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Thank you both. I have some follow-up questions to clarify. When I run
the original configuration the resulting design matrix (see attached
"design.png") only contains columns for the four conditions. Is it
invalid to use this model to test the conjunction null using the
contrasts depicted in attached "contrast.png"? If so, why is it
invalid?

Donald: when you say "subject...needs to be in the model", do you mean
that I need to add the main effect of subject, or is the way I had it
originally set up sufficient (where the subject factor is explicitly
defined and correctly specified in the factor matrix). If the former,
it's unclear to me how to add the main effect of subject without
making the design rank deficient.

Thanks again for your help.

On Tue, Sep 13, 2011 at 9:04 AM, MCLAREN, Donald
<[log in to unmask]> wrote:
> (1) I think subject should be set to equal variance AND it needs to be
> in the model.
>
> (2) Some of the conjunctions are impossible, some are possible, here is why:
> A1: 1 1 0 0
> B1: 1 0 1 0
> A2: 0 0 1 1
> B2 0 1 0 1
> A1>B1: 0 1 -1 0
> A2>B2: 0 -1 1 0
> The conjunction of these two is 0 since they can't overlap!!!
>
> A1>A2: 1 1 -1 -1
> B1>B2: 1 -1 1 -1
> The conjunction of these two is possible since they can overlap.
>
>
> 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 5:07 AM, Cyril Pernet <[log in to unmask]> wrote:
>> Hi Bob
>>
>> looks ok - once you 'run' make sure the subjects factors appear in the
>> design matrix (as the factor_matrix.png only showed the factors)
>> conjunctions will be between contrasts 1 0 -1 0 & 0 1 0 -1 and between 1 -1
>> & 1 -1
>>
>> Hope this helps
>> Cyril
>>
>>
>>> Dear SPM experts,
>>>
>>> I am trying to setup a group-level model to test the conjunction of
>>> simple effects. Namely, I have a 2 X 2 within-subjects factorial
>>> design, with factors A (two levels, A1 and A2) and B (two levels, B1
>>> and B2). My current understanding is that it is most appropriate to
>>> model this using a flexible factorial design, with the following
>>> factors:
>>>
>>> 1. Subject
>>> 2. Factor A
>>> 3. Factor B
>>>
>>> I've used the attached parameters (pictured in params.png) and factor
>>> matrix (pictured in factor_matrix.png). As you can see, I've defined
>>> only the interaction among A and B. In this model, my primary interest
>>> is in interrogating the conjunction of the simple effects, e.g. A1>
>>> B1&  A2>  B2, and also A1>  A2&  B1>  B2.
>>>
>>> Is this model correct? I realize this may be a simple-minded question,
>>> but I'm still living in the days of the one-sample t-test and am
>>> unsure about how to appropriately use the flexible factorial model.
>>>
>>> Sincerely,
>>>
>>> Bob Spunt
>>> Postdoctoral Fellow
>>> Social Cognitive Neuroscience Lab - www.scn.ucla.edu
>>> Department of Psychology
>>> University of California, Los Angeles
>>
>>
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>> The University of Edinburgh is a charitable body, registered in
>> Scotland, with registration number SC005336.
>>
>