The R Book, 2nd Edition

Chapter 11

Analysis of Variance

Instead of fitting continuous, measured variables to data (as in regression), many experiments involve exposing experimental material to a range of discrete levels of one or more categorical variables known as factors. Thus, a factor might be drug treatment for a particular cancer, with five levels corresponding to a placebo plus four new pharmaceuticals. Alternatively, a factor might be mineral fertilizer, where the four levels represent four different mixtures of nitrogen, phosphorus and potassium. Factors are often used in experimental designs to represent statistical blocks; these are internally homogeneous units in which each of the experimental treatments is repeated. Blocks may be different fields in an agricultural trial, different genotypes in a plant physiology experiment, or different growth chambers in a study of insect photoperiodism.

It is important to understand that regression and analysis of variance (ANOVA) are identical approaches except for the nature of the explanatory variables. For example, it is a small step from having three levels of a shade factor (say light, medium and heavy shade cloths) then carrying out a one-way ANOVA, to measuring the light intensity in the three treatments and carrying out a regression with light intensity as the explanatory variable. As we shall see later on, some experiments combine regression and ANOVA by fitting a series of regression lines, one in each of several levels of a given factor (this ...