Nonparametric hypotheses for the two-sample location problem

Abstract

Students in an applied statistics course offering some nonparametric methods are often (subconsciously) restricted in modeling their research problems by what they have learned from the t-test. When moving from parametric to nonparametric models, they do not have a good idea of the variety and richness of general location models. In this paper, the simple context of the Wilcoxon-Mann-Whitney (WMW) test is used to illustrate alternatives where "one distribution is to the right of the other." For those situations, it is also argued (and demonstrated by examples) that a plausible research question about a real-world experiment needs a precise formulation, and that hypotheses about a single parameter may need additional assumptions. A full and explicit description of underlying models is not always available in standard textbooks.