In the ideal case where the regressors (columns) of your design matrix are orthogonal (e.g, if you have a 2nd-level design with equal numbers of subjects in each condition A to C), and the error is i.i.d (white), then all that matters is whether your contrast weights are orthogonal.
If so, then taking your first example, and assuming your conditions are ordered [A B C], then you cannot use contrast weights [1 -1 0] to select a region from which to extract data (or use for SVC) for a second contrast with weights [1 0 -1] without inducing some statistical bias (since [1 -1 0]*[1 0 -1]' ~= 0).
In your second example, where you split condition A into two halves A1 and A2, and use contrast weights [1/2 1/2 0 -1] (ordered [A1 A2 B C]) to select a region for subsequent testing of [1 -1 0 0], then the contrast weights (and regressors) are orthogonal, but the error may not be i.i.d (variance associated with the A1 and A2 estimates is likely to be greater). The deviation from i.i.d. is unlikely to be large though.
If you have correlated regressors (e.g, in a 1st-level fMRI design), then you could use the conjunction option to create orthogonal contrasts (contrasts are a function of the contrast weights and the design matrix). There may also be (auto)correlation in the error, but again this should be small. For a more precise answer, see Karl's email:
From: SPM (Statistical Parametric Mapping) [[log in to unmask]] on behalf of elise metereau [[log in to unmask]]
Sent: 20 May 2010 18:59
To: [log in to unmask]
Subject: [SPM] non independent analyses ?
Dear SPM experts,
I have made some reading on the issue of non-independent analyses and
"double dipping", and now I'm wondering about non independence -and thus
validity- of the following analyses:
1) Let's say I have an fMRI experiment with 3 conditions A, B and C. The
contrast A>B gives a significant cluster. Now I want to make sure that
the contrast A>C is also significant in this region, and to this aim I
extract the % signal change from the above cluster (separately for each
particpant and each condition) and compare the A and C conditions using
a paired t-test. Is such an ROI analysis valid or considered a case of
non independence ? (I could also use a whole-brain mask, but considering
I'm focusing on one particular cluster, I'm wondering whether the less
conservative ROI approach might not be sufficient)
2) Let's say I'm comparing condition A versus a control condition C and
find a significant cluster. Let's now imagine that condition A can
actually be split into 2 categories A1 and A2, and that I want to
determine whether activity in the previous cluster is modulated by these
categories. Similarly, is it valid to compare A1 versus A2 in this ROI,
or is it a case of non independence ?
Any insight will be greatly appreciated.