This manuscript presents some general comments about the Wilcoxon rank sum test. Even the most casual reader will gather that I am not too impressed with the scientific usefulness of the Wilcoxon test. However, the actual motivation is more to illustrate differences between parametric, semiparametric, and nonparametric (distribution-free) inference, and to use this example to illustrate how many misconceptions have been propagated through a focus on (semi)parametric probability models as the basis for evaluating commonly used statistical analysis models. The document itself arose as a teaching tool for courses aimed at graduate students in biostatistics and statistics, with parts of the document originally written for applied biostatistics classes and parts written for a course in mathematical statistics. Hence, some of the material is also meant to provide an illustration of common methods of deriving moments of distributions, etc.
Emerson, Scott S., "Some Observations on the Wilcoxon Rank Sum Test" (August 2011). UW Biostatistics Working Paper Series. Working Paper 380.