Kruskal-Wallis H Test Calculator
The Kruskal-Wallis test compares three or more independent groups using ranks — the non-parametric alternative to one-way ANOVA for skewed data, ordinal outcomes or unequal small samples. Enter one group per line and get the tie-corrected H statistic, its chi-square degrees of freedom, the p-value and the epsilon-squared effect size, alongside every group's n and median. Results match R's kruskal.test() to at least four significant digits, tie correction included. A significant H says at least one group differs — pairwise Mann-Whitney tests (with a multiple-comparison correction) or Dunn's test then locate where.
AI Report
Let AI interpret your results: a downloadable Word document in APA 7 / business report format.
Frequently asked questions
How do I report a Kruskal-Wallis test in APA 7 format?
Report H (often written as χ² or H with df), the p-value and an effect size, e.g.: "Scores differed across the three conditions, H(2) = 7.62, p = .022, ε² = .32", typically with the group medians. The AI Report button produces the full APA 7 results paragraph.
When should I use Kruskal-Wallis instead of one-way ANOVA?
When ANOVA's assumptions fail: clearly non-normal residuals, ordinal outcomes, or small groups with outliers or very unequal variances. With roughly normal data ANOVA has more power and gives you Tukey post-hoc tests directly — check normality per group first (see our ANOVA tool).
The test is significant — how do I find which groups differ?
Follow up with pairwise comparisons: Dunn's test is standard, or pairwise Mann-Whitney U tests with a Bonferroni (or Holm) correction to the α level. Our Mann-Whitney tool handles each pair; divide 0.05 by the number of comparisons for the Bonferroni threshold.