According to the documentation (link):

MannWhitneyTest[{data1,data2}] tests whether the medians of data1 and data2 are equal.

However, as per discussion on Stack Exchange (link), this test is not verifying an important assumption prior to doing the test, nor is it stated anywhere in the documentation that this is assumed: both data1 and data2 should exhibit similar shapes so that the MannWhitneyTest effectively compares medians.

I believe this is an important problem in this test and should be easily fixed by running for instance the Kolmogorov-Smirnov test prior to the Mann-Whitney test.

I would appreciate if you could let me know if I am wrong or could provide any insight regarding this issue.

Thanks