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Just a note

In pooling samples A&B you force the nil hypothesis to be true. So, provided no two values in A and B are the same, if you were to randomly class one of that pooled set of values as 'A' and class another as 'B', you are equally likely to observe A>B as B>A. In which case A-B is equally likely to be positive as negative. In other words P(A>B) = P(B>A) = 0.5. Similarly, we would expect the median difference between those pairs of randomly selected values, M(A-B), will equal zero. Expressed as a parameter of the null model, this Hodges-Lehmann difference, HLδ = 0.

If however we randomly select one value from sample A and compare it with a randomly selected value from sample B, and repeat that enough times, we are likely to find P(A>B) differs substantially from 0.5 and M(A-B) is not 0. In that case their observed median difference, HLd, will deviate from HLδ. Of course the null model assumes values from the null population are assigned to samples A&B at random so, if that model is correct, any difference between HLd and HLδ has arisen by simple chance.

The WMW test assesses the probability, under this nil hypothesis, of observing a value as or more deviant than the observed HLd.