Kruskal-Wallis Test calculator

Run a non-parametric Kruskal-Wallis test online. Compare multiple groups with skewed data or ordinal scales with Dunn-Holm post-hocs.

What it does

The rank-based analogue of ANOVA — asks whether some of 3+ independent groups systematically outrank others, without assuming any distribution shape.

Cautions

• Interpreting a significant result as "medians differ" requires similar distribution shapes across groups — check with a per-group ECDF overlay.
• A significant omnibus result should be followed by Dunn's post-hoc test (Holm-adjusted), not uncorrected pairwise Mann-Whitney comparisons — the card will show it automatically.

Alternatives

• Welch's ANOVA — assumptions for the parametric test are fine

How to read the output

H statistic (χ² approximation)

Compares the average rank of each group against the average rank overall; compared to a χ² distribution with groups − 1 df. This does not compare medians. It compares whether values in one group tend to exceed the other's. The two coincide only when the distributions have the same shape, so a significant result with differently-shaped distributions means 'these differ', not 'the median differs by X'.

p-value

How surprising a difference at least this large would be IF the groups really were identical on this measure. A small p means the data would be surprising under that assumption. It is not the probability that the result is due to chance, and not the probability that the groups are the same — those read the conditional backwards. It also answers 'would this be surprising?', never 'is this big enough to matter?': with a large sample a trivial difference returns a small p, and the result looks identical to an important one.

Dunn's test (post-hoc) and the correction menu

Pairwise rank comparisons following a significant H, using the ranks from the full analysis. The correction dropdown re-adjusts them without refitting anything. Holm is the default and dominates Bonferroni — same guarantee, more power, no reason to prefer Bonferroni except matching a published protocol. Benjamini–Hochberg controls the false discovery rate instead, which is a different and weaker promise: fine for screening, not for a confirmatory claim. Choosing the correction after seeing which one makes a pair significant invalidates all of them.

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