Oops! I thought that the system would link the original post to mine. Here it is again with the original question and the response from 2004.
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I was wondering if I can get your insight on several questions I had about this approach to modeling a 2x2 within and between design.
1. Given the contrasts and F-tests Arun proposed (below), what is the difference between the third contrast (EV1, EV2, EV3, EV4 = 0, 0, 1, 0) and the third F-test (off, off, on)?
> 1 2 3 4
> C1 1 0 0 0
> C2 0 1 0 0
> C3 0 0 1 0
>
> and the F-tests are (with their interpretation)
>
> F1 F2 F3
> C1 on off off - main effect of task
> C2 off on off - main effect of group
> C3 off off on- interaction between the two factors
2. Dr. Smith proposes tweaking Arun's design by replacing "EV4 with a set of EVs, one for each subject ID, in the manner of the paired t-test." My interpretation of this tweak is that it is an attempt to "model-out" the individual means of each subject separately in contrast to modeling out the grand mean. Is this interpretation correct?
3. Are both ways of modeling a 2x2 repeated measures design (Arun's original versus Dr. Smith's tweak) interpreted the same. My understanding is that Arun's original suggestion is similar to an unpaired t-test, while the addition of the tweak would be like a paired t-test. Is Arun's original method more susceptible to more Type II error than the tweaked method?
Thanks a million,
Omar
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Hi Arun, I think this looks fine. Both your factors are fixed, surely (you
are getting representative samples of both levels of both factors)?
The only tweaking I can possibly see, is that you probably get slightly
better modelling if you replace EV4 with a set of EVs, one for each
subject ID, in the manner of the paired t-test - does that improve things?
Cheers.
On Tue, 10 Aug 2004, Arun Bokde wrote:
> Hello,
>
> I would like to set up a repeated measures 2x2 anova at the second level
> and examine the interaction. I have two groups of subjects (group 1 and
> 2) and each subject did 2 tasks (task A and B). The repeated measure
> would be the tasks (2 levels). I would like to ask the question: are
> there any task by group interactions ? I have set up things as
> described below and I have a few questions.
>
> I already have the COPE images for every subjects and task. I was
> thinking of setting up the second level analysis as follows (with
> smaller number of subjects for simplification). Each row represents a
> COPE image from one subject.
>
> group EV1 EV2 EV3 EV4
> group_1_task_A_subj1 1 1 1 1 1
> group_1_task_A_subj2 1 1 1 1 1
> group_1_task_A_subj3 1 1 1 1 1
> group_1_task_A_subj4 1 1 1 1 1
> group_2_task_A_subj1 2 1 -1 -1 1
> group_2_task_A_subj2 2 1 -1 -1 1
> group_2_task_A_subj3 2 1 -1 -1 1
> group_1_task_B_subj1 1 -1 1 -1 1
> group_1_task_B_subj2 1 -1 1 -1 1
> group_1_task_B_subj3 1 -1 1 -1 1
> group_1_task_B_subj4 1 -1 1 -1 1
> group_2_task_B_subj1 2 -1 -1 1 1
> group_2_task_B_subj2 2 -1 -1 1 1
> group_2_task_B_subj3 2 -1 -1 1 1
>
> EV1 models task, EV2 models effects of group membership, EV3 the group x
> task interaction, and EV4 is the grand mean.
>
> The contrasts that I am thinking of implementing are as follows:
> 1 2 3 4
> C1 1 0 0 0
> C2 0 1 0 0
> C3 0 0 1 0
>
> and the F-tests are (with their interpretation)
>
> F1 F2 F3
> C1 on off off - main effect of task
> C2 off on off - main effect of group
> C3 off off on - interaction between the two factors
>
>
> Question: is the repeated measures factor (task) the same as considering
> this variable as fixed and the other factor (group) as random ? I
> believe the F-tests above will not give me the exact test that I want
> but I am not sure.
>
>
> Thanks in advance,
>
> Arun
>
Stephen M. Smith DPhil
Associate Director, FMRIB and Analysis Research Coordinator
Oxford University Centre for Functional MRI of the Brain
John Radcliffe Hospital, Headington, Oxford OX3 9DU, UK
+44 (0) 1865 222726 (fax 222717)
[log in to unmask] http://www.fmrib.ox.ac.uk/~steve
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