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.