Nonparametric Hypothesis Testing: Rank and Permutation Methods with Applications in R

4 Paired samples and repeated measures

4.1 Introduction

In this chapter, location problems in the presence of two or more related samples are presented. In related sample designs the compared samples are not independent in the sense that the ith statistical unit (observation) of one sample is associated with the ith statistical unit (observation) of each of the other samples. For example, in the two-sample test, a typical problem with related samples is the so called case-control clinical study. In this type of study, a group of cases (patients with a specific disease or risk factor) are compared with a group of controls (people who do not have the disease or the risk factor). To reduce the effect on the results of possible confounding factors, the controls are selected with the matching technique: that is for each case there is a control who is similar according to one or more variables (age, gender, ethnic group, etc.). The typical multisample problem with related samples concerns the case of repeated measure designs. In these problems data are collected on the same n statistical units in C > 2 different occasions, such that each time j corresponds to n sample data observed on the same n units. Certainly in problems with related samples only the balanced case is possible.

By assuming that n is the sample size and C the number of dependent samples, the dataset is represented by {X_ji; i = 1, …, n; j = 1, …, C}, where X_1i, represent the C data observed on the ith unit. Section ...