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Subject:

Re: repeated measures 2x2 anova

From:

Omar Alhassoon <[log in to unmask]>

Reply-To:

FSL - FMRIB's Software Library <[log in to unmask]>

Date:

Sat, 17 Apr 2010 23:08:04 +0100

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text/plain

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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.
-------------

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

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