I use Stata to perform a Kruskal-Wallis test on four groups of data (not normally distributed), and the results are shown below:
Kruskal-Wallis equality-of-populations rank test
+------------------------+
| group | Obs | Rank Sum |
|----------+-----+-------|
| 1 | 7 | 136.00 |
| 2 | 7 | 64.50 |
| 3 | 7 | 134.00 |
| 4 | 7 | 71.50 |
+------------------------+
chi-squared = 9.533 with 3 d.f.
probability = 0.0230
chi-squared with ties = 9.538 with 3 d.f.
probability = 0.0229
It is fine to conclude from above that there is significant difference between these 4 groups of data. But I wonder how to interpret the rank sums output by this test as shown above: can we actually say that group 1
and group 3
$>$ group 2
and group 4
based on the ranks above? If not, what does a difference in the rank sum between two groups mean here?