ANOVA vs Kruskal-Wallis: Which Test to Use
When you compare a numeric outcome across three or more independent groups, two tests dominate the choice: one-way ANOVA and the Kruskal–Wallis test. Both answer "do the groups differ?", but they rest on different assumptions — and picking the wrong one either costs you power or invalidates your p-value.
ANOVA compares group means and assumes approximately normal residuals with roughly equal variances. Kruskal–Wallis is its rank-based counterpart: it makes no normality assumption, which makes it the safer choice for skewed data, ordinal outcomes, or small samples with outliers.
Quick decision
| One-way ANOVA | Kruskal–Wallis | |
|---|---|---|
| Outcome scale | Interval / ratio | Ordinal or non-normal |
| Key assumption | Normal residuals, equal variance | Independent observations |
| Compares | Means | Mean ranks (distributions) |
| Post-hoc | Tukey HSD | Dunn (Bonferroni / BH) |
| Effect size | η², ω² | ε², η²H |
What Kruskal–Wallis actually tests
A common myth is that Kruskal–Wallis "compares medians." It compares mean ranks; it becomes a clean test of medians only when the group distributions share the same shape. Word your conclusion accordingly.
Checking the ANOVA assumptions
Before trusting ANOVA, verify normality of the residuals (not the raw data) and homogeneity of variance — and consider Welch's ANOVA when variances differ.
Effect size and post-hoc
Always report an effect size, and if the omnibus test is significant, follow up with the matching post-hoc test under a multiple-comparisons correction.
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