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  • Current: Dec 28, 2021

Post-hoc test

In statistics, a post-hoc test typically refers to a test conducted after analysis of variance (ANOVA). “Post-hoc” means “after this” in Latin.

Becuse the null hypothesis of ANOVA is that there is no difference among group means, ANOVA does not analyze differences between group means. Post-hoc tests are used to test the differences between group means in multiple comparison.

Below is a typical figure of multiple comparison [1].

Multiple comparison example

Common post-hoc tests include the following.

Tukey HSD

HSD stands for “honest significant difference.”

Dunnet's test

Comparison between the control group vs. several experimental groups.

Duncan's multiple range test

Not recommended because of the high probability of type I error.


Definitions in the literature

  • Post-hoc tests may be a priori (comparisons that were planned before the ANOVA was performed) or a posteriori (run after the ANOVA is performed and run only if the F statistic from the ANOVA is significant). These types of contrasts are tested using different methods [2].

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