Pierre -
> Reading SPM 99 documentation, I have understood that the statistics
> corresponding
> to "random effect" are done using a two-stage approach, i.e. calculating
> one contrast image for each subject (as if only one determination has been
> performed on each subject, so that the residual df is number_of_subject-1)
> and then running a second level analysis (I did not find out how this
> analysis is performed. Is it by comparing the mean t value to 0?). Is this
> correct?
Yes, the t (and F) tests are against the null hypothesis of zero mean,
using the one (or two)-sample t-test option in SPM99.
> In books concerning variance analysis, the random effect (mixed models) is
> generally performed by calculating a F value as the ratio : (main effect
> linked variance) / (interaction variance). Then, the interaction df is:
> (number_of_subject-1)*(number_of_replication_per_subject - 1). The
> contrasts of interest are then calculated in the same way than in SPM but
> the interaction variance is taken as residual variance.
>
> 1) Did I correctly understood the random analysis in SPM?
Yes. In the special case of two conditions (two levels of your main
effect)
and one replication per subject (or data averaged over balanced
replications),
the "conventional" F-test you describe and the F-contrast [1] on an SPM
one-
sample t-test are equivalent. Because the con*imgs already contain the
effect
parameters for each subject, the residual error in the SPM model is
identical
to the subject x effect interaction, the denominator of the conventional
repeated
measures ANOVA.
When there are more than two levels of your factor and you want an
omnibus F-test (rather than a specific planned comparison, ie
t-contrast),
you must use a PET design. However, the resulting analysis uses a
pooled error term (even for factorial designs) and there is currently
no correction for sphericity violations (so your p-values may be
invalid).
This is why we advise keeping second-level models to one/two-sample
t-tests
on specific t-contrast images.
> 2) As the number of values for the contrast is always low (the number
> of subjects), is it better to use a non parametric test to compare the mean
> t value to 0?
It may be, particularly with ~10 or less subjects - see:
http://www.mailbase.ac.uk/lists/spm/2000-07/0053.html
(though if you use permutation tests, as in SnPM, you are not really
treating subjects as a random effect - but then again how often are
subject samples for imaging experiments true random samples from the
population?)
> 3) Is the first order risk (false positive) in the two-stage approach in
> SPM the same (or lower or greater) as in the classical approach (one_stage
> analysis, F determination and contrasts deducting using of interaction
> variance in place of between replicates variance)?
>
> 4) The same question for second order risk (power).
They are the same in both cases (if I have understood you correctly),
for
the reasons given above.
Rik
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DR R HENSON
Wellcome Department of Cognitive Neurology
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