Dear Sabira,
Nice to hear from you. I recognize this question from the SPM
helpline (to which Karl copied his reply to Elaine Anderson) and I
will try to clarify what Karl said further. I hope that you won't
mind my copying this message to the helpline as well.
>Our paradigm is a block design with 4 different active blocks each
> followed by its respective null block, i.e. I have 4 different null
> blocks. How do I go about specifying the design matrix for a second
> level analysis taking these different null blocks into account?
>
>e.g.
>if my 4 active blocks are: A1 A2 A3 A4
>and my 4 null blocks are: N1 N2 N3 N4
>
>If I specify blocks 1-8 in the following order: A1 N1 A2 N2 A3 N3 A4 N4
>
>how do I contrast [A1-N1]-[A2-N2]? or vice versa? i.e perform a 2nd order
>contrast.
The first issue is exactly what question you are asking. [A1-N1] vs
[A2-N2] looks like an interaction, and I think that this is what you
are after. You can think of it as comparing the 'simple main effect'
Ax-Nx in two contexts, x=1 and x=2. Put another way, the
interaction is the 'A-specific activity' in context 1 compared with
the 'A-specific activity' in context 2, each being compared with its
own baseline. Let me know if this is not what you need.
>Would the appropriate contrast be A1-N1-A2+A1?
No, it would be A1-N1-A2+N2 (I suspect that this is what you meant
and that the A1 on the end is just a typo). Thus with your
covariates ordered as specified above, your contrast will be 1 -1 -1
1 0 0 0 0). As Karl pointed out (but for a different contrast), you
now need to perform this contrast on each of your subjects, within
the 'fixed effects' design matrix:
Subject 1: 1 -1 -1 1 0 0 0 0 0 0 0 0 0 0 0 0 ...
Subject 2: 0 0 0 0 0 0 0 0 1 -1 -1 1 0 0 0 0 ...
etc.
Each contrast image generated (i.e. one for each subject) gets
entered into a one-sample t test in the 'second level' analysis. The
question which you now ask of every voxel is whether its value
departs significantly from zero (which is its expected value under
the null hypothesis).
Incidentally it may be worth just mentioning an alternative (less
good) approach, which I suspect that you might have been considering.
(You can ignore this bit if you like.) You could specify the simple
main effect contrasts A1-N1 and A2-N2, and test for the difference
between them. Thus your contrasts would be
Subject 1 (A1-N1): 1 -1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ...
Subject 1 (A2-N2): 0 0 1 -1 0 0 0 0 0 0 0 0 0 0 0 0 ...
Subject 2 (A1-N1): 0 0 0 0 0 0 0 0 1 -1 0 0 0 0 0 0 ...
Subject 2 (A2-N2): 0 0 0 0 0 0 0 0 0 0 0 1 -1 0 0 0 ...
In this case, the second level analysis would test whether the A1-N1
contrasts, as a population, are significantly greater than the A2-N2
contrasts. The reason why this is less good than the first approach
outlined above is that it is equivalent to an unpaired t test (in
which you just compare an 'A1-N1' population with an 'A2-N2'
population) whereas your data are obviously paired (i.e. each A1-N1
estimate goes with the A2-N2 estimate for the same subject).
[However, if you can do a paired t test, then as I understand it the
result should be exactly the same as the first analysis - I've never
tried this so I don't know if it is possible within SPM99.]
> I know this is a very simple question but I am not sure how to do it.
Alas, nothing in functional imaging is simple; I hope that I haven't
made it even more complicated than it needs to be! If you are not in
fact after the interaction contrast (which I have assumed is the one
that you want) please feel free to contact me again.
>Many thanks,
>Sabira
You are more than welcome!
Best wishes,
Richard.
--
from: Dr Richard Perry,
Clinical Research Fellow, Wellcome Department of Cognitive Neurology,
Darwin Building, University College London, Gower Street, London WC1E
6BT.
Tel: 0171 504 2187; e mail: [log in to unmask]
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