Kruskal–Wallis Test Calculator
Non-parametric one-way comparison of three or more groups — H statistic with tie correction, degrees of freedom, p-value and epsilon-squared effect size.
How it works
H = 12 ÷ [n(n+1)] · Σ Rᵢ²/nᵢ − 3(n+1), divided by 1 − Σ(t³−t)/(n³−n) for ties; H ~ χ² with k−1 df
Kruskal–Wallis extends the Mann–Whitney test to several groups: all values are ranked together and the test asks whether the mean ranks differ more than chance allows. It replaces one-way ANOVA when data are skewed, ordinal or have outliers. A significant H says at least one group differs — pairwise comparisons (Dunn’s test with a multiplicity correction) show which. The chi-square approximation is reliable with five or more observations per group.
Worked example
Three groups of six: H = 5.69 on 2 df, p = 0.058 — suggestive but not significant at 5%.
Frequently asked questions
ANOVA or Kruskal–Wallis?
ANOVA when residuals are roughly normal with similar spread; Kruskal–Wallis otherwise. With normal data ANOVA is only slightly more powerful.
What is epsilon-squared?
The rank analogue of eta-squared: the share of rank variance explained by group membership (0.01 small, 0.08 medium, 0.26 large).
Related calculators
For education — check assumptions (sample size, distribution, independence) before using a test result in a real decision.