Kruskal Wallis Calculator
kruskal-wallis calculator. Get instant, accurate results. Enter values for instant results with step-by-step formulas.
Reviewed for accuracy by Manoj Kumar, Mathematics Educator
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Formula: H = (12/(N(N+1))) ร ฮฃ(Rแตขยฒ/nแตข) - 3(N+1)
Worked example โ H value
H = (12/(N(N+1))) ร ฮฃ(Rแตขยฒ/nแตข) - 3(N+1)
Non-parametric alternative to one-way ANOVA for comparing 3+ groups.
Problem:G1:[3,4,6] G2:[8,10,12] G3:[15,18,20]
Solution:H statistic with ranks
Result:H value
The Kruskal-Wallis H test determines whether three or more independent groups come from the same distribution. It works by replacing raw values with their overall ranks and comparing the average ranks across groups. A large H statistic indicates that at least one group's distribution differs from the others.
Choose Kruskal-Wallis when your data is ordinal, when group distributions are clearly non-normal (especially with small samples), or when variances are very unequal across groups. If ANOVA assumptions are met, ANOVA has more statistical power. If the result is significant, use post-hoc Dunn's test to identify which specific pairs differ.
The groups must be independent; observations within each group must be independent; each group should have at least 5 observations for the chi-square approximation of H to be reliable; and observations should be from continuous or at least ordinal distributions. Unlike one-way ANOVA, normality and equal variance are not required.
Reviewed for accuracy by Manoj Kumar, Mathematics Educator ยท Editorial policy
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