Introduction

This chapter describes two slightly more complex ANOVA models often used by life scientists, but an understanding of these is not essential if you are reading this book as an introduction to biostatistics. If, however, you need to use more complex models, the explanations given here for two factor ANOVA without replication and nested ANOVA are straightforward extensions of the pictorial descriptions in Chapters 9 and 11 and will help with many of the ANOVA models used to analyse more complex designs.

Two factor ANOVA without replication

This is a special case of the two factor ANOVA described in Chapter 11. Sometimes an orthogonal experiment with two independent factors has to be done without replication, because there is a shortage of experimental subjects or the treatments are very expensive to administer. The simplest case of ANOVA without replication is a two factor design. You cannot do a one factor ANOVA without replication.

The data in Table 13.1 are for a preliminary trial of two experimental drugs ‘Proshib’ and ‘Testoblock’, which were being evaluated, together with a control treatment, for their effect on the growth of solid tumours of the prostate, in combination with three levels of radiation therapy (high, medium, and low). The researcher had only nine consenting volunteers with advanced prostate cancer, so an orthogonal design was only possible without replication.