Nonparametric comparison workspace
Compare groups or paired measurements with rank tests: Mann-Whitney U, Wilcoxon signed-rank, Kruskal-Wallis with Dunn comparisons, or Friedman. Get exact p-values for small samples, tie corrections and Hodges-Lehmann estimates with confidence intervals.
Runs locally in your browser in a background worker; nothing is uploaded. CSV up to 1,000,000 characters and 10,000 data rows. Exact Mann-Whitney needs both groups of at most 50 without ties or a total of at most 100 with ties; the exact signed-rank test allows up to 200 nonzero differences. Hodges-Lehmann values are computed when there are at most 1,000,000 pairwise differences or Walsh averages, for example 1,000 x 1,000 values or 1,413 pairs. Kruskal-Wallis and Friedman allow 2 to 20 groups or conditions. Confidence level 0.5 to 0.9999. Setting numbers are plain decimals with a digit before the point, such as 0.95, without exponents. In CSV with two or more columns a blank line between rows is rejected, and in one-column CSV it is a blank cell; blank lines after the last row are ignored. Downloads: a JSON report and CSV tables. Paste one row per observation, or paired columns such as before,after. Up to 1,000,000 characters. Review the settings before running.
Your result
How to use Nonparametric comparison workspace
- Choose the test that matches your design.
- Paste the CSV and name the group and value columns, the paired columns or the condition columns.
- Pick the alternative, the p-value method and the confidence level.
- Run the test, review the ranks and the Hodges-Lehmann interval, and download the report.
Useful next steps
Two-sample and paired tests
Mann-Whitney W is the rank sum of the first group minus n1(n1 + 1)/2 (Mann and Whitney 1947, Annals of Mathematical Statistics 18:50), and the signed-rank V is the sum of ranks of positive differences (Wilcoxon 1945, Biometrics Bulletin 1:80), as in R wilcox.test. Automatic mode uses the exact distribution when both groups are under 50 (or under 50 pairs) and there are no ties or zero differences, otherwise the normal approximation with tie and optional continuity correction. Zero differences are dropped. Paired differences and differences from the null value are computed exactly from the decimal values you enter (up to 15 significant digits), so equal differences such as 1.3 - 1.2 and 1.4 - 1.3 count as ties and zeros; R subtracts in binary floating point, which can split such ties. The exact option with ties uses the distribution conditional on the observed ranks, which differs from R, which switches to the normal approximation.
Hodges-Lehmann estimate and interval
The estimate is the median of the pairwise differences (two groups) or Walsh averages (paired or one sample) (Hodges and Lehmann 1963, Annals of Mathematical Statistics 34:598). The interval inverts the same test: for exact tests it takes order statistics of those differences (Bauer 1972, JASA 67:687; Hollander, Wolfe and Chicken 2014, Nonparametric Statistical Methods, 3rd ed.), otherwise it takes the difference where the normal statistic crosses the critical value. R finds that point with uniroot to within 0.0001; this tool returns the exact difference. The achieved confidence of exact intervals is reported.
More than two groups
Kruskal-Wallis (Kruskal and Wallis 1952, JASA 47:583) uses the chi-square approximation with tie correction and epsilon squared, followed by Dunn z tests (Dunn 1964, Technometrics 6:241) with Holm or Bonferroni adjustment. Friedman (Friedman 1937, JASA 32:675) ranks within each subject, with R's tie correction and Kendall's W.
Limits
Rank tests compare distributions, not means. The Hodges-Lehmann shift is a fair summary only when the groups have a similar shape. Conventions for ties and continuity corrections differ between programs, so the method used is always labelled.