Dunn Post Hoc Test Calculator

Calculator

Alpha

P-value adjustment Holm Bonferroni Benjamini-Hochberg None

Add Group Load Example

Group 1 Remove

Group name

Values 12 15 14 11 13

Group 2 Remove

Group name

Values 19 18 20 17 21

Group 3 Remove

Group name

Values 14 16 15 13 17

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Example Data Table

Formula Used

Dunn testing compares the mean rank of each group pair after all observations are ranked together.

Mean rank for group i: R̄_i = rank sum of group i / n_i

Dunn z statistic: z = |R̄_i − R̄_j| / √[V × (1/n_i + 1/n_j)]

Tie-adjusted variance term: V = [N(N + 1) − Σ(t³ − t)/(N − 1)] / 12

Here, N is the total sample size and t is the size of each tie block. Raw two-sided p-values come from the standard normal distribution. The selected correction method then adjusts all pairwise p-values.

How to Use This Calculator

1. Enter one group per panel and give each group a clear name.
2. Paste numeric values using commas, spaces, or line breaks.
3. Choose an alpha threshold and a p-value adjustment method.
4. Run the test to place results above the form.
5. Review the omnibus summary, mean ranks, and pairwise comparisons.
6. Download CSV for spreadsheet work or PDF for reporting.

Frequently Asked Questions

1. What does Dunn post hoc testing measure?

Dunn testing checks whether two groups differ in their average rank after all observations are ranked together. It is commonly used after a rank-based omnibus test.

2. When should I use this method?

Use it when you need pairwise comparisons for independent groups and the data are ordinal, skewed, or unsuitable for equal-variance normal methods.

3. Do I need equal group sizes?

No. Dunn comparisons can handle unequal sample sizes. The denominator already accounts for the size of each group in every pairwise comparison.

4. Why are p-values adjusted?

Multiple comparisons increase false positive risk. Adjustment methods such as Holm or Bonferroni control that risk across all tested group pairs.

5. What happens when ties exist?

The calculator applies a tie correction in the variance term. That makes the z statistics more appropriate when repeated values appear across groups.

6. Can I run the test without a significant omnibus result?

You can compute it, but many analysts prefer first confirming an overall difference. Interpret isolated pairwise findings carefully when the omnibus result is not significant.

7. What does the direction field mean?

It shows which group has the higher mean rank in each pair. Higher mean rank usually indicates larger observed values for that group.

8. What should I report from the output?

Report the omnibus statistic, adjustment method, each pairwise z value, adjusted p-value, significance decision, and the direction or mean rank difference.