I have a four distributions: A,B,C,D. A has 55 observations, B has 30, C has 110, and D has 13. the four distributions are non normal and have unequal variance.

I would like to test to see if the means between any of the four are significantly different. I as wondering what is a robust way of testing this.

I came across doing a permutation test. However, in the cases that I saw, this was done between two distributions. Would a permutation test be appropriate in my case?

  • $\begingroup$ Yes, something like bootstrap or permutation test would be suitable here. $\endgroup$ – stans Feb 4 '18 at 5:47
  • $\begingroup$ Possible duplicate of How to test for differences between two group means when the data is not normally distributed? $\endgroup$ – yoav_aaa Feb 4 '18 at 7:26
  • $\begingroup$ The proposed duplicate looks at comparing two samples (i.e., at alternatives to t-tests), whereas the present question looks at four (i.e., alternatives to ANOVA). Since you are asking about "means between any of the four", you could run six t-tests (or alternatives as per the proposed duplicate) and correct for multiple tests. Conversely, if you are really looking whether all four of your means are equal (note that this is a different question!), we can write up a simple permutation analogue of ANOVA. Please clarify if the dupe is enough. $\endgroup$ – Stephan Kolassa Feb 4 '18 at 9:09

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