Definition
Post-hoc tests follow a significant ANOVA and compare groups pairwise to show which ones really differ. At the same time they control the risk of a falsely significant result, which grows with many simultaneous comparisons. The most used are Tukey's HSD, Scheffé's test, Bonferroni and Fisher's LSD.
Statistical tests
Without correction, with 6 groups (15 pairs) at least one pair would come out "significant" almost surely even with no real difference. Tukey's test keeps the overall error at the chosen level and suits all pairs with similar group sizes; Scheffé is more conservative and also covers complex contrasts; Dunnett's test compares every group with a single control.
The output is a matrix of p-values or homogeneous groups (letters a, b, c) that read well in a plot of means. For nonparametric ANOVA there are analogous multiple comparisons of mean ranks.
In Statistica
In the ANOVA module the post-hoc tests sit on the Post-hoc tab of the results dialog: Tukey HSD (also for unequal n), Scheffé, Bonferroni, Newman–Keuls, Duncan, Dunnett and LSD, output as a p-value matrix or homogeneous groups. The nonparametric variant is in the Nonparametrics module.
Related terms
- ANOVA (analysis of variance)ANOVA (analysis of variance) tests whether the means of three or more groups differ.
- Significance level and Type I / Type II errorsThe significance level α is the maximum risk of a Type I error — rejecting a null hypothesis that is actually true (a false alarm).
- t-testThe t-test compares means: the one-sample version compares a mean with a fixed value, the two-sample version the means…
Knowledgebase guides
FAQ
- Which post-hoc test should I choose?
- Tukey for all pairwise comparisons; Dunnett when comparing with a control; when unsure, Scheffé is safely conservative.
- Can I run several t-tests instead?
- Not without correction — every extra t-test raises the chance of a false alarm. Post-hoc tests handle that systematically.
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Statistical tests
Updated: September 2026.