Fundamentals of Statistical Experimental Design and Analysis

6Randomized Complete Block Design

Introduction

As discussed in Chapter 2, blocking of the experimental units in an experiment can be crucial to an experiment’s success and value. The choice of blocks defines the scope of the experiment and the conclusions it supports. Blocking can also increase the precision with which treatments are compared, relative to an unblocked experiment spanning the same set of experimental units. We will see later in this chapter a dramatic demonstration of the efficiency of the blocked design in the context of the boys’ shoes experiment in Chapter 3.

The randomized block design (RBD) is constructed like a collection of b separate completely randomized designs (CRD) for comparing k treatments, where b is the number of blocks. In each block, each of k treatments is randomly assigned to one or more experimental units, as in a CRD. In the simplest situation, the number of treatments equals the number of experimental units (eus) in a block, so each treatment is assigned to only one eu in each block. (As discussed later (p. 203), it is possible for there to be fewer than k eus in a block, so that not all treatments can be run in each block.) We have already seen an example of this type of a randomized block experiment: the aforementioned boys’ shoes material experiment in Chapter 3. In that experiment, there were 10 blocks (boys), each of which (whom) contained two experimental units (feet). The two treatments, shoe sole materials A and B, were assigned ...