and suggests Student's t
Boundary caseInput
10 values
| value |
|---|
| 95.82 |
| 70.27 |
| 105.2 |
| 83.04 |
| 111 |
| 107.3 |
| 134.2 |
| 111 |
| 107 |
| 99.81 |
Against USEPA ProUCL (ProUCL 5.2.0)
| Value | USEPA ProUCL | EnviroAutomate | Difference | Agreement band | Verdict |
|---|---|---|---|---|---|
| Sample size (n) n | 10 | 10 | 0 | exact match | Agree |
| Mean mean | 102.46399999999998 | 102.46399999999998 | 0 | within 0.000001 relative | Agree |
| Standard deviation sd | 17.221691877138873 | 17.221691877138873 | 0 | within 0.000001 relative | Agree |
| Skewness skewness | -0.20594043617318858 | -0.20594043617318847 | 1.11e-16 | within 0.000001 relative | Agree |
| 95% UCL - Student's t ucl.studentT | 112.44709121259781 | 112.44709114340172 | 6.92e-8 | within 0.000001 relative | Agree |
| 95% UCL - Modified t (Johnson) ucl.modifiedT | 112.3879805003175 | 112.38798043112142 | 6.92e-8 | within 0.000001 relative | Agree |
| 95% UCL - Central limit theorem ucl.clt | 111.42183527174848 | 111.42183526638335 | 5.37e-9 | within 0.000001 relative | Agree |
| 95% UCL - Land's H ucl.landsH | 114.5486634897012 | 114.5486634897012 | 0 | within 0.02 relative | Agree |
| 95% UCL - approximateGamma ucl.approximateGamma | 113.7947399714912 | 113.79474005843919 | 8.69e-8 | within 0.005 relative | Agree |
| 95% UCL - adjustedGamma ucl.adjustedGamma | 115.91185052163387 | 115.91185071426371 | 1.93e-7 | within 0.005 relative | Agree |
| Distribution used distributionUsed | normal | normal | - | exact match | Agree |
| Recommended method recommendedMethod | studentT | studentT | - | exact match | Agree |
| 95% UCL - Chebyshev, 95% ucl.chebyshev95 | 126.20246404279581 | 126.20246404279581 | 0 | within 0.000001 relative | Agree |
| 95% UCL - Chebyshev, 97.5% ucl.chebyshev975 | 136.47411639693888 | 136.47411639693888 | 0 | within 0.000001 relative | Agree |
| 95% UCL - Chebyshev, 99% ucl.chebyshev99 | 156.65078846360979 | 156.65078846360979 | 0 | within 0.000001 relative | Agree |
Drawn from a normal distribution, CV 0.1, n = 100: ProUCL 5.2 finds normal and suggests Student's t
Boundary caseInput
100 values
| value |
|---|
| 111 |
| 98.54 |
| 98.08 |
| 98.19 |
| 101.9 |
| 95.59 |
| 102.9 |
| 85.8 |
| 112.2 |
| 113 |
| 100.3 |
| 119.7 |
| 122.1 |
| 100.4 |
| 102.9 |
| 113.5 |
| 94.41 |
| 92.25 |
| 98.72 |
| 94.5 |
| 106.3 |
| 112 |
| 102 |
| 90.41 |
| 91.33 |
| 103.6 |
| 101.2 |
| 100.1 |
| 87.49 |
| 96 |
| 93.69 |
| 93.52 |
| 106.3 |
| 101.7 |
| 106.2 |
| 88.11 |
| 82.57 |
| 84.91 |
| 98.92 |
| 99.63 |
| 105.6 |
| 83.09 |
| 91.49 |
| 99.06 |
| 112.2 |
| 99.74 |
| 98.73 |
| 100.7 |
| 104.2 |
| 92.82 |
| 100.8 |
| 95.17 |
| 112.2 |
| 101.6 |
| 106.1 |
| 107.7 |
| 90.27 |
| 103.5 |
| 103.7 |
| 102.9 |
| 109.7 |
| 83.29 |
| 91.46 |
| 96.48 |
| 113.1 |
| 96.56 |
| 112.6 |
| 95.18 |
| 96.13 |
| 110.6 |
| 100.5 |
| 79.95 |
| 93.63 |
| 114 |
| 111 |
| 100.7 |
| 108 |
| 79 |
| 110.5 |
| 106.7 |
| 111 |
| 101.6 |
| 99.95 |
| 117.2 |
| 88.75 |
| 95.94 |
| 102.2 |
| 96.6 |
| 100.6 |
| 101.4 |
| 87.17 |
| 98.26 |
| 111.4 |
| 100.7 |
| 76.62 |
| 120.7 |
| 98.02 |
| 124.7 |
| 103.1 |
| 112.9 |
Against USEPA ProUCL (ProUCL 5.2.0)
| Value | USEPA ProUCL | EnviroAutomate | Difference | Agreement band | Verdict |
|---|---|---|---|---|---|
| Sample size (n) n | 100 | 100 | 0 | exact match | Agree |
| Mean mean | 100.71420000000008 | 100.71420000000008 | 0 | within 0.000001 relative | Agree |
| Standard deviation sd | 9.654312814446811 | 9.654312814446811 | 0 | within 0.000001 relative | Agree |
| Skewness skewness | -0.05203003286770162 | -0.05203003286770167 | 4.86e-17 | within 0.000001 relative | Agree |
| 95% UCL - Student's t ucl.studentT | 102.31719338930789 | 102.31719356145332 | 1.72e-7 | within 0.000001 relative | Agree |
| 95% UCL - Modified t (Johnson) ucl.modifiedT | 102.3163561989528 | 102.31635637109824 | 1.72e-7 | within 0.000001 relative | Agree |
| 95% UCL - Central limit theorem ucl.clt | 102.30219314580786 | 102.30219314485677 | 9.51e-10 | within 0.000001 relative | Agree |
| 95% UCL - approximateGamma ucl.approximateGamma | 102.35172835367194 | 102.35172835268824 | 9.84e-10 | within 0.005 relative | Agree |
| 95% UCL - adjustedGamma ucl.adjustedGamma | 102.3755638995706 | 102.37556389846063 | 1.11e-9 | within 0.005 relative | Agree |
| Distribution used distributionUsed | normal | normal | - | exact match | Agree |
| Recommended method recommendedMethod | studentT | studentT | - | exact match | Agree |
| 95% UCL - Chebyshev, 95% ucl.chebyshev95 | 104.92241739275042 | 104.92241739275042 | 0 | within 0.000001 relative | Agree |
| 95% UCL - Chebyshev, 97.5% ucl.chebyshev975 | 106.7433164202133 | 106.7433164202133 | 0 | within 0.000001 relative | Agree |
| 95% UCL - Chebyshev, 99% ucl.chebyshev99 | 110.32011996427211 | 110.32011996427211 | 0 | within 0.000001 relative | Agree |
Drawn from a normal distribution, CV 0.1, n = 30: ProUCL 5.2 finds normal and suggests Student's t
Boundary caseInput
30 values
| value |
|---|
| 82.84 |
| 103.8 |
| 93.8 |
| 109.2 |
| 78.07 |
| 110.4 |
| 104.3 |
| 82.5 |
| 109.8 |
| 96.49 |
| 102.5 |
| 104 |
| 86.58 |
| 98.5 |
| 117.7 |
| 101.6 |
| 100.8 |
| 105.2 |
| 86.99 |
| 93.02 |
| 101 |
| 94.97 |
| 116.4 |
| 114.8 |
| 101.7 |
| 98.34 |
| 130.7 |
| 85.71 |
| 104.6 |
| 108.8 |
Against USEPA ProUCL (ProUCL 5.2.0)
| Value | USEPA ProUCL | EnviroAutomate | Difference | Agreement band | Verdict |
|---|---|---|---|---|---|
| Sample size (n) n | 30 | 30 | 0 | exact match | Agree |
| Mean mean | 100.83699999999997 | 100.83699999999999 | 1.42e-14 | within 0.000001 relative | Agree |
| Standard deviation sd | 11.69217396675937 | 11.69217396675937 | 0 | within 0.000001 relative | Agree |
| Skewness skewness | 0.15938784258078786 | 0.15938784258078778 | 8.33e-17 | within 0.000001 relative | Agree |
| 95% UCL - Student's t ucl.studentT | 104.4641078639456 | 104.46410801547789 | 1.52e-7 | within 0.000001 relative | Agree |
| 95% UCL - Modified t (Johnson) ucl.modifiedT | 104.4744611438547 | 104.474461295387 | 1.52e-7 | within 0.000001 relative | Agree |
| 95% UCL - Central limit theorem ucl.clt | 104.34825118076022 | 104.34825117865724 | 2.10e-9 | within 0.000001 relative | Agree |
| 95% UCL - Land's H ucl.landsH | 104.69009871903548 | 104.69009871903548 | 0 | within 0.02 relative | Agree |
| 95% UCL - approximateGamma ucl.approximateGamma | 104.59266463928309 | 104.59266463714695 | 2.14e-9 | within 0.005 relative | Agree |
| 95% UCL - adjustedGamma ucl.adjustedGamma | 104.81270634558066 | 104.81270634385604 | 1.72e-9 | within 0.005 relative | Agree |
| Distribution used distributionUsed | normal | normal | - | exact match | Agree |
| Recommended method recommendedMethod | studentT | studentT | - | exact match | Agree |
| 95% UCL - Chebyshev, 95% ucl.chebyshev95 | 110.14189424856679 | 110.14189424856679 | 0 | within 0.000001 relative | Agree |
| 95% UCL - Chebyshev, 97.5% ucl.chebyshev975 | 114.16812942288293 | 114.16812942288293 | 0 | within 0.000001 relative | Agree |
| 95% UCL - Chebyshev, 99% ucl.chebyshev99 | 122.07688879037707 | 122.07688879037707 | 0 | within 0.000001 relative | Agree |
Drawn from a normal distribution, CV 0.1, n = 5: ProUCL 5.2 finds normal and suggests Student's t
Boundary caseInput
5 values
| value |
|---|
| 102.5 |
| 83.66 |
| 102.9 |
| 93.71 |
| 118.3 |
Against USEPA ProUCL (ProUCL 5.2.0)
| Value | USEPA ProUCL | EnviroAutomate | Difference | Agreement band | Verdict |
|---|---|---|---|---|---|
| Sample size (n) n | 5 | 5 | 0 | exact match | Agree |
| Mean mean | 100.214 | 100.214 | 0 | within 0.000001 relative | Agree |
| Standard deviation sd | 12.805084146541171 | 12.805084146541171 | 0 | within 0.000001 relative | Agree |
| Skewness skewness | 0.22539653967589682 | 0.22539653967589682 | 0 | within 0.000001 relative | Agree |
| 95% UCL - Student's t ucl.studentT | 112.42225032404549 | 112.42225026838824 | 5.57e-8 | within 0.000001 relative | Agree |
| 95% UCL - Modified t (Johnson) ucl.modifiedT | 112.51845771260847 | 112.51845765695121 | 5.57e-8 | within 0.000001 relative | Agree |
| 95% UCL - Central limit theorem ucl.clt | 109.63343148706176 | 109.63343148142016 | 5.64e-9 | within 0.000001 relative | Agree |
| 95% UCL - Land's H ucl.landsH | 114.65835320824414 | 114.65835320824412 | 1.42e-14 | within 0.02 relative | Agree |
| 95% UCL - approximateGamma ucl.approximateGamma | 115.03613393529449 | 115.22131009754932 | 0.185 | within 0.005 relative | Agree |
| 95% UCL - adjustedGamma ucl.adjustedGamma | 122.50341732844066 | 122.53308585034037 | 0.0297 | within 0.005 relative | Agree |
| 95% UCL - Chebyshev, 95% ucl.chebyshev95 | 125.17570434886206 | 125.17570434886207 | 1.42e-14 | within 0.000001 relative | Agree |
| 95% UCL - Chebyshev, 97.5% ucl.chebyshev975 | 135.9766537605922 | 135.9766537605922 | 0 | within 0.000001 relative | Agree |
| 95% UCL - Chebyshev, 99% ucl.chebyshev99 | 157.19302740482675 | 157.19302740482675 | 0 | within 0.000001 relative | Agree |
Drawn from a very widely spread lognormal distribution, n = 100: ProUCL 5.2 finds lognormal and suggests Land's H
Boundary caseInput
100 values
| value |
|---|
| 2.104 |
| 1.769 |
| 69.35 |
| 0.5107 |
| 0.1535 |
| 0.03594 |
| 1693 |
| 2361 |
| 15.34 |
| 223.6 |
| 5.042 |
| 21.34 |
| 0.2293 |
| 36.2 |
| 26090 |
| 1.712 |
| 17.62 |
| 0.9385 |
| 3.251 |
| 17.23 |
| 679 |
| 3.396 |
| 44490 |
| 0.4698 |
| 3.523 |
| 44.31 |
| 0.2135 |
| 6.195 |
| 0.1742 |
| 2.255 |
| 170.4 |
| 22.01 |
| 83.29 |
| 30.68 |
| 290.6 |
| 18.33 |
| 0.1503 |
| 25.8 |
| 1061 |
| 0.09735 |
| 175.2 |
| 29.89 |
| 15.98 |
| 31.92 |
| 1.493 |
| 1.174 |
| 16940 |
| 1.134 |
| 409.2 |
| 5.093 |
| 0.2126 |
| 5416 |
| 11.29 |
| 3.626 |
| 61.91 |
| 1212 |
| 4757 |
| 2437 |
| 3.092 |
| 0.04148 |
| 1.411 |
| 34.93 |
| 176.5 |
| 0.3488 |
| 0.4042 |
| 106.3 |
| 0.7268 |
| 12.35 |
| 0.1212 |
| 44.29 |
| 158.2 |
| 0.007856 |
| 43.05 |
| 7.551 |
| 2.829 |
| 47.58 |
| 155.4 |
| 4.855 |
| 1160 |
| 5.954 |
| 3.219 |
| 40.66 |
| 3.242 |
| 146.7 |
| 4.733 |
| 0.5606 |
| 25.1 |
| 0.4228 |
| 19.2 |
| 5.985 |
| 5.832 |
| 27.73 |
| 2234 |
| 2323 |
| 0.003107 |
| 12.39 |
| 23.05 |
| 1893 |
| 1383 |
| 0.4877 |
Against USEPA ProUCL (ProUCL 5.2.0)
| Value | USEPA ProUCL | EnviroAutomate | Difference | Agreement band | Verdict |
|---|---|---|---|---|---|
| Sample size (n) n | 100 | 100 | 0 | exact match | Agree |
| Mean mean | 1191.2070023299993 | 1191.2070023299993 | 0 | within 0.000001 relative | Agree |
| Standard deviation sd | 5405.059518753479 | 5405.059518753479 | 0 | within 0.000001 relative | Agree |
| Skewness skewness | 6.560926138690802 | 6.560926138690799 | 3.55e-15 | within 0.000001 relative | Agree |
| 95% UCL - Student's t ucl.studentT | 2088.6582082212935 | 2088.6583045985635 | 9.64e-5 | within 0.000001 relative | Agree |
| 95% UCL - Modified t (Johnson) ucl.modifiedT | 2147.7618686842425 | 2147.761965061512 | 9.64e-5 | within 0.000001 relative | Agree |
| 95% UCL - Central limit theorem ucl.clt | 2080.2601781935055 | 2080.2601776610236 | 5.32e-7 | within 0.000001 relative | Agree |
| 95% UCL - Land's H ucl.landsH | 20264.25355410028 | 20264.25355410028 | 0 | within 0.02 relative | Agree |
| 95% UCL - approximateGamma ucl.approximateGamma | 1864.8394377857915 | 1864.848341986383 | 0.0089 | within 0.005 relative | Agree |
| 95% UCL - adjustedGamma ucl.adjustedGamma | 1877.243278794067 | 1877.2527940722714 | 0.00952 | within 0.005 relative | Agree |
| Distribution used distributionUsed | lognormal | lognormal | - | exact match | Agree |
| Recommended method recommendedMethod | landsH | landsH | - | exact match | Agree |
| 95% UCL - Chebyshev, 95% ucl.chebyshev95 | 3547.2178249368985 | 3547.2178249368985 | 0 | within 0.000001 relative | Agree |
| 95% UCL - Chebyshev, 97.5% ucl.chebyshev975 | 4566.665589913967 | 4566.665589913967 | 0 | within 0.000001 relative | Agree |
| 95% UCL - Chebyshev, 99% ucl.chebyshev99 | 6569.173320303263 | 6569.173320303263 | 0 | within 0.000001 relative | Agree |
Drawn from a very widely spread lognormal distribution, n = 150: ProUCL 5.2 finds no discernible distribution and suggests Student's t
Boundary caseInput
150 values
| value |
|---|
| 23.54 |
| 3335 |
| 5976 |
| 0.03027 |
| 1026 |
| 4134 |
| 1.099 |
| 275.3 |
| 2771 |
| 132.7 |
| 0.6869 |
| 84.72 |
| 167.1 |
| 49.96 |
| 10.77 |
| 4.221 |
| 2769 |
| 156.1 |
| 5061 |
| 13.17 |
| 0.07985 |
| 235.4 |
| 0.2484 |
| 30.53 |
| 46.99 |
| 47340 |
| 1.128 |
| 0.3947 |
| 693.4 |
| 5.037 |
| 1.909 |
| 0.5968 |
| 23970 |
| 1.614 |
| 3358 |
| 2.716 |
| 107.4 |
| 29.32 |
| 2.97 |
| 9.212 |
| 56860 |
| 692.5 |
| 0.0211 |
| 26.7 |
| 147.2 |
| 46.81 |
| 4.254 |
| 1.987 |
| 12.19 |
| 0.4037 |
| 30.65 |
| 12260 |
| 5489 |
| 4.347 |
| 2.959 |
| 2.65 |
| 3758 |
| 1.725 |
| 5.837 |
| 42450 |
| 62.62 |
| 13.37 |
| 12800 |
| 20.03 |
| 0.4045 |
| 140.9 |
| 1.217 |
| 75.79 |
| 1.494 |
| 840.5 |
| 158.9 |
| 20910 |
| 13 |
| 337.7 |
| 5.102 |
| 4.524 |
| 0.1906 |
| 1.279 |
| 34.16 |
| 2.897 |
| 0.00122 |
| 24.74 |
| 0.0387 |
| 4.065 |
| 3146 |
| 26.81 |
| 1.853 |
| 1.571 |
| 17.29 |
| 1.65 |
| 3.263 |
| 0.9741 |
| 7.863 |
| 32870 |
| 760.6 |
| 28.86 |
| 1445 |
| 4.494 |
| 24.15 |
| 0.09508 |
| 2369 |
| 2.674 |
| 63.42 |
| 75.33 |
| 36.9 |
| 66.21 |
| 3401 |
| 11.95 |
| 14.19 |
| 37.99 |
| 0.9584 |
| 28.64 |
| 107.2 |
| 14.76 |
| 28.93 |
| 99.78 |
| 53.71 |
| 23.58 |
| 0.5629 |
| 0.2888 |
| 103.2 |
| 1.61 |
| 54.68 |
| 26.84 |
| 0.002409 |
| 64.61 |
| 18.73 |
| 2892 |
| 58.67 |
| 22.95 |
| 327.2 |
| 5218 |
| 0.0008722 |
| 1.934 |
| 31.62 |
| 16.06 |
| 14.39 |
| 1970 |
| 0.007671 |
| 2030 |
| 20.23 |
| 1.989 |
| 64.13 |
| 2.47 |
| 113.3 |
| 14.59 |
| 13.4 |
| 3519 |
| 59.61 |
| 30.8 |
Against USEPA ProUCL (ProUCL 5.2.0)
| Value | USEPA ProUCL | EnviroAutomate | Difference | Agreement band | Verdict |
|---|---|---|---|---|---|
| Sample size (n) n | 150 | 150 | 0 | exact match | Agree |
| Mean mean | 2136.987139814668 | 2136.987139814668 | 0 | within 0.000001 relative | Agree |
| Standard deviation sd | 7877.833793323665 | 7877.833793323666 | 9.09e-13 | within 0.000001 relative | Agree |
| Skewness skewness | 5.135411769675308 | 5.1354117696753105 | 2.66e-15 | within 0.000001 relative | Agree |
| 95% UCL - Student's t ucl.studentT | 3201.613132042078 | 3201.613238339572 | 0.000106 | within 0.000001 relative | Agree |
| 95% UCL - Modified t (Johnson) ucl.modifiedT | 3246.564154688501 | 3246.5642609859947 | 0.000106 | within 0.000001 relative | Agree |
| 95% UCL - Central limit theorem ucl.clt | 3194.9938968061942 | 3194.993896172521 | 6.34e-7 | within 0.000001 relative | Agree |
| 95% UCL - Land's H ucl.landsH | 64563.31355199791 | 64563.313551997795 | 1.16e-10 | within 0.02 relative | Agree |
| 95% UCL - approximateGamma ucl.approximateGamma | 3053.794653851799 | 3053.798419806081 | 0.00377 | within 0.005 relative | Agree |
| 95% UCL - adjustedGamma ucl.adjustedGamma | 3064.4293537947037 | 3064.4332853245332 | 0.00393 | within 0.005 relative | Agree |
| Distribution used distributionUsed | nonparametric | nonparametric | - | exact match | Agree |
| Recommended method recommendedMethod | studentT | studentT | - | exact match | Agree |
| 95% UCL - Chebyshev, 95% ucl.chebyshev95 | 4940.728735408447 | 4940.728735408447 | 0 | within 0.000001 relative | Agree |
| 95% UCL - Chebyshev, 97.5% ucl.chebyshev975 | 6153.90996351447 | 6153.90996351447 | 0 | within 0.000001 relative | Agree |
| 95% UCL - Chebyshev, 99% ucl.chebyshev99 | 8536.969568044711 | 8536.969568044711 | 0 | within 0.000001 relative | Agree |
Drawn from a very widely spread lognormal distribution, n = 200: ProUCL 5.2 finds lognormal and suggests Land's H
Boundary caseInput
200 values
| value |
|---|
| 0.08717 |
| 4.492 |
| 2.884 |
| 18.93 |
| 30.16 |
| 594.4 |
| 917.6 |
| 4.756 |
| 32.88 |
| 180.3 |
| 220.8 |
| 0.406 |
| 118.2 |
| 4.426 |
| 1532 |
| 0.02093 |
| 0.895 |
| 3.794 |
| 0.02625 |
| 0.3169 |
| 32300 |
| 0.119 |
| 0.8502 |
| 3.322 |
| 303.7 |
| 212.4 |
| 137 |
| 5.317 |
| 0.1804 |
| 11.71 |
| 42.27 |
| 1308 |
| 25.63 |
| 148.7 |
| 0.2634 |
| 1566 |
| 0.01321 |
| 3112 |
| 1.89 |
| 0.08753 |
| 23.88 |
| 184.4 |
| 19.69 |
| 23.04 |
| 2882 |
| 0.1042 |
| 474.2 |
| 2.13 |
| 670.4 |
| 23.54 |
| 11.06 |
| 42.27 |
| 865.1 |
| 594.9 |
| 398.6 |
| 2598 |
| 47.52 |
| 0.6009 |
| 1918 |
| 39.15 |
| 81.95 |
| 0.5568 |
| 131 |
| 50.64 |
| 404.3 |
| 22.98 |
| 0.4463 |
| 1.065 |
| 0.3691 |
| 53370 |
| 0.1697 |
| 16.97 |
| 74.08 |
| 0.09193 |
| 3469 |
| 224.2 |
| 0.8708 |
| 105.8 |
| 22.19 |
| 0.1619 |
| 5.209 |
| 15.67 |
| 79.79 |
| 679.7 |
| 85.69 |
| 1.226 |
| 689 |
| 143.9 |
| 32.3 |
| 7109 |
| 311 |
| 1478 |
| 336 |
| 20.63 |
| 229.3 |
| 4683 |
| 2106 |
| 347.8 |
| 2.981 |
| 1.891 |
| 4.563 |
| 945.1 |
| 689.4 |
| 302.7 |
| 224.1 |
| 0.3478 |
| 0.01416 |
| 831.7 |
| 2977 |
| 93190 |
| 50.16 |
| 172.3 |
| 3.793 |
| 65.12 |
| 129.9 |
| 72.28 |
| 0.1437 |
| 0.4015 |
| 54.98 |
| 16.64 |
| 15.11 |
| 2.674 |
| 18.69 |
| 0.1596 |
| 32.48 |
| 658.1 |
| 4.081 |
| 0.2243 |
| 36.27 |
| 11.17 |
| 20.12 |
| 734.8 |
| 3.679 |
| 194.8 |
| 1.173 |
| 0.3595 |
| 34060 |
| 7.003 |
| 1.192 |
| 1.011 |
| 43.21 |
| 466.7 |
| 0.0056 |
| 31.51 |
| 0.2012 |
| 12.6 |
| 28.99 |
| 0.1742 |
| 546.1 |
| 142.8 |
| 534.3 |
| 12060 |
| 0.7063 |
| 0.02419 |
| 31 |
| 105.2 |
| 25.78 |
| 15.86 |
| 64.29 |
| 281.6 |
| 9.876 |
| 18.37 |
| 0.415 |
| 229.6 |
| 0.006036 |
| 5.862 |
| 812.8 |
| 4445 |
| 0.7016 |
| 3 |
| 23.39 |
| 362.2 |
| 3.763 |
| 0.6688 |
| 37.77 |
| 0.3113 |
| 0.0571 |
| 420000 |
| 29.2 |
| 623.3 |
| 387.5 |
| 6.031 |
| 84.89 |
| 6964 |
| 0.1309 |
| 47.38 |
| 22.52 |
| 883.2 |
| 89.75 |
| 6121 |
| 3885 |
| 369.5 |
| 14.76 |
| 24.7 |
| 1.349 |
| 0.08987 |
| 6315 |
| 9.056 |
| 44680 |
| 48.44 |
Against USEPA ProUCL (ProUCL 5.2.0)
| Value | USEPA ProUCL | EnviroAutomate | Difference | Agreement band | Verdict |
|---|---|---|---|---|---|
| Sample size (n) n | 200 | 200 | 0 | exact match | Agree |
| Mean mean | 3882.4285963799994 | 3882.428596379999 | 4.55e-13 | within 0.000001 relative | Agree |
| Standard deviation sd | 30864.463030922812 | 30864.463030922812 | 0 | within 0.000001 relative | Agree |
| Skewness skewness | 12.601754120872839 | 12.601754120872839 | 0 | within 0.000001 relative | Agree |
| 95% UCL - Student's t ucl.studentT | 7489.025255121203 | 7489.0244678214685 | 0.000787 | within 0.000001 relative | Agree |
| 95% UCL - Modified t (Johnson) ucl.modifiedT | 7813.147233611586 | 7813.146446311852 | 0.000787 | within 0.000001 relative | Agree |
| 95% UCL - Central limit theorem ucl.clt | 7472.234644169541 | 7472.234642019494 | 2.15e-6 | within 0.000001 relative | Agree |
| 95% UCL - Land's H ucl.landsH | 48396.45442624609 | 48396.454426246084 | 7.28e-12 | within 0.02 relative | Agree |
| 95% UCL - approximateGamma ucl.approximateGamma | 5366.929133799345 | 5366.932835988251 | 0.0037 | within 0.005 relative | Agree |
| 95% UCL - adjustedGamma ucl.adjustedGamma | 5379.568234230883 | 5379.572056574131 | 0.00382 | within 0.005 relative | Agree |
| Distribution used distributionUsed | lognormal | lognormal | - | exact match | Agree |
| Recommended method recommendedMethod | landsH | landsH | - | exact match | Agree |
| 95% UCL - Chebyshev, 95% ucl.chebyshev95 | 13395.495001476938 | 13395.495001476938 | 0 | within 0.000001 relative | Agree |
| 95% UCL - Chebyshev, 97.5% ucl.chebyshev975 | 17511.806434216327 | 17511.806434216327 | 0 | within 0.000001 relative | Agree |
| 95% UCL - Chebyshev, 99% ucl.chebyshev99 | 25597.50316918919 | 25597.50316918919 | 0 | within 0.000001 relative | Agree |
Eight results, six of them non-detects, no distribution identified
Boundary caseInput
8 values
| value | non-detect | reporting limit |
|---|---|---|
| 11.906 | yes | 11.906 |
| 11.906 | yes | 11.906 |
| 11.906 | yes | 11.906 |
| 11.906 | yes | 11.906 |
| 11.906 | yes | 11.906 |
| 11.906 | yes | 11.906 |
| 13.157 | no | |
| 14.673 | no |
Settings: nonDetectMethod = kaplanMeier
Against USEPA ProUCL (ProUCL 5.2.0)
| Value | USEPA ProUCL | EnviroAutomate | Difference | Agreement band | Verdict |
|---|---|---|---|---|---|
| Sample size (n) n | 8 | 8 | 0 | exact match | Agree |
| Mean mean | 12.40825 | 12.40825 | 0 | within 0.000001 relative | Agree |
| Standard deviation sd | 0.948897353510905 | 0.9488973535109051 | 1.11e-16 | within 0.000001 relative | Agree |
| Standard error of the mean standardError | 0.4744486767554525 | 0.4744486767554525 | 0 | within 0.000001 relative | Agree |
| 95% UCL - Chebyshev, 95% ucl.chebyshev95 | 14.47632383587361 | 14.476323835873611 | 1.78e-15 | within 0.000001 relative | Agree |
| Distribution used distributionUsed | nonparametric | nonparametric | - | exact match | Agree |
| Recommended method recommendedMethod | studentT | studentT | - | exact match | Agree |
| 95% UCL - Student's t ucl.studentT | 13.307130303121042 | 13.307130312194145 | 9.07e-9 | within 0.000001 relative | Agree |
Fifty results, where the approximate gamma limit takes over
Boundary caseInput
50 values
| value | non-detect | reporting limit |
|---|---|---|
| 0.584 | yes | 0.584 |
| 0.584 | yes | 0.584 |
| 0.584 | yes | 0.584 |
| 0.584 | yes | 0.584 |
| 0.584 | yes | 0.584 |
| 0.612 | no | |
| 0.702 | no | |
| 0.746 | no | |
| 0.757 | no | |
| 0.881 | no | |
| 1.066 | no | |
| 1.093 | no | |
| 1.128 | no | |
| 1.146 | no | |
| 1.32 | no | |
| 1.36 | no | |
| 1.446 | no | |
| 1.521 | no | |
| 1.676 | no | |
| 1.736 | no | |
| 1.814 | no | |
| 1.917 | no | |
| 1.987 | no | |
| 2.517 | no | |
| 2.58 | no | |
| 2.604 | no | |
| 2.619 | no | |
| 2.699 | no | |
| 3.009 | no | |
| 3.337 | no | |
| 3.47 | no | |
| 3.84 | no | |
| 3.906 | no | |
| 4.712 | no | |
| 4.815 | no | |
| 5.231 | no | |
| 5.419 | no | |
| 5.573 | no | |
| 5.574 | no | |
| 6.831 | no | |
| 7.556 | no | |
| 7.716 | no | |
| 8.651 | no | |
| 9.12 | no | |
| 10.128 | no | |
| 11.673 | no | |
| 12.104 | no | |
| 15.721 | no | |
| 22.376 | no | |
| 37.741 | no |
Settings: nonDetectMethod = kaplanMeier
Against USEPA ProUCL (ProUCL 5.2.0)
| Value | USEPA ProUCL | EnviroAutomate | Difference | Agreement band | Verdict |
|---|---|---|---|---|---|
| Sample size (n) n | 50 | 50 | 0 | exact match | Agree |
| Mean mean | 4.747000000000002 | 4.7470000000000026 | 8.88e-16 | within 0.000001 relative | Agree |
| Standard deviation sd | 6.397948768159997 | 6.397948768159997 | 0 | within 0.000001 relative | Agree |
| Standard error of the mean standardError | 0.9150307197525716 | 0.9150307197525714 | 1.11e-16 | within 0.000001 relative | Agree |
| 95% UCL - Chebyshev, 95% ucl.chebyshev95 | 8.735526437636745 | 8.735526437636747 | 1.78e-15 | within 0.000001 relative | Agree |
| Distribution used distributionUsed | gamma | gamma | - | exact match | Agree |
| Recommended method recommendedMethod | approximateGamma | approximateGamma | - | exact match | Agree |
| 95% UCL - approximateGamma ucl.approximateGamma | 6.747 | 6.747451145753031 | 0.000451 | within 0.005 relative | Agree |
Gamma data with a comfortable shape - the approximate gamma UCL
Boundary caseInput
60 values
| value |
|---|
| 10.5495 |
| 2.634 |
| 2.8427 |
| 11.067 |
| 3.9059 |
| 4.8471 |
| 2.6756 |
| 3.247 |
| 7.5206 |
| 0.8072 |
| 4.663 |
| 3.4504 |
| 3.3872 |
| 4.5914 |
| 6.3398 |
| 7.0968 |
| 5.8554 |
| 1.3913 |
| 3.858 |
| 8.644 |
| 3.0659 |
| 5.587 |
| 11.2053 |
| 1.7691 |
| 3.3279 |
| 12.6565 |
| 2.9073 |
| 9.6474 |
| 1.0388 |
| 5.6201 |
| 1.9476 |
| 15.6764 |
| 2.656 |
| 4.9371 |
| 14.2585 |
| 2.3175 |
| 4.6068 |
| 1.5909 |
| 1.738 |
| 4.9563 |
| 2.0597 |
| 6.6443 |
| 2.9905 |
| 4.4709 |
| 2.0886 |
| 7.2782 |
| 5.025 |
| 4.3931 |
| 4.7116 |
| 4.4932 |
| 6.909 |
| 3.8235 |
| 3.3961 |
| 3.5981 |
| 6.5676 |
| 10.7602 |
| 5.993 |
| 3.0522 |
| 5.7463 |
| 5.3074 |
Against USEPA ProUCL (ProUCL 5.2.0)
| Value | USEPA ProUCL | EnviroAutomate | Difference | Agreement band | Verdict |
|---|---|---|---|---|---|
| Sample size (n) n | 60 | 60 | 0 | exact match | Agree |
| Mean mean | 5.169880000000001 | 5.169880000000001 | 0 | within 0.000001 relative | Agree |
| Standard deviation sd | 3.2700001741460585 | 3.2700001741460585 | 0 | within 0.000001 relative | Agree |
| Skewness skewness | 1.3381246899863022 | 1.338124689986302 | 2.22e-16 | within 0.000001 relative | Agree |
| 95% UCL - Student's t ucl.studentT | 5.875340604675027 | 5.875340625249703 | 2.06e-8 | within 0.000001 relative | Agree |
| 95% UCL - Modified t (Johnson) ucl.modifiedT | 5.887495237923039 | 5.887495258497715 | 2.06e-8 | within 0.000001 relative | Agree |
| 95% UCL - Central limit theorem ucl.clt | 5.864263524146129 | 5.864263523730242 | 4.16e-10 | within 0.000001 relative | Agree |
| 95% UCL - Land's H ucl.landsH | 6.165001152421691 | 6.165001152421691 | 0 | within 0.02 relative | Agree |
| 95% UCL - approximateGamma ucl.approximateGamma | 5.912794348217808 | 5.912794369376121 | 2.12e-8 | within 0.005 relative | Agree |
| 95% UCL - adjustedGamma ucl.adjustedGamma | 5.93230812665995 | 5.932308150052728 | 2.34e-8 | within 0.005 relative | Agree |
| Distribution used distributionUsed | gamma | gamma | - | exact match | Agree |
| Recommended method recommendedMethod | approximateGamma | approximateGamma | - | exact match | Agree |
| 95% UCL - Chebyshev, 95% ucl.chebyshev95 | 7.0100118867560814 | 7.0100118867560814 | 0 | within 0.000001 relative | Agree |
| 95% UCL - Chebyshev, 97.5% ucl.chebyshev975 | 7.806238424094666 | 7.8062384240946665 | 8.88e-16 | within 0.000001 relative | Agree |
| 95% UCL - Chebyshev, 99% ucl.chebyshev99 | 9.370271276918158 | 9.37027127691816 | 1.78e-15 | within 0.000001 relative | Agree |
Against R EnvStats / nortest (EnvStats 3.1.0, nortest 1.0-4, R 4.6.1)
| Value | R EnvStats / nortest | EnviroAutomate | Difference | Agreement band | Verdict |
|---|---|---|---|---|---|
| Sample size (n) n | 60 | 60 | 0 | exact match | Agree |
| Mean mean | 5.16988 | 5.169880000000001 | 8.88e-16 | within 0.000001 relative | Agree |
| Standard deviation sd | 3.270000174146058 | 3.2700001741460585 | 4.44e-16 | within 0.000001 relative | Agree |
| Median median | 4.5423 | 4.5423 | 0 | within 0.000001 relative | Agree |
| Minimum min | 0.8072 | 0.8072 | 0 | within 0.000001 relative | Agree |
| Maximum max | 15.6764 | 15.6764 | 0 | within 0.000001 relative | Agree |
| Coefficient of variation cv | 0.6325098791743827 | 0.6325098791743827 | 0 | within 0.000001 relative | Agree |
| Skewness skewness | 1.3381246899863026 | 1.338124689986302 | 6.66e-16 | within 0.000001 relative | Agree |
| 95% UCL - Student's t ucl.studentT | 5.875340625249659 | 5.875340625249703 | 4.44e-14 | within 0.000001 relative | Agree |
