Dunn's Post Hoc Test

Dunn's test is a post hoc procedure that compares mean ranks between every pair of groups after a Kruskal-Wallis test, using a tie-corrected standard error and adjusted p-values.

Dunn 검정은 Kruskal-Wallis 검정 뒤에 모든 집단 쌍의 평균 순위 차이를 동순위 보정 표준오차로 나누어 비교하고 다중비교를 보정하는 사후검정이다.

My Kruskal-Wallis test was significant; how do I find which groups differ?

Kruskal-Wallis 검정이 유의하게 나왔는데 어느 집단끼리 다른지 어떻게 알 수 있나요?

Dunn's test reuses the ranks from the full Kruskal-Wallis ranking, divides each pairwise difference in mean ranks by a tie-corrected standard error to obtain z, and adjusts the resulting p-values for multiple comparisons. Holm adjustment controls the familywise error rate with more power than Bonferroni, while Benjamini-Hochberg controls the false discovery rate.

When to use Dunn's Post Hoc Test

• A Kruskal-Wallis test across three or more groups was significant.
• You need all pairwise comparisons between groups.
• The outcome is ordinal or non-normal.

When to use something else

• The data meet ANOVA assumptions; use Tukey HSD or Games-Howell instead.
• The groups are repeated measurements on the same subjects; use the Nemenyi or Conover test after a Friedman test instead.

Assumptions and requirements

• Observations are independent.
• Groups are compared on the same ranking used for the Kruskal-Wallis test.
• Group distributions have similar shapes if conclusions are about medians.

What the analysis reports

• Mean rank of each group
• Pairwise z statistics
• Unadjusted and adjusted p-values
• Effect size r = z/√N

How to report it

Following a significant Kruskal-Wallis test, H([df]) = [value], p = [value], Dunn's test with Holm adjustment showed that [group A] differed from [group B], z = [value], adjusted p = [value].

Related methods

• Kruskal-Wallis Test
• Nemenyi Post Hoc Test
• Holm-Bonferroni Correction

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