Alex, Will, Andreas,
The first question: The difference between Full Factorial and Flexible
Factorial Model
(a) Flex. Fact. has a subject factor that is missing in the full
factorial model. The result of this is an increase in the degrees of
freedom. This should only be done if there is no subject effect.
(b) The variance components are same, but not the hyperparameters.
(c) The voxels used to compute the hyperparameters and the
hyperparameters are going to be different. Not sure what effect this
has on the data though.
The second question: within-subject versus between-subject effect
Andreas was correct, at least based on my testing, that
between-subject effects (NOTE: group*condition is a within-subject
effect) need to be tested in a separate model or using a model that
allows for partitioned variance.
The test to determine this was: one-way ANOVA testing for the average
effect of condition compared to a one-sample t-test. Both the
t-statistic and df are higher in the one-way ANOVA, which gives
inflated results. In a between-subject analysis, the observations are
considered independent - so you can't have df larger than the number
of subjects-1. The contrast images are almost identical (they differ
by <.0001). I think this could be attributable to rounding errors
depending on when averaging was done and when images were written out
to disk.
Best Regards, Donald McLaren
=================
D.G. McLaren, Ph.D.
Postdoctoral Research Fellow, GRECC, Bedford VA
Research Fellow, Department of Neurology, Massachusetts General Hospital and
Harvard Medical School
Office: (773) 406-2464
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On Tue, Sep 13, 2011 at 10:00 AM, Penny, William <[log in to unmask]> wrote:
> Dear Alec and Gil,
>
> Yes you can process your data like this and, in the effects you can test for, there will only be a minor difference between doing it like this and doing eg a one way ANOVA within-subjects (with three levels ctrl, con1, con2) at the second level.
>
> With this way of processing the data you won't be able to immediately look at eg the control condition itself. But then perhaps this is not of interest to you.
>
> Best, Will.
>
> -----Original Message-----
> From: SPM (Statistical Parametric Mapping) [mailto:[log in to unmask]] On Behalf Of Alec Sproten
> Sent: 13 September 2011 14:05
> To: [log in to unmask]
> Subject: [SPM] Flexible Vs Full factorial design - one understanding question
>
> Dear Will and the other SPM Experts,
>
> Following the thread in the SPM-Archive forum by Will Penny, the advices regarding how to set an analysis to investigate both within-subject effects (condition) and between-subject effects (group) we wanted to ask you for a confirmation if we understood the issues discussed correctly so that our design is fit for our planned analyses.
>
> Our data:
> 2 groups: A and B (A=25 subjects, B=21 subjects).
> 3 conditions: ctrl, con1, con2.
>
> We are interested to investigate both the effects of within- and between- subjects effects.
>
> In the first level analysis we made the following differential contrasts: d1=con1-ctrl and d2=con2-ctrl for each subject.
>
> To our understanding, this can solve the problem of accounting the within-subjects variability and so we can avoid creating a flexible-factorial design in order to investigate the within-subject effects (by including the factor subjects) in the model.
>
> Instead (we hope it is correct), we now can set a 2x2 full factorial design and only with 2 factors: group (with 2 levels: A,B) and condition (with 2 levels: d1,d2).
>
> This way we can construct contrasts to investigate the effect of condition (within-subject effects) but we can also construct contrasts to investigate the effect of group (between-subject effects) in the same model.
>
> Please let us know if we understood the issue correctly or we need to modify any part of our planned design.
>
> Thank you very much in advance,
> Alec & Gil
>
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