Conover-Iman Post-Hoc Test
Conover-Iman Post-Hoc Multiple Comparison Test · Also known as: Conover-Iman post-hoc test, Conover post-hoc test, Conover-Iman Post-Hoc Testi
The Conover-Iman test is a rank-based post-hoc procedure, introduced by Conover and Iman in 1979, that identifies which pairs of groups differ after a significant Kruskal-Wallis or Friedman test. It builds a t-style statistic on the pooled ranks and is generally more powerful than the comparable Dunn test.
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When to use it
Use the Conover-Iman test as a follow-up after a significant Kruskal-Wallis test (independent groups) or Friedman test (repeated measures), when the outcome is continuous or ordinal and not normally distributed. It assumes the omnibus test was significant and, for the Kruskal-Wallis case, independent groups; a total sample of at least about 20 observations is recommended. With fewer than about 10 observations its power is low and a permutation test is preferable; below 5 observations rank-based comparison is not meaningful.
Strengths & limitations
- More powerful than the comparable Dunn test for detecting which group pairs differ.
- Distribution-free: works on continuous or ordinal outcomes without a normality assumption.
- Reuses the ranks and statistic from the omnibus Kruskal-Wallis or Friedman test, so it follows naturally from the analysis already run.
- Supports multiple-comparison correction (such as Holm) to control the family-wise error rate across all pairs.
- Only valid as a post-hoc step: it requires a significant Kruskal-Wallis or Friedman result first.
- Power is low with very small samples (n < 10), where a permutation test is preferred.
- Below about 5 observations, rank-based multiple comparison is not meaningful.
- For independent-group comparisons it assumes the groups are independent.
Frequently asked
How does Conover-Iman differ from the Dunn test?
Both are rank-based post-hoc tests after Kruskal-Wallis, but Conover-Iman builds a t-style statistic using the pooled rank variance and N − k degrees of freedom, which generally gives it more power to detect real pairwise differences than the more conservative Dunn test.
Do I always need a significant omnibus test first?
Yes. Conover-Iman is a post-hoc procedure; it is only valid after a significant Kruskal-Wallis (independent groups) or Friedman (repeated measures) test. Without that, the pairwise comparisons are not justified.
Why do I need a multiple-comparison correction?
Comparing every pair of groups runs many tests at once, which inflates the chance of a false positive. Applying a correction such as Holm to the pairwise p-values keeps the overall (family-wise) error rate controlled.
What should I do if my sample is very small?
With fewer than about 10 observations the test has low power, so a permutation test is preferred. Below about 5 observations a rank-based multiple comparison is not meaningful at all.
Sources
- Conover, W. J. & Iman, R. L. (1979). On Multiple-Comparisons Procedures. Technical Report LA-7677-MS, Los Alamos Scientific Laboratory. link ↗
- Hollander, M., Wolfe, D. A. & Chicken, E. (2014). Nonparametric Statistical Methods (3rd ed.). Wiley. ISBN: 978-0470387375
How to cite this page
ScholarGate. (2026, June 1). Conover-Iman Post-Hoc Multiple Comparison Test. ScholarGate. https://scholargate.app/en/statistics/conover-iman-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.
- Dunn TestStatistics↔ compare
- Friedman testStatistics↔ compare
- Nemenyi TestStatistics↔ compare