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Tukey HSD test calculator

Paste groups to compare after analysis of variance. Empty optional fields are ignored.

Smallest adjusted p-value: —

Fill in the fields above — the result is computed on this page.

Groups
—
Comparisons
—
Error df
—
Error MS
—
Largest q
—

Pairwise comparisons

Pair Mean 1 Mean 2 Difference q Adjusted p
Fill in the fields above — the result is computed on this page.
What do these numbers mean?
  • Review every pair in the table, not only the smallest p.
  • Plan post-hoc comparisons after the overall ANOVA test.

P-values are approximate and may differ from software using the exact studentized-range distribution. Variance assumptions match classical ANOVA.

How do I use this page?
  1. Paste at least two groups.
  2. Check the pooled error MS.
  3. Compare differences, q and adjusted p for every pair.

What this page does not do: P-values are approximate and may differ from software using the exact studentized-range distribution. Variance assumptions match classical ANOVA.

Further reading

Theory — what is the Tukey HSD test?

The Tukey HSD procedure compares all pairs of means after an analysis of variance, using a pooled estimate of within-group variance. The q statistic scales the absolute difference between two means by its standard error, showing which pairs differ significantly. The calculator also handles unequal group sizes with an adjusted formula. It is worth noting that the p-value is an explicitly labelled conservative approximation rather than an exact tabulated value.

Frequently asked questions

Is this an exact Tukey test?
The q statistic uses Tukey–Kramer, while p is clearly labelled as a conservative approximation.
Can it be used without ANOVA?
It can be computed, but post-hoc interpretation should follow a planned analysis.

See also

← All calculators

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