Complete Block Designs

Just as a oneway anova is a generalization of a two-sample

t

-test, a randomized complete block (RCB) design is a generalization of a paired

t

-test. In this first section we review some basics and do a small example, and show how to build up an RCB from pairwise

t

-tests.

In this book we discuss two types of block effects, fixed and random. In most textbooks blocks are treated as a random effect without much discussion of options, but there are clear instances where blocks are not random (see Example 4.1). However, in such cases these factors are still blocks because of the randomization pattern they induce and, in particular, the covariance structure they induce. We focus on this, and look very carefully at how to model the covariance, which we find is the overwhelmingly important concern. Whether the block is fixed or random is a function of the particular experiment, as long as the covariance is correctly accounted for then valid inferences can be drawn.

In this chapter we will mainly concentrate on the classical approach with the blocks considered as random, leaving details of fixed blocks models and implications to Chapter 4.