GLM Introductory Overview - One-Way Within-Subject Designs
The example algebra skills study with the Time repeated measures factor (see also Within-Subjects Design Overview) illustrates a one-way within-subject design. In such designs, orthonormal contrast transformations of the scores on the original dependent Y variables are performed via the M transformation (orthonormal transformations correspond to orthogonal rotations of the original variable axes). If any b0 coefficient in the regression of a transformed T variable on the intercept is non-zero, this indicates a change in responses across the levels of the repeated measures factor, that is, the presence of a main effect for the repeated measure factor on responses.
What if the between design includes effects other than the intercept? If any of the b1 through bk coefficients in the regression of a transformed T variable on X are non-zero, this indicates a different change in responses across the levels of the repeated measures factor for different levels of the corresponding between effect, i.e., the presence of a within by between interaction effect on responses.
The same between-subject effects that can be tested in designs with no repeated-measures factors can also be tested in designs that do include repeated-measures factors. This is accomplished by creating a transformed dependent variable which is the sum of the original dependent variables divided by the square root of the number of original dependent variables. The same tests of between-subject effects that are performed in designs with no repeated-measures factors (including tests of the between intercept) are performed on this transformed dependent variable.
Between-subject designs
Within-subject (repeated measures) designs
Multivariate designs