Some issues in the simulation of ANOVA by multiple regression techniques

Abstract

A major contribution to research in psychology and education was made by Cohen (1968) in a clear and convincing demonstration of the equivalence of analysis of variance (AV) and multiple regression (MR) techniques. Cohen's appealing thesis consisted of two simple points. Firstly, any AV solution can be simulated using MR. Secondly, and more importantly, MR offers a number of practical advantages not realisable within the AV framework. Fundamentally, MR differs from AV in terms of the added f lexibi l i ty it offers the researcher. For example, within the AV framework, any continuous independent variable like IQ must be reduced to a number of "pseudo<lualitative" categories (Hurst, 1970, p. 541). But Cohen (1968, p. 441) has claimed that this "wi l ful degradation of available measurement information has a direct consequence in the loss of statistical power", while Kerlinger and Pedhazur (1973, Ch. 10) have provided numerical examples illustrating this loss of power. By permitting the use of continuous predictor variables, MR overcomes this important l imitation present with AV. MR not only allows the inclusion of the same interactions which are found with AV but, also, permits the option of excluding some interactions when desired. This point has been graphically illustrated in Cohen's following remarks: