← 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
- 33
- Values agreeing
- 472
- Values differing
- 0
- 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 method is compared against the method ProUCL's interface reports, for both uncensored and censored data. ProUCL applies a separate decision tree to censored data: it fits the distribution to the detected results only, accepts a sample that passes either normality test, and recommends only Kaplan-Meier methods. Nine scenarios sit one result either side of each threshold in that tree.
Scenarios
- 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
- Detected results below the reporting limit - Kaplan-Meier stops matching substitutionBoundary case
- Detects that pass one normality test and both gamma testsBoundary 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
- Lognormal data, wide spread and a small sample - Chebyshev instead of Land's HBoundary case
- n = 37, sitting on a Shapiro-Wilk critical value that does not follow the trend of its neighboursBoundary case
- Neither normal, gamma nor lognormal - a distribution-free limitBoundary case
- Nine results - one below the size at which ProUCL will recommend a UCLBoundary case
- Normal data - ProUCL recommends Student's tBoundary case
- Not normal and fewer than ten results - no recommendation at allBoundary 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 data - the regime where the recommended method changesBoundary 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
- 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
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 |
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 |
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 | gamma | gamma | - | exact match | Agree |
| Recommended method recommendedMethod | approximateGamma | approximateGamma | - | 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 |
Lognormal data, wide spread and a small sample - Chebyshev instead of Land's H
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 | approximateGamma | approximateGamma | - | 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 |
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 | gamma | - | exact match | Agree |
| Recommended method recommendedMethod | adjustedGamma | adjustedGamma | - | exact match | Agree |
| 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 |
Neither normal, gamma nor lognormal - a distribution-free limit
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 | nonparametric | nonparametric | - | exact match | Agree |
| Recommended method recommendedMethod | chebyshev99 | chebyshev99 | - | 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 |
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 |
| Distribution used distributionUsed | normal | normal | - | exact match | Agree |
| Recommended method recommendedMethod | studentT | studentT | - | exact match | 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 |
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 |
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 |
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 data - the regime where the recommended method changes
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 | nonparametric | nonparametric | - | exact match | Agree |
| Recommended method recommendedMethod | chebyshev95 | chebyshev95 | - | 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 |
| Distribution used distributionUsed | nonparametric | nonparametric | - | exact match | 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 |
| Distribution used distributionUsed | normal | normal | - | exact match | Agree |
| Recommended method recommendedMethod | studentT | studentT | - | exact match | 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 |
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.