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Kruskal Wallis Test Calculator

Work out kruskal wallis test instantly with clear inputs, formula shown and shareable results.

About Kruskal Wallis Test Calculator

Kruskal-Wallis extends Mann-Whitney to three or more groups. It ranks all observations together and asks whether the rank sums differ more than chance allows, comparing H against chi-square on k − 1 degrees of freedom.

Formula

Kruskal-Wallis H

H = [12/(N(N+1))]·Σ(Rᵏ²/nᵏ) − 3(N + 1)

Worked example

With the default values below, Kruskal Wallis Test Calculator returns Kruskal-Wallis H of 6.50000000. Change any input above and every figure here is recalculated in your browser.

Inputs used

First group
12, 15, 18, 21
Second group
22, 25, 28, 30
Third group
16, 19, 23, 26

Results

Kruskal-Wallis H
6.50000000
p value
0.03877421
Degrees of freedom
2
Rank sums by group
13, 39, 26

Step by step

  1. 1Values used
  2. 2Kruskal-Wallis H
  3. 3Kruskal-Wallis H= 6.50000000
  4. 4p value= 0.03877421
  5. 5Degrees of freedom= 2
  6. 6Rank sums by group= 13, 39, 26

Assumptions and limits

  • The result is derived only from the 3 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 8 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

For the three sample groups?

H ≈ 5.6538 on 2 df, giving p ≈ 0.0592 — borderline evidence of a difference.

What follows a significant result?

Post-hoc pairwise comparisons such as Dunn's test, with a correction for multiple testing.

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