Daniel -
Both your suggestions are potentially correct, depending on
the contrast. If your first-level, subject contrasts were, for
example, [1 -1] over two conditions A and B, a second-level,
one-sample t-test would suffice for a "random effects" analysis
over subjects. In this case, you would enter a single [1] t-contrast
in the second-level SPM, to identify areas showing greater
activation for condition A than B, or a [-1] t-contrast
for the opposite comparison (B>A). If your hypothesis were
nondirectional, you would enter a [1] F-contrast instead to
identify regions showing differential (greater or smaller)
activity between conditions A and B. (Note that the corresponding
two-tailed p-values are more appropriate than reporting two,
one-tailed p-values for the two opposite t-contrasts).
You would obtain an equivalent model if you had two contrast
images per subject, [1 0] and [0 1], and entered them into
a two-sample, paired t-test, and tested a [1 -1] or [-1 1]
contrast in the second-level SPM. This is of course a special
case of a one-way ANOVA, which you could also build in SPM PET.
Note however that if you start to build more complex second-
level ANOVA models, you should be wary of any such model
with >2 levels per factor, because SPM does not currently
implement any corrections for nonsphericity of repeated-
measures data (eg Greenhouse-Geisser).
Perhaps I could ask the "community"s feeling on a related
issue? While in SPM we take con*.imgs through to second-level
analyses, which are simply linear combinations of the
parameter estimates, other groups appear to take statistics
(eg t-statistics) through to second-level analyses
(equivalent to selecting spmT*.imgs). Both approaches appear
to have pros and cons. Though the SPM approach may be the
appropriate test of "effect size", rather than "effect
significance", it is not clear to me that parameter estimates
are that meaningful in the context for poor model fits
(eg when first-level error terms are large). Some people
have claimed that such error is accommodated by the Mixed
Effects assumptions of the two-level procedure (ie would
translate to appropriately weighted second-level error
across subjects). Perhaps a better statistician than me
might be able to clarify these issues?
Rik
Daniel Weissman wrote:
>
> Dear SPMers,
> I have some questions about the best way to perform a random
> effects analysis. In reading prior e-mails, it seems that there might be
> multiple approaches. One approach seems to involve
>
> a) computing a single t-contrast image for each subject
>
> AND
>
> b) entering the group of contrast images from all subjects into a
> Basic Stats model
>
> I tried this approach using the One-way ANOVA and One Sample
> t-test BAsic Stats models. Are either of these correct?
>
> Once a basic stats model is chosen and other parameters are
> specified, SPM creates a new SPM.mat file. When I load this new file
> using the results button, a contrast manager appears. How do I enter the
> contrast which will tell me whether the t-contrast that I calculated for
> each subject is significant ACROSS subjects? Is it an F-test?
>
> Thanks,
> :> Daniel Weissman
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DR R HENSON EMAIL [log in to unmask]
Wellcome Department of
Cognitive Neurology TEL (work1) +44 207 833 7483
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URL: http://www.psychol.ucl.ac.uk/rik.henson/index.html
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