Kruskal-Wallis Test Calculator

In short Kruskal-Wallis is the non-parametric alternative to one-way ANOVA: it ranks every value across all groups together and asks whether the rank sums are further apart than chance would produce. The three groups loaded above give H = 9.8462 on 2 degrees of freedom and p = 0.0073, against a critical chi-square of 5.9915. Because it uses ranks rather than values, it needs no normality assumption and is unbothered by outliers — an extreme value simply becomes the highest rank rather than dragging a mean around. Two structural facts are worth carrying. Every rank from 1 to N is used exactly once, so the group rank sums must total N(N+1)/2, which is an arithmetic check you can do by hand. And with exactly two groups this IS the Mann-Whitney test — H comes out as precisely the square of that test's z, so Kruskal-Wallis generalises it to more groups and collapses back to it at two. Use it when the variances differ wildly between groups, when the data is ordinal, or when the samples are small and non-normal. As with ANOVA, a significant result says only that the groups are not all alike: finding which pair differs needs a follow-up such as Dunn's test, and running plain Mann-Whitney on every pair without adjusting inflates the false-positive rate.