ABSTRACT
In this chapter, the author considers only one qualitative predictor. Although this may seem like a simple situation, he sees it holds some interest as well as forming the basis. Linear models with only categorical predictors (or factors) have traditionally been called analysis of variance (ANOVA) problems. The idea is to partition the overall variance in the response due to each of the factors and the error. This traditional approach is exemplified by Scheffé. Some insight can be gained by considering the problem from this perspective, but historically this required an increasingly complex set of specialized formulae for each type of model depending on the configuration of factors. Unbalanced designs due to missing or observational data caused a particular difficulty. The Bonferroni correction is known to be conservative, but even were the readers to use one of the more generous alternatives, the family-wise error rate restriction imposes a high bar on the identification of significant effects.
