I have seen recent genetics articles that use principal components analysis
to calculate the number of independent statistical comparisons that result when
a large number of correlations are carried out. This reduces the
number that must
be used for multiple comparisons correction.
In that vein, I wonder how many independent statistical contrasts
result from the following scenarios, in which steps 1) 2) and 3) are
performed on the same fMRI data set:
1) whole-brain group correlation of activation with behavioral variable A.
2) whole-brain group correlation of activation with behavioral variable B.
3) whole-brain group partial correlation of activation, putting both A and
B in the model and using a contrast of [1 0] so that the variance of B is
taken into account before correlating the residuals with A.
If A and B are independent, I think there are 2 independent contrasts,
since the [1 0] contrast will be identical to the correlation with A, because
the partial correlation with B won't remove any variance related to A.
If A and B are completely dependent, i.e. identical, then 1) and 2) between them
generate 1 independent contrast. 3) is everywhere 0 and I'm not sure
it counts as
a contrast, but if it does, at most there are 2 independent contrasts.
Finally, I wonder about the middle ground where A and B are somewhat dependent.
1) and 2) would yield LESS than 2 independent contrasts, because of their
dependence, and I wonder if the limit on independent contrasts is still 2?
Many Thanks in Advance!