Ben,

I have one follow up question. How come EV1 serves as the mean for the third group (in this case controls)? Why wouldn't I set up a fourth variable that is "0's" for everyone but "1" for the last 3 subjects (in my example from the past email). Does this not allow for a proper ANOVA? I guess I was able to extract the steps, but I'm just missing a piece of the logic behind setting up this matrix.

Grp EV1 (control) EV2 (PtGrp1) EV3 (PtGrp2)
1 1 1 0
1 1 1 0
1 1 1 0
1 1 0 1
1 1 0 1
1 1 0 1
1 1 0 0
1 1 0 0
1 1 0 0

Setting up a fourth variable would lead to a linearly-dependent design matrix. I.e. the sum of EV2, EV3 and (your proposed) EV4 would equal EV1. If you dropped the grand mean covariate, you could take the approach you suggest, and, in fact, that's the dummy variable approach taken in http://www.fmrib.ox.ac.uk/fsl/feat5/detail.html#FTests .

-Tom

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Thomas Nichols, PhD
Director, Modelling & Genetics
GlaxoSmithKline Clinical Imaging Centre

Senior Research Fellow
Oxford University FMRIB Centre