# About Kruskal-Wallis, Mann-Whitney U and multiple comparisons correction

I have 5 independent samples which I want to compare, to define if there are significant differences in the distribution of values across samples.

The samples' sizes are: 4562, 1116, 314, 151, 77

I don't assume that the samples are normally distributed, so I've decided to use:

• Kruskal-Wallis test to have an overall suggestion that some samples are differently distributed
• If Kruskal-Wallis p is significant ($<0.01$), I run post-hoc Mann-Whitney U test to compare each group to another
• I am running several tests, so I want to correct for multiple comparisons. I was thinking of using Benjamini-Hochberg FDR

I have several questions:

• Does the choice of these tests together make sense? Did I miss something?
• Do I have to test if the tests are sufficiently powered?
• How can I test for effect size between the samples? Just taking the difference between the medians?
• If the choice of tests makes sense, since I want to run Mann-Whitney U test on the same data used for Kruskal-Wallis, do I have to account also for that in the correction for multiple comparisons, and if yes how can I do it?
• Hey, sorry for bringing up old thread! I'm wondering on the multiple comparisons correction, did you end up applying it on top of Kruskal-Wallis, or only on your post-hoc analysis? Mar 26 at 4:38