5.1. Introduction

In many experiments, several treatments are applied to the same experimental unit at different time points, or only a single treatment is applied to a subject but the measurements on the same characteristic or set of characteristics are taken on more than one occasion. The data collected under these or similar kinds of experimental setups are often referred to as repeated measures data and require extra care in their analyses.

A common reason for taking repeated measures on the same subject in many biological, medical, psychological, and sociological experiments is the fact that there is usually more variability in the measurements between the subjects than within a given subject. Thus, to control the variability, subjects are taken as the blocks. As a result, treatments applied to the same subject provide a more comparable set of measurements than several parallel groups subjected to different treatments. The analysis, however, is complicated by the fact that the measurements taken on the same subject will most likely be correlated. The obvious lack of ability to randomize in such situations often prevents one from using the standard block design related experimental design methodology. Therefore it is necessary to incorporate this special feature of the data in the modeling and analysis.

Within the domain of repeated measures, there are certain subtle differences in the analyses, depending on the design and the data collection scheme. For example, a situation in which three different drugs are all tried on a group of 30 patients at different time periods (and possibly in different sequences) is different in design and analysis from the one in which each of the three drugs is given to a different group of ten patients who are all observed over a certain period of time. These features are very important in choosing an appropriate model, in deciding the appropriate hypotheses to be tested, and in constructing the corresponding statistical tests.

Repeated measures designs also arise naturally in many other research or industrial contexts. For example, an auto maker may be interested in the number of problems various models of cars may have over time. In order to study this, he may decide to follow up on a specific group of cars in each model for a given length of time. Similarly a soft drink manufacturer may want to compare her drink with those from some of her competitors and to do so she may decide to conduct a double-blind taste test on a group of potential consumers. A psychologist may be interested in comparing the performance of students at various schools and may administer a battery of several tests to sample groups of students from these schools. The common aspect in all these problems is that the data are multivariate in nature: on each subject we have a vector of repeated measurements which are correlated within themselves but are independent for different subjects.

This chapter considers various experimental situations where repeated measures data may arise, and concentrates on the analysis of such data. Of course, the particular approach to these analyses depends on the particular data collection scheme and therefore, various sections have been arranged by the designs under which data are collected. While most of the chapter emphasizes analyses under various designs, at the end of this chapter we also provide certain methods to generate certain relatively complex crossover designs which are extensively used in repeated measures studies.