GRM Introductory Overview - Main Effect ANOVA

Main effect ANOVA designs contain separate one-way ANOVA designs for 2 or more categorical predictors. A good example of main effect ANOVA would be the typical analysis performed on screening designs as described in the context of the Experimental Design module.

Consider 2 categorical predictor variables A and B each with 2 categories. Using the sigma-restricted coding, the X matrix defining the between design is

Note: if there are equal numbers of cases in each group, the sum of the cross-products of values for the X1 and X2 columns is 0, for example, with 1 case in each group (1*1)+(1*-1)+(-1*1)+(-1*-1) = 0.

Between-subject designs

Multivariate designs