ABSTRACT
There are several reasons to discuss the analysis of variance here. First, it can be developed as an extension of multiple regression, in a form known as the general linear model. The geometry of this approach gives considerable insight into the analysis of multifactor designs, particularly those in which the groups have unequal sizes. Second, integration of the analysis of variance into the regression framework allows examining a mixture of categorical and graded variables within a single analysis. Finally, the analysis of variance provides the framework for two techniques that are truly multivariate: the analysis of covariance and the multivariate analysis of variance. The flexibility of the regression-based analysis of variance allows it to treat data from unequally sized groups in a way that the conventional formulation of the analysis of variance cannot do. Most analysis-of-variance designs have a rich organization of the groups; in a factorial design, the groups are classified along two or more dimensions or factors.
