In this chapter, the authors discuss one-way analysis of variance models or, equivalently, models with a single categorical predictor. For any given categorical predictor, there are an infinite number of sets of contrast codes that could be used. Serious interpretative errors can ensue if one thinks that a given categorical predictor codes a particular mean difference when it is embedded in a nonorthogonal set. The important point is that predictors that code the levels of a categorical independent variable will not yield coefficients that equal the expected mean differences and their associated squares reduced unless a full set of orthogonal contrast-coded predictors is used. The authors’ also discuss the general strategy for testing any mean difference that was of interest in designs with multiple levels of a categorical independent variable. The intercept in the augmented model, the one making predictions conditional on group, is the mean of the group means.