Hi Libby,
I might be talking nonsense, but I think your last three F-tests will
be equivalent. An F-contrast K specifies a reduced model K'beta=0.
First, with your F1, this ends up as beta1=0 and beta2=0 and beta3=0.
Now, if you also had a constant/mean EV (e.g. a fourth column, after
three columns for groups A,B,C) then this reduced model would just
have the mean, which I believe would be the usual "main effect of
group" contrast. I think that would also be true if the data are
de-meaned, and there is only the three group columns. Otherwise
(please forgive my lack of familiarity with FEAT to know whether this
is usual or not...) if you have non-zero mean data, and only three
group EVs in the design, then I think this contrast is actually
testing the hypothesis that all groups have zero mean, as opposed to
the usual "main effect of group" test, which has H0 that they are all
equal (but possibly non-zero).
Now, for the other contrasts, their K'*beta=0 equations reduce to
(F2): A-B=0 and A-C=0, (F3): B-A=0 and B-C=0, and (F4): C-A=0 and
C-B=0. In all three of these cases, the equations imply A=B=C. So here
(with or without a separate mean, as far as I can tell) all your F2-F4
will test the usual "main effect of group hypothesis" that all groups
have equal (possibly non-zero) mean.
I hope that's clear (and correct!). I think you'll need to be more
specific about the other null hypotheses you want to test, in order to
decide what the correct F- (or t-) contrasts are required. E.g. what
do you mean "main effect of groupA"? The t-contrast c1 would test
whether A's mean is greater than zero. A (t-) contrast like [2 -1 -1]
would test whether group A was greater than the average of groups B
and C, etc. etc.
Hope that helps,
Ged.
Libby OHare wrote:
> Hello,
>
> I have a question concerning the set-up and interpretation of F tests. In my higher-level analysis,
> I have 3 groups of subjects (A, B, and C), and I’m interested in examining the effects of group
> membership on activation. I set up these contrasts to look at the 3 group means and 6 pair-wise
> comparisons between groups:
>
> c1 A mean 1 0 0
> c2 B mean 0 1 0
> c3 C mean 0 0 1
> c4 A>B 1 -1 0
> c5 A>C 1 0 -1
> c6 B>A -1 1 0
> c7 B>C 0 1 -1
> c8 C>A -1 0 1
> c9 C>B 0 -1 1
>
> I’m thinking that I want to use these F tests:
>
> F1 F2 F3 F4
> c1 x
> c2 x
> c3 x
> c4 x
> c5 x
> c6 x
> c7 x
> c8 x
> c9 x
>
> I’m confident that F1 will give me the interaction for all three groups, but I’m less certain about
> the interpretation of F2, F3, and F4. For example, will F2 be the main effect of group A (and F3
> the main effect of group B, etc.)? Is there a more efficient way of setting up this analysis?
>
> Thanks in advance,
> Libby
>
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