Calculator
Enter at least three independent groups. Each group needs two or more values. Use commas, spaces, semicolons, or new lines between numbers.
Example data table
These example values match the default sample loaded into the calculator.
| Observation | Method A | Method B | Method C | Method D |
|---|---|---|---|---|
| 1 | 10 | 15 | 8 | 18 |
| 2 | 12 | 14 | 9 | 17 |
| 3 | 9 | 13 | 7 | 16 |
| 4 | 11 | 16 | 10 | 19 |
| 5 | 13 | 14 | 8 | 18 |
Formula used
1) Rank all observations together.
Combine every value from all groups, sort them, and assign average ranks to tied values.
2) Kruskal-Wallis omnibus statistic.
H = [12 / (N(N+1))] × Σ(Ri² / ni) − 3(N+1)
Here, Ri is the rank sum for group i, ni is that group size, and N is the total sample size.
3) Tie correction.
C = 1 − Σ(t³ − t) / (N³ − N)
The corrected Kruskal-Wallis value is H* = H / C, where t is each tie block size.
4) Conover-Imán pairwise statistic.
t(i,j) = |R̄i − R̄j| / √[ s² × ((N−1−H*) / (N−k)) × (1/ni + 1/nj) ]
s² = [Σ(r²) − N(N+1)² / 4] / (N−1)
R̄i and R̄j are mean ranks for groups i and j. The calculator uses the Student t distribution with N − k degrees of freedom.
5) Multiple-comparison adjustment.
Adjusted p-values can be reported with None, Bonferroni, Holm, or Benjamini-Hochberg correction, depending on your selected option.
How to use this calculator
- Enter each independent group in its own card.
- Type a group name, then paste its observations.
- Separate values with spaces, commas, semicolons, or new lines.
- Choose the significance level and p-value adjustment method.
- Set the number of decimals you want displayed.
- Click Run Conover Imán Test.
- Read the omnibus Kruskal-Wallis result first.
- Then inspect the pairwise table, charts, and exports.
Frequently asked questions
1) What does the Conover Imán test do?
It compares every pair of groups after a Kruskal-Wallis analysis. The method uses pooled rank information to identify which specific group pairs differ.
2) When should I use this calculator?
Use it when you have three or more independent groups, ordinal or nonnormal data, and you want post hoc pairwise comparisons after rank-based testing.
3) Do group sizes need to match?
No. Unequal group sizes are allowed. The calculator uses each group’s own sample count inside the standard error term.
4) How are ties handled?
Tied observations receive average ranks. A tie-correction factor is also applied to the Kruskal-Wallis step so the omnibus result stays properly adjusted.
5) Which p-value adjustment should I choose?
Holm is a strong default for familywise error control. Bonferroni is stricter. Benjamini-Hochberg is useful when controlling false discovery rate is more appropriate.
6) What if the omnibus test is not significant?
Pairwise outputs can still be viewed, but interpretation should be cautious. Many analysts prefer strong pairwise claims only when the overall test shows evidence of group differences.
7) Why does the calculator show mean ranks?
The Conover-Imán procedure compares groups through ranks, not raw means. Mean ranks help you see which groups tend to hold higher or lower positions overall.
8) Can I export the results?
Yes. The page includes CSV export for pairwise results and PDF export for the results report area, making documentation and sharing easier.