| 95% UCL - Land's H ucl.landsH | 6.148559579563049 | 6.165001152421691 | 0.0164 | within 0.02 relative | Agree |
Gamma data with a low shape - the adjusted gamma UCL
Boundary caseInput
25 values
| value |
|---|
| 0.0002 |
| 0.2199 |
| 0.7523 |
| 0.0287 |
| 1.8154 |
| 0.0155 |
| 0.2525 |
| 0.0933 |
| 1.788 |
| 0.2516 |
| 0.0347 |
| 0.2946 |
| 0.2196 |
| 0.0344 |
| 0.7148 |
| 0.6871 |
| 0.6397 |
| 0.0788 |
| 0.4578 |
| 0.0762 |
| 2.1604 |
| 0.0048 |
| 0.0082 |
| 0.0001 |
| 1.295 |
Against USEPA ProUCL (ProUCL 5.2.0)
| Value | USEPA ProUCL | EnviroAutomate | Difference | Agreement band | Verdict |
|---|---|---|---|---|---|
| Sample size (n) n | 25 | 25 | 0 | exact match | Agree |
| Mean mean | 0.476944 | 0.47694400000000003 | 5.55e-17 | within 0.000001 relative | Agree |
| Standard deviation sd | 0.6341849474456696 | 0.6341849474456696 | 0 | within 0.000001 relative | Agree |
| Skewness skewness | 1.595295515811521 | 1.595295515811521 | 0 | within 0.000001 relative | Agree |
| 95% UCL - Student's t ucl.studentT | 0.693947124342754 | 0.6939471323866131 | 8.04e-9 | within 0.000001 relative | Agree |
| 95% UCL - Modified t (Johnson) ucl.modifiedT | 0.7006918736951223 | 0.7006918817389813 | 8.04e-9 | within 0.000001 relative | Agree |
| 95% UCL - Central limit theorem ucl.clt | 0.6855722823177617 | 0.6855722821928077 | 1.25e-10 | within 0.000001 relative | Agree |
| 95% UCL - Land's H ucl.landsH | 44.198605933694076 | 44.19860593369407 | 7.11e-15 | within 0.02 relative | Agree |
| 95% UCL - approximateGamma ucl.approximateGamma | 0.8784778624224293 | 0.8785042881045121 | 2.64e-5 | within 0.005 relative | Agree |
| 95% UCL - adjustedGamma ucl.adjustedGamma | 0.917232621320544 | 0.917268850265371 | 3.62e-5 | within 0.005 relative | Agree |
| Distribution used distributionUsed | gamma | gamma | - | exact match | Agree |
| Recommended method recommendedMethod | adjustedGamma | adjustedGamma | - | exact match | Agree |
| 95% UCL - Chebyshev, 95% ucl.chebyshev95 | 1.029813619486065 | 1.029813619486065 | 0 | within 0.000001 relative | Agree |
| 95% UCL - Chebyshev, 97.5% ucl.chebyshev975 | 1.2690407454825197 | 1.2690407454825197 | 0 | within 0.000001 relative | Agree |
| 95% UCL - Chebyshev, 99% ucl.chebyshev99 | 1.738956111021126 | 1.738956111021126 | 0 | within 0.000001 relative | Agree |
Against R EnvStats / nortest (EnvStats 3.1.0, nortest 1.0-4, R 4.6.1)
| Value | R EnvStats / nortest | EnviroAutomate | Difference | Agreement band | Verdict |
|---|---|---|---|---|---|
| Sample size (n) n | 25 | 25 | 0 | exact match | Agree |
| Mean mean | 0.476944 | 0.47694400000000003 | 5.55e-17 | within 0.000001 relative | Agree |
| Standard deviation sd | 0.6341849474456696 | 0.6341849474456696 | 0 | within 0.000001 relative | Agree |
| Median median | 0.2199 | 0.2199 | 0 | within 0.000001 relative | Agree |
| Minimum min | 0.0001 | 0.0001 | 0 | within 0.000001 relative | Agree |
| Maximum max | 2.1604 | 2.1604 | 0 | within 0.000001 relative | Agree |
| Coefficient of variation cv | 1.3296842972040106 | 1.3296842972040104 | 2.22e-16 | within 0.000001 relative | Agree |
| Skewness skewness | 1.5952955158115212 | 1.595295515811521 | 2.22e-16 | within 0.000001 relative | Agree |
| 95% UCL - Student's t ucl.studentT | 0.6939471323866196 | 0.6939471323866131 | 6.55e-15 | within 0.000001 relative | Agree |
| 95% UCL - Land's H ucl.landsH | 44.20218650499962 | 44.19860593369407 | 0.00358 | within 0.02 relative | Agree |
Gamma detects at forty-nine results, still the adjusted limit
Boundary caseInput
49 values
| value | non-detect | reporting limit |
|---|---|---|
| 0.706 | yes | 0.706 |
| 0.706 | yes | 0.706 |
| 0.706 | yes | 0.706 |
| 0.706 | yes | 0.706 |
| 0.706 | yes | 0.706 |
| 0.843 | no | |
| 0.969 | no | |
| 1.051 | no | |
| 1.101 | no | |
| 1.125 | no | |
| 1.135 | no | |
| 1.157 | no | |
| 1.216 | no | |
| 1.217 | no | |
| 1.231 | no | |
| 1.364 | no | |
| 1.459 | no | |
| 1.48 | no | |
| 1.506 | no | |
| 1.513 | no | |
| 1.677 | no | |
| 1.718 | no | |
| 1.752 | no | |
| 1.847 | no | |
| 1.936 | no | |
| 2.003 | no | |
| 2.097 | no | |
| 2.128 | no | |
| 2.164 | no | |
| 2.376 | no | |
| 2.382 | no | |
| 2.562 | no | |
| 2.639 | no | |
| 2.71 | no | |
| 2.734 | no | |
| 2.741 | no | |
| 2.919 | no | |
| 2.947 | no | |
| 2.976 | no | |
| 3.106 | no | |
| 3.344 | no | |
| 3.846 | no | |
| 4.023 | no | |
| 4.053 | no | |
| 4.192 | no | |
| 4.55 | no | |
| 6.014 | no | |
| 6.109 | no | |
| 8.429 | no |
Settings: nonDetectMethod = kaplanMeier
Against USEPA ProUCL (ProUCL 5.2.0)
| Value | USEPA ProUCL | EnviroAutomate | Difference | Agreement band | Verdict |
|---|---|---|---|---|---|
| Sample size (n) n | 49 | 49 | 0 | exact match | Agree |
| Mean mean | 2.3238979591836744 | 2.323897959183675 | 4.44e-16 | within 0.000001 relative | Agree |
| Standard deviation sd | 1.5573224699149366 | 1.5573224699149368 | 2.22e-16 | within 0.000001 relative | Agree |
| Standard error of the mean standardError | 0.22504668514588788 | 0.2250466851458878 | 8.33e-17 | within 0.000001 relative | Agree |
| 95% UCL - Chebyshev, 95% ucl.chebyshev95 | 3.3048537173134154 | 3.3048537173134154 | 0 | within 0.000001 relative | Agree |
| Distribution used distributionUsed | gamma | gamma | - | exact match | Agree |
| Recommended method recommendedMethod | adjustedGamma | adjustedGamma | - | exact match | Agree |
| 95% UCL - adjustedGamma ucl.adjustedGamma | 2.769 | 2.768642396134268 | 0.000358 | within 0.005 relative | Agree |
Gamma-distributed detects, shape at or below one, fourteen results
Boundary caseInput
14 values
| value | non-detect | reporting limit |
|---|---|---|
| 0.662 | yes | 0.662 |
| 0.662 | yes | 0.662 |
| 0.662 | yes | 0.662 |
| 1.509 | no | |
| 1.539 | no | |
| 3.034 | no | |
| 4.777 | no | |
| 4.965 | no | |
| 6.17 | no | |
| 14.868 | no | |
| 28.802 | no | |
| 29.645 | no | |
| 61.441 | no | |
| 367.352 | no |
Settings: nonDetectMethod = kaplanMeier
Against USEPA ProUCL (ProUCL 5.2.0)
| Value | USEPA ProUCL | EnviroAutomate | Difference | Agreement band | Verdict |
|---|---|---|---|---|---|
| Sample size (n) n | 14 | 14 | 0 | exact match | Agree |
| Mean mean | 37.57771428571427 | 37.577714285714265 | 7.11e-15 | within 0.000001 relative | Agree |
| Standard deviation sd | 92.9606091036325 | 92.9606091036325 | 0 | within 0.000001 relative | Agree |
| Standard error of the mean standardError | 26.05741233919851 | 26.057412339198514 | 3.55e-15 | within 0.000001 relative | Agree |
| 95% UCL - Chebyshev, 95% ucl.chebyshev95 | 151.1593414024503 | 151.1593414024503 | 0 | within 0.000001 relative | Agree |
| Distribution used distributionUsed | gamma | gamma | - | exact match | Agree |
| Recommended method recommendedMethod | chebyshev99 | chebyshev99 | - | exact match | Agree |
Land's H off a tabulated sample size - where ProUCL's own interpolation goes the wrong way
Boundary caseInput
30 values
| value |
|---|
| 7.3191 |
| 15.5826 |
| 2.4015 |
| 17.7837 |
| 6.0233 |
| 4.0151 |
| 21.5596 |
| 2.7121 |
| 10.7429 |
| 11.2159 |
| 2.6572 |
| 21.2828 |
| 4.1769 |
| 5.7563 |
| 18.277 |
| 2.4135 |
| 15.0507 |
| 7.6654 |
| 3.3248 |
| 22.3758 |
| 3.1006 |
| 8.4966 |
| 13.8656 |
| 2.4574 |
| 19.3195 |
| 5.2095 |
| 4.5781 |
| 20.5415 |
| 2.5544 |
| 12.3165 |
Against USEPA ProUCL (ProUCL 5.2.0)
| Value | USEPA ProUCL | EnviroAutomate | Difference | Agreement band | Verdict |
|---|---|---|---|---|---|
| Sample size (n) n | 30 | 30 | 0 | exact match | Agree |
| Mean mean | 9.825863333333334 | 9.825863333333334 | 0 | within 0.000001 relative | Agree |
| Standard deviation sd | 6.989811588920635 | 6.989811588920635 | 0 | within 0.000001 relative | Agree |
| Skewness skewness | 0.5441248573013786 | 0.5441248573013785 | 1.11e-16 | within 0.000001 relative | Agree |
| 95% UCL - Student's t ucl.studentT | 11.99421976163741 | 11.994219852226388 | 9.06e-8 | within 0.000001 relative | Agree |
| 95% UCL - Modified t (Johnson) ucl.modifiedT | 12.015349374045105 | 12.015349464634083 | 9.06e-8 | within 0.000001 relative | Agree |
| 95% UCL - Central limit theorem ucl.clt | 11.92495835746353 | 11.924958356206314 | 1.26e-9 | within 0.000001 relative | Agree |
| 95% UCL - Land's H ucl.landsH | 14.193950607311416 | 14.193950607311416 | 0 | within 0.02 relative | Agree |
| 95% UCL - approximateGamma ucl.approximateGamma | 12.541101092093632 | 12.541102694682877 | 1.60e-6 | within 0.005 relative | Agree |
| 95% UCL - adjustedGamma ucl.adjustedGamma | 12.720421400086297 | 12.72042343815073 | 2.04e-6 | within 0.005 relative | Agree |
| Distribution used distributionUsed | normal | normal | - | exact match | Agree |
| Recommended method recommendedMethod | studentT | studentT | - | exact match | Agree |
| 95% UCL - Chebyshev, 95% ucl.chebyshev95 | 15.38851214759312 | 15.38851214759312 | 0 | within 0.000001 relative | Agree |
| 95% UCL - Chebyshev, 97.5% ucl.chebyshev975 | 17.795474733093798 | 17.795474733093798 | 0 | within 0.000001 relative | Agree |
| 95% UCL - Chebyshev, 99% ucl.chebyshev99 | 22.523486652695517 | 22.523486652695517 | 0 | within 0.000001 relative | Agree |
Against R EnvStats / nortest (EnvStats 3.1.0, nortest 1.0-4, R 4.6.1)
| Value | R EnvStats / nortest | EnviroAutomate | Difference | Agreement band | Verdict |
|---|---|---|---|---|---|
| Sample size (n) n | 30 | 30 | 0 | exact match | Agree |
| Mean mean | 9.825863333333334 | 9.825863333333334 | 0 | within 0.000001 relative | Agree |
| Standard deviation sd | 6.989811588920634 | 6.989811588920635 | 1.78e-15 | within 0.000001 relative | Agree |
| Median median | 7.49225 | 7.49225 | 0 | within 0.000001 relative | Agree |
| Minimum min | 2.4015 | 2.4015 | 0 | within 0.000001 relative | Agree |
| Maximum max | 22.3758 | 22.3758 | 0 | within 0.000001 relative | Agree |
| Coefficient of variation cv | 0.7113686962455852 | 0.7113686962455853 | 1.11e-16 | within 0.000001 relative | Agree |
| Skewness skewness | 0.5441248573013786 | 0.5441248573013785 | 1.11e-16 | within 0.000001 relative | Agree |
| 95% UCL - Student's t ucl.studentT | 11.994219852226584 | 11.994219852226388 | 1.95e-13 | within 0.000001 relative | Agree |
| 95% UCL - Land's H ucl.landsH | 14.12790123930072 | 14.193950607311416 | 0.066 | within 0.02 relative | Agree |
Nine results - one below the size at which ProUCL will recommend a UCL
Boundary caseInput
9 values
| value |
|---|
| 4.2 |
| 5.1 |
| 6.3 |
| 7.8 |
| 9.1 |
| 11.4 |
| 3.3 |
| 8.8 |
| 12.1 |
Settings: confidenceLevel = 0.95
Against R EnvStats / nortest (EnvStats 3.1.0, nortest 1.0-4, R 4.6.1)
| Value | R EnvStats / nortest | EnviroAutomate | Difference | Agreement band | Verdict |
|---|---|---|---|---|---|
| Sample size (n) n | 9 | 9 | 0 | exact match | Agree |
| Mean mean | 7.566666666666666 | 7.566666666666666 | 0 | within 0.000001 relative | Agree |
| Standard deviation sd | 3.0903074280724887 | 3.0903074280724887 | 0 | within 0.000001 relative | Agree |
| Median median | 7.8 | 7.8 | 0 | within 0.000001 relative | Agree |
| Minimum min | 3.3 | 3.3 | 0 | within 0.000001 relative | Agree |
| Maximum max | 12.1 | 12.1 | 0 | within 0.000001 relative | Agree |
| Coefficient of variation cv | 0.4084106733135448 | 0.4084106733135448 | 0 | within 0.000001 relative | Agree |
| Skewness skewness | 0.1204322817491478 | 0.1204322817491478 | 0 | within 0.000001 relative | Agree |
| 95% UCL - Student's t ucl.studentT | 9.482191704413117 | 9.482191704413124 | 7.11e-15 | within 0.000001 relative | Agree |
| 95% UCL - Land's H ucl.landsH | 10.909151052457746 | 10.87808244308314 | 0.0311 | within 0.02 relative | Agree |
Against USEPA ProUCL (ProUCL 5.2.0)
| Value | USEPA ProUCL | EnviroAutomate | Difference | Agreement band | Verdict |
|---|---|---|---|---|---|
| Sample size (n) n | 9 | 9 | 0 | exact match | Agree |
| Mean mean | 7.566666666666667 | 7.566666666666666 | 8.88e-16 | within 0.000001 relative | Agree |
| Standard deviation sd | 3.0903074280724887 | 3.0903074280724887 | 0 | within 0.000001 relative | Agree |
| Skewness skewness | 0.12043228174914782 | 0.1204322817491478 | 1.39e-17 | within 0.000001 relative | Agree |
| 95% UCL - Student's t ucl.studentT | 9.48219169665234 | 9.482191704413124 | 7.76e-9 | within 0.000001 relative | Agree |
| 95% UCL - Modified t (Johnson) ucl.modifiedT | 9.489083785075842 | 9.489083792836626 | 7.76e-9 | within 0.000001 relative | Agree |
| 95% UCL - Central limit theorem ucl.clt | 9.261034461501513 | 9.261034460486703 | 1.01e-9 | within 0.000001 relative | Agree |
| 95% UCL - Land's H ucl.landsH | 10.87808244308314 | 10.87808244308314 | 0 | within 0.02 relative | Agree |
| 95% UCL - approximateGamma ucl.approximateGamma | 10.120344700483615 | 10.120348384508043 | 3.68e-6 | within 0.005 relative | Agree |
| 95% UCL - adjustedGamma ucl.adjustedGamma | 10.78118805730451 | 10.781196303329585 | 8.25e-6 | within 0.005 relative | Agree |
| 95% UCL - Chebyshev, 95% ucl.chebyshev95 | 12.05677926114702 | 12.05677926114702 | 0 | within 0.000001 relative | Agree |
| 95% UCL - Chebyshev, 97.5% ucl.chebyshev975 | 13.999654567582795 | 13.999654567582795 | 0 | within 0.000001 relative | Agree |
| 95% UCL - Chebyshev, 99% ucl.chebyshev99 | 17.816056892431313 | 17.816056892431313 | 0 | within 0.000001 relative | Agree |
