Tukey HSD Calculator (Post-Hoc Test)
Find which pairs of groups differ after a significant ANOVA.
What Tukey’s HSD does
When a one-way ANOVA is significant, it says that some group means differ, but not which ones. Tukey’s honestly significant difference (HSD) test compares every pair of groups and adjusts the p-values so that the chance of any false positive across all the comparisons stays at 5%. With unequal group sizes it uses the Tukey–Kramer version, which this calculator applies automatically.
Worked example
Four groups of 6, 6, 6 and 7 scores give an ANOVA of F(3, 21) = 22.76, p < .001. The Tukey comparisons show which pairs differ:
| Groups | Mean difference | Adjusted p | Significant at 0.05? |
|---|---|---|---|
| 1 − 2 | -7.17 | < 0.0001 | Yes |
| 1 − 3 | -2.00 | 0.3996 | No |
| 1 − 4 | 2.50 | 0.1932 | No |
| 2 − 3 | 5.17 | 0.0025 | Yes |
| 2 − 4 | 9.67 | < 0.0001 | Yes |
| 3 − 4 | 4.50 | 0.0062 | Yes |
The 95% critical value of the studentized range for 4 groups and 21 degrees of freedom is q = 3.942.
How it is calculated
- MSW is the pooled within-group variance from the ANOVA, with N − k degrees of freedom.
- For each pair, q = |mean difference| ÷ √((MSW ÷ 2) × (1/nᵢ + 1/nⱼ)).
- The adjusted p-value is the right tail of the studentized range distribution with k groups and N − k degrees of freedom.
- The 95% confidence interval for a difference is the difference ± q-critical × the same standard error.
Assumptions are the same as for ANOVA: independent observations, roughly normal data and similar variances. If variances are very unequal, use the Games-Howell test. For data that is not normal, use Kruskal-Wallis with Dunn’s test.
How to cite this page
CalcPulse. (2026). Tukey HSD Calculator. https://calcpulse.com/tukey-hsd-calculator/
Frequently asked questions
What is Tukey's HSD test?
A post-hoc test that compares all pairs of group means after an ANOVA, while controlling the overall error rate.
When should I use a post-hoc test?
After a significant ANOVA, to see which groups differ. If the ANOVA is not significant, you usually stop there.
What is the Tukey-Kramer test?
The version of Tukey's test for groups of unequal size. This calculator uses it automatically.
What is the studentized range?
A distribution that describes the largest difference between group means, in standard error units. It is used to get the adjusted p-values.
What if the group variances differ?
Use the Games-Howell test, which does not assume equal variances.
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