Introduction

The previous two chapters have been concerned with relatively simple experiments involving for the most part the comparison between a control group and a treated group of experimental units. In the present chapter the discussion turns to designs that can be used to compare either the effects of several levels of a single type of treatment or several levels of different types of treatment. The designs to be discussed have quite complex structures in some cases, with correspondingly complex analyses of data. As such, a detailed review of all methods of analysis is beyond the scope of this book. Instead, the treatment here will be largely restricted to the description of the designs and to the assumptions involved in their use. It is assumed that most researchers will have at their disposal one of the standard computer packages for analysing the results of designed experiments, so that what is important is a knowledge of which designs can be used and a general knowledge of the principles that are used for their analysis rather than the ability to carry out the calculations.

Factorial experiments and the analysis of variance

In the terminology of experimental design a factor is simply a classification of experimental units, and a factorial experiment is one in which all combinations of the factors being considered are tested. Three examples are as follows:

1. (a) Thirty subjects are allocated at random to three groups of ten subjects, each group is given a different dose of a drug, and the mean scores for the three groups are compared. This is a one factor experiment

2. […]