When is the Wilcoxon-Mann-Whitney procedure a test of location? Implications for effect-size measures.

The Wilcoxon-Mann-Whitney procedure is invariant under monotone transformations but its use as a test of location or shift is said not to be so. It tests location only under the shift model, the assumption of parallel cumulative distribution functions (cdfs). We show that infinitely many monotone transformations of the measured variable produce parallel cdfs, so long as the original cdfs intersect nowhere or everywhere.