A Handbook for Data Analysis in the Behavioral Sciences: Statistical Issues

By Gideon Keren; Charles Lewis | Go to book overview

1 Elements of the General Linear Model

Maurice Tatsuoka Educational Testing Service


INTRODUCTION

It has been commonplace at least since the mid- 1960s to hear of the general linear model (or the general linear hypothesis) being used in computer programs for carrying out significance tests in the analysis of variance (ANOVA) or analysis of covariance (ANCOVA) and their multivariate counterparts (MANOVA and MANCOVA). This may seem to some readers like a major departure from the customary F ratio (MSh/MSe) approach to significance testing in this field. The two approaches are, however, very closely related. It might be more accurate to say that the general linear model is just an alternative, more general and more rational way to get to the significance-test F ratio than is the "traditional" way of partitioning the total sum of squares somewhat arbitrarily into various components.

The word "traditional" used in referring to the customary partitioning of sums of squares is placed in quotation marks because, in a way, the general linear model approach (or a precursor of it) is the older and hence the more traditional approach. This is because Fisher, the originator of ANOVA (and many other statistical techniques) initially used multiple regression analysis (which is basically what the general linear model is) to carry out multigroup significance testing. The multiple regression approach was feasible for the simplest cases (i.e., one-way design problems) of ANOVA, but for factorial and more complicated designs the computational difficulty proved to be insurmountable in the precomputer days. It was largely for this reason that Fisher invented what we now know as the traditional variance-partitioning approach to ANOVA. It may thus be said that the widespread availability of computers has restored multiple

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