Jessica -

You could do a (type of) multifactorial 2nd-level ANOVA using
the Full Monty option - but it is not the same as a conventional
(eg repeated-measures) ANOVA given by, for example, SPSS.
This (and the related issue of nonsphericity, see below) is why
Andrew labelled it "Dodgy population inference".

In conventional repeated-measures ANOVAs, different error
terms are used for different contrasts (main effects/interactions),
namely the effect-by-subject interaction (with error df related to the
number of subjects). This is a form of variance component estimation,
which is not currently implemented in SPM, which always assumes
a single ("pooled") error term (with error df related to the number
of scans).

However, if you perform your contrasts (main effects/interactions)
at the first-level and take these contrast images (as many as you
have subjects) into a second-level one- (or two-sample) t-test, the
resulting F-contrast will give you exactly the same answer as the
equivalent F-valie in a multifactorial repeated-measures ANOVA
(since the SPM residual error IS now the effect-by-subject interaction).
Thus, although it is more work (requiring multiple one/two-sample
SPM analyses), it is formally equivalent.

The problem comes when you have >2 levels for >2 factors,
for which you cannot create first-level contrasts that allow an
F-contrast in a second-level one/two-sample t-test to produce
a test equivalent to an F-test in a multifactorial ANOVA. However,
we are currently extending SPM_devel to variance component
estimation, and this will hopefully be possible in the future
(together with appropriate corrections for nonsphericity in
such >2 level multifactorial ANOVAs, eg Greenhouse-Geisser)

Rik


> > We have done an fMRI experiment  with young and elderly subjects performing
> > two different motor tasks. The paradigm is a blockdesign with rest 40s,
> > first activation 32s, rest 48s, second activation 40s and rest 56s. I would
> > like to perform a 2 way ANOVA in SPM to study the interaction effect of age
> > and performance of the two tasks. How should we choose the right contrasts?
> > Regards,
> >
> > Patrizia
>
> I'd like to hear an answer to this one, too; I've got a mixed design myself,
> two groups each doing a 2x2 design in an MRI study. I could do a whole bunch of
> t-tests but that seems inelegant; I'd rather do an omnibus F test and then
> break it down by interactions, main effects and simple effects the way I would
> if it were behavioral data.
>
> Is it possible to do a multi-factor ANOVA in SPM99 on MRI data? I keep being
> told it's not possible, but I'm not sure if that's true because the statistics
> haven't been developed yet, or whether it can be done but the programs aren't
> readily available. Or whether it can be done, but it's buried in the Full Monty
> section of the PET models...?

--
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DR RICHARD HENSON
Wellcome Department of Imaging Neuroscience
& Institute of Cognitive Neuroscience
Institute of Neurology
University College London
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England

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URL:    http://www.fil.ion.ucl.ac.uk/~rhenson

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