The Two-Sample Location Problem
In this chapter the data consist of two random samples, a sample from the control population and an independent sample from the treatment population. On the basis of these samples, we wish to investigate the presence of a treatment effect that results in a shift of location. The basic hypothesis is that of no treatment effect; that is, the samples can be thought of as a single sample from one population.
Section 4.1 presents a distribution-free rank sum test for the hypothesis of no treatment effect; Section 4.2, a point estimator associated with the rank sum statistic; and Section 4.3, a related distribution-free confidence interval that emanates from the rank sum test. The basic model for Sections 4.1, 4.2 and 4.3 assumes the populations differ only by a location shift. In Section 4.4 we present a test for location differences that allows the population dispersions to differ. Section 4.5 considers the asymptotic relative efficiencies for translation alternatives of the procedures based on the rank sum statistic with respect to their normal theory counterparts based on sample means.