Kruskal-Wallis H Test Calculator

Calculator Input

Example Data Table

Formula Used

Step 1: Rank all observations together from smallest to largest.

Step 2: Add the ranks within each group.

Step 3: Compute the raw test statistic.

H = [12 / (N(N + 1))] × Σ(Ri² / ni) − 3(N + 1)

Ri is the sum of ranks for group i.

ni is the sample size for group i.

N is the total sample size across all groups.

Tie correction:

T = 1 − Σ(t³ − t) / (N³ − N)

Corrected H = H / T

The calculator reports the corrected H statistic, chi-square approximation, p value, critical value, and effect sizes.

How to Use This Calculator

1. Enter one group per line inside the textarea.
2. Add a label, then a colon or equals sign.
3. Separate group values with commas, spaces, or semicolons.
4. Choose alpha, decimal places, graph metric, and graph order.
5. Press the button to calculate the test.
6. Review the summary, tables, and Plotly graph.
7. Use the CSV or PDF button to export results.

About the Kruskal-Wallis H Test

The Kruskal-Wallis H test compares three or more independent groups without assuming a normal distribution. It works by ranking all values together and then testing whether rank totals differ more than expected by chance.

This method is useful when data are skewed, ordinal, or affected by outliers. It is often treated as the nonparametric alternative to one-way ANOVA. The test evaluates whether group distributions differ in location.

The calculator computes pooled ranks, applies tie correction, estimates the p value from the chi-square distribution, and returns effect sizes for practical interpretation. It also shows group medians, means, rank sums, and mean ranks.

Use it when groups are independent and the measurement scale supports ranking. When the overall result is significant, follow-up pairwise procedures such as Dunn testing can help identify which groups differ.

FAQs

1. What does this calculator test?

It tests whether three or more independent groups differ in their ranked outcomes. It does not assume normality and is useful for ordinal or non-normal numeric data.

2. When should I use Kruskal-Wallis instead of ANOVA?

Use it when your data are skewed, ordinal, contain outliers, or do not meet normality assumptions. It is a common nonparametric alternative to one-way ANOVA.

3. Can I compare only two groups?

You can, but Mann-Whitney U is usually more direct for two groups. Kruskal-Wallis is most helpful when comparing three or more independent groups.

4. Does the calculator handle tied values?

Yes. It applies the standard tie correction factor and reports both the raw and corrected H statistic when repeated values exist.

5. What does a small p value mean?

A small p value suggests the group rank distributions are unlikely to be equal under the null hypothesis. It supports a statistically significant difference somewhere among the groups.

6. What do the effect sizes mean?

Epsilon squared and eta squared estimate practical magnitude. Higher values indicate stronger group separation, even when sample size changes the p value.

7. Does this calculator identify which groups differ?

No. Kruskal-Wallis is an overall test. If the result is significant, follow-up pairwise procedures are needed to locate the specific differences.

8. What input format should I use?

Enter one group per line, such as Group A: 12, 14, 16. Labels are optional, but using them makes the tables and graph easier to read.