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Which of my conditions differ from each other?

Compare three or more groups

ANOVA, its non-parametric equivalents, and what to do about post-hoc tests.

One-way ANOVA asks a single question: is anything different anywhere. It does not tell you which groups differ, which is what you actually wanted, so it is followed by a post-hoc test — Tukey when comparing everything against everything, Dunnett when comparing each treatment against one control. Dunnett is the right choice far more often than it is used, and it is more powerful because it asks for less.

Two factors, such as treatment and time, call for two-way ANOVA. Repeated measurements on the same subjects call for a repeated-measures design or a mixed model. Kruskal–Wallis is the non-parametric one-way equivalent.

Running a t-test between every pair instead of an ANOVA inflates your false positive rate: with five groups that is ten tests, and roughly a 40% chance of at least one spurious result at p < 0.05.

What to use

Drafted from the literature and not yet reviewed by a specialist. Treat it as a starting point, and tell us if something here is wrong. Last touched .

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