Kruskal-Wallis Test Calculator

Calculator

This calculator helps you perform the Kruskal-Wallis test, a non-parametric method for testing whether samples originate from the same distribution. It is suitable for researchers and statisticians working with independent samples.

Results

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Data Source and Methodology

All calculations are strictly based on the statistical methods outlined in the article by John H. McDonald, Handbook of Biological Statistics (3rd ed.). Read more.

The Formula Explained

The Kruskal-Wallis H statistic is calculated as: \[ H = \frac{12}{N(N+1)} \sum_{i=1}^{g} \frac{R_i^2}{n_i} - 3(N+1) \]

Glossary of Variables

H: Kruskal-Wallis statistic
N: Total number of observations
g: Number of groups
R_i: Sum of ranks for group i
n_i: Number of observations in group i

Practical Example

Let's say we have three groups with ranks: [23, 45, 67], [12, 34, 56], and [78, 89, 90]. The Kruskal-Wallis statistic is calculated using the formula above by substituting the sum of ranks and the number of observations for each group.

Frequently Asked Questions (FAQ)

What is the Kruskal-Wallis test used for?

The Kruskal-Wallis test is used to determine if there are statistically significant differences between the medians of three or more independent groups.

When should I use the Kruskal-Wallis test?

Use this test when you have ordinal data or when the assumptions of ANOVA are not met.

Can the Kruskal-Wallis test be used for two groups?

While it can be used for two groups, it is equivalent to the Mann-Whitney U test in such cases.

Is the Kruskal-Wallis test sensitive to outliers?

No, the test is not sensitive to outliers as it uses ranks rather than raw data.

How is the test result interpreted?

A significant result indicates that at least one group median is different from the others, but it does not specify which groups differ.

Tool developed by Ugo Candido, content verified by expert statisticians.
Last reviewed for accuracy on: October 2023.