GLM Introductory Overview - Main Effect ANOVA

Main effect ANOVA designs contain 2 or more categorical predictors that are assumed to affect the response additively, that is, without any interactions. 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. Using the overparameterized model, the matrix X defining the between design is

Comparing the two types of coding, it can be seen that the overparameterized coding takes almost twice as many values as the sigma-restricted coding to convey the same information.

Between-subject designs

Within-subject (repeated measures) designs

Multivariate designs