Dunn's Multiple Comparison Test
Also known as: Dunn's post-hoc test, Kruskal-Wallis post-hoc, Dunn Testi — Kruskal-Wallis Post-Hoc
Dunn's test is a nonparametric post-hoc procedure introduced by Olive Jean Dunn in 1964 to identify which specific pairs of groups differ significantly after a Kruskal-Wallis test has returned a significant overall result. It compares groups pairwise using rank sums and applies a multiple-comparison correction — most commonly Bonferroni or Holm — to control the family-wise error rate.
Key highlights
- Distribution-free: requires no normality assumption, making it safe for skewed or ordinal data.
- Directly extends the Kruskal-Wallis rank framework, so pairwise comparisons are consistent with the omnibus test.
- Multiple-comparison control via Bonferroni or Holm keeps family-wise Type I error at the nominal level.
- Simple to compute and widely implemented; effect size r = z / √N is straightforward to interpret.
Intuition
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How it works
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When to use it
Apply Dunn's test as a follow-up to a statistically significant Kruskal-Wallis test when you have three or more independent groups measured on a continuous or ordinal outcome and the normality assumption for one-way ANOVA cannot be met. Prerequisites are: (1) the omnibus Kruskal-Wallis test is significant (p < 0.05), (2) groups are independent, and (3) each group contains at least five observations. Do not run Dunn's test after a non-significant Kruskal-Wallis result, as the omnibus test must establish that a difference exists before post-hoc comparisons are warranted.
Strengths & limitations
- Distribution-free: requires no normality assumption, making it safe for skewed or ordinal data.
- Directly extends the Kruskal-Wallis rank framework, so pairwise comparisons are consistent with the omnibus test.
- Multiple-comparison control via Bonferroni or Holm keeps family-wise Type I error at the nominal level.
- Simple to compute and widely implemented; effect size r = z / √N is straightforward to interpret.
- Can only be used after a significant Kruskal-Wallis test; it is not a stand-alone comparison procedure.
- Less powerful than parametric post-hoc tests (e.g. Tukey's HSD) when data genuinely follow a normal distribution.
- Bonferroni correction becomes conservative with many groups, reducing power; Holm's method is preferable in those cases.
- Does not directly test medians — it tests rank-sum equality, which may differ from median equality when distributions have different shapes.
Common pitfalls
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Applications
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Frequently asked
Do I need to run Kruskal-Wallis first?
Yes. Dunn's test is a post-hoc procedure and should only be run after a statistically significant Kruskal-Wallis result. Running it without a significant omnibus test increases the probability of spurious findings.
Bonferroni or Holm — which correction should I use?
Holm's step-down method is generally preferred because it is uniformly more powerful than Bonferroni while still controlling the family-wise error rate at the same nominal level. Bonferroni is simpler and widely accepted, but with many groups it becomes increasingly conservative. Report whichever you use and be consistent.
How do I report effect size?
For each significant pair, calculate r = z / √N, where z is the pairwise z statistic and N is the total sample size across the two groups in the comparison. Values around 0.1, 0.3, and 0.5 are conventionally interpreted as small, medium, and large effects respectively.
Why not just run multiple Mann-Whitney U tests instead?
Running multiple Mann-Whitney tests without correction inflates the family-wise Type I error. Dunn's test uses the same pooled ranking as Kruskal-Wallis and applies a proper multiple-comparison correction, making it both conceptually consistent and statistically rigorous.
Sources
- 1.Dunn, O.J. (1964). Multiple Comparisons Using Rank Sums. Technometrics, 6(3), 241–252.
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Cite this page
ScholarGate. (2026, June 1). Dunn Test. ScholarGate. https://scholargate.app/statistics/dunn-test