Permutation test vs Mann–Whitney U test I am wondering if there exist any advantage of using the Mann-Whitney U test over a permutation test in the following setting:
Suppose I have a group of animals with eggs in their brood chamber, from this group I assign some to a control vessel and some to a treatment vessel. Then I wait till the newborns hatch in each vessel and I measure the size of the newborns.
I want to test the hypothesis that the newborns came from the same population, i.e, there is no effect of the treatment with respect to control in the size of newborns. Under this hypothesis, I can construct a permutation test to assess if the mean difference between the size of the animals in each vessel is just random or there is evidence that suggest that the difference could not have happened by chance.
Is there any reason to use Mann–Whitney U test over just this simple permutation test?

There are important reasons to use the Wilcoxon-Mann-Whitney two-sample rank-sum test in this context.  The most important reason is that the test is transformation-invariant, i.e., you get the same inference whether you log-transform the weights or not.  Secondly, this rank test is more robust to outliers.  Third, it extends to more complex situations such as needing covariate adjustment (the proportional odds model is the generalization of the Wilcoxon test).
