INTRODUCTION

The focus in the previous chapters in Part II was on completely randomized experiments, where, in a fixed sample with N units, Nt are randomly choosen to receive the active treatment and the remaining Nc = N − Nt are assigned to receive the control treatment. We considered four modes of inference: Fisher's exact p-values and associated intervals, Neyman's unbiased estimates and repeated sampling-based large-N confidence intervals, regression methods, and model-based imputation. In addition, we considered the benefits of observing covariates, that is, measurements on the units unaffected by the treatments, such as pre-treatment characteristics. In this chapter we consider the same issues for a different class of randomized experiments, stratified randomized experiments, also referred to as randomized blocks experiments to use the terminology of classical experimental design. In stratified randomized experiments, units are stratified (or grouped or blocked) according to the values of (a function of) the covariates. Within the strata, independent completely randomized experiments are conducted but possibly with different relative sizes of treatment and control groups.

Part of the motivation for considering alternative structures for randomized experiments is interest in such experiments per se. But there are other, arguably equally important reasons. In the discussion of observational studies in Parts III, IV, V, and VI of this text, we consider methods for (non-randomized) observational data that can be viewed in some way as analyzing the data as if they arose from hypothetical stratified randomized experiments. Understanding these methods in the context of randomized experiments will aid their interpretation and implementation in observational studies.

The main part of this chapter describes how the methods developed in the previous four chapters can be modified to apply in the context of stratified randomized experiments. In most cases these modifications are conceptually straightforward. We also discuss some design issues in relation to stratification. Specifically, we assess the benefits of stratification relative to complete randomization.

In the next section we describe the data used to illustrate the concepts discussed in this chapter.