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In general, this is how a conjunction would work. Howevever, the underlying statistics are invalid.

When you setup the mixed-design as above (group, subject, conditions) you need to remember the following things:
(1) You need the main effect of subject, group, and condition in addition to the interaction terms. Statistical theory says that if you include the interaction, then you need the main effects in the model.

(2) The mixed-designs are invalid for between-subject comparisons (e.g. group1>group2), but valid for within-subject comparisons (e.g. condition1>condtion2). In brief, the between-subject effects should use the between-subject error term (Sums of Squares of Subjects - Sums of Squares of Group Factor); while the within-subject effects should use the within-subject error term (Sums of Squares of Subject-by-Condition). In SPM, there is only one error term and in the mixed -design it is the Sums of Squares of Subject-by-Condition. Thus, between-subject comparisons are statistically invalid.

If you your going to OHBM, drop by my poster for more detail.

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, Jun 21, 2011 at 5:52 AM, Raphael Hilgenstock <[log in to unmask]> wrote:
Hello Mayuresh,

your approach looks perfectly valid to me. Good luck with your analysis.

Best regards
Raphael

Am 21.06.2011 07:20, schrieb Mayuresh K:

Hello SPMers,

I am working on data from three fMRI tasks for two groups of subjects. The two groups are significantly different in several brain areas for individual group analyses for each of the 3 tasks. I am interested in identifying if there is an overlap in brain regions (with group1>group2) across the three tasks.  I would appreciate if someone can review my model setup and validate if this approach is correct?

I have setup this analysis using a "Flexible factorial model" with factors:
1. subject (independence, equal variance) ;
2. group (independence, unequal variance) and
3. task (dependent, equal variance).

I have specified all the subjects such that:
1. each subject belonging to group 1 has a factor matrix: [1, 1; 1, 2; 1, 3]
2. each subject belonging to group 2 has a factor matrix: [2, 1; 2, 2; 2, 3]
i.e. first row for group membership & second row for task.

Main Effect: subject
Interaction: [2 3] i.e. group by task

The resulting design matrix has the following columns: N1 + N2 + 3 task columns group 1 + 3 task columns group 2. (N1&N2 are number of subjects in group1 and group2 resp)

I have defined three contrasts - one for each task (group1>group2):
1. task 1 - ones(1,N1)/N1 -ones(1,N2)/N2 1 0 0 -1 0 0
2. task 2 - ones(1,N1)/N1 -ones(1,N2)/N2 0 1 0 0 -1 0
3. task 3 - ones(1,N1)/N1 -ones(1,N2)/N2 0 0 1 0 0 -1

to achieve the conjunction, I select all the three contrasts for interrogation.
Is this a valid approach?

Thanks,
Mayuresh