Thank Roger. I am familiar with this program and I
have used it before. So the test really test both
hypotheses: that the difference between the median is
zero, and that the degree of non-overlap of the two
populations is zero. i.e. whether the degree of
overlap between the two populations is significantly
different than would be expected by chance alone. Is
this correct?
No and yes. The Wilcoxon ranksum test does indeed test the hypopthesis that
Somers' D is zero, where Somers' D is the difference between 2
probabilities, namely the probability that a randomly-chosen member of
Subpopulation A has a higher outcome value than a randomly-chosen member of
Subpopulation B and the probability that a randomly-chosen member of
Subpopulation B has a higher outcome value than a randomly-chosen member of
Subpopulation A. If these 2 probabilities are equal, then you can argue
that (in Ricardo's words) "the degree of non-overlap of the two populations
is zero". However, the Hodges-Lehmann median difference is not always the
difference between the 2 subpopulation medians. The Hodges-Lehmann median
difference is the median difference between 2 outcome values, assuming that
the first is sampled at random from Subpopulation A and the second is
sampled at random from Subpopulation B.
