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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

Comparison between a 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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