Hi everyone,
I have an dependent ordinal variable (five point Likert item) and a nominal grouping variable with five categories and want to test for differences in the responses on the dependent variables between the categories.
For that purpose I considered applying a Kruskal-Wallis with subsequent Dunn's tests.
The problem is that by inspecting of the boxplots the distributions of the responses differ quite a much between groups.
How robust is KW to the violation of the sameness of distribution shape assumption?
What are possible alternatives to the KW in this case?
Perhaps you may try using "The two-sample Kolmogorov-Smirnov test"
described, e.g., here
https://www.mathworks.com/help/stats/kstest2.html
https://www.mathworks.com/help/stats/kstest2.html#btno0q9
Stefan Becker, just one more thing, along with robustness of a test, the power-of-a-test might also help when choosing among different statistical tests - good luck.
https://en.wikipedia.org/wiki/Power_of_a_test
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