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SPM  January 2009

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Subject:

Re: multi-subjects multi-conditions : within-subject ANOVA or one-sample t-tests ?

From:

Volkmar Glauche <[log in to unmask]>

Reply-To:

Volkmar Glauche <[log in to unmask]>

Date:

Wed, 28 Jan 2009 11:05:30 +0100

Content-Type:

text/plain

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text/plain (64 lines)

Dear Camille,

there is one likely explanation for the increase of the number of
significant voxels in an ANOVA with multiple conditions compared to a
series of one-sample t-test: the ANOVA model has much higher degrees of
freedom (if I'm right there should be 27 for 10 subjects and 4
conditions) than the one-sample t-test (9).
There are other differences between the two models as well: in a
one-sample t-test the only source of variance is between-subject,
whereas in the ANOVA model there is both between-subject and
within-subject variance.
To compare 2 conditions, one could even model differences between
conditions on the 1st level and take the resulting con images to the 2nd
level. (This holds for any t-contrast that can be computed on 1st
level.)
There is a lot more to say about the implications of different models on
the results, but as a rule of thumb you should only include those
conditions in your 2nd level that you are using in your contrasts.

Volkmar

Am Dienstag, den 27.01.2009, 17:22 +0000 schrieb Camille Maumet:
> Dear SPMers,
> 
> I have 10 subjects and 4 different conditions. First level stats give me one
> contrast image per subject per condition. My question arises with the
> second-level statistical analysis. I want to find the effect of each
> condition on my group of subjects.
> 
> I first performed four different one-sample t-test to test each condition on
> my group of subjects. This worked fine, however I thought that it would be
> better to use a one-way ANOVA (flexible factorial) in order to take into
> consideration the effect of each subject.
> 
> To this aim, I used the "flexible factorial" design with two factors :
> subject and condition and two main effects subject and condition. To isolate
> the effect of one condition I used the following T-contrasts :
> Condition 1 : [ones(1,10)/10 1 0 0 0]
> Condition 2 : [ones(1,10)/10 0 1 0 0]
> Condition 3 : [ones(1,10)/10 0 0 1 0]
> Condition 4 : [ones(1,10)/10 0 0 0 1]
> 
> The ANOVA leads to much more voxels activated with a FWE-corrected threshold
> than the solution using 4 different one-sample t-test. I wonder if that can
> be explained by the fact that subjects variability have been identified in
> the model ?
> 
> Furthermore, I wonder if this approach is right on a statistical point of
> view ? I searched the mailing list and only found examples in which one-way
> within-subject ANOVA was used for conjunction analysis or difference
> between-conditions.
> 
> Any thought on this would be highly appreciated,
> 
> Camille
> 
-- 
Volkmar Glauche
-
Department of Neurology         [log in to unmask]
Universitaetsklinikum Freiburg  Phone   49(0)761-270-5331
Breisacher Str. 64              Fax     49(0)761-270-5416
79106 Freiburg                  http://fbi.uniklinik-freiburg.de/

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