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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?

Silverfish
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Sam
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  • Yes, something like bootstrap or permutation test would be suitable here. – stans Feb 04 '18 at 05:47
  • Possible duplicate of [How to test for differences between two group means when the data is not normally distributed?](https://stats.stackexchange.com/questions/15664/how-to-test-for-differences-between-two-group-means-when-the-data-is-not-normall) – yoav_aaa Feb 04 '18 at 07:26
  • [The proposed duplicate](https://stats.stackexchange.com/q/15664/1352) 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. – Stephan Kolassa Feb 04 '18 at 09:09

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