Loading...
Loading...
The exact critical value of H for comparing three small groups by rank, computed exactly rather than by the chi-square approximation.
| n1, n2, n3 | α = 0.1 | α = 0.05 | α = 0.01 |
|---|---|---|---|
| 2, 2, 2 | 4.5714 | — | — |
| 2, 2, 3 | 4.5000 | 4.7143 | — |
| 2, 2, 4 | 4.4583 | 5.3333 | — |
| 2, 2, 5 | 4.3733 | 5.1600 | 6.5333 |
| 2, 3, 3 | 4.5556 | 5.3611 | — |
| 2, 3, 4 | 4.5111 | 5.4444 | 6.4444 |
| 2, 3, 5 | 4.6509 | 5.2509 | 6.9091 |
| 2, 4, 4 | 4.5545 | 5.4545 | 7.0364 |
| 2, 4, 5 | 4.5409 | 5.2727 | 7.2045 |
| 2, 5, 5 | 4.6231 | 5.3385 | 7.3385 |
| 3, 3, 3 | 4.6222 | 5.6000 | 7.2000 |
| 3, 3, 4 | 4.7091 | 5.7909 | 6.7455 |
| 3, 3, 5 | 4.5333 | 5.6485 | 7.0788 |
| 3, 4, 4 | 4.5455 | 5.5985 | 7.1439 |
| 3, 4, 5 | 4.5487 | 5.6564 | 7.4449 |
| 3, 5, 5 | 4.5451 | 5.7055 | 7.5780 |
| 4, 4, 4 | 4.6538 | 5.6923 | 7.6538 |
| 4, 4, 5 | 4.6681 | 5.6571 | 7.7604 |
| 4, 5, 5 | 4.5229 | 5.6657 | 7.8229 |
| 5, 5, 5 | 4.5600 | 5.7800 | 8.0000 |
n1, n2, n3 are your three group sizes, listed smallest to largest — look up your sizes in that sorted order regardless of which group is which, since H doesn't depend on group labeling. A dash means no value of H is significant at that α with such small samples. Reject the null hypothesis of no group difference if your computed H is at or above the tabled value. For sample sizes outside this table, use the chi-square distribution with k−1 degrees of freedom as an approximation.