クラスカル・ウォリスH検定計算ツール

What is the Kruskal-Wallis H Test?

The Kruskal-Wallis H test is a rank-based non-parametric test used to determine whether there are statistically significant differences between three or more independent groups. It extends the Mann-Whitney U test to more than two groups and serves as the non-parametric alternative to one-way ANOVA. Developed by William Kruskal and W. Allen Wallis in 1952, it ranks all observations regardless of group membership and tests whether the rank distributions differ across groups.

When to Use the Kruskal-Wallis H Test

Use the Kruskal-Wallis H test when you want to compare three or more independent groups and one or more of the following conditions apply: your data are measured on an ordinal scale (e.g., Likert-type items), the assumption of normality is violated, your sample sizes are very small, or your data contain outliers that would distort parametric results. It is commonly used in medical research, psychology, education, and quality control studies.

Kruskal-Wallis H Test vs. One-Way ANOVA

Assumptions of the Kruskal-Wallis H Test

While the Kruskal-Wallis H test is less restrictive than ANOVA, it still has assumptions that should be verified:

Understanding Eta-Squared H (η²_H)

Eta-squared H (η²_H) is the effect size measure for the Kruskal-Wallis test. It estimates the proportion of variance in ranks explained by group membership, analogous to η² in ANOVA.

How to Report Kruskal-Wallis Results in APA Format

According to APA 7th edition guidelines, report the H statistic, degrees of freedom, p-value, effect size, and descriptive statistics (medians and sample sizes) for each group:

Note: Report H to two decimal places, degrees of freedom as an integer, and p to three decimal places. Use p < .001 when the value is below .001. Always include η²_H as the effect size measure and follow up with post-hoc results when the omnibus test is significant.

Common Mistakes to Avoid

• Using ANOVA on non-normal data: If your data are ordinal or clearly non-normal with small samples, ANOVA may give misleading results. Use the Kruskal-Wallis H test instead.
• Skipping post-hoc tests: A significant Kruskal-Wallis result only tells you that at least one group differs. Always follow up with Dunn's post-hoc test to identify which specific pairs of groups differ.
• Using Kruskal-Wallis for related groups: If your data are paired, matched, or represent repeated measures, use the Friedman test instead. The Kruskal-Wallis test is strictly for independent groups.
• Ignoring effect size: A significant p-value alone does not tell you the magnitude of the difference. Always report η²_H alongside the test result.
• Forgetting Bonferroni correction: When performing multiple pairwise comparisons, failing to apply correction for multiple testing inflates the Type I error rate.