ANOVA Post-hoc Multiple Comparison (Tukey HSD / Bonferroni / Holm)
After ANOVA shows a difference among several groups, post-hoc pairwise comparison identifies which groups differ. This tool first runs a one-way ANOVA, then gives each pair's mean difference, Tukey-Kramer HSD (with 95% simultaneous confidence intervals), and Bonferroni- and Holm-corrected P values. Computed locally in your browser; data are not uploaded.
① Enter data
One group per row (≥3 groups), numbers within a group separated by space or comma. You may write "GroupName:" at the start of a line — it is ignored automatically.
How to use & methodology
Why do post-hoc tests after ANOVA?
One-way ANOVA only answers "at least one group differs from the others" and does not tell you which. Post-hoc pairwise comparison judges each pair while controlling the false-positive inflation from multiple comparisons, usually after a significant ANOVA (P<0.05).
How to choose among Tukey, Bonferroni, Holm?
Tukey HSD (this tool uses the Tukey-Kramer method, compatible with unequal samples) is the classic method for all pairwise comparisons and gives simultaneous CIs; Bonferroni divides the significance threshold by the number of comparisons — simple but conservative; Holm improves on Bonferroni and is more powerful. Generally report Tukey; if only a few pairs matter or for consistency with other analyses, use Bonferroni/Holm.
How to read the 95% confidence interval?
The 95% CI in the table is Tukey's simultaneous CI (already corrected for multiple comparisons). If a comparison's CI does not contain 0, that pair's mean difference is significant at the 0.05 level, consistent with Tukey P<0.05.
What if variances are unequal?
Tukey/Bonferroni both assume homogeneous variances. If group variances clearly differ, use a method that does not assume equal variances such as Games-Howell (not provided here), or test for homogeneity of variance first.