Dear Richard,
In relation to your reply to Timm Strotmann I just wanted to confirm
that I agree with everything you said. The design is multifactorial in
that there is a condition factor (Levels A,B) and a parametric factor.
The design is unbalanced in that the parametric factor is 0 under level
A of the the condition factor. This renders the simple main effect of
parameter (under B) and the difference (under A and B, i.e. the
interaction) the same. Therefore there are only two effects (i.e. the
two contrasts you described). Your point about mean correcting the
parameter within level B is crucial and corresponds to orthogonalizing
the parametric factor w.r.t. the condition factor so that the modelled
variance is partitioned in an orthogonal way and the ensuing contrasts
are sensible.
Best wishes and thanks - Karl
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