>Martin wrote:
> I have two groups: controls and schizophrenics. I used the canonical hrf +
> the two derivatives in my model. I created the following contrasts for the
> difference between A and B for each subject from each group:
>
> [1 0 0 -1 0 0] canonical HRF A-B
> [0 1 0 0 -1 0] temporal derivative A-B
> [0 0 1 0 0 -1] dispersion derivative A-B
>
> I was then able to examine the overall effect for _each group_ separately
> using a one-way ANOVA (without constant term), modelling the three contrast
> images as three groups using the F-contrast:
> [1 0 0
> 0 1 0
> 0 0 1]
> Antonia wrote:
> I think this step is a mistake (one I was making until yesterday!).
> This ANOVA means that you are looking for areas where the HRF, temp
> and disp differ from each other, not where they differ from zero. So
> if you had a giant effect with positive values for all 3 contrasts,
> you wouldn't find it in this analysis. Can anyone confirm and suggest
> the proper analysis, because I don't know what it is?
No, Martin is correct. If the contrast images are already
differences between conditions, then the F-contrast
[1 0 0; 0 1 0; 0 0 1] is CORRECT for testing any
differences between the conditions in the shape of
the HRF (at least those shape differences that can be
captured by the three basis functions).
You are correct that an F-contrast that tested for
differences between the basis functions would NOT
be appropriate. However, such an F-contrast would be
some rotation of [1 -0.5 -0.5; -0.5 1 -0.5; -0.5 -0.5 1]
instead.
And this is why it is important NOT to include a constant
term in the ANOVA. If you do include one, you will
find that you cannot evaluate the F-contrast [1 0 0; 0 1 0; 0 0 1],
because the design matrix is now rank deficient and the
contrast weights will need to sum to 1. You will also see
that the default "effects of interest" contrast looks like
[1 -0.5 -0.5; -0.5 1 -0.5; -0.5 -0.5 1], and so is not
appropriate. You would need to redo without a constant.
Finally, note that you should use "full" nonsphericity correction
(ie non-identically distributed and non-independent (correlated
errors)), because the (contrasts of) basis functions come from
the same subjects, and have quite difference scalings, so both
the variance and covariance of errors are likely to be nonspherical.
> Martin wrote:
> What if I want to compare the two groups now? Do I do a one-way ANOVA where
> I enter six groups - one for each contrast for each group and then do an
> F-contrast like:
> [1 0 0 -1 0 0
> 0 1 0 0 -1 0
> 0 0 1 0 0 -1]
> to get the overall effect?
Yes. (If the contrast images were already differences between
two conditions, then this would actually test the "Group X Condition
interaction". To test the "main effect of Group", perform another
ANOVA, but this time with the contrast images being the average
(sum) of the two conditions, for each basis function).
There is a slight problem here that this ANOVA really consists of
one within-subject factor (basis function) and one between-subject
factor (group), yet the SPM2 GUI does not allow you to specify a
error covariance basis set (for nonsphericity correction) with only
some (but not all) of the off-diagonal terms included. You can do this
by hand in matlab (in a batch script), or you can wait until (hopefully)
the whole "second-level" stats GUI options in SPM5 are over-hauled (about time!).
But for now, I doubt there would be much harm in allowing "full"
nonsphericity correction anyway, and hopefully ReML will estimate
covariance terms close to zero for the between-subject covariances.
> Can I do an equivalent of the t-test above, such as:
> [1 0 0 -1 0 0] to find A>B group 1>2?
Yes.
Rik
----------------------------------------
Dr Richard Henson
MRC Cognition & Brain Sciences Unit
15 Chaucer Road
Cambridge
CB2 2EF, UK
Tel: +44 (0)1223 355 294 x522
Fax: +44 (0)1223 359 062
http://www.mrc-cbu.cam.ac.uk/~rik.henson
----------------------------------------
|