No discernible distribution (bimodal), n = 10: ProUCL 5.2 finds no discernible distribution and suggests Student's t
Boundary caseInput
10 values
| value |
|---|
| 19.12 |
| 211.9 |
| 22.6 |
| 204.4 |
| 21.77 |
| 178.5 |
| 17.05 |
| 177.5 |
| 22.74 |
| 195.7 |
Against USEPA ProUCL (ProUCL 5.2.0)
| Value | USEPA ProUCL | EnviroAutomate | Difference | Agreement band | Verdict |
|---|---|---|---|---|---|
| Sample size (n) n | 10 | 10 | 0 | exact match | Agree |
| Mean mean | 107.128 | 107.128 | 0 | within 0.000001 relative | Agree |
| Standard deviation sd | 91.7375202290632 | 91.7375202290632 | 0 | within 0.000001 relative | Agree |
| Skewness skewness | 0.04281664863446035 | 0.04281664863446033 | 2.08e-17 | within 0.000001 relative | Agree |
| 95% UCL - Student's t ucl.studentT | 160.3065168726655 | 160.3065165040677 | 3.69e-7 | within 0.000001 relative | Agree |
| 95% UCL - Modified t (Johnson) ucl.modifiedT | 160.37198175883623 | 160.37198139023843 | 3.69e-7 | within 0.000001 relative | Agree |
| 95% UCL - Central limit theorem ucl.clt | 154.84512328342785 | 154.84512325484855 | 2.86e-8 | within 0.000001 relative | Agree |
| 95% UCL - Land's H ucl.landsH | 506.0511287974662 | 506.0511287974658 | 3.98e-13 | within 0.02 relative | Agree |
| 95% UCL - approximateGamma ucl.approximateGamma | 213.0286500083797 | 213.04159511097745 | 0.0129 | within 0.005 relative | Agree |
| 95% UCL - adjustedGamma ucl.adjustedGamma | 241.8523798174497 | 241.88068061724326 | 0.0283 | within 0.005 relative | Agree |
| Distribution used distributionUsed | nonparametric | nonparametric | - | exact match | Agree |
| Recommended method recommendedMethod | studentT | studentT | - | exact match | Agree |
| 95% UCL - Chebyshev, 95% ucl.chebyshev95 | 233.57944512332693 | 233.57944512332693 | 0 | within 0.000001 relative | Agree |
| 95% UCL - Chebyshev, 97.5% ucl.chebyshev975 | 288.29508644048263 | 288.29508644048263 | 0 | within 0.000001 relative | Agree |
| 95% UCL - Chebyshev, 99% ucl.chebyshev99 | 395.77336877628915 | 395.7733687762891 | 5.68e-14 | within 0.000001 relative | Agree |
No discernible distribution (bimodal), n = 150: ProUCL 5.2 finds no discernible distribution and suggests Student's t
Boundary caseInput
150 values
| value |
|---|
| 18.58 |
| 194 |
| 21.11 |
| 191.6 |
| 20.49 |
| 188.6 |
| 21.56 |
| 217.9 |
| 21.73 |
| 226.9 |
| 21.48 |
| 202.4 |
| 17.65 |
| 191 |
| 19.61 |
| 173.1 |
| 17.15 |
| 198.3 |
| 19.14 |
| 204.7 |
| 21.04 |
| 187.8 |
| 22.92 |
| 215.8 |
| 19.52 |
| 201.6 |
| 18.42 |
| 181.4 |
| 20.58 |
| 224 |
| 23.94 |
| 189.1 |
| 21.05 |
| 220.6 |
| 23.32 |
| 230.8 |
| 20.2 |
| 213.7 |
| 14.64 |
| 203.4 |
| 21.86 |
| 157.5 |
| 20.39 |
| 206.8 |
| 21.54 |
| 204.2 |
| 19.08 |
| 198.7 |
| 24.52 |
| 164.2 |
| 25.08 |
| 183.2 |
| 19.71 |
| 194.4 |
| 23.12 |
| 179.3 |
| 20.38 |
| 217.3 |
| 23.14 |
| 235.7 |
| 23.02 |
| 157 |
| 21.6 |
| 218 |
| 19.29 |
| 179.5 |
| 16.05 |
| 192.4 |
| 16.7 |
| 190.6 |
| 16.9 |
| 192.9 |
| 22.57 |
| 179.5 |
| 19.09 |
| 216.9 |
| 21.37 |
| 202.3 |
| 22.22 |
| 194.2 |
| 18.23 |
| 200.3 |
| 18.13 |
| 170.8 |
| 19.44 |
| 216.9 |
| 19.5 |
| 228.2 |
| 24.18 |
| 198.6 |
| 21.12 |
| 174.3 |
| 20.73 |
| 226.9 |
| 16.9 |
| 206.3 |
| 19.55 |
| 193.6 |
| 20.35 |
| 208.5 |
| 20.77 |
| 202.3 |
| 20.15 |
| 213.1 |
| 18.87 |
| 163.3 |
| 22.1 |
| 196.6 |
| 18.63 |
| 221.9 |
| 20.21 |
| 197.2 |
| 18.33 |
| 238.8 |
| 20.73 |
| 184.4 |
| 17.47 |
| 184.5 |
| 20.15 |
| 174.4 |
| 21.34 |
| 224.4 |
| 18.62 |
| 186.3 |
| 19.78 |
| 173.1 |
| 24.45 |
| 206.7 |
| 16.07 |
| 161.7 |
| 19.48 |
| 217.5 |
| 17.78 |
| 222.6 |
| 18.97 |
| 192.1 |
| 18.57 |
| 188.3 |
| 19.66 |
| 186.4 |
| 17.39 |
| 168.7 |
| 19.93 |
| 152 |
| 22.64 |
| 225.2 |
| 20.59 |
| 206.5 |
| 16.12 |
| 193.8 |
Against USEPA ProUCL (ProUCL 5.2.0)
| Value | USEPA ProUCL | EnviroAutomate | Difference | Agreement band | Verdict |
|---|---|---|---|---|---|
| Sample size (n) n | 150 | 150 | 0 | exact match | Agree |
| Mean mean | 108.9079333333333 | 108.90793333333332 | 1.42e-14 | within 0.000001 relative | Agree |
| Standard deviation sd | 90.2294147658557 | 90.2294147658557 | 0 | within 0.000001 relative | Agree |
| Skewness skewness | 0.07254453282462807 | 0.07254453282462808 | 1.39e-17 | within 0.000001 relative | Agree |
| 95% UCL - Student's t ucl.studentT | 121.10171435783366 | 121.10171557532071 | 1.22e-6 | within 0.000001 relative | Agree |
| 95% UCL - Modified t (Johnson) ucl.modifiedT | 121.10898730310169 | 121.10898852058874 | 1.22e-6 | within 0.000001 relative | Agree |
| 95% UCL - Central limit theorem ucl.clt | 121.02590040475972 | 121.02590039750189 | 7.26e-9 | within 0.000001 relative | Agree |
| 95% UCL - Land's H ucl.landsH | 151.92350190711215 | 151.92350190711215 | 0 | within 0.02 relative | Agree |
| 95% UCL - approximateGamma ucl.approximateGamma | 125.02177086049478 | 125.13581513015923 | 0.114 | within 0.005 relative | Agree |
| 95% UCL - adjustedGamma ucl.adjustedGamma | 125.18781750135058 | 125.13581513015923 | 0.052 | within 0.005 relative | Agree |
| Distribution used distributionUsed | nonparametric | nonparametric | - | exact match | Agree |
| Recommended method recommendedMethod | studentT | studentT | - | exact match | Agree |
| 95% UCL - Chebyshev, 95% ucl.chebyshev95 | 141.020817403001 | 141.020817403001 | 0 | within 0.000001 relative | Agree |
| 95% UCL - Chebyshev, 97.5% ucl.chebyshev975 | 154.9160879924488 | 154.9160879924488 | 0 | within 0.000001 relative | Agree |
| 95% UCL - Chebyshev, 99% ucl.chebyshev99 | 182.21065641189716 | 182.21065641189716 | 0 | within 0.000001 relative | Agree |
No discernible distribution (bimodal), n = 30: ProUCL 5.2 finds no discernible distribution and suggests Student's t
Boundary caseInput
30 values
| value |
|---|
| 22.93 |
| 192.8 |
| 21.82 |
| 212.1 |
| 16.73 |
| 192.8 |
| 22.19 |
| 195.7 |
| 19.96 |
| 182.8 |
| 19.04 |
| 209.7 |
| 20.55 |
| 230.2 |
| 22 |
| 207.6 |
| 18.83 |
| 186.6 |
| 20.5 |
| 225.8 |
| 20.49 |
| 205.5 |
| 22.86 |
| 204.8 |
| 18.89 |
| 181 |
| 21.26 |
| 214 |
| 17.99 |
| 232.1 |
Against USEPA ProUCL (ProUCL 5.2.0)
| Value | USEPA ProUCL | EnviroAutomate | Difference | Agreement band | Verdict |
|---|---|---|---|---|---|
| Sample size (n) n | 30 | 30 | 0 | exact match | Agree |
| Mean mean | 112.65133333333333 | 112.65133333333333 | 0 | within 0.000001 relative | Agree |
| Standard deviation sd | 94.52159639134231 | 94.52159639134231 | 0 | within 0.000001 relative | Agree |
| Skewness skewness | 0.045397505405558515 | 0.04539750540555855 | 3.47e-17 | within 0.000001 relative | Agree |
| 95% UCL - Student's t ucl.studentT | 141.97351298601544 | 141.97351421102914 | 1.23e-6 | within 0.000001 relative | Agree |
| 95% UCL - Modified t (Johnson) ucl.modifiedT | 141.99735212314388 | 141.9973533481576 | 1.23e-6 | within 0.000001 relative | Agree |
| 95% UCL - Central limit theorem ucl.clt | 141.03690712653875 | 141.03690710953774 | 1.70e-8 | within 0.000001 relative | Agree |
| 95% UCL - Land's H ucl.landsH | 232.63230363881874 | 232.63230363881874 | 0 | within 0.02 relative | Agree |
| 95% UCL - approximateGamma ucl.approximateGamma | 158.00775111801212 | 158.00789273169707 | 0.000142 | within 0.005 relative | Agree |
| 95% UCL - adjustedGamma ucl.adjustedGamma | 161.16895779217742 | 161.1691390779868 | 0.000181 | within 0.005 relative | Agree |
| Distribution used distributionUsed | nonparametric | nonparametric | - | exact match | Agree |
| Recommended method recommendedMethod | studentT | studentT | - | exact match | Agree |
| 95% UCL - Chebyshev, 95% ucl.chebyshev95 | 187.87373945965277 | 187.8737394596528 | 2.84e-14 | within 0.000001 relative | Agree |
| 95% UCL - Chebyshev, 97.5% ucl.chebyshev975 | 220.42253467988115 | 220.42253467988115 | 0 | within 0.000001 relative | Agree |
| 95% UCL - Chebyshev, 99% ucl.chebyshev99 | 284.35834020379787 | 284.3583402037979 | 5.68e-14 | within 0.000001 relative | Agree |
No discernible distribution (bimodal), n = 8: ProUCL 5.2 finds normal and suggests Student's t
Boundary caseInput
8 values
| value |
|---|
| 19.33 |
| 230.7 |
| 18.98 |
| 194.6 |
| 16.41 |
| 181.1 |
| 18.15 |
| 185.4 |
Against USEPA ProUCL (ProUCL 5.2.0)
| Value | USEPA ProUCL | EnviroAutomate | Difference | Agreement band | Verdict |
|---|---|---|---|---|---|
| Sample size (n) n | 8 | 8 | 0 | exact match | Agree |
| Mean mean | 108.08375 | 108.08375 | 0 | within 0.000001 relative | Agree |
| Standard deviation sd | 97.20217794995277 | 97.20217794995277 | 0 | within 0.000001 relative | Agree |
| Skewness skewness | 0.09087236230682877 | 0.09087236230682876 | 1.39e-17 | within 0.000001 relative | Agree |
| 95% UCL - Student's t ucl.studentT | 173.19314003592496 | 173.19314069312506 | 6.57e-7 | within 0.000001 relative | Agree |
| 95% UCL - Modified t (Johnson) ucl.modifiedT | 173.377160692835 | 173.37716135003507 | 6.57e-7 | within 0.000001 relative | Agree |
| 95% UCL - Central limit theorem ucl.clt | 164.611052275348 | 164.61105224149205 | 3.39e-8 | within 0.000001 relative | Agree |
| 95% UCL - Land's H ucl.landsH | 996.0321051715584 | 996.0321051715584 | 0 | within 0.02 relative | Agree |
| 95% UCL - approximateGamma ucl.approximateGamma | 258.23320748125417 | 258.29754693243774 | 0.0643 | within 0.005 relative | Agree |
| 95% UCL - adjustedGamma ucl.adjustedGamma | 328.85519059264885 | 329.0644948702817 | 0.209 | within 0.005 relative | Agree |
| 95% UCL - Chebyshev, 95% ucl.chebyshev95 | 257.8823667184427 | 257.8823667184427 | 0 | within 0.000001 relative | Agree |
| 95% UCL - Chebyshev, 97.5% ucl.chebyshev975 | 322.700347835057 | 322.700347835057 | 0 | within 0.000001 relative | Agree |
| 95% UCL - Chebyshev, 99% ucl.chebyshev99 | 450.0227205092148 | 450.0227205092148 | 0 | within 0.000001 relative | Agree |
No discernible distribution (cluster outliers), n = 8: not normal and under ten results, so ProUCL 5.2 makes no suggestion
Boundary caseInput
8 values
| value |
|---|
| 499.2 |
| 491.1 |
| 500.8 |
| 506.1 |
| 526.2 |
| 505.8 |
| 529.6 |
| 2971 |
Against USEPA ProUCL (ProUCL 5.2.0)
| Value | USEPA ProUCL | EnviroAutomate | Difference | Agreement band | Verdict |
|---|---|---|---|---|---|
| Sample size (n) n | 8 | 8 | 0 | exact match | Agree |
| Mean mean | 816.2249999999998 | 816.2249999999999 | 1.14e-13 | within 0.000001 relative | Agree |
| Standard deviation sd | 870.7606637712963 | 870.7606637712963 | 0 | within 0.000001 relative | Agree |
| Skewness skewness | 2.82712943224754 | 2.82712943224754 | 0 | within 0.000001 relative | Agree |
| 95% UCL - Student's t ucl.studentT | 1399.49069302405 | 1399.490698911408 | 5.89e-6 | within 0.000001 relative | Agree |
| 95% UCL - Modified t (Johnson) ucl.modifiedT | 1450.7772159613673 | 1450.7772218487253 | 5.89e-6 | within 0.000001 relative | Agree |
| 95% UCL - Central limit theorem ucl.clt | 1322.610271282974 | 1322.6102709796842 | 3.03e-7 | within 0.000001 relative | Agree |
| 95% UCL - Land's H ucl.landsH | 1417.3923715768738 | 1417.3923715768738 | 0 | within 0.02 relative | Agree |
| 95% UCL - approximateGamma ucl.approximateGamma | 1442.172289622006 | 1442.2008141587917 | 0.0285 | within 0.005 relative | Agree |
| 95% UCL - adjustedGamma ucl.adjustedGamma | 1681.4135603424515 | 1681.4952501982925 | 0.0817 | within 0.005 relative | Agree |
| 95% UCL - Chebyshev, 95% ucl.chebyshev95 | 2158.1573072465844 | 2158.1573072465844 | 0 | within 0.000001 relative | Agree |
| 95% UCL - Chebyshev, 97.5% ucl.chebyshev975 | 2738.812488558248 | 2738.812488558248 | 0 | within 0.000001 relative | Agree |
| 95% UCL - Chebyshev, 99% ucl.chebyshev99 | 3879.3971552903977 | 3879.3971552903977 | 0 | within 0.000001 relative | Agree |
No discernible distribution, n = 10: ProUCL 5.2 finds no discernible distribution and suggests Student's t
Boundary caseInput
10 values
| value |
|---|
| 492.5 |
| 515.1 |
| 516 |
| 499.6 |
| 500.7 |
| 491.6 |
| 517.5 |
| 496.5 |
| 5402 |
| 3811 |
Against USEPA ProUCL (ProUCL 5.2.0)
| Value | USEPA ProUCL | EnviroAutomate | Difference | Agreement band | Verdict |
|---|---|---|---|---|---|
| Sample size (n) n | 10 | 10 | 0 | exact match | Agree |
| Mean mean | 1324.25 | 1324.25 | 0 | within 0.000001 relative | Agree |
| Standard deviation sd | 1770.102769929224 | 1770.102769929224 | 0 | within 0.000001 relative | Agree |
| Skewness skewness | 1.97234281617478 | 1.97234281617478 | 0 | within 0.000001 relative | Agree |
| 95% UCL - Student's t ucl.studentT | 2350.345318273183 | 2350.345311160979 | 7.11e-6 | within 0.000001 relative | Agree |
| 95% UCL - Modified t (Johnson) ucl.modifiedT | 2408.532809642533 | 2408.532802530329 | 7.11e-6 | within 0.000001 relative | Agree |
| 95% UCL - Central limit theorem ucl.clt | 2244.9661027041902 | 2244.9661021527445 | 5.51e-7 | within 0.000001 relative | Agree |
| 95% UCL - Land's H ucl.landsH | 3022.208438210116 | 3022.208438210116 | 0 | within 0.02 relative | Agree |
| 95% UCL - approximateGamma ucl.approximateGamma | 2626.1650819408146 | 2626.3209382760892 | 0.156 | within 0.005 relative | Agree |
| 95% UCL - adjustedGamma ucl.adjustedGamma | 2979.909765432083 | 2980.2502437724593 | 0.34 | within 0.005 relative | Agree |
| Distribution used distributionUsed | nonparametric | nonparametric | - | exact match | Agree |
| Recommended method recommendedMethod | studentT | studentT | - | exact match | Agree |
