Dear Dr. William,
Thanks for your reply. However, what I'm not sure is, whether the question that asks,
(b) if there's anything in AY# > BY# is larger than AX# > BX#,
is different from the question which asks,
(c) if there's anything in BX# > AX# is larger than BY# > AY#.
I think they are different, as the brain activation pattern resulted in (b) can be different from that in (c). E.g. (b) can give a result on Insula while (c) can give a result on Thalamus, is that correct? If so, then how may I obtain these different results with the same t-contrast for this 3-way interaction* (for new readers, please see * below or my previous email to understand my original 3-way design)?
Thanks for your attention :)
Best wishes,
Meikei
*The 3-way Design:
factor 1 - A, B
factor 2 - X, Y
factor 3 - 1, 2
which gives rise to these 8 cells:
AX1 AX2 BX1 BX2 AY1 AY2 BY1 BY2
for simplicity, I assume:
(AX1 - AX2) = AX#
(BX1 - BX2) = BX#
(AY1 - AY2) = AY#
(BY1 - BY2) = BY#
________________________________________
From: Penny, William [[log in to unmask]]
Sent: Tuesday, October 18, 2011 11:24 PM
To: mmkleung; [log in to unmask]
Subject: RE: t-contrast for 3-way interaction
Dear Meikei,
In a 3-way ANOVA there are 8 independent tests. These look for
1. The overall effect
2. The 3 main effects
3. The 3 two-way interactions
4. One three-way interaction
To find out which contrast to use to test for each you can use the SPM function
Con=spm_make_contrasts([2 2 2]);
assuming you have two levels for each factor (which you do here). If you had a 3-by-3-by-2 ANOVA you'd type in [3 3 2].
The three-way interaction is
>> Con(8)
ans =
c: [1 -1 -1 1 -1 1 1 -1]
name: 'Interaction, factor 1 x 2 x 3'
which is identical to what you have.
Con(1) to Con(7) will contain the other effects.
Best wishes,
Will.
-----Original Message-----
From: SPM (Statistical Parametric Mapping) [mailto:[log in to unmask]] On Behalf Of mmkleung
Sent: 18 October 2011 14:31
To: [log in to unmask]
Subject: [SPM] t-contrast for 3-way interaction
Dear all,
I can't get around with the t-contrast for 3-way interaction effect, it would be great if you could help me with this.
The Design:
factor 1 - A, B
factor 2 - X, Y
factor 3 - 1, 2
First, I got two different t-contrasts for the 3-way interaction as follow:
AX1 AX2 BX1 BX2 AY1 AY2 BY1 BY2
(a) 1 -1 -1 1 -1 1 1 -1 for [(AX1 - AX2) - (BX1 - BX2)] - [(AY1 - AY2) - (BY1 - BY2)] --> positive interaction
(b) -1 1 1 -1 1 -1 -1 1 for [(AY1 - AY2) - (BY1 - BY2)] - [(AX1 - AX2) - (BX1 - BX2)] --> negative interaction
Then when I want to explore for other contrasts, I found that no matter how I change the combinations, they will be the same as either one of the above two situations, for example:
(c) -1 1 1 -1 1 -1 -1 1 for [(BX1 - BX2) - (AX1 - AX2)] - [(BY1 - BY2) - (AY1 - AY2)] --> same as the negative interaction
I understand that the formula in (b) and (c) are the same mathematically, but it seems that what is asked by them are different. But if I assume (AX1 - AX2) = AX#, (BX1 - BX2) = BX#, (AY1 - AY2) = AY#, (BY1 - BY2) = BY#, then it seems that by asking:
(b) if there's anything in AY# > BY# is larger than AX# > BX#,
is different from the question which asks
(c) if there's anything in BX# > AX# is larger than BY# > AY#.
Am I correct? If so, how to know which formula the result will be referring to if I use the t-contrast in (b)/(c)? Hope my question is clear... I tried to make it the simpliest I can. Thanks for your time and help!
Best wishes,
Meikei
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