Dear Antonia,
since I’m not a real SPM expert please consider my suggestions with caution:
If the order of condition in your design matrix is AB, Ab, aB, ab
the main effect of A (A-a) is computed by 1 1 -1 -1 and
the main effect of B (B-b) by -1 -1 1 1.
The interaction results in voxels that are differentially affected by A and
B, i.e. in which the difference of A-a in B significantly differs from A-a
in b (a difference in the difference):
(AB-aB)-(Ab-ab): 1 -1 -1 1
(aB-AB)-(ab-Ab): -1 1 1 -1
If you are interested in the voxels that are activated in A-a AND B-b then
separately compute the main effect of A and B for each subject. Determine
your contrast for A at the designated threshold on the second level using a
one-sample t-test and create a binary mask using imcalc (i1>0). Then
calculate the main effect for B explicitly masked with your A-a-Mask.
On the same way you can again create a second mask (A-a AND B-b-Mask) and
mask a third contrast.
However, as far as I know, it is also allowed to calculate a conjunction
analysis on the second level with SPM99 if there is no reason to assume a
violation of the sphericity assumption. In SPM2 you have the possibility to
take into account such violations.
I hope this is all correct and helps…
Stefan
-----------------------------------------
Dipl.-Psych. Stefan Fischer
University Clinics Innsbruck
Department of General Psychiatry
Sleep Laboratory
Anichstraße 35
6020 Innsbruck
Austria
Phone: +43 512 504 23621
Fax: +43 512 504 23628
Email: [log in to unmask]
-----Ursprüngliche Nachricht-----
Von: SPM (Statistical Parametric Mapping) [mailto:[log in to unmask]] Im
Auftrag von Antonia Hamilton
Gesendet: Freitag, 20. August 2004 16:27
An: [log in to unmask]
Betreff: [SPM] combination of main effects
I hope this question isn't too foolish, but it is one that has been
annoying me for a while. Is it valid, or does anyone ever look for a
combination of main effects?
For example, I have a 2x2 factorial design with factors Alpha and Beta, so
I have 4 conditions AB, Ab, aB and ab. I know how to get the following:
Main effect of A: (AB + Ab) - (aB + ab) Main effect of B: (AB + aB) - (Ab
+ ab)
Interaction Effect: (AB + ab) - (Ab + aB)
but really what I want to find is brain areas which are particularly
involved in condition AB rather than in any of the others, i.e. voxels
where A > a AND B > b. For example, if I look at my main effect A at a low-
ish threshold, I get the brain region I am interested in, and if I look at
the main effect of B at a low-ish threshold, I get the same region, so I
want to combine these main effects to show that this region is specific to
my task. The interaction doesn't give me this because all the areas I'm
interested in have no activity at all in ab, and I don't think this is a
conjunction because A and B are part of the same factorial design and
aren't independent conditions. Is that right?
While I think I could get almost what I want by masking one main effect
with the other, I want to use the results to mask a third contrast, and too
many masks get confusing. So I wanted to ask - am I doing something
reasonable and how should I set up my contrasts? Or do I have to use
masks? At the moment I'm creating a con.img for each subject and each main
effect at the first level and then doing 2nd level t-tests on them (spm99).
Thanks very much for your help,
Antonia.
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