| 95% UCL - Chebyshev, 95% ucl.chebyshev95 | 3764.168287691435 | 3764.168287691435 | 0 | within 0.000001 relative | Agree |
| 95% UCL - Chebyshev, 97.5% ucl.chebyshev975 | 4819.922879837775 | 4819.922879837775 | 0 | within 0.000001 relative | Agree |
| 95% UCL - Chebyshev, 99% ucl.chebyshev99 | 6893.74834181679 | 6893.74834181679 | 0 | within 0.000001 relative | Agree |
No discernible distribution, n = 200: ProUCL 5.2 finds no discernible distribution and suggests Student's t
Boundary caseInput
200 values
| value |
|---|
| 505 |
| 503.4 |
| 491.1 |
| 458.2 |
| 500.2 |
| 521.1 |
| 498.5 |
| 519.5 |
| 502.5 |
| 490.6 |
| 499.7 |
| 477.7 |
| 504.8 |
| 512.4 |
| 519.7 |
| 504 |
| 461.9 |
| 533 |
| 507.6 |
| 524.2 |
| 485.9 |
| 517.1 |
| 490.3 |
| 494.7 |
| 522.6 |
| 497.4 |
| 504.6 |
| 490.2 |
| 514.1 |
| 515 |
| 522 |
| 518.8 |
| 481.8 |
| 513.1 |
| 488.3 |
| 509.7 |
| 507.5 |
| 496.8 |
| 474.6 |
| 520.1 |
| 496.1 |
| 499.7 |
| 504.2 |
| 506 |
| 481 |
| 489.1 |
| 467.8 |
| 527.2 |
| 514.7 |
| 493.5 |
| 512.1 |
| 473.9 |
| 512.2 |
| 512.3 |
| 473.4 |
| 509.5 |
| 501 |
| 497.8 |
| 504.6 |
| 477.8 |
| 491.3 |
| 497.7 |
| 532.6 |
| 504.3 |
| 475.7 |
| 499.9 |
| 487.9 |
| 507.4 |
| 519.3 |
| 516.7 |
| 490.7 |
| 502 |
| 499 |
| 486.2 |
| 491.9 |
| 534.2 |
| 506 |
| 513.6 |
| 502.3 |
| 488.3 |
| 494.8 |
| 479.1 |
| 507.4 |
| 500.9 |
| 502.8 |
| 507.8 |
| 497.6 |
| 522.5 |
| 517.5 |
| 498.1 |
| 516.1 |
| 516.4 |
| 499.6 |
| 496.7 |
| 487.5 |
| 494.3 |
| 522.8 |
| 516 |
| 483.6 |
| 496.9 |
| 512.2 |
| 504.9 |
| 498 |
| 510.3 |
| 529.2 |
| 504.3 |
| 468.7 |
| 504 |
| 489.2 |
| 489.2 |
| 492.9 |
| 477.3 |
| 506.5 |
| 490.5 |
| 522.7 |
| 481.8 |
| 502.3 |
| 504.1 |
| 506.2 |
| 476.3 |
| 468.7 |
| 469.3 |
| 498.7 |
| 489.6 |
| 504.6 |
| 504.5 |
| 504.4 |
| 545.5 |
| 511.6 |
| 470.9 |
| 495.5 |
| 523.6 |
| 496.4 |
| 529.2 |
| 507.1 |
| 516.1 |
| 505.2 |
| 490.4 |
| 497.7 |
| 505.7 |
| 506.6 |
| 518.2 |
| 519.8 |
| 500.6 |
| 493.1 |
| 498.2 |
| 482.2 |
| 511.1 |
| 511.1 |
| 502.9 |
| 489.5 |
| 491.1 |
| 518.6 |
| 510.7 |
| 497.1 |
| 486.1 |
| 522.5 |
| 494.8 |
| 519.4 |
| 476.6 |
| 6842 |
| 6127 |
| 4943 |
| 6676 |
| 6271 |
| 1751 |
| 6897 |
| 5490 |
| 4830 |
| 2072 |
| 5026 |
| 3312 |
| 3151 |
| 2379 |
| 4653 |
| 4164 |
| 3755 |
| 3160 |
| 5970 |
| 5201 |
| 4718 |
| 2319 |
| 7950 |
| 2090 |
| 1841 |
| 2631 |
| 7176 |
| 5392 |
| 6525 |
| 4525 |
| 5401 |
| 4830 |
| 6279 |
| 3457 |
| 4653 |
| 4809 |
| 6904 |
| 4968 |
| 2121 |
| 1692 |
Against USEPA ProUCL (ProUCL 5.2.0)
| Value | USEPA ProUCL | EnviroAutomate | Difference | Agreement band | Verdict |
|---|---|---|---|---|---|
| Sample size (n) n | 200 | 200 | 0 | exact match | Agree |
| Mean mean | 1315.8275 | 1315.8275 | 0 | within 0.000001 relative | Agree |
| Standard deviation sd | 1807.4886141397885 | 1807.4886141397885 | 0 | within 0.000001 relative | Agree |
| Skewness skewness | 2.0975914519985297 | 2.0975914519985284 | 1.33e-15 | within 0.000001 relative | Agree |
| 95% UCL - Student's t ucl.studentT | 1527.0374727747776 | 1527.0374266688302 | 4.61e-5 | within 0.000001 relative | Agree |
| 95% UCL - Modified t (Johnson) ucl.modifiedT | 1530.1969499969478 | 1530.1969038910004 | 4.61e-5 | within 0.000001 relative | Agree |
| 95% UCL - Central limit theorem ucl.clt | 1526.0541788781954 | 1526.0541787522843 | 1.26e-7 | within 0.000001 relative | Agree |
| 95% UCL - Land's H ucl.landsH | 1277.9343166427877 | 1277.9343166427877 | 0 | within 0.02 relative | Agree |
| 95% UCL - approximateGamma ucl.approximateGamma | 1479.8401218982037 | 1479.8401242374264 | 2.34e-6 | within 0.005 relative | Agree |
| 95% UCL - adjustedGamma ucl.adjustedGamma | 1481.0892420962127 | 1481.0892445017444 | 2.41e-6 | within 0.005 relative | Agree |
| Distribution used distributionUsed | nonparametric | nonparametric | - | exact match | Agree |
| Recommended method recommendedMethod | studentT | studentT | - | exact match | Agree |
| 95% UCL - Chebyshev, 95% ucl.chebyshev95 | 1872.932906160515 | 1872.932906160515 | 0 | within 0.000001 relative | Agree |
| 95% UCL - Chebyshev, 97.5% ucl.chebyshev975 | 2113.992860434647 | 2113.992860434647 | 0 | within 0.000001 relative | Agree |
| 95% UCL - Chebyshev, 99% ucl.chebyshev99 | 2587.508462219401 | 2587.508462219401 | 0 | within 0.000001 relative | Agree |
No discernible distribution, n = 9: not normal and under ten results, so ProUCL 5.2 makes no suggestion
Boundary caseInput
9 values
| value |
|---|
| 513.4 |
| 472.4 |
| 487.1 |
| 516.1 |
| 474.1 |
| 501.7 |
| 541.7 |
| 474.5 |
| 3025 |
Against USEPA ProUCL (ProUCL 5.2.0)
| Value | USEPA ProUCL | EnviroAutomate | Difference | Agreement band | Verdict |
|---|---|---|---|---|---|
| Sample size (n) n | 9 | 9 | 0 | exact match | Agree |
| Mean mean | 778.4444444444445 | 778.4444444444445 | 0 | within 0.000001 relative | Agree |
| Standard deviation sd | 842.7835577879873 | 842.7835577879874 | 1.14e-13 | within 0.000001 relative | Agree |
| Skewness skewness | 2.9955508930357078 | 2.9955508930357078 | 0 | within 0.000001 relative | Agree |
| 95% UCL - Student's t ucl.studentT | 1300.8432793105915 | 1300.8432814270996 | 2.12e-6 | within 0.000001 relative | Agree |
| 95% UCL - Modified t (Johnson) ucl.modifiedT | 1347.5951504062882 | 1347.595152522796 | 2.12e-6 | within 0.000001 relative | Agree |
| 95% UCL - Central limit theorem ucl.clt | 1240.529641975414 | 1240.5296416986569 | 2.77e-7 | within 0.000001 relative | Agree |
| 95% UCL - Land's H ucl.landsH | 1228.913616950396 | 1228.913616950396 | 0 | within 0.02 relative | Agree |
| 95% UCL - approximateGamma ucl.approximateGamma | 1296.2284562271723 | 1296.2417843764074 | 0.0133 | within 0.005 relative | Agree |
| 95% UCL - adjustedGamma ucl.adjustedGamma | 1451.5351245066463 | 1451.5670786991138 | 0.032 | within 0.005 relative | Agree |
| 95% UCL - Chebyshev, 95% ucl.chebyshev95 | 2002.9805643362804 | 2002.9805643362802 | 2.27e-13 | within 0.000001 relative | Agree |
| 95% UCL - Chebyshev, 97.5% ucl.chebyshev975 | 2532.838321600798 | 2532.838321600798 | 0 | within 0.000001 relative | Agree |
| 95% UCL - Chebyshev, 99% ucl.chebyshev99 | 3573.6412851080054 | 3573.6412851080054 | 0 | within 0.000001 relative | Agree |
Normal data - ProUCL recommends Student's t
Boundary caseInput
15 values
| value |
|---|
| 9.8 |
| 10.4 |
| 11.2 |
| 9.1 |
| 10.8 |
| 12 |
| 8.7 |
| 10.1 |
| 11.6 |
| 9.5 |
| 10.9 |
| 10.3 |
| 10 |
| 9.9 |
| 10.6 |
Against USEPA ProUCL (ProUCL 5.2.0)
| Value | USEPA ProUCL | EnviroAutomate | Difference | Agreement band | Verdict |
|---|---|---|---|---|---|
| Sample size (n) n | 15 | 15 | 0 | exact match | Agree |
| Mean mean | 10.326666666666664 | 10.326666666666664 | 0 | within 0.000001 relative | Agree |
| Standard deviation sd | 0.8971913847961208 | 0.8971913847961208 | 0 | within 0.000001 relative | Agree |
| Skewness skewness | 0.08515334733141469 | 0.08515334733141472 | 2.78e-17 | within 0.000001 relative | Agree |
| 95% UCL - Student's t ucl.studentT | 10.734680892852985 | 10.734680886846242 | 6.01e-9 | within 0.000001 relative | Agree |
| 95% UCL - Modified t (Johnson) ucl.modifiedT | 10.735529768959786 | 10.735529762953044 | 6.01e-9 | within 0.000001 relative | Agree |
| 95% UCL - Central limit theorem ucl.clt | 10.707703292006276 | 10.70770329177806 | 2.28e-10 | within 0.000001 relative | Agree |
| 95% UCL - approximateGamma ucl.approximateGamma | 10.752198187708894 | 10.752198187477958 | 2.31e-10 | within 0.005 relative | Agree |
| 95% UCL - adjustedGamma ucl.adjustedGamma | 10.8059175970647 | 10.805917597326486 | 2.62e-10 | within 0.005 relative | Agree |
| Distribution used distributionUsed | normal | normal | - | exact match | Agree |
| Recommended method recommendedMethod | studentT | studentT | - | exact match | Agree |
| 95% UCL - Chebyshev, 95% ucl.chebyshev95 | 11.33642225551297 | 11.33642225551297 | 0 | within 0.000001 relative | Agree |
| 95% UCL - Chebyshev, 97.5% ucl.chebyshev975 | 11.77334430542251 | 11.77334430542251 | 0 | within 0.000001 relative | Agree |
| 95% UCL - Chebyshev, 99% ucl.chebyshev99 | 12.631593067722827 | 12.631593067722825 | 1.78e-15 | within 0.000001 relative | Agree |
Against R EnvStats / nortest (EnvStats 3.1.0, nortest 1.0-4, R 4.6.1)
| Value | R EnvStats / nortest | EnviroAutomate | Difference | Agreement band | Verdict |
|---|---|---|---|---|---|
| Sample size (n) n | 15 | 15 | 0 | exact match | Agree |
| Mean mean | 10.326666666666666 | 10.326666666666664 | 1.78e-15 | within 0.000001 relative | Agree |
| Standard deviation sd | 0.8971913847961207 | 0.8971913847961208 | 1.11e-16 | within 0.000001 relative | Agree |
| Median median | 10.3 | 10.3 | 0 | within 0.000001 relative | Agree |
| Minimum min | 8.7 | 8.7 | 0 | within 0.000001 relative | Agree |
| Maximum max | 12 | 12 | 0 | within 0.000001 relative | Agree |
| Coefficient of variation cv | 0.08688102499639645 | 0.08688102499639648 | 2.78e-17 | within 0.000001 relative | Agree |
| Skewness skewness | 0.08515334733140789 | 0.08515334733141472 | 6.83e-15 | within 0.000001 relative | Agree |
| 95% UCL - Student's t ucl.studentT | 10.734680886846245 | 10.734680886846242 | 3.55e-15 | within 0.000001 relative | Agree |
Normal data with one mild outlier, n = 10: ProUCL 5.2 finds normal and suggests Student's t
Boundary caseInput
10 values
| value |
|---|
| 96.28 |
| 99.81 |
| 82.47 |
| 105.4 |
| 95.62 |
| 102.9 |
| 112.4 |
| 108.5 |
| 112.8 |
| 126.3 |
Against USEPA ProUCL (ProUCL 5.2.0)
| Value | USEPA ProUCL | EnviroAutomate | Difference | Agreement band | Verdict |
|---|---|---|---|---|---|
| Sample size (n) n | 10 | 10 | 0 | exact match | Agree |
| Mean mean | 104.248 | 104.248 | 0 | within 0.000001 relative | Agree |
| Standard deviation sd | 11.921105280598402 | 11.921105280598402 | 0 | within 0.000001 relative | Agree |
| Skewness skewness | 0.03298670376300828 | 0.03298670376300829 | 6.94e-18 | within 0.000001 relative | Agree |
| 95% UCL - Student's t ucl.studentT | 111.15844075229194 | 111.1584407043934 | 4.79e-8 | within 0.000001 relative | Agree |
| 95% UCL - Modified t (Johnson) ucl.modifiedT | 111.16499471843225 | 111.16499467053372 | 4.79e-8 | within 0.000001 relative | Agree |
| 95% UCL - Central limit theorem ucl.clt | 110.44874369711187 | 110.44874369339806 | 3.71e-9 | within 0.000001 relative | Agree |
| 95% UCL - Land's H ucl.landsH | 111.89344553299274 | 111.89344553299273 | 1.42e-14 | within 0.02 relative | Agree |
| 95% UCL - approximateGamma ucl.approximateGamma | 111.72047237788432 | 111.72047238093192 | 3.05e-9 | within 0.005 relative | Agree |
| 95% UCL - adjustedGamma ucl.adjustedGamma | 113.08430111292314 | 113.08430113699235 | 2.41e-8 | within 0.005 relative | Agree |
| Distribution used distributionUsed | normal | normal | - | exact match | Agree |
| Recommended method recommendedMethod | studentT | studentT | - | exact match | Agree |
| 95% UCL - Chebyshev, 95% ucl.chebyshev95 | 120.68010963665685 | 120.68010963665685 | 0 | within 0.000001 relative | Agree |
| 95% UCL - Chebyshev, 97.5% ucl.chebyshev975 | 127.79029660278141 | 127.79029660278141 | 0 | within 0.000001 relative | Agree |
| 95% UCL - Chebyshev, 99% ucl.chebyshev99 | 141.75688209477855 | 141.75688209477855 | 0 | within 0.000001 relative | Agree |
Normal data with one mild outlier, n = 30: ProUCL 5.2 finds normal and suggests Student's t
Boundary caseInput
30 values
| value |
|---|
| 90.91 |
| 88.52 |
| 100.8 |
| 108.9 |
| 88.71 |
| 97.28 |
| 91.26 |
| 101.7 |
| 104.9 |
| 107.1 |
| 83.47 |
| 105.6 |
| 84.47 |
| 81.96 |
| 108 |
| 91.44 |
| 104.2 |
| 92.44 |
| 97.34 |
| 98.92 |
| 108.7 |
| 97.53 |
| 105.3 |
| 122.8 |
| 98.02 |
| 87.52 |
| 79.91 |
| 79.72 |
| 100.6 |
| 130.9 |
Against USEPA ProUCL (ProUCL 5.2.0)
| Value | USEPA ProUCL | EnviroAutomate | Difference | Agreement band | Verdict |
|---|---|---|---|---|---|
| Sample size (n) n | 30 | 30 | 0 | exact match | Agree |
| Mean mean | 97.964 | 97.964 | 0 | within 0.000001 relative | Agree |
| Standard deviation sd | 11.903998922413747 | 11.903998922413745 | 1.78e-15 | within 0.000001 relative | Agree |
| Skewness skewness | 0.6887285791291946 | 0.6887285791291946 | 0 | within 0.000001 relative | Agree |
| 95% UCL - Student's t ucl.studentT | 101.65681950701715 | 101.6568196612947 | 1.54e-7 | within 0.000001 relative | Agree |
| 95% UCL - Modified t (Johnson) ucl.modifiedT | 101.70236741959376 | 101.70236757387131 | 1.54e-7 | within 0.000001 relative | Agree |
| 95% UCL - Central limit theorem ucl.clt | 101.53886386970674 | 101.53886386756565 | 2.14e-9 | within 0.000001 relative | Agree |
| 95% UCL - Land's H ucl.landsH | 101.76714291069293 | 101.76714291069293 | 0 | within 0.02 relative | Agree |
| 95% UCL - approximateGamma ucl.approximateGamma | 101.71820332946488 | 101.71820332735102 | 2.11e-9 | within 0.005 relative | Agree |
| 95% UCL - adjustedGamma ucl.adjustedGamma | 101.93829207286205 | 101.9382920711679 | 1.69e-9 | within 0.005 relative | Agree |
| Distribution used distributionUsed | normal | normal | - | exact match | Agree |
| Recommended method recommendedMethod | studentT | studentT | - | exact match | Agree |
| 95% UCL - Chebyshev, 95% ucl.chebyshev95 | 107.43746929861094 | 107.43746929861094 | 0 | within 0.000001 relative | Agree |
