I have a relatively simple dataset comparing continuous data between 4 groups. There is heteroscedasticity between groups and the data and ANOVA residuals are not normally distributed, so I figured I would run a Kruskal-Wallis with Dunn Bonferroni post-hoc. I get significant differences between some groups as expected, but for some of these differences, the order of the difference is the opposite of what would be expected based on box-plots.
For example: the median of group 1 is 2.8 en the median of groups 2 is 9.6. The Dunn post-hoc table indicates a significant difference between both groups and gives a test statistic of (Group 2 - Group 1)= -12.58. Intuitively, I would interpret this result as " the median of group 1 is higher compared to the median of group 2", but that is clearly not true, just looking at my data. So what exactly does the test statistic learn me? I've found that Kruskal-Wallis does not test the difference between medians, but between distributions. Is it then fair to say that the median of group 2 is higher compared to the median of group 1, regardles of the test statistic?
Interestingly, when I run a Welch with Games-Howell on the same data, the results do make sense, even though Welch assumes normality and my data are not normally distributed.
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