Fundamentals of Statistical Experimental Design and Analysis

4Completely Randomized Design

Introduction

In both of the tomato fertilizer experiments in Chapter 3, the gardener set out several tomato plants in her garden and randomly assigned one of two fertilizers to each of them. Her experiment is the simplest example of the experimental design that is called the “completely randomized design (CRD),” which is the topic of this and the following chapter. The tomato experiment had a single qualitative treatment factor (fertilizer), and this factor had two discrete, qualitative levels (brands A and B in the first experiment, brands A and C in the second).

In the general case of a CRD, there are k (= two or more) treatments. In this chapter, these k treatments are the k selected levels of a single treatment factor. Chapter 5 addresses the situation in which the treatments are combinations of various levels of two or more factors. The experimental units (eus) to which the treatments are applied are a single group of essentially homogeneous entities, like laboratory mice, plots of land, or people in a certain demographic or medical group. There are no distinguishing characteristics on which one might group, or block, the experimental units. Blocked designs are addressed in Chapters 6 and 7.

In a CRD, the assignment of treatments to experimental units is, as the label implies, completely randomized: n_i eus are selected at random to receive level i of the treatment factor, i = 1, …, k. The numbers of eus that receive each treatment are often ...