On Thu, 31 Jan 2013 00:50:03 -0800 (PST), "Mickey M." <firstname.lastname@example.org> wrote:
>Yes, >the point was, that the weaker null hypothesis >H0: P(X>Y) = 0.5 was satisfies for both A and B. >but the distributions U1 for A and B were different. > >This casts some doubt on what is written on e.g. wikipedia: > >http://en.wikipedia.org/wiki/Mann%E2%80%93Whitney_U > >"If one is only interested in stochastic ordering of the two populations (i.e., the concordance probability P(Y > X)), the U test can be used even if the shapes of the distributions are different." > >But here is still some chance, that the test can be used "approximately" >even though the exact distribution of U1 is different than under standard >null hypothesis (equality of distributions of Xi and Yi).
Yes. Wikip seems to overstate.
By the way -- for years I have been somewhat disparaging towards rank tests. Now it turns out that I underestimated how bad they could be.