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I have two samples of observations drawn from distributions with different variances. To test whether they have the same mean, I plan to use the function wilcox.test in R to perform a Mann-Whitney U test. I was wondering whether R's implementation of the Mann-Whitney U test only valid if the variance of the two samples are equal?

Henry
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    Why is your question particular to the R function for the WIlcoxon-Mann-Whitney test? Do you think it implements a test that is somehow not equivalent to its implementation in other packages - one with different assumptions? Or is your question not about implementation, and actually about the assumptions of the test itself? – Glen_b Nov 17 '18 at 14:45
  • I am unsure whether there are many slightly different types of Mann-Whitney U test. If there are, I would like to know whether the type implemented by wilcox.test requires the variances of the two-samples to be equal. If there are not many different types, I will edit my question to make it more general. – Henry Nov 17 '18 at 14:57
  • There are different versions of the test statistic (though correctly-calculated p-values will correspond across test statistics; the tests should be equivalent). In addition some implementations use asymptotic approximation of the null distribution rather than exact calculations (in which case there can be some variation in p-values), but they don't differ in their assumptions, which are common to all the implementations. – Glen_b Nov 17 '18 at 15:08
  • Oh okay, thank you. So is one of the assumptions that the two samples have the same variance? It doesn't mention that they must on wikipedia, but I have read in other places that it is a necessary assumption. – Henry Nov 17 '18 at 15:13
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    If you are testing dominance, you don't need to make assumptions about variance. If you want to compare medians, then both groups should only differ in location, variances should be the same. See assumptions section of aforementioned Wikipedia article https://en.wikipedia.org/wiki/Mann%E2%80%93Whitney_U_test – Heteroskedastic Jim Nov 17 '18 at 16:15
  • @Henry several questions on site discuss the assumptions of the test. I'll try to locate some for you . (Edit: one is here but there are better ones around; I'll try again later) – Glen_b Nov 17 '18 at 22:57

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