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.

Keywords:

• Median
• Stochastic ordering
• Teaching statistics
• Wilcoxon-Mann-Whitney

Acknowledgments

Discussions with D. P. Harrington (Harvard School of Public Health) were very helpful while preparing this paper. Constructive remarks made by the referees are gratefully acknowledged. Substantial help from the Editor greatly improved the readability of the paper.