Kruskal-Wallis Test Calculator
Compare 2–10 groups of raw data with the Kruskal-Wallis test (tie-corrected H, chi-square p-value, epsilon-squared) and Bonferroni-adjusted Dunn post hoc pairs.
Related Calculators
Mann-Whitney U Test Calculator
Compare two independent samples with the Mann-Whitney U (Wilcoxon rank-sum) test: exact or asymptotic p-value, rank table, and effect sizes.
ANOVA Calculator
Run one-way ANOVA calculations and inspect variance across groups.
Wilcoxon Signed-Rank Test Calculator
Paired or one-sample Wilcoxon signed-rank test with zero handling, tie correction, exact p for small n, and a signed-rank table.
Hypotheses
H = (12/(N(N+1))) · Σ (R_i²/n_i) − 3(N+1)
H* = H / T with tie correction T on pooled ranks
ε² = (H − df)/(N − 1)
Worked example (Load example)
Groups [8,10,12], [5,7,9], [14,16,18]: H ≈ 6.489, df = 2, p ≈ 0.039, ε² ≈ 0.561. Dunn: B vs C is significant after Bonferroni at α = 0.05.
When to use ANOVA
Parametric alternative: one-way ANOVA calculator. For two groups only, Mann-Whitney U is equivalent to Kruskal-Wallis with k = 2.
Related guides and calculators
The Kruskal-Wallis test is the rank-based counterpart of one-way ANOVA; for two groups use the Mann-Whitney U test. The Levene test checks whether the groups have equal spread, and the Bonferroni correction adjusts p-values when you compare pairs of groups afterwards. Read parametric vs nonparametric tests, multiple comparisons explained and which statistical test to use.
Frequently Asked Questions
What is the Kruskal-Wallis test?
It is a nonparametric one-way layout test: H0 is that all groups share the same distribution; the statistic compares mean ranks across groups.
How is H computed with ties?
H = (12/(N(N+1))) Σ (R_i²/n_i) − 3(N+1), divided by tie correction T from pooled average ranks, then compared to χ² with k−1 df.
What is Dunn post hoc?
Pairwise z tests on mean rank differences with variance (N(N+1)/12)·T·(1/n_i + 1/n_j); p-values are Bonferroni-adjusted for k(k−1)/2 comparisons.
When use ANOVA instead?
One-way ANOVA targets means under normality and homoscedasticity; Kruskal-Wallis is safer when those assumptions fail.
How many groups can I enter?
Between 2 and 10 groups, each with at least one value, up to 10,000 observations total.
Software equivalents?
R: kruskal.test(x ~ g). Python: scipy.stats.kruskal(*groups).
What does epsilon-squared ε² mean?
ε² = (H − df)/(N − 1) is a rank-based effect size for how much mean ranks differ across groups; larger values mean stronger separation.
Bonferroni vs Holm on Dunn pairs?
Bonferroni multiplies each raw two-sided p by the number of pairs; Holm step-down is less conservative while still controlling family-wise error at α.
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