GLM Introductory Overview - Multivariate Approach to Repeated Measures
When the repeated measures factor has more than 2 levels, then the M matrix will have more than a single column. For example, for a repeated measures factor with 3 levels (e.g., Time 1, Time 2, Time3), the M matrix will have 2 columns (e.g., the two transformations of the dependent variables could be (1) Time 1 vs. Time 2 and Time 3 combined, and (2) Time 2 vs. Time 3). Consequently, the nature of the design is really multivariate, that is, there are two simultaneous dependent variables, which are transformations of the original dependent variables. Therefore, when testing repeated measures effects involving more than a single degree of freedom (e.g., a repeated measures main effect with more than 2 levels), you can compute multivariate test statistics to test the respective hypotheses. This is a different (and usually the preferred) approach than the univariate method that is still widely used. For a further discussion of the multivariate approach to testing repeated measures effects, and a comparison to the traditional univariate approach, see the Sphericity and Compound Symmetry topic of the ANOVA/MANOVA module.
Between-subject designs
Within-subject (repeated measures) designs
Multivariate designs