ProUCL is a free statistical package by the U.S. EPA and it can be downloaded along with manuals etc from https://www.epa.gov/land-research/proucl-software
Here are some of the task it can do:
Upper Cofidence Levels (Note: see the important note at the bottom of page)
Graphs (Notched Box, histograms, Multi QQ plots, timeseries with confidence and prediction limits)
Trend analysis by Mann Kendall and Theil-Sen (Note: You have to normalize your non-dects manually also It will report a trend and it will report a trend with 100% non-detects)
Normality / Goodness of fit by Shapiro-Wilks and Lilliefores
Outlier Test
ANOVA
Estimation of non-detect values.
Hypothesis Testing (Single Sample)
t-Test
Propotion
Sign Test
Wilcoxon Signed Rank Test
Hypothesis Testing (Two Sample)
t-Test
Wilcoxon-Mann
Quantile test
In March 2011, EPA offered a 2 part webinar about using ProUCL. Below are links to the PDFs of the webinar with my notes on them (also have the times on them so it is easy to jump around on the audio files) and a link to the audio files
Part 1 Notes and Audio
Part 2 Notes and Audio
EPA also offered another webinar titled ProUCL Utilization 2020: Part 1: ProUCL A to Z in January 2020.
IMPORTANT NOTE!!
Issues with ProUCL ver. 5.2 calculations of 95% UCL when data is lognormal.
A while back the Risk Assessor that I work with mentioned that West Virginia and Florida had put out guidance to not use ProUCL 5.2 but to stay with ProUCL 5.1.
The Florida review states:
Based on simulations performed by Neptune, the 95 UCL estimate suggested by ProUCL Version 5.2 for a dataset with a SDlog in the range of 0.5 to 1.5 and a sample size of 10 (the minimum required sample size for the calculation of a 95 UCL in Chapter 62-780, F.A.C.) provides an 80% coverage rate (e.g., Figures B5 to B7 of the Technical Guide). In other words, the 95 UCL is really an 80 UCL.
The WVDEP memo dated May 25, 2023 with the subject The use of ProUCL 5.2 to calculate Upper Confidence Limits (UCL) for OER sites states:
When the updated lognormal Decision Tree focuses on the H-UCL and t-UCL the resulting coverage goes down with decreasing sample size and increasing SDlog. Thus, the effective UCL is now ~80% (instead of 95%) when the sample size is 10 and the SDlog is ~1.5, thereby increasing the likelihood of false negative decisions due to lower EPC values for the lognormal datasets frequently seen at OER sites.........
OER no longer approves the ProUCL 5.2 Decision Tree process.......
At this time, no other issues with ProUCL 5.2 are known for other statistical calculations, such as Mann-Kendall trend analyses, and it may continue to be used for these other analyses.
Also, Section 4.1 (page 117 of 383 in the PDF) of the West Virginia Voluntary Remediation Program Guidance Manual states:
Per a WVDEP memo dated May 25, 2023, ProUCL 5.2 radically altered the UCL Decision Tree, leading to smaller sample sizes having reduced coverage. The term “coverage” is the effective confidence level in the upper estimate of the mean. For example, a 95% confidence level means the probability of the UCL underestimating the population mean (Type I error) is less than or equal to 5%. In ProUCL 5.2, that confidence can be reduced from 95% to 80% with sample sizes ~10 due to the Decision Tree excluding non-parametric UCL parameters, such as the Chebyshev and Bootstrap methods.
Also note the document Analysis of UCL Simulations at the Lognormal Distribution Performance of the Chebyshev UCL Estimators and Improved Recommendation Rules document NAC-0175_R0 prepared by Neptune and Company, Inc dated January 6, 2022 in section 6.0 Conclusion states:
The results of this study provide clear and convincing evidence that neither the Chebyshev 95% UCL nor the Chebyshev 90% UCL are useful procedures for constructing UCLs for data deemed to be lognormal.
Furthermore, analysis of the lognormal UCL simulation study data using RPart classification trees for risk minimization allows formulation of a simple tentative recommendation rule for UCLs in data classified as lognormal by ProUCL 5.2. That rule may be simply stated as:
H-UCL when 𝑁 ≥ 28 or log-scale SD ≤ 1.4, and the t-UCL otherwise.
It is important that this recommendation for lognormal data be confirmed by simulations with other right-skewed distributions and by accounting for the effects of detection limit censoring.