Can I use a Mann-Whitney U Test with a very small sample? I want to compare differences between two independent groups (female and male) when dependent variables are continuous. However, my sample size is very small (N=6). I have done a Mann-Whitney U Test and I am not sure if the results are meaningful given the small sample.

This has been discussed at length on this site.  Briefly, the test is valid.  But no test is especially helpful because of our inability to interpret large p-values, which do not indicate "no difference".  Instead I would replace a test with a confidence interval or Bayesian credible interval.  These have interpretations regardless of sample size and regardless of whether a null hypothesis is true.
