Non-Parametric Tests (Mann-Whitney / Wilcoxon / Kruskal-Wallis)
The first choice for comparing groups when data are non-normal or ordinal. Two independent groups automatically run a Mann-Whitney U test; check "paired" for a Wilcoxon signed-rank test; 3 or more groups automatically run a Kruskal-Wallis H test. All include tie correction and medians.
① Enter data
One group per line, numbers within a group separated by spaces or commas. 2 groups = Mann-Whitney (or check paired), ≥3 groups = Kruskal-Wallis.
How to use & methodology
When should I use a non-parametric test instead of a t-test?
When data clearly depart from normal, are ordinal (grades, scores), have extreme outliers, or the sample is very small, non-parametric tests are more robust. When data are approximately normal, prefer t-tests/ANOVA for higher efficiency.
Mann-Whitney, Wilcoxon signed-rank, or Kruskal-Wallis?
Two independent groups → Mann-Whitney U; two paired groups (before/after, one-to-one) → Wilcoxon signed-rank (check 'paired'); three or more independent groups → Kruskal-Wallis H. This tool selects automatically by group count and pairing.
Why does the p-value differ slightly from statistical software?
This tool uses a normal approximation with tie and continuity corrections, suitable for typical samples; for small samples (n < 8 per group) the exact test and the approximation differ, and the software's exact p is more accurate. For borderline results, verify with the exact test.
What to do after a significant Kruskal-Wallis?
The H test only says 'at least one group differs'. If P<0.05, run post-hoc pairwise comparisons (commonly Dunn's test with multiple-comparison correction) to determine which specific groups differ.