| 95% UCL - Chebyshev, 97.5% ucl.chebyshev975 | 111.53664703174275 | 111.53664703174276 | 1.42e-14 | within 0.000001 relative | Agree |
| 95% UCL - Chebyshev, 99% ucl.chebyshev99 | 119.58868793157328 | 119.58868793157328 | 0 | within 0.000001 relative | Agree |
Normal data with one mild outlier, n = 5: ProUCL 5.2 finds normal and suggests Student's t
Boundary caseInput
5 values
| value |
|---|
| 107.6 |
| 87.83 |
| 103.1 |
| 82.77 |
| 128 |
Against USEPA ProUCL (ProUCL 5.2.0)
| Value | USEPA ProUCL | EnviroAutomate | Difference | Agreement band | Verdict |
|---|---|---|---|---|---|
| Sample size (n) n | 5 | 5 | 0 | exact match | Agree |
| Mean mean | 101.85999999999999 | 101.85999999999999 | 0 | within 0.000001 relative | Agree |
| Standard deviation sd | 17.881930824158783 | 17.881930824158783 | 0 | within 0.000001 relative | Agree |
| Skewness skewness | 0.6072843638326758 | 0.607284363832676 | 2.22e-16 | within 0.000001 relative | Agree |
| 95% UCL - Student's t ucl.studentT | 118.90846959850418 | 118.90846952078046 | 7.77e-8 | within 0.000001 relative | Agree |
| 95% UCL - Modified t (Johnson) ucl.modifiedT | 119.27045016465917 | 119.27045008693543 | 7.77e-8 | within 0.000001 relative | Agree |
| 95% UCL - Central limit theorem ucl.clt | 115.01396449776854 | 115.01396448989021 | 7.88e-9 | within 0.000001 relative | Agree |
| 95% UCL - Land's H ucl.landsH | 123.0238084144219 | 123.0238084144219 | 0 | within 0.02 relative | Agree |
| 95% UCL - approximateGamma ucl.approximateGamma | 123.11390416045494 | 123.11390763517007 | 3.47e-6 | within 0.005 relative | Agree |
| 95% UCL - adjustedGamma ucl.adjustedGamma | 134.29950997665543 | 134.29952433482646 | 1.44e-5 | within 0.005 relative | Agree |
| 95% UCL - Chebyshev, 95% ucl.chebyshev95 | 136.71830044623516 | 136.71830044623516 | 0 | within 0.000001 relative | Agree |
| 95% UCL - Chebyshev, 97.5% ucl.chebyshev975 | 151.80151489492482 | 151.80151489492482 | 0 | within 0.000001 relative | Agree |
| 95% UCL - Chebyshev, 99% ucl.chebyshev99 | 181.42956899468533 | 181.42956899468535 | 2.84e-14 | within 0.000001 relative | Agree |
Not normal and fewer than ten results - no recommendation at all
Boundary caseInput
9 values
| value |
|---|
| 0.4 |
| 0.6 |
| 1.1 |
| 2.8 |
| 14 |
| 52 |
| 0.5 |
| 0.9 |
| 7 |
Against USEPA ProUCL (ProUCL 5.2.0)
| Value | USEPA ProUCL | EnviroAutomate | Difference | Agreement band | Verdict |
|---|---|---|---|---|---|
| Sample size (n) n | 9 | 9 | 0 | exact match | Agree |
| Mean mean | 8.811111111111112 | 8.811111111111112 | 0 | within 0.000001 relative | Agree |
| Standard deviation sd | 16.81111570096141 | 16.81111570096141 | 0 | within 0.000001 relative | Agree |
| Skewness skewness | 2.631733764362207 | 2.6317337643622065 | 4.44e-16 | within 0.000001 relative | Agree |
| 95% UCL - Student's t ucl.studentT | 19.231470139035434 | 19.23147018125369 | 4.22e-8 | within 0.000001 relative | Agree |
| 95% UCL - Modified t (Johnson) ucl.modifiedT | 20.05077348730987 | 20.050773529528133 | 4.22e-8 | within 0.000001 relative | Agree |
| 95% UCL - Central limit theorem ucl.clt | 18.02838599457403 | 18.02838598905352 | 5.52e-9 | within 0.000001 relative | Agree |
| 95% UCL - Land's H ucl.landsH | 180.80889731182043 | 180.80889731182043 | 0 | within 0.02 relative | Agree |
| 95% UCL - approximateGamma ucl.approximateGamma | 28.33350070151364 | 28.374608746326082 | 0.0411 | within 0.005 relative | Agree |
| 95% UCL - adjustedGamma ucl.adjustedGamma | 37.264772083016034 | 37.38910349941701 | 0.124 | within 0.005 relative | Agree |
| 95% UCL - Chebyshev, 95% ucl.chebyshev95 | 33.237095933998006 | 33.237095933998006 | 0 | within 0.000001 relative | Agree |
| 95% UCL - Chebyshev, 97.5% ucl.chebyshev975 | 43.806239078893725 | 43.806239078893725 | 0 | within 0.000001 relative | Agree |
| 95% UCL - Chebyshev, 99% ucl.chebyshev99 | 64.5672741984526 | 64.5672741984526 | 0 | within 0.000001 relative | Agree |
Against R EnvStats / nortest (EnvStats 3.1.0, nortest 1.0-4, R 4.6.1)
| Value | R EnvStats / nortest | EnviroAutomate | Difference | Agreement band | Verdict |
|---|---|---|---|---|---|
| Sample size (n) n | 9 | 9 | 0 | exact match | Agree |
| Mean mean | 8.811111111111112 | 8.811111111111112 | 0 | within 0.000001 relative | Agree |
| Standard deviation sd | 16.811115700961405 | 16.81111570096141 | 3.55e-15 | within 0.000001 relative | Agree |
| Median median | 1.1 | 1.1 | 0 | within 0.000001 relative | Agree |
| Minimum min | 0.4 | 0.4 | 0 | within 0.000001 relative | Agree |
| Maximum max | 52 | 52 | 0 | within 0.000001 relative | Agree |
| Coefficient of variation cv | 1.907945035418066 | 1.9079450354180665 | 4.44e-16 | within 0.000001 relative | Agree |
| Skewness skewness | 2.6317337643622065 | 2.6317337643622065 | 0 | within 0.000001 relative | Agree |
| 95% UCL - Student's t ucl.studentT | 19.231470181253655 | 19.23147018125369 | 3.55e-14 | within 0.000001 relative | Agree |
| 95% UCL - Land's H ucl.landsH | 180.44409479242998 | 180.80889731182043 | 0.365 | within 0.02 relative | Agree |
Packed lead soil results (synthetic), n = 15: ProUCL 5.2 finds no discernible distribution and suggests Student's t
Boundary caseInput
15 values
| value |
|---|
| 50 |
| 200 |
| 510 |
| 520 |
| 530 |
| 540 |
| 550 |
| 555 |
| 558 |
| 562 |
| 570 |
| 700 |
| 700 |
| 2000 |
| 7000 |
Against USEPA ProUCL (ProUCL 5.2.0)
| Value | USEPA ProUCL | EnviroAutomate | Difference | Agreement band | Verdict |
|---|---|---|---|---|---|
| Sample size (n) n | 15 | 15 | 0 | exact match | Agree |
| Mean mean | 1036.3333333333333 | 1036.3333333333333 | 0 | within 0.000001 relative | Agree |
| Standard deviation sd | 1702.4841373990062 | 1702.4841373990062 | 0 | within 0.000001 relative | Agree |
| Skewness skewness | 3.512353539683608 | 3.512353539683609 | 8.88e-16 | within 0.000001 relative | Agree |
| 95% UCL - Student's t ucl.studentT | 1810.5691983747604 | 1810.5691869765396 | 1.14e-5 | within 0.000001 relative | Agree |
| 95% UCL - Modified t (Johnson) ucl.modifiedT | 1877.010600444189 | 1877.0105890459686 | 1.14e-5 | within 0.000001 relative | Agree |
| 95% UCL - Central limit theorem ucl.clt | 1759.377291848548 | 1759.3772914154945 | 4.33e-7 | within 0.000001 relative | Agree |
| 95% UCL - Land's H ucl.landsH | 2150.43185839632 | 2150.43185839632 | 0 | within 0.02 relative | Agree |
| 95% UCL - approximateGamma ucl.approximateGamma | 1768.204628126814 | 1768.2286234102169 | 0.024 | within 0.005 relative | Agree |
| 95% UCL - adjustedGamma ucl.adjustedGamma | 1893.4064954731134 | 1893.4476280508425 | 0.0411 | within 0.005 relative | Agree |
| Distribution used distributionUsed | nonparametric | nonparametric | - | exact match | Agree |
| Recommended method recommendedMethod | studentT | studentT | - | exact match | Agree |
| 95% UCL - Chebyshev, 95% ucl.chebyshev95 | 2952.416012896152 | 2952.416012896152 | 0 | within 0.000001 relative | Agree |
| 95% UCL - Chebyshev, 97.5% ucl.chebyshev975 | 3781.5065189534344 | 3781.5065189534344 | 0 | within 0.000001 relative | Agree |
| 95% UCL - Chebyshev, 99% ucl.chebyshev99 | 5410.094274608994 | 5410.094274608994 | 0 | within 0.000001 relative | Agree |
Robust ROS at seventy-five per cent censoring, two reporting limits
Boundary caseInput
12 values
| value | non-detect | reporting limit |
|---|---|---|
| 0.2 | yes | 0.2 |
| 0.2 | yes | 0.2 |
| 0.5 | yes | 0.5 |
| 0.2 | yes | 0.2 |
| 1.4 | no | |
| 0.5 | yes | 0.5 |
| 0.2 | yes | 0.2 |
| 2.8 | no | |
| 0.5 | yes | 0.5 |
| 0.2 | yes | 0.2 |
| 0.5 | yes | 0.5 |
| 3.9 | no |
Settings: nonDetectMethod = robustRos
Against R NADA (NADA 1.6.1.2, R 4.6.1)
| Value | R NADA | EnviroAutomate | Difference | Agreement band | Verdict |
|---|---|---|---|---|---|
| Sample size (n) n | 12 | 12 | 0 | exact match | Agree |
| Detected results nDetected | 3 | 3 | 0 | exact match | Agree |
| Non-detects nCensored | 9 | 9 | 0 | exact match | Agree |
| Mean mean | 0.899633642398952 | 0.8996336423989524 | 3.33e-16 | within 0.000001 relative | Agree |
| Standard deviation sd | 1.2235888142536313 | 1.223588814253631 | 2.22e-16 | within 0.000001 relative | Agree |
| Median median | 0.36591468128418825 | 0.3659146812841887 | 4.44e-16 | within 0.000001 relative | Agree |
| Minimum min | 0.06890383684433658 | 0.06890383684433671 | 1.25e-16 | within 0.000001 relative | Agree |
| Maximum max | 3.9 | 3.9 | 0 | within 0.000001 relative | Agree |
| Coefficient of variation cv | 1.3600967733830234 | 1.3600967733830225 | 8.88e-16 | within 0.000001 relative | Agree |
| Standard error of the mean standardError | 0.35321966564337454 | 0.3532196656433745 | 5.55e-17 | within 0.000001 relative | Agree |
| Fitted non-detect, result 1 ros.fitted.0 | 0.06890383684433658 | 0.06890383684433671 | 1.25e-16 | within 0.000001 relative | Agree |
| Fitted non-detect, result 2 ros.fitted.1 | 0.14277739856103192 | 0.14277739856103216 | 2.50e-16 | within 0.000001 relative | Agree |
| Fitted non-detect, result 3 ros.fitted.2 | 0.08203330625246699 | 0.08203330625246717 | 1.80e-16 | within 0.000001 relative | Agree |
| Fitted non-detect, result 4 ros.fitted.3 | 0.24619378902023334 | 0.24619378902023373 | 3.89e-16 | within 0.000001 relative | Agree |
| Fitted non-detect, result 6 ros.fitted.5 | 0.1796632112005937 | 0.179663211200594 | 3.05e-16 | within 0.000001 relative | Agree |
| Fitted non-detect, result 7 ros.fitted.6 | 0.40100684197262254 | 0.401006841972623 | 4.44e-16 | within 0.000001 relative | Agree |
| Fitted non-detect, result 9 ros.fitted.8 | 0.3308225205957539 | 0.33082252059575434 | 4.44e-16 | within 0.000001 relative | Agree |
| Fitted non-detect, result 10 ros.fitted.9 | 0.6531703661120387 | 0.6531703661120393 | 5.55e-16 | within 0.000001 relative | Agree |
| Fitted non-detect, result 11 ros.fitted.10 | 0.5910324382283475 | 0.5910324382283481 | 5.55e-16 | within 0.000001 relative | Agree |
Robust ROS with detected results below the reporting limit
Boundary caseInput
12 values
| value | non-detect | reporting limit |
|---|---|---|
| 0.3 | no | |
| 2.4 | no | |
| 1 | yes | 1 |
| 3.1 | no | |
| 1 | yes | 1 |
| 4.7 | no | |
| 1 | yes | 1 |
| 0.7 | no | |
| 5.9 | no | |
| 3.3 | no | |
| 1 | yes | 1 |
| 2 | no |
Settings: nonDetectMethod = robustRos
Against R NADA (NADA 1.6.1.2, R 4.6.1)
| Value | R NADA | EnviroAutomate | Difference | Agreement band | Verdict |
|---|---|---|---|---|---|
| Sample size (n) n | 12 | 12 | 0 | exact match | Agree |
| Detected results nDetected | 8 | 8 | 0 | exact match | Agree |
| Non-detects nCensored | 4 | 4 | 0 | exact match | Agree |
| Mean mean | 2.0559408814567477 | 2.0559408814567477 | 0 | within 0.000001 relative | Agree |
| Standard deviation sd | 1.8721064997140042 | 1.8721064997140042 | 0 | within 0.000001 relative | Agree |
| Median median | 1.459871583281115 | 1.459871583281115 | 0 | within 0.000001 relative | Agree |
| Minimum min | 0.2547094878833023 | 0.2547094878833023 | 0 | within 0.000001 relative | Agree |
| Maximum max | 5.9 | 5.9 | 0 | within 0.000001 relative | Agree |
| Coefficient of variation cv | 0.9105838191161962 | 0.9105838191161962 | 0 | within 0.000001 relative | Agree |
| Standard error of the mean standardError | 0.5404305957807642 | 0.5404305957807642 | 0 | within 0.000001 relative | Agree |
| Fitted non-detect, result 3 ros.fitted.2 | 0.2547094878833023 | 0.2547094878833023 | 0 | within 0.000001 relative | Agree |
| Fitted non-detect, result 5 ros.fitted.4 | 0.4411949549534958 | 0.44119495495349575 | 5.55e-17 | within 0.000001 relative | Agree |
| Fitted non-detect, result 7 ros.fitted.6 | 0.6556429680819429 | 0.6556429680819428 | 1.11e-16 | within 0.000001 relative | Agree |
| Fitted non-detect, result 11 ros.fitted.10 | 0.9197431665622303 | 0.9197431665622302 | 1.11e-16 | within 0.000001 relative | Agree |
Seven results, two detected, below the recommendation floor
Boundary caseInput
7 values
| value | non-detect | reporting limit |
|---|---|---|
| 0.5 | yes | 0.5 |
| 0.5 | yes | 0.5 |
| 0.5 | yes | 0.5 |
| 0.5 | yes | 0.5 |
| 0.5 | yes | 0.5 |
| 3.4 | no | |
| 6.1 | no |
Settings: nonDetectMethod = kaplanMeier
Against USEPA ProUCL (ProUCL 5.2.0)
| Value | USEPA ProUCL | EnviroAutomate | Difference | Agreement band | Verdict |
|---|---|---|---|---|---|
| Sample size (n) n | 7 | 7 | 0 | exact match | Agree |
| Mean mean | 1.714285714285714 | 1.7142857142857137 | 2.22e-16 | within 0.000001 relative | Agree |
| Standard deviation sd | 2.0510823424500058 | 2.0510823424500058 | 0 | within 0.000001 relative | Agree |
| Standard error of the mean standardError | 1.0963496282156664 | 1.0963496282156664 | 0 | within 0.000001 relative | Agree |
| 95% UCL - Chebyshev, 95% ucl.chebyshev95 | 6.493162950466189 | 6.493162950466189 | 0 | within 0.000001 relative | Agree |
| Distribution used distributionUsed | nonparametric | nonparametric | - | exact match | Agree |
Seventy-five per cent non-detects across two reporting limits
Boundary caseInput
12 values
| value | non-detect | reporting limit |
|---|---|---|
| 0.2 | yes | 0.2 |
| 0.2 | yes | 0.2 |
| 0.5 | yes | 0.5 |
| 0.2 | yes | 0.2 |
| 1.4 | no | |
| 0.5 | yes | 0.5 |
| 0.2 | yes | 0.2 |
| 2.8 | no | |
| 0.5 | yes | 0.5 |
| 0.2 | yes | 0.2 |
| 0.5 | yes | 0.5 |
| 3.9 | no |
Settings: nonDetectMethod = kaplanMeier
Against USEPA ProUCL (ProUCL 5.2.0)
