Nonparametric Statistical Methods, 3rd Edition

Chapter 3

The One-Sample Location Problem

Introduction

The procedures of this chapter are designed for statistical analyses in which primary interest is centered on the location (median) of a population. We encounter two types of data for which such analyses are important. The first of these, referred to as paired replicates data, represents pairs of “pretreatment” and “posttreatment” observations; here, we are concerned with a shift in location due to the application of the “treatment.” The second type of data, referred to as one-sample data, consists of observations from a single population about whose location we wish to make inferences.

In Sections 3.1–3.3, procedures are considered for analyzing paired replicates data using signed ranks. In particular, Section 3.1 presents a distribution-free signed rank test; Section 3.2, a point estimator associated with the signed rank statistic; and Section 3.3, a related distribution-free confidence interval. In Section 3.7, these procedures are applied to some one-sample data. An asymptotically distribution-free test for symmetry of the underlying population (one of the assumptions in Sections 3.1–3.3 and 3.7) is considered in Section 3.9. A distribution-free test for exchangeability of the paired replicates data is discussed in Section 3.10.

Procedures for analyzing paired replicates data using signs are discussed in Sections 3.4–3.6. A distribution-free sign test is considered in Section 3.4, a point estimator associated with the sign ...