Dear List members,
I was wondering if anyone could help me understand the difference between similar design matrices (second level) or point me to the right references. In the first case, we have one categorical variable with two levels, one continuous variable, their interaction and say a further nuisance variable.
Two test the interaction, in Design 1: [0 0 1 -1 0], in Design 2 [0 0 1 0]. They yield similar results, but are they equivalent? (C & D are centred, otherwise please ignore the actual numbers). Each row is one participant.
Design 1
A B C*A C*B D
1 0 -20 0 -4
1 0 5 0 5
0 1 0 20 -5
0 1 0 -5 4
0 1 0 0 0
Design 2
GROUP C GROUP*C D
1 -20 -20 -4
1 5 5 5
-1 20 -20 -5
-1 -5 5 4
-1 0 0 0
In the case of two categorical variables, would Design 3 (to test interaction: [0 0 1]) be equivalent to Design 4 (where the interaction is tested by contrast [1 -1 -1 1]? (And similar for main effects, if the interaction is not significant: e.g. for A, in design 3: [1 0] (A*B has been dropped), in design 4: [1 1 -1 -1].)
Design 3
A B A*B
1 1 1
1 -1 -1
-1 1 -1
-1 -1 1
Design 4
A1B1 A1B2 A2B1 A2B2
1 0 0 0
0 1 0 0
0 0 1 0
0 0 0 1
Many thanks for your help!
Yannis
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