Analysis of Variance: Multiple Regression Approaches

Abstract

Abstract One‐way and factorial independent‐means analysis of variance (ANOVA) can be accomplished via a multiple regression analysis (MRA) in which the dependent variable is predicted from sets of level‐membership variables or, preferably, contrast variables representing the factors. Doing so can be useful in the two‐group design in that it provides an easily interpretable and often remarkably low estimate of the proportion of variance in the dependent variable, that is accounted for by an experimental manipulation. It also helps in the choice among alternative approaches to analyzing unequal‐ n factorial designs by showing that full‐model analyses involve the comparison of unweighted means and that testing an effect uncorrected for any other effects implies making comparisons among weighted means. Furthermore, testing an effect corrected for confounds with some, but not all, other effects involves comparisons among the means that are difficult to characterize, require hand computations beyond those provided by ANOVA computer programs, and are unlikely to be of any real interest to the researcher. SPSS commands for carrying out factorial ANOVA via the MANOVA and REGRESSION commands are provided.