Dear Rik,
Thank you very much for your detailed and clear response, it helps a
lot. If you don't mind I have a quick related question which actually
concerns the use of unbiased statistics in the context of forward
inferences. Let's say I identified, based on a whole-brain analysis, 2
regions that respond to opposite contrasts (i.e. A>B in region 1 and B>A
in region 2). If I want to make the point of a qualitative difference
between regions 1 & 2, I need to show a common activation/deactivation
of A or B vs C in both regions 1 & 2 (eg A>C in regions 1 & 2). Now if I
correctly understand your previous response, it seems that testing the
A>C difference in regions 1 & 2 only (by means of an ROI analysis) is
not correct, and that I should instead use a whole-brain mask of the A>C
contrast to avoid any statistical bias. Am I correct ?
Thanks a lot again for your time and help, I really appreciate it.
Sincerely,
Elise
Le 20/05/2010 21:11, Rik Henson a écrit :
> Elise -
>
> 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:
>
> https://www.jiscmail.ac.uk/cgi-bin/wa.exe?A2=ind0904&L=SPM&P=R89389&I=-3
>
> Best wishes
> Rik
>
> ________________________________________
> 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.
> Best,
>
> Elise
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