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Subject:

Re: ANOVA design matrix

From:

Rik Henson <[log in to unmask]>

Reply-To:

Rik Henson <[log in to unmask]>

Date:

Thu, 25 May 2006 21:36:22 +0100

Content-Type:

text/plain

Parts/Attachments:

Parts/Attachments

text/plain (1437 lines)

Bernhard -

There was no attachment (at least for the message I received), but I assume
you had 3 columns for your 3 conditions, plus 16 extra columns to model the
subject effects (ie differences in mean across conditions for each subject)
- given that you selected a "within-subject" ANOVA? If so, then yes, the
betas for each column are not uniquely estimiable, because the design matrix
is rank deficient. This means you cannot estimate contrasts like [1 0 0...].
Indeed, your contrasts will have to sum to zero. But this is not necessarily
a problem, since I assume that, if you intend to do classic "Analysis of
Variance", you are only interested in differences between the three
condition means, in which case F-contrasts like [1 -1 0....; 0 1 -1....]
("main effect of condition"), or [1 -1 0 ...], can still be estimated fine.
(If this is not making any sense, I suggest you consult the SPM course
slides, or a textbook, about the basic GLM).

In situations where your data for the ANOVA (ie contrast images) are already
subtractions of conditions for each subject (more precisely, 1st-level
contrasts that are orthogonal to the mean across all conditions entering the
ANOVA), then these contrasts have already effectively removed differences in
the mean activity for each subject (ie by using "difference scores"), so
there is no need to add the subject columns in the 2nd-level design.

Note that many people find the user-interface for 2nd-level designs (eg
ANOVAs) in SPM2 very confusing. This reflects the fact that it was a relic
of the old PET GUI. I would recommend SPM5, where Will Penny and Stefan
Kiebel have implemented a much more logical and general interface (in terms
of factors and levels), that avoids menus of "ad hoc" designs.

Sorry to continue my boring rants...
Rik





>-----Original Message-----
>From: SPM (Statistical Parametric Mapping)
>[mailto:[log in to unmask]] On Behalf Of Bernhard Staresina
>Sent: 25 May 2006 19:46
>To: [log in to unmask]
>Subject: [SPM] ANOVA design matrix
>
>
>Dear SPM experts,
>
>I'm trying to set up a within subjects ANOVA in SPM2, with
>beta values for certain conditions as
>dependent measures. I have 16 subjects and three conditions of
>interest. Correspondingly, I enter 16
>subjects and 3 conditions at the prompts, and then load up the
>3 beta images of interest, subject
>after subject. However, when I look at the resulting design
>matrix (attached as 'anova_matrix'), it
>doesn't look like the example provided by Rik Henson and Will
>Penny (attached as
>'r_henson_example'), and importantly it says that the betas
>are not uniquely specified. My question is
>whether I did something wrong with the setup and/or whether I
>should be worried about the 'not
>uniquely specified' statement.
>
>Thanks a lot for your help!
>
>Cheers,
>Bernhard
>
>
>
>
>
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