What does the p-value mean?

A p-value below your chosen significance level (commonly 0.05) indicates that at least one group differs significantly from the others. A high p-value means you lack evidence to conclude any group is different.

How is this different from one-way ANOVA?

One-way ANOVA assumes the data in each group are normally distributed and have equal variances. The Kruskal-Wallis test makes neither assumption — it works on ranks and is suitable for ordinal data or skewed distributions.

What is the H statistic?

H measures how much the rank sums of each group deviate from what would be expected if all groups were identical. A larger H indicates greater differences between groups. Under the null hypothesis, H follows an approximate chi-squared distribution with k-1 degrees of freedom, where k is the number of groups.

How are ties handled?

When multiple observations share the same value they receive the average of the ranks they would have occupied. A standard tie-correction factor is applied to H, slightly increasing its value to maintain accuracy.

How many observations do I need?

The chi-squared approximation is generally reliable when each group has at least 5 observations. For very small groups (n < 5), consider using exact critical-value tables.

Which groups differ if the test is significant?

The Kruskal-Wallis test only tells you that at least one group differs — it does not identify which pairs. Follow up with pairwise Mann-Whitney U tests (with a Bonferroni correction) to pinpoint the differing groups.

Kruskal-Wallis Test Calculator

Enter up to 6 independent groups to compute the Kruskal-Wallis H statistic and p-value without assuming normality.

Group Data

Significance Level (α)

Enter data for at least 2 groups, then click "Run Test"

H Statistic

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p-value

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N (total)

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Group Rank Summary

Group	n	Rank Sum	Mean Rank	Median

Summary

The Kruskal-Wallis H test is a non-parametric alternative to one-way ANOVA that determines whether two or more independent groups come from the same distribution. It ranks all observations jointly and compares rank sums across groups. This calculator accepts up to 6 groups, computes the H statistic with tie correction, and reports an approximate p-value using the chi-squared distribution.

How it works

Enter values for each group (one value per line or comma-separated).
Add or remove groups as needed — between 2 and 6 groups are supported.
Click "Run Test" to pool and rank all observations jointly.
The tool sums the ranks for each group and applies the Kruskal-Wallis H formula.
A tie-correction factor is applied when tied ranks are present.
The H statistic is compared to the chi-squared distribution to produce a p-value.

Use cases

Compare customer satisfaction scores across multiple product categories.
Test whether three or more teaching methods produce different exam results.
Analyze pain-scale ratings from multiple treatment groups in a clinical study.
Assess whether website session durations differ across device types.
Non-parametric replacement for one-way ANOVA when normality cannot be assumed.
Evaluate Likert-scale survey responses across demographic segments.
Compare response times for multiple algorithm variants without assuming normality.
Test whether plant growth differs under several fertilizer conditions.

Frequently Asked Questions

Last updated: 2026-06-13 · Reviewed by Nham Vu