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

____________________
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