The H Statistic

This Kruskal-Wallis test calculator pools all observations, ranks them from smallest to largest (averaging ranks for ties), and computes the H statistic from each group's rank sum: H = 12/(N(N+1)) · Σ(Rᵢ²/nᵢ) − 3(N+1). A tie-correction factor is applied when repeated values are present.

The P-Value

Under the null hypothesis that all groups share the same distribution, H follows a chi-square distribution with k − 1 degrees of freedom. The p-value — computed here from the incomplete gamma function — is the probability of an H this large by chance alone.

Reading the Result

If the p-value falls below 0.05, the test rejects the null and concludes that at least one group's values tend to rank higher or lower than the others. It does not say which groups differ — follow-up pairwise comparisons do that.