| Value | USEPA ProUCL | EnviroAutomate | Difference | Agreement band | Verdict |
|---|---|---|---|---|---|
| Sample size (n) n | 12 | 12 | 0 | exact match | Agree |
| Mean mean | 0.8250000000000002 | 0.8250000000000002 | 0 | within 0.000001 relative | Agree |
| Standard deviation sd | 1.1973060037712444 | 1.1973060037712444 | 0 | within 0.000001 relative | Agree |
| Standard error of the mean standardError | 0.4233115972110063 | 0.4233115972110063 | 0 | within 0.000001 relative | Agree |
| 95% UCL - Chebyshev, 95% ucl.chebyshev95 | 2.67017247387157 | 2.6701724738715695 | 4.44e-16 | within 0.000001 relative | Agree |
| Distribution used distributionUsed | normal | normal | - | exact match | Agree |
| Recommended method recommendedMethod | studentT | studentT | - | exact match | Agree |
| 95% UCL - Student's t ucl.studentT | 1.5852188691635547 | 1.5852188710126038 | 1.85e-9 | within 0.000001 relative | Agree |
Strongly right-skewed lognormal data - Land's H
Boundary caseInput
15 values
| value |
|---|
| 0.8 |
| 1.1 |
| 1.3 |
| 1.6 |
| 1.9 |
| 2.4 |
| 3.1 |
| 4.6 |
| 8.2 |
| 19.7 |
| 41.5 |
| 0.9 |
| 1.2 |
| 2 |
| 2.8 |
Settings: confidenceLevel = 0.95
Against R EnvStats / nortest (EnvStats 3.1.0, nortest 1.0-4, R 4.6.1)
| Value | R EnvStats / nortest | EnviroAutomate | Difference | Agreement band | Verdict |
|---|---|---|---|---|---|
| Sample size (n) n | 15 | 15 | 0 | exact match | Agree |
| Mean mean | 6.206666666666667 | 6.206666666666667 | 0 | within 0.000001 relative | Agree |
| Standard deviation sd | 10.889278256724866 | 10.889278256724868 | 1.78e-15 | within 0.000001 relative | Agree |
| Median median | 2 | 2 | 0 | within 0.000001 relative | Agree |
| Minimum min | 0.8 | 0.8 | 0 | within 0.000001 relative | Agree |
| Maximum max | 41.5 | 41.5 | 0 | within 0.000001 relative | Agree |
| Coefficient of variation cv | 1.7544486987204402 | 1.7544486987204406 | 4.44e-16 | within 0.000001 relative | Agree |
| Skewness skewness | 2.895410473052349 | 2.895410473052349 | 0 | within 0.000001 relative | Agree |
| 95% UCL - Student's t ucl.studentT | 11.158765462449999 | 11.158765462449963 | 3.55e-14 | within 0.000001 relative | Agree |
| 95% UCL - Land's H ucl.landsH | 13.151002526154675 | 13.14714561459168 | 0.00386 | within 0.02 relative | Agree |
Against USEPA ProUCL (ProUCL 5.2.0)
| Value | USEPA ProUCL | EnviroAutomate | Difference | Agreement band | Verdict |
|---|---|---|---|---|---|
| Sample size (n) n | 15 | 15 | 0 | exact match | Agree |
| Mean mean | 6.206666666666667 | 6.206666666666667 | 0 | within 0.000001 relative | Agree |
| Standard deviation sd | 10.88927825672487 | 10.889278256724868 | 1.78e-15 | within 0.000001 relative | Agree |
| Skewness skewness | 2.8954104730523484 | 2.895410473052349 | 4.44e-16 | within 0.000001 relative | Agree |
| 95% UCL - Student's t ucl.studentT | 11.158765535354252 | 11.158765462449963 | 7.29e-8 | within 0.000001 relative | Agree |
| 95% UCL - Modified t (Johnson) ucl.modifiedT | 11.509086983226503 | 11.509086910322212 | 7.29e-8 | within 0.000001 relative | Agree |
| 95% UCL - Central limit theorem ucl.clt | 10.831336396714635 | 10.831336393944774 | 2.77e-9 | within 0.000001 relative | Agree |
| 95% UCL - Land's H ucl.landsH | 13.14714561459168 | 13.14714561459168 | 0 | within 0.02 relative | Agree |
| 95% UCL - approximateGamma ucl.approximateGamma | 11.587709476809811 | 11.58810657332431 | 0.000397 | within 0.005 relative | Agree |
| 95% UCL - adjustedGamma ucl.adjustedGamma | 12.559312157492988 | 12.560004282140383 | 0.000692 | within 0.005 relative | Agree |
| Distribution used distributionUsed | lognormal | lognormal | - | exact match | Agree |
| Recommended method recommendedMethod | landsH | landsH | - | exact match | Agree |
| 95% UCL - Chebyshev, 95% ucl.chebyshev95 | 18.462145001123837 | 18.462145001123837 | 0 | within 0.000001 relative | Agree |
| 95% UCL - Chebyshev, 97.5% ucl.chebyshev975 | 23.765100266398456 | 23.765100266398456 | 0 | within 0.000001 relative | Agree |
| 95% UCL - Chebyshev, 99% ucl.chebyshev99 | 34.18172903095307 | 34.18172903095307 | 0 | within 0.000001 relative | Agree |
Ten identical results - zero variance
Boundary caseInput
10 values
| value |
|---|
| 7 |
| 7 |
| 7 |
| 7 |
| 7 |
| 7 |
| 7 |
| 7 |
| 7 |
| 7 |
Settings: confidenceLevel = 0.95
Against USEPA ProUCL (ProUCL 5.2.0)
| Value | USEPA ProUCL | EnviroAutomate | Difference | Agreement band | Verdict |
|---|---|---|---|---|---|
| Sample size (n) n | 10 | 10 | 0 | exact match | Agree |
| Mean mean | 7 | 7 | 0 | within 0.000001 relative | Agree |
| Standard deviation sd | 0 | 0 | 0 | within 0.000001 relative | Agree |
| 95% UCL - Student's t ucl.studentT | 7 | 7 | 0 | within 0.000001 relative | Agree |
| 95% UCL - Central limit theorem ucl.clt | 7 | 7 | 0 | within 0.000001 relative | Agree |
| 95% UCL - Chebyshev, 95% ucl.chebyshev95 | 7 | 7 | 0 | within 0.000001 relative | Agree |
| 95% UCL - Chebyshev, 97.5% ucl.chebyshev975 | 7 | 7 | 0 | within 0.000001 relative | Agree |
| 95% UCL - Chebyshev, 99% ucl.chebyshev99 | 7 | 7 | 0 | within 0.000001 relative | Agree |
Not run for this scenario
- R EnvStats / nortest - EnvStats cannot fit a sample with no variation at all
The same shape, one result later, where the gamma limit is used
Boundary caseInput
15 values
| value | non-detect | reporting limit |
|---|---|---|
| 0.601 | yes | 0.601 |
| 0.601 | yes | 0.601 |
| 0.601 | yes | 0.601 |
| 1.333 | no | |
| 1.379 | no | |
| 2.636 | no | |
| 4.071 | no | |
| 4.134 | no | |
| 4.989 | no | |
| 11.564 | no | |
| 19.419 | no | |
| 21.815 | no | |
| 35.069 | no | |
| 126.643 | no | |
| 191.472 | no |
Settings: nonDetectMethod = kaplanMeier
Against USEPA ProUCL (ProUCL 5.2.0)
| Value | USEPA ProUCL | EnviroAutomate | Difference | Agreement band | Verdict |
|---|---|---|---|---|---|
| Sample size (n) n | 15 | 15 | 0 | exact match | Agree |
| Mean mean | 28.421799999999998 | 28.421799999999994 | 3.55e-15 | within 0.000001 relative | Agree |
| Standard deviation sd | 53.46014833150639 | 53.4601483315064 | 1.42e-14 | within 0.000001 relative | Agree |
| Standard error of the mean standardError | 14.417129860946455 | 14.417129860946456 | 1.78e-15 | within 0.000001 relative | Agree |
| 95% UCL - Chebyshev, 95% ucl.chebyshev95 | 91.26461211976817 | 91.26461211976817 | 0 | within 0.000001 relative | Agree |
| Distribution used distributionUsed | gamma | gamma | - | exact match | Agree |
| Recommended method recommendedMethod | adjustedGamma | adjustedGamma | - | exact match | Agree |
| 95% UCL - adjustedGamma ucl.adjustedGamma | 94.84 | 94.96595983931 | 0.126 | within 0.005 relative | Agree |
The same spread at twenty-eight results, where Land’s H returns
Boundary caseInput
28 values
| value | non-detect | reporting limit |
|---|---|---|
| 0.753 | yes | 0.753 |
| 0.753 | yes | 0.753 |
| 0.753 | yes | 0.753 |
| 0.753 | yes | 0.753 |
| 0.753 | yes | 0.753 |
| 0.753 | yes | 0.753 |
| 0.988 | no | |
| 0.996 | no | |
| 1.425 | no | |
| 2.199 | no | |
| 2.957 | no | |
| 3.019 | no | |
| 3.198 | no | |
| 3.456 | no | |
| 5.694 | no | |
| 6.018 | no | |
| 9.552 | no | |
| 11.262 | no | |
| 13.459 | no | |
| 13.777 | no | |
| 15.702 | no | |
| 23.121 | no | |
| 31.904 | no | |
| 38.764 | no | |
| 109.582 | no | |
| 137.593 | no | |
| 192.561 | no | |
| 325.07 | no |
Settings: nonDetectMethod = kaplanMeier
Against USEPA ProUCL (ProUCL 5.2.0)
| Value | USEPA ProUCL | EnviroAutomate | Difference | Agreement band | Verdict |
|---|---|---|---|---|---|
| Sample size (n) n | 28 | 28 | 0 | exact match | Agree |
| Mean mean | 34.17196428571428 | 34.17196428571427 | 1.42e-14 | within 0.000001 relative | Agree |
| Standard deviation sd | 71.96368574569999 | 71.96368574569999 | 0 | within 0.000001 relative | Agree |
| Standard error of the mean standardError | 13.919898731838579 | 13.919898731838583 | 3.55e-15 | within 0.000001 relative | Agree |
| 95% UCL - Chebyshev, 95% ucl.chebyshev95 | 94.8473961621186 | 94.8473961621186 | 0 | within 0.000001 relative | Agree |
| Distribution used distributionUsed | lognormal | lognormal | - | exact match | Agree |
| Recommended method recommendedMethod | landsH | landsH | - | exact match | Agree |
| 95% UCL - Land's H ucl.landsH | 120.34545944451052 | 120.34545944451052 | 0 | within 0.02 relative | Agree |
Three results - the documented minimum
Boundary caseInput
3 values
| value |
|---|
| 2.5 |
| 6.1 |
| 9.8 |
Settings: confidenceLevel = 0.95
Against R EnvStats / nortest (EnvStats 3.1.0, nortest 1.0-4, R 4.6.1)
| Value | R EnvStats / nortest | EnviroAutomate | Difference | Agreement band | Verdict |
|---|---|---|---|---|---|
| Sample size (n) n | 3 | 3 | 0 | exact match | Agree |
| Mean mean | 6.133333333333334 | 6.133333333333333 | 8.88e-16 | within 0.000001 relative | Agree |
| Standard deviation sd | 3.6501141534660717 | 3.6501141534660717 | 0 | within 0.000001 relative | Agree |
| Median median | 6.1 | 6.1 | 0 | within 0.000001 relative | Agree |
| Minimum min | 2.5 | 2.5 | 0 | within 0.000001 relative | Agree |
| Maximum max | 9.8 | 9.8 | 0 | within 0.000001 relative | Agree |
| Coefficient of variation cv | 0.5951273076303377 | 0.5951273076303378 | 1.11e-16 | within 0.000001 relative | Agree |
| Skewness skewness | 0.041091178059606034 | 0.04109117805960845 | 2.41e-15 | within 0.000001 relative | Agree |
| 95% UCL - Student's t ucl.studentT | 12.286894561555059 | 12.28689456155507 | 1.07e-14 | within 0.000001 relative | Agree |
| 95% UCL - Land's H ucl.landsH | 567.7273934409031 | 567.6096926889293 | 0.118 | within 0.02 relative | Agree |
Against USEPA ProUCL (ProUCL 5.2.0)
| Value | USEPA ProUCL | EnviroAutomate | Difference | Agreement band | Verdict |
|---|---|---|---|---|---|
| Sample size (n) n | 3 | 3 | 0 | exact match | Agree |
| Mean mean | 6.133333333333333 | 6.133333333333333 | 0 | within 0.000001 relative | Agree |
| Standard deviation sd | 3.650114153466072 | 3.6501141534660717 | 4.44e-16 | within 0.000001 relative | Agree |
| Skewness skewness | 0.041091178059608435 | 0.04109117805960845 | 1.39e-17 | within 0.000001 relative | Agree |
| 95% UCL - Student's t ucl.studentT | 12.286894460267307 | 12.28689456155507 | 1.01e-7 | within 0.000001 relative | Agree |
| 95% UCL - Modified t (Johnson) ucl.modifiedT | 12.295227098634971 | 12.295227199922733 | 1.01e-7 | within 0.000001 relative | Agree |
| 95% UCL - Central limit theorem ucl.clt | 9.599688639699103 | 9.599688637622997 | 2.08e-9 | within 0.000001 relative | Agree |
| 95% UCL - Land's H ucl.landsH | 567.6096926889293 | 567.6096926889293 | 0 | within 0.02 relative | Agree |
| 95% UCL - Chebyshev, 95% ucl.chebyshev95 | 15.319252509502421 | 15.319252509502427 | 5.33e-15 | within 0.000001 relative | Agree |
| 95% UCL - Chebyshev, 97.5% ucl.chebyshev975 | 19.29400707495208 | 19.294007074952084 | 3.55e-15 | within 0.000001 relative | Agree |
| 95% UCL - Chebyshev, 99% ucl.chebyshev99 | 27.101642754934296 | 27.1016427549343 | 3.55e-15 | within 0.000001 relative | Agree |
Widely spread lognormal detects at twenty-seven results
Boundary caseInput
27 values
| value | non-detect | reporting limit |
|---|---|---|
| 0.609 | yes | 0.609 |
| 0.609 | yes | 0.609 |
| 0.609 | yes | 0.609 |
| 0.609 | yes | 0.609 |
| 0.609 | yes | 0.609 |
| 0.973 | no | |
| 1.24 | no | |
| 1.321 | no | |
| 1.362 | no | |
| 2.65 | no | |
| 2.996 | no | |
| 4.017 | no | |
| 4.197 | no | |
| 5.46 | no | |
| 6.71 | no | |
| 7.165 | no | |
| 9.233 | no | |
| 9.423 | no | |
| 18.777 | no | |
| 18.793 | no | |
| 21.021 | no | |
| 40.512 | no | |
| 47.919 | no | |
| 58.083 | no | |
| 70.03 | no | |
| 144.069 | no | |
| 255.098 | no |
Settings: nonDetectMethod = kaplanMeier
Against USEPA ProUCL (ProUCL 5.2.0)
| Value | USEPA ProUCL | EnviroAutomate | Difference | Agreement band | Verdict |
|---|---|---|---|---|---|
| Sample size (n) n | 27 | 27 | 0 | exact match | Agree |
| Mean mean | 27.18866666666665 | 27.188666666666638 | 1.07e-14 | within 0.000001 relative | Agree |
| Standard deviation sd | 54.29434708519298 | 54.29434708519298 | 0 | within 0.000001 relative | Agree |
| Standard error of the mean standardError | 10.694843303958736 | 10.694843303958734 | 1.78e-15 | within 0.000001 relative | Agree |
| 95% UCL - Chebyshev, 95% ucl.chebyshev95 | 73.8064078456254 | 73.80640784562539 | 1.42e-14 | within 0.000001 relative | Agree |
| Distribution used distributionUsed | lognormal | lognormal | - | exact match | Agree |
| Recommended method recommendedMethod | studentT | studentT | - | exact match | Agree |
| 95% UCL - Student's t ucl.studentT | 45.42998374487132 | 45.429983054915226 | 6.90e-7 | within 0.000001 relative | Agree |
Widely spread small sample that ProUCL 5.2 reads as gamma - the adjusted gamma UCL, not a Chebyshev limit
Boundary caseInput
15 values
| value |
|---|
| 6.5469 |
| 36.3492 |
| 0.5226 |
| 49.0528 |
| 4.208 |
| 1.6769 |
| 75.919 |
| 0.6886 |
| 15.6351 |
| 17.2405 |
| 0.6574 |
| 73.7259 |
| 1.8342 |
| 3.7966 |
| 52.1943 |
Against USEPA ProUCL (ProUCL 5.2.0)
| Value | USEPA ProUCL | EnviroAutomate | Difference | Agreement band | Verdict |
|---|---|---|---|---|---|
| Sample size (n) n | 15 | 15 | 0 | exact match | Agree |
| Mean mean | 22.669866666666667 | 22.669866666666667 | 0 | within 0.000001 relative | Agree |
