>Dear Experts,
>
>I've red your documentation ANOVAs and SPM and I'm trying to
>applay it to my
>simple design. I've a 2x2 within subjects design A (a1, a2) x
>B (b1, b2) so
>the design matrix has four regressor a1b1, a1b2, a2b1, a2b2, and I'm
>interesting in main effect of A, main effect of B and interaction AxB.
>
>I implement a two stage procedure: at first level I get three sets of
>con.img (differential effects) and at second level I run one
>sample t-tests
>for each set. I think that in this case the errors are
>partitioned (more
>sensitive inferences). Is this correct?
Yes.
For a single voxel, partitioned error can be more "sensitive", though it
depends on the data, and is really a question of model selection.
>If yes, total sum of square (SStot) of my design can be partitioned as
>follw?
>SStot = SSA + SSB + SSAxB + SSsubjects + SSAxsubjects + SSBxsubjects +
>SSAxBxsubjects
>where,
>SSA: main effect of A
>SSB: main effect of B
>SSAxB: interaction of factors A and B
>SSsubjects: main effect of subjects (the modelling of subject effect
>increases the sensitivity of inference)
>SSAxsubjects: interaction of factors A and subjects (error
>term for main
>effect of A)
>SSBxsubjects: interaction of factors B and subjects (error
>term for main
>effect of B)
>SSAxBxsubjects, interaction of factors A, B and subjects
>(error term for
>interaction of A and B).
Yes.
>I think also that if at 1-st level I get four sets of con.img
>and at second
>level I run paired t-tests the errors are partitioned in the
>same manner.
>The difference is that in the first case the subject effect is
>modeled at
>1-st level with con.img (differential effects) while in the
>second one the
>subject effect is modelled at 2-nd level. Is this correct?
If the four sets of con.imgs from the 1st-level that you talk about
are differences, eg one con.img for a1b1-a1b2 and another for
a2b1-a2b2, then a [1 -1] contrast within paired t-test on these two,
equivalent to the interaction, will give the same answers as a one-sample
t-test on the single con.img at the 1st level (a1b1-a1b2)-(a2b1-a2b2), yes.
Rik
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