Enter Group Data
Use commas, spaces, semicolons, or line breaks between numbers.
Example Data Table
This example mirrors the prefilled values shown in the calculator.
| Group | Values | Count |
|---|---|---|
| Control | 12, 15, 14, 10, 13 | 5 |
| Method A | 18, 21, 17, 19, 20 | 5 |
| Method B | 25, 24, 27, 26, 23 | 5 |
| Method C | 14, 16, 15, 13, 17 | 5 |
Formula Used
1) Rank all pooled observations
Combine every value from every group, sort them, and assign average ranks when ties occur.
2) Compute each group mean rank
Mean Rank_i = Rank Sum_i / n_i
3) Dunn z statistic
z = (Mean Rank_i - Mean Rank_j) / sqrt(V × (1/n_i + 1/n_j))
4) Tie-adjusted variance base
V = N(N+1)/12 - Σ(t³ - t) / [12(N-1)]
5) Two-sided p-value
p = 2 × (1 - Φ(|z|)), where Φ is the standard normal cumulative function.
6) Multiple-comparison adjustment
This page supports Holm, Bonferroni, Benjamini-Hochberg, or no correction.
How to Use This Calculator
- Enter at least three groups. Keep each group in its own box.
- Separate values with commas, spaces, semicolons, or line breaks.
- Choose your preferred multiple-testing adjustment method.
- Set the alpha level and display precision.
- Click Run Dunn Test to compute all pairwise comparisons.
- Review the summary table, significance table, and chart.
- Download CSV for spreadsheet work or PDF for reports.
- Use the example button if you want a ready-made demonstration dataset.
Frequently Asked Questions
1) What does the Dunn test measure?
It compares group mean ranks after pooled ranking. It helps identify which specific pairs differ after a Kruskal-Wallis analysis suggests that not all groups behave the same.
2) When should I use this calculator?
Use it for independent groups when data are ordinal, skewed, or non-normal. It is especially useful after Kruskal-Wallis when you need pairwise follow-up comparisons.
3) Why are there adjusted p-values?
Many pairwise tests increase false-positive risk. Adjustment methods reduce that risk by making significance decisions more conservative or better controlled across all comparisons.
4) Which adjustment method should I choose?
Holm is a strong general choice. Bonferroni is stricter. Benjamini-Hochberg controls false discovery rate and is often useful when you expect several real differences.
5) Can I include tied values?
Yes. The calculator applies tie-adjusted variance and tie correction. That makes the ranking-based comparison more appropriate when repeated values appear across groups.
6) Does a larger mean rank imply a larger raw value distribution?
Usually yes in a rank-based sense. A larger mean rank indicates that observations from that group tend to appear higher when all observations are ranked together.
7) Is this calculator suitable for paired samples?
No. Dunn testing here is for independent groups. For repeated or paired data, use a method designed for matched observations instead.
8) What should I report from the results?
Report the Kruskal-Wallis result, the chosen adjustment method, each pairwise comparison, z scores, adjusted p-values, and which comparisons stayed significant at your selected alpha.