To this point we have relied on regression models where the predictor variables have been treated as continuous variables. Our purpose in this chapter and the following two is to examine our basic approach to data analysis when predictors are categorical variables. In the language of traditional statistics books, earlier chapters concerned multiple regression. The present chapter concerns oneway analysis of variance (ANOVA) models or, equivalently, models with a single categorical predictor. In the next chapter we consider models having multiple categorical predictors, or higher order ANOVA models. Chapter 10 is devoted to models in which some predictors are categorical and some are continuous. Such models have been traditionally labeled analysis of covariance models. By integrating these into a common approach, we will not only explore these traditional topics but also consider others that considerably extend the sorts of questions that we are able to ask of our data, in the context of categorical predictor variables. Throughout we will continue to use our basic approach to statistical inference, testing null hypotheses by the comparison of augmented and compact models.