Introduction

In this chapter we describe some methods that can be used to diagnose qualitative relationships between a quantitative response variable, that is, a variable measured on a continuous scale, and one or more factors that are classified, perhaps according to level, or perhaps only according to their presence or absence. Our purpose is to introduce only some of the concepts of experimental design and analysis of variance (ANOVA). We illustrate the general patterns of analysis and thought with these methods using a couple of examples from the climate literature. Our coverage of the subject is necessarily far from complete. A more complete treatment of the topic can be found in Box, Hunter, and Hunter [59]. Cochran and Cox [87] provide a classical treatment. Anderson and McLean [13] provide a good description of ANOVA for nonspecialists.

Terminology and Purpose of Experimental Design. The classical setting for ANOVA and experimental design methods is agricultural experiments, so much of the associated terminology has its roots in agriculture.

For example, a typical agricultural experiment might be designed to determine the effect of two factors, say, fertilizer (applied at one of three different levels) and tillage (the land is either tilled, or not tilled before seeding) on crop yield. The experiment might be conducted as a factorial experiment in which each possible treatment combination is applied to a separate plot of land according to an experimental design.