Hi Ian,
> hi all,
> i have a question about conjunctions that i'm sure has been tackled before,
> but i can't seem to find the answer.
> i have two contrasts across four conditions and all four conditions are
> in every session:
> task1hit task1miss task2hit task2miss
> 1 -1 0 0
> 1 1 -1 -1
>
> in terms of anova, my understanding is
> that these two contrasts are mutually
> orthogonal in that the rows sum to 0 and the products
> of the columns also sum to zero. however when i select
> these two contrasts in spm99 on the individual in order
> to get the conjunction, it orthogonalizes one with respect
> to the other. my question is why is it doing this given that
> they are already orthogonal....or are they not?
Your "contrast weight vectors", i.e. the row-vectors of ones and zeros above,
are orthogonal. However, the "contrast" is better thought of as the regressor
resulting from the multplication of the design matrix with the contrast weight
vector. So, for example your first "contrast" above could be thought of as the
regressor resulting from subtracting the second column from the first column
of your design matrix. Even though the contrast weight vectors are orthogonal,
the constrasts may not be.
To take a really extreme, and silly, example. Lets say you have two
regressors, a and b, and that you construct a design matrix X = [a b b b].
Your first contrast weight vector above would the result in the "contrast"
a-b, and your second contrast weight vector in the contrast a+b-b-b=a-b. Not
exactly orthogonal.
The above explanation is a bit simplified, but the main point is. Do not mix
orthogonality of contrast weight vectors with orthogonality of contrasts.
Good luck Jesper
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