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Kruskal Wallis Calculator

Perform a Kruskal-Wallis test comparing three or more independent groups.

About Kruskal Wallis Calculator

Kruskal-Wallis extends the Mann-Whitney test to more than two groups and follows a chi-square distribution under the null. A significant result identifies that some group differs but not which. A significant H requires post-hoc pairwise tests with multiplicity correction to locate the difference, exactly as ANOVA does.

Formula

Kruskal Wallis

H is compared against a chi-square distribution with k − 1 degrees of freedom

H
Rank-based test statistic, the non-parametric analogue of the F ratio
epsilon squared
Proportion of variability explained by group membership

Worked example

With the default values below, Kruskal Wallis Calculator returns H Statistic of 8.40000. Change any input above and every figure here is recalculated in your browser.

Inputs used

H statisticminimum 0
8.4
Number of groupsaccepts 2–20
3
Total sample sizeminimum 4
45
Significance levelaccepts 0.1–20 %
5 %

Results

H Statistic
8.40000
Degrees of Freedom
2
Approximate Critical Value
6.6400
Effect Size
0.19091
Decision
Reject H0 — at least one group differs

Step by step

  1. 1Values used
  2. 2Kruskal Wallis
  3. 3H Statistic= 8.40000
  4. 4Degrees of Freedom= 2
  5. 5Approximate Critical Value= 6.6400
  6. 6Effect Size= 0.19091
  7. 7Decision= Reject H0 — at least one group differs

Assumptions and limits

  • The result is derived only from the 4 inputs listed above. Anything not among them is not part of the calculation.
  • In particular, this calculator does not take inflation, tax, fees or charges or compounding frequency into account.
  • Figures are rounded for display to 5 decimal places, so totals built from several rounded parts can differ slightly from the unrounded arithmetic.

How these calculators are built and tested is described on the Methodology page. If a figure looks wrong, please report it.

Frequently Asked Questions

How is Kruskal Wallis calculated?

H is compared against a chi-square distribution with k − 1 degrees of freedom Kruskal-Wallis extends the Mann-Whitney test to more than two groups and follows a chi-square distribution under the null. A significant result identifies that some group differs but not which.

Why does Kruskal Wallis matter?

A significant H requires post-hoc pairwise tests with multiplicity correction to locate the difference, exactly as ANOVA does.

What values do I need to enter?

This calculator takes 4 inputs: H statistic, Number of groups, Total sample size, Significance level. The pre-filled defaults are a realistic starting point — replace them with figures from your own environment for a result you can act on.

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