| Standard deviation sd | 27.47216359812931 | 27.472163598129306 | 3.55e-15 | within 0.000001 relative | Agree |
| Skewness skewness | 1.0437389444899698 | 1.0437389444899696 | 2.22e-16 | within 0.000001 relative | Agree |
| 95% UCL - Student's t ucl.studentT | 35.16333657966843 | 35.163336395740856 | 1.84e-7 | within 0.000001 relative | Agree |
| 95% UCL - Modified t (Johnson) ucl.modifiedT | 35.48193399118807 | 35.48193380726049 | 1.84e-7 | within 0.000001 relative | Agree |
| 95% UCL - Central limit theorem ucl.clt | 34.33727752860625 | 34.33727752161827 | 6.99e-9 | within 0.000001 relative | Agree |
| 95% UCL - Land's H ucl.landsH | 278.434989781978 | 278.4349897819778 | 2.27e-13 | within 0.02 relative | Agree |
| 95% UCL - approximateGamma ucl.approximateGamma | 47.23539450704596 | 47.23964009926553 | 0.00425 | within 0.005 relative | Agree |
| 95% UCL - adjustedGamma ucl.adjustedGamma | 51.968865385529774 | 51.976421484560355 | 0.00756 | within 0.005 relative | Agree |
| Distribution used distributionUsed | gamma | gamma | - | exact match | Agree |
| Recommended method recommendedMethod | adjustedGamma | adjustedGamma | - | exact match | Agree |
| 95% UCL - Chebyshev, 95% ucl.chebyshev95 | 53.588766692902205 | 53.58876669290221 | 7.11e-15 | within 0.000001 relative | Agree |
| 95% UCL - Chebyshev, 97.5% ucl.chebyshev975 | 66.96739943297533 | 66.96739943297533 | 0 | within 0.000001 relative | Agree |
| 95% UCL - Chebyshev, 99% ucl.chebyshev99 | 93.2471328380884 | 93.24713283808839 | 1.42e-14 | within 0.000001 relative | Agree |
Against R EnvStats / nortest (EnvStats 3.1.0, nortest 1.0-4, R 4.6.1)
| Value | R EnvStats / nortest | EnviroAutomate | Difference | Agreement band | Verdict |
|---|---|---|---|---|---|
| Sample size (n) n | 15 | 15 | 0 | exact match | Agree |
| Mean mean | 22.669866666666667 | 22.669866666666667 | 0 | within 0.000001 relative | Agree |
| Standard deviation sd | 27.472163598129306 | 27.472163598129306 | 0 | within 0.000001 relative | Agree |
| Median median | 6.5469 | 6.5469 | 0 | within 0.000001 relative | Agree |
| Minimum min | 0.5226 | 0.5226 | 0 | within 0.000001 relative | Agree |
| Maximum max | 75.919 | 75.919 | 0 | within 0.000001 relative | Agree |
| Coefficient of variation cv | 1.2118361348160835 | 1.2118361348160835 | 0 | within 0.000001 relative | Agree |
| Skewness skewness | 1.0437389444899696 | 1.0437389444899696 | 0 | within 0.000001 relative | Agree |
| 95% UCL - Student's t ucl.studentT | 35.16333639574094 | 35.163336395740856 | 8.53e-14 | within 0.000001 relative | Agree |
| 95% UCL - Land's H ucl.landsH | 278.4794208366666 | 278.4349897819778 | 0.0444 | within 0.02 relative | Agree |
Benzo(a)pyrene, five-analyte SME cross-check (was Land's H mismatch before the KM H-UCL fix)
regressionInput
56 values
| value | non-detect | reporting limit |
|---|---|---|
| 0.5 | yes | 0.5 |
| 0.5 | yes | 0.5 |
| 0.5 | yes | 0.5 |
| 0.5 | yes | 0.5 |
| 46 | no | |
| 0.5 | yes | 0.5 |
| 0.5 | yes | 0.5 |
| 0.5 | yes | 0.5 |
| 0.5 | yes | 0.5 |
| 0.5 | yes | 0.5 |
| 85 | no | |
| 0.5 | yes | 0.5 |
| 0.5 | yes | 0.5 |
| 0.5 | yes | 0.5 |
| 0.5 | yes | 0.5 |
| 0.5 | yes | 0.5 |
| 0.5 | yes | 0.5 |
| 0.05 | yes | 0.05 |
| 5.3 | no | |
| 0.5 | yes | 0.5 |
| 0.5 | yes | 0.5 |
| 0.5 | yes | 0.5 |
| 61 | no | |
| 13 | no | |
| 0.5 | yes | 0.5 |
| 0.9 | no | |
| 0.5 | yes | 0.5 |
| 0.5 | yes | 0.5 |
| 34 | no | |
| 38 | no | |
| 0.5 | yes | 0.5 |
| 0.5 | yes | 0.5 |
| 2.8 | no | |
| 0.5 | yes | 0.5 |
| 5.9 | no | |
| 0.5 | yes | 0.5 |
| 40 | no | |
| 5.9 | no | |
| 0.6 | no | |
| 3 | no | |
| 15 | no | |
| 40 | no | |
| 0.5 | yes | 0.5 |
| 3.5 | no | |
| 0.5 | yes | 0.5 |
| 2.1 | no | |
| 0.5 | yes | 0.5 |
| 0.5 | yes | 0.5 |
| 0.5 | yes | 0.5 |
| 3.6 | no | |
| 8 | no | |
| 7.6 | no | |
| 6.9 | no | |
| 5.9 | no | |
| 5.5 | no | |
| 7.3 | no |
Settings: nonDetectMethod = kaplanMeier
Against USEPA ProUCL (ProUCL 5.2.0)
| Value | USEPA ProUCL | EnviroAutomate | Difference | Agreement band | Verdict |
|---|---|---|---|---|---|
| Sample size (n) n | 56 | 56 | 0 | exact match | Agree |
| Mean mean | 8.006250000000007 | 8.006250000000007 | 0 | within 0.000001 relative | Agree |
| Standard deviation sd | 16.95558026164038 | 16.95558026164038 | 0 | within 0.000001 relative | Agree |
| Standard error of the mean standardError | 2.312506845263873 | 2.312506845263873 | 0 | within 0.000001 relative | Agree |
| 95% UCL - Chebyshev, 95% ucl.chebyshev95 | 18.086233644751275 | 18.086233644751275 | 0 | within 0.000001 relative | Agree |
| Distribution used distributionUsed | lognormal | lognormal | - | exact match | Agree |
| Recommended method recommendedMethod | landsH | landsH | - | exact match | Agree |
| 95% UCL - Land's H ucl.landsH | 111.77107808175877 | 111.77107808175887 | 9.95e-14 | within 0.02 relative | Agree |
Copper, five-analyte SME cross-check (matches ProUCL)
regressionInput
56 values
| value | non-detect | reporting limit |
|---|---|---|
| 5.5 | no | |
| 5 | yes | 5 |
| 35 | no | |
| 5 | yes | 5 |
| 5 | yes | 5 |
| 5 | yes | 5 |
| 24 | no | |
| 5 | yes | 5 |
| 5 | yes | 5 |
| 5 | yes | 5 |
| 6.2 | no | |
| 5 | yes | 5 |
| 29 | no | |
| 5 | yes | 5 |
| 7.8 | no | |
| 5 | yes | 5 |
| 5 | yes | 5 |
| 1 | yes | 1 |
| 5 | yes | 5 |
| 5 | yes | 5 |
| 13 | no | |
| 16 | no | |
| 16 | no | |
| 14 | no | |
| 23 | no | |
| 8.3 | no | |
| 20 | no | |
| 5 | yes | 5 |
| 5 | yes | 5 |
| 5 | yes | 5 |
| 5.1 | no | |
| 9.3 | no | |
| 6.1 | no | |
| 5 | yes | 5 |
| 8 | no | |
| 5 | yes | 5 |
| 32 | no | |
| 5 | yes | 5 |
| 5 | yes | 5 |
| 12 | no | |
| 5 | yes | 5 |
| 5 | yes | 5 |
| 5 | yes | 5 |
| 16 | no | |
| 5 | yes | 5 |
| 30 | no | |
| 11 | no | |
| 80 | no | |
| 5.9 | no | |
| 22 | no | |
| 22 | no | |
| 21 | no | |
| 21 | no | |
| 19 | no | |
| 670 | no | |
| 33 | no |
Settings: nonDetectMethod = kaplanMeier
Against USEPA ProUCL (ProUCL 5.2.0)
| Value | USEPA ProUCL | EnviroAutomate | Difference | Agreement band | Verdict |
|---|---|---|---|---|---|
| Sample size (n) n | 56 | 56 | 0 | exact match | Agree |
| Mean mean | 22.61071428571432 | 22.610714285714327 | 7.11e-15 | within 0.000001 relative | Agree |
| Standard deviation sd | 88.3717041789385 | 88.37170417893849 | 1.42e-14 | within 0.000001 relative | Agree |
| Standard error of the mean standardError | 12.004371750389016 | 12.004371750389014 | 1.78e-15 | within 0.000001 relative | Agree |
| 95% UCL - Chebyshev, 95% ucl.chebyshev95 | 74.93655762635449 | 74.93655762635449 | 0 | within 0.000001 relative | Agree |
| Distribution used distributionUsed | nonparametric | nonparametric | - | exact match | Agree |
| Recommended method recommendedMethod | studentT | studentT | - | exact match | Agree |
| 95% UCL - Student's t ucl.studentT | 42.694435234238235 | 42.694435956086195 | 7.22e-7 | within 0.000001 relative | Agree |
Lead, five-analyte SME cross-check (was Land's H mismatch before the KM H-UCL fix)
regressionInput
56 values
| value | non-detect | reporting limit |
|---|---|---|
| 5 | yes | 5 |
| 5 | yes | 5 |
| 33 | no | |
| 15 | no | |
| 5 | yes | 5 |
| 5 | yes | 5 |
| 16 | no | |
| 5 | yes | 5 |
| 5 | yes | 5 |
| 5 | yes | 5 |
| 13 | no | |
| 5 | yes | 5 |
| 23 | no | |
| 5 | yes | 5 |
| 79 | no | |
| 5 | yes | 5 |
| 5 | yes | 5 |
| 2 | no | |
| 5 | yes | 5 |
| 5 | yes | 5 |
| 44 | no | |
| 5.6 | no | |
| 120 | no | |
| 150 | no | |
| 21 | no | |
| 6.9 | no | |
| 21 | no | |
| 5 | yes | 5 |
| 5 | yes | 5 |
| 5 | yes | 5 |
| 12 | no | |
| 33 | no | |
| 30 | no | |
| 5 | yes | 5 |
| 11 | no | |
| 13 | no | |
| 200 | no | |
| 5 | yes | 5 |
| 19 | no | |
| 16 | no | |
| 5 | yes | 5 |
| 12 | no | |
| 8 | no | |
| 190 | no | |
| 5 | yes | 5 |
| 120 | no | |
| 56 | no | |
| 93 | no | |
| 5 | yes | 5 |
| 80 | no | |
| 70 | no | |
| 110 | no | |
| 95 | no | |
| 100 | no | |
| 7300 | no | |
| 79 | no |
Settings: nonDetectMethod = kaplanMeier
Against USEPA ProUCL (ProUCL 5.2.0)
| Value | USEPA ProUCL | EnviroAutomate | Difference | Agreement band | Verdict |
|---|---|---|---|---|---|
| Sample size (n) n | 56 | 56 | 0 | exact match | Agree |
| Mean mean | 164.97321428571462 | 164.97321428571462 | 0 | within 0.000001 relative | Agree |
| Standard deviation sd | 963.3320886550638 | 963.3320886550639 | 1.14e-13 | within 0.000001 relative | Agree |
| Standard error of the mean standardError | 130.61004438959063 | 130.61004438959066 | 2.84e-14 | within 0.000001 relative | Agree |
| 95% UCL - Chebyshev, 95% ucl.chebyshev95 | 734.2891987913015 | 734.2891987913015 | 0 | within 0.000001 relative | Agree |
| Distribution used distributionUsed | lognormal | lognormal | - | exact match | Agree |
| Recommended method recommendedMethod | landsH | landsH | - | exact match | Agree |
| 95% UCL - Land's H ucl.landsH | 154.7788054359823 | 154.7788054359824 | 1.14e-13 | within 0.02 relative | Agree |
Mercury, five-analyte SME cross-check (matches ProUCL)
regressionInput
56 values
| value | non-detect | reporting limit |
|---|---|---|
| 0.21 | no | |
| 0.05 | yes | 0.05 |
| 0.07 | no | |
| 0.05 | yes | 0.05 |
| 0.05 | yes | 0.05 |
| 0.05 | yes | 0.05 |
| 0.05 | yes | 0.05 |
| 0.05 | yes | 0.05 |
| 0.05 | yes | 0.05 |
| 0.06 | no | |
| 0.09 | no | |
| 0.05 | yes | 0.05 |
| 0.06 | no | |
| 0.05 | yes | 0.05 |
| 0.14 | no | |
| 0.05 | yes | 0.05 |
| 0.05 | yes | 0.05 |
| 0.1 | yes | 0.1 |
| 0.05 | yes | 0.05 |
| 0.05 | yes | 0.05 |
| 0.1 | no | |
| 0.05 | yes | 0.05 |
| 0.08 | no | |
| 0.05 | no | |
| 0.2 | no | |
| 0.6 | no | |
| 0.05 | yes | 0.05 |
| 0.05 | yes | 0.05 |
| 0.05 | yes | 0.05 |
| 0.05 | yes | 0.05 |
| 0.05 | yes | 0.05 |
| 0.07 | no | |
| 0.06 | no | |
| 0.05 | yes | 0.05 |
| 0.05 | yes | 0.05 |
| 0.05 | yes | 0.05 |
| 0.11 | no | |
| 0.12 | no | |
| 0.05 | yes | 0.05 |
| 0.05 | yes | 0.05 |
| 0.05 | yes | 0.05 |
| 0.15 | no | |
| 0.24 | no | |
| 3.9 | no | |
| 0.05 | yes | 0.05 |
| 0.25 | no | |
| 0.14 | no | |
| 0.1 | no | |
| 0.05 | yes | 0.05 |
| 0.1 | yes | 0.1 |
| 0.1 | yes | 0.1 |
| 0.12 | no | |
| 0.12 | no | |
| 0.1 | no | |
| 0.43 | no | |
| 0.12 | no |
Settings: nonDetectMethod = kaplanMeier
Against USEPA ProUCL (ProUCL 5.2.0)
| Value | USEPA ProUCL | EnviroAutomate | Difference | Agreement band | Verdict |
|---|---|---|---|---|---|
| Sample size (n) n | 56 | 56 | 0 | exact match | Agree |
| Mean mean | 0.1643214285714287 | 0.16432142857142878 | 8.33e-17 | within 0.000001 relative | Agree |
| Standard deviation sd | 0.5127398878593721 | 0.5127398878593721 | 0 | within 0.000001 relative | Agree |
| Standard error of the mean standardError | 0.06987533979945079 | 0.06987533979945079 | 0 | within 0.000001 relative | Agree |
| 95% UCL - Chebyshev, 95% ucl.chebyshev95 | 0.46890097340280024 | 0.4689009734028003 | 5.55e-17 | within 0.000001 relative | Agree |
| Distribution used distributionUsed | nonparametric | nonparametric | - | exact match | Agree |
| Recommended method recommendedMethod | studentT | studentT | - | exact match | Agree |
| 95% UCL - Student's t ucl.studentT | 0.28122524119035897 | 0.2812252453921092 | 4.20e-9 | within 0.000001 relative | Agree |
TRH fraction, five-analyte SME cross-check (matches ProUCL)
regressionInput
56 values
| value | non-detect | reporting limit |
|---|---|---|
| 100 | yes | 100 |
| 100 | yes | 100 |
| 100 | yes | 100 |
| 100 | yes | 100 |
| 2500 | no | |
| 100 | yes | 100 |
| 100 | yes | 100 |
| 100 | yes | 100 |
| 100 | yes | 100 |
| 100 | yes | 100 |
| 4800 | no | |
| 100 | yes | 100 |
| 100 | yes | 100 |
| 100 | yes | 100 |
| 130 | no | |
| 100 | yes | 100 |
| 100 | yes | 100 |
| 100 | yes | 100 |
| 100 | yes | 100 |
| 100 | yes | 100 |
| 100 | no | |
| 100 | yes | 100 |
| 480 | no | |
| 100 | yes | 100 |
| 100 | yes | 100 |
| 100 | yes | 100 |
| 100 | yes | 100 |
| 100 | yes | 100 |
| 980 | no | |
| 280 | no | |
| 100 | yes | 100 |
| 100 | yes | 100 |
| 100 | yes | 100 |
| 100 | yes | 100 |
| 190 | no | |
| 100 | yes | 100 |
| 400 | no | |
| 180 | no | |
| 100 | yes | 100 |
| 260 | no | |
| 720 | no | |
| 840 | no | |
| 100 | yes | 100 |
| 160 | no | |
| 100 | yes | 100 |
| 1400 | no | |
| 100 | yes | 100 |
| 100 | yes | 100 |
| 100 | yes | 100 |
| 110 | no | |
| 160 | no | |
| 290 | no | |
| 280 | no | |
| 250 | no | |
| 280 | no | |
| 380 | no |
Settings: nonDetectMethod = kaplanMeier
Against USEPA ProUCL (ProUCL 5.2.0)
| Value | USEPA ProUCL | EnviroAutomate | Difference | Agreement band | Verdict |
|---|---|---|---|---|---|
| Sample size (n) n | 56 | 56 | 0 | exact match | Agree |
| Mean mean | 331.6071428571432 | 331.6071428571433 | 1.14e-13 | within 0.000001 relative | Agree |
| Standard deviation sd | 716.6309490189758 | 716.6309490189758 | 0 | within 0.000001 relative | Agree |
| Standard error of the mean standardError | 98.01741383541672 | 98.01741383541672 | 0 | within 0.000001 relative | Agree |
| 95% UCL - Chebyshev, 95% ucl.chebyshev95 | 758.85514447293 | 758.8551444729301 | 1.14e-13 | within 0.000001 relative | Agree |
| Distribution used distributionUsed | nonparametric | nonparametric | - | exact match | Agree |
| Recommended method recommendedMethod | studentT | studentT | - | exact match | Agree |
| 95% UCL - Student's t ucl.studentT | 495.59359949971616 | 495.59360539370823 | 5.89e-6 | within 0.000001 relative | Agree |
Evidence generated 2026-08-26 from a full comparison run against the versions named above.