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From here and here I see that we cannot use Mann-Whitney test if symmetry assumption is violated. Which test(s) can we use instead of Mann-Whitney test for non-parametric continues data if symmetry assumption is violated? I want to compare two continues independent variables which are non-normally distributed which violates the assumption for t-test. Null hypothesis: median/mean (depending on which of them the test can for test; I think median is better in that case) of one group is similar to another. Alternative hypothesis: median/mean of groups are different.

I do not have actual data yet. I may have it soon and I need to be prepared in case I will not be able to use Mann-Whitney test if symmetry assumption is violated.

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    $\begingroup$ What are you actually testing? What are your null and alternative hypotheses? $\endgroup$ – jbowman Jan 14 at 18:16
  • $\begingroup$ @jbowman Added that information to question. $\endgroup$ – vasili111 Jan 14 at 18:32
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    $\begingroup$ "Non-parametric" can be a property of a probability model but it's not a characteristic of a variable. If you would like reasonable advice, then please supply some information about (a) the empirical distributions of these variables and (b) the null hypothesis you wish to test. $\endgroup$ – whuber Jan 14 at 18:35
  • $\begingroup$ @whuber I updated the question and I think now it looks better. If it looks good then please reopen it or please let me know what else can be added. Thank you. $\endgroup$ – vasili111 Jan 14 at 18:45
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    $\begingroup$ @whuber I do not have actual data yet. I may have it soon and I need to be prepared in case I will not be able to use Mann-Whitney test if symmetry assumption is violated. I understand that you want to make question as best as possible and I really appropriate it (no irony of any kind here). Of course it will be better to add data description to it too but as I said I do not have it and even in this state I think my question is currently valid. $\endgroup$ – vasili111 Jan 15 at 0:31
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The Mann-Whitney two-sample test does not require symmetry, and actually the two links that you give don't claim that it does. The first reference addresses the question when Mann-Whitney is a powerful test for equality of medians, but this doesn't mean you can't use it otherwise. The second link doesn't mention the term "symmetry" at all.

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