Kruskal-Wallis Test

The Kruskal-Wallis test is a rank-based nonparametric test of whether three or more independent groups come from the same distribution, used as an alternative to one-way ANOVA.

크러스컬-월리스 검정은 서로 독립인 세 개 이상의 집단이 같은 분포에서 나왔는지를 순위로 검정하는 비모수 검정으로, 일원분산분석의 대안으로 쓰인다.

How do I compare three or more groups when my data are not normally distributed?

데이터가 정규분포가 아닐 때 세 개 이상 집단을 어떻게 비교하나요?

The Kruskal-Wallis test compares three or more independent groups using ranks instead of raw values, so it does not require normally distributed outcomes. It fits ordinal outcomes or skewed continuous outcomes, and a significant result is usually followed by Dunn's pairwise tests with adjusted p-values.

When to use Kruskal-Wallis Test

• One ordinal or continuous outcome compared across three or more independent groups
• Skewed outcomes or outliers that make one-way ANOVA questionable
• Small groups where normality cannot be checked reliably

When to use something else

• Only two groups; use the Mann-Whitney U test
• Repeated measurements on the same participants; use the Friedman test

Assumptions and requirements

• Independent observations within and between groups
• Ordinal or continuous outcome
• Similar distribution shapes across groups if the result is to be read as a difference in medians

What the analysis reports

• H statistic (chi-square approximation) with degrees of freedom
• p-value
• Mean ranks or medians by group
• Effect size such as epsilon-squared
• Dunn post hoc comparisons

How to report it

A Kruskal-Wallis test showed a significant difference in [outcome] across groups, H([df]) = [value], p = [value].

Related methods

• One-Way ANOVA
• Mann-Whitney U Test
• Dunn's Test

Run Kruskal-Wallis Test on Quorant