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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?

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    $\begingroup$ @whuber, thank you for pointing me to a related question which solves parts of my questions. Still, how do we interpret the rank sums in the output of Kruskal-Wallis test? What does a difference between two groups in rank sum mean here? $\endgroup$ – skyork Oct 29 '14 at 8:45
  • $\begingroup$ That's a good question. If you would edit your post to focus on this issue of post hoc testing, I would be glad to vote to reopen it. $\endgroup$ – whuber Oct 29 '14 at 13:32
  • $\begingroup$ @whuber, done, I have edited the question to focus on the rank sums part. $\endgroup$ – skyork Oct 29 '14 at 16:48

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