About Tukey HSD Calculator
This Tukey HSD calculator compares every pair of group means after a one-way ANOVA and keeps the overall error rate at your chosen α. It opens on four fertilisers with uneven group sizes, so it uses the Tukey-Kramer form. It is free, needs no sign-up and runs in your browser, so nothing you enter is uploaded.
For each pair the calculator gives the mean difference, the studentized range statistic q and an adjusted p-value from the studentized range distribution. A pair is flagged when p is below α.
Tukey HSD is for pairwise comparisons made after the fact. The ANOVA table sits just below the Tukey table in this view, so you can check that F is significant first.
How to use Tukey HSD Calculator
- Paste your data with one group per column. A text first row names the groups. Use "Groups in rows" if your groups run across the page.
- Choose the significance level α, usually 0.05.
- Read the ANOVA table: F is the ratio of between-group to within-group variance, and p says how surprising that ratio is if all group means were equal.
- If p is below α, read the Tukey HSD table to see which pairs of groups differ.
- Check the group statistics and the box plots. Very different spreads or heavy outliers weaken the test.
- Copy the summary line for your report.
Features
- One-way ANOVA table with SS, df, MS, F and p.
- Effect size η², the share of the total variance that is between groups.
- Tukey HSD post-hoc test for every pair, with Tukey-Kramer for unequal group sizes.
- Group sizes, means and standard deviations.
- Box plots by group with whiskers and outliers.
- Paste columns straight from a spreadsheet, with blank cells for uneven groups.
- Plain-English reading of the result.
- Three bundled examples to try.
Tukey HSD statistic
For groups i and j the statistic uses the within-group mean square MSW from the ANOVA table.
q = |mean_i − mean_j| / sqrt((MSW / 2) × (1/n_i + 1/n_j))
p = P(studentized range with k groups and N − k df > q)Worked examples
Four fertilisers, groups of 5, 6, 4 and 5 gives 4 of 6 pairs differ at the 5% level
F(3, 16) = 19.04, p = < 0.0001. Fertiliser 1 vs Fertiliser 2 (difference 5.3, p = 0.0006); Fertiliser 2 vs Fertiliser 3 (difference 8, p < 0.0001); Fertiliser 2 vs Fertiliser 4 (difference 3.5, p = 0.019); Fertiliser 3 vs Fertiliser 4 (difference 4.5, p = 0.006).
Privacy: how it works
- Everything is calculated by code running in your browser tab. Your data is not sent to Ulkaa or to any other server, and there is nothing to sign in to.
Tips
- With only two groups, ANOVA gives the same p-value as a two-sided t test with equal variances, and F equals t squared.
- Do not run many separate t tests on the same groups. The chance of a false positive grows, which is the problem Tukey HSD solves.
- Report F with both degrees of freedom, the p-value and η², for example F(2, 15) = 9.26, p = 0.002, η² = 0.55.
- Make sure each column is a different group of independent people or items, not the same people measured repeatedly.
Frequently asked questions
Is it really free?
Yes. There is no price, no trial and no credit card. Ulkaa Tool does the work with your own device, so there is no server bill to pass on to you.
Do I need an account?
No. There is no sign-up and no login. Open the page and use it. An Ulkaa account is not needed for anything on this tool.
Does it run in my browser?
Yes. Your data are processed by code running in your browser tab, on your own device.
Is my data uploaded?
No. Your data are never sent to Ulkaa or to anyone else. You can check this yourself by watching the Network tab in your browser developer tools while you use the tool.
What does HSD stand for?
Honestly significant difference. It is the smallest difference between two means that Tukey regards as significant across all comparisons.
Why is the Tukey p-value larger than a plain t test p-value?
Tukey adjusts for making many comparisons at once. The adjustment makes each pair harder to declare significant, which protects against false positives.
Do I need a significant ANOVA first?
It is customary and sensible, but Tukey HSD has its own error control. If F is not significant, treat any single pair that Tukey flags with caution.
What if the group sizes are unequal?
The calculator uses the Tukey-Kramer adjustment, which uses both group sizes in each comparison.