Nemenyi Post-Hoc Test for Friedman
Also known as: Nemenyi Testi — Friedman Post-Hoc, Nemenyi multiple comparison test, Nemenyi procedure
The Nemenyi test is a nonparametric post-hoc multiple comparison procedure introduced by Peter Nemenyi in his 1963 Princeton doctoral thesis. It is applied after a significant Friedman test to identify which specific pairs of conditions differ from each other in a repeated-measures or blocked design.
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When to use it
Use the Nemenyi test when you have already obtained a significant Friedman test result in a repeated-measures or randomised complete block design with three or more conditions, and you need to determine which specific pairs differ. The data should be continuous or ordinal. Three assumptions must hold: the Friedman test has produced a significant result, the design is a repeated-measures or related-groups layout, and observations within each block are independent of one another. If you have independent (not related) groups, use the Dunn or Conover–Iman test after Kruskal-Wallis instead.
Strengths & limitations
- Makes no normality assumption — safe for ordinal data and small samples.
- Controls the family-wise error rate across all pairwise comparisons simultaneously.
- Conceptually straightforward: ranks replace raw values, and the decision rule mirrors Tukey's HSD logic.
- Can be conservative relative to alternatives such as the Conover–Iman test, meaning it may miss real differences when the number of conditions is large.
- Only applicable after a significant Friedman omnibus test — running it on a non-significant Friedman result inflates the Type I error.
- Does not provide an effect size estimate directly; a rank-biserial correlation must be computed separately for each pair.
Frequently asked
When should I choose the Nemenyi test over the Conover–Iman test?
The Nemenyi test is more conservative but has a longer pedigree and is appropriate when you prefer a procedure that closely mirrors the Tukey HSD logic. The Conover–Iman test is more powerful but slightly more complex. For standard repeated-measures comparisons with moderate k, both are acceptable; when power is a concern or k is large, Conover–Iman is generally preferred.
Can I run the Nemenyi test if my Friedman test was not significant?
No. Performing post-hoc comparisons after a non-significant omnibus test inflates the family-wise Type I error rate. The Friedman test must reach significance before any pairwise Nemenyi comparisons are conducted.
Does the Nemenyi test work for independent groups?
No. It is designed for repeated-measures or randomised complete block designs where the same subjects (or matched units) appear under every condition. For independent groups, run a Kruskal-Wallis test first and use the Dunn or Conover–Iman test as the post-hoc procedure.
How do I report the results?
Report the Friedman chi-square and p-value first, then present the Nemenyi pairwise p-value matrix. State the mean rank for each condition and identify which pairs differ significantly. Adding a rank-biserial correlation as an effect size for each significant pair is recommended for interpretability.
Sources
- Nemenyi, P. (1963). Distribution-Free Multiple Comparisons. PhD thesis, Princeton University. link ↗
How to cite this page
ScholarGate. (2026, June 1). Nemenyi Post-Hoc Test for Friedman. ScholarGate. https://scholargate.app/en/statistics/nemenyi-test
Which method?
Set this method beside its closest kin and read them side by side — the library lays the books on the table; the choice is yours.
- Conover-Iman TestStatistics↔ compare
- Friedman testStatistics↔ compare
- Kruskal-Wallis testStatistics↔ compare
- Repeated-measures ANOVAStatistics↔ compare
- Wilcoxon signed-rank testStatistics↔ compare