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

Name: Kruskal-Wallis Test Calculator
Availability: InStock
Author: Nham Vu

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

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

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: 2026-06-10 · Reviewed by Nham Vu