Kruskal-Wallis Test
Statistics & analysis
The non-parametric alternative to one-way ANOVA: compares three or more independent groups using ranks instead of means.
The Kruskal-Wallis test compares three or more independent groups on a ranked outcome, serving as the non-parametric alternative to one-way ANOVA. It pools all observations, converts them to ranks, and tests whether mean ranks differ across the groups.
It is the appropriate choice when the outcome is ordinal, or when ANOVA's normality assumption is clearly violated and transformation does not help. As with ANOVA, a significant result indicates only that at least one group differs from the others, not which pair is responsible.
Follow a significant test with pairwise post-hoc comparisons — Dunn's test with a Bonferroni or Benjamini-Hochberg adjustment is standard — and report the H statistic, degrees of freedom, p-value, group medians and an effect size such as epsilon squared.
Where it's used
- Comparing satisfaction across three departments when scores are skewed
- Ordinal-outcome comparisons across multiple groups
Software used
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