> We have been struggling a little trying to figure out how best to perform a
> 2x2 within subjects Anova. All of our subjects perform all 4 conditions.
> What we have done is used the following t-contrasts at the 1st level:
> main effect A (1 1 -1 -1)
> main effect B (1 -1 1 -1)
> interaction (1 -1 -1 1)
>
> Then we use a one-sample t-test on the resulting contrasts at the 2nd level.
>
> My questions are:
> 1. Does this analysis account for the variance across subjects? Is it a
> within-subject analysis?
It is a within-subject analysis because "subject effects" (ie differences
due to different subject means) have already been "subtracted out"
in your 1st level contrasts.
It will give you exactly the same results as a conventional repeated-measures
ANOVA in something like SPSS, where each effect has a separate error
term (the "effect-by-subject" interaction, in fact).
> 2. Is this the most appropriate way to perform an anova?
You could do a 2nd-level ANOVA with all four conditions (using [1 0 0 0],
[0 1 0 0], ... contrasts at the 1st level). For this, you would need to also
add "subject effects" (by selecting the "ANOVA (within-subjects)" option
under Basic Stats in SPM2). However, subsequent main effect and
interaction contrasts like those above will be using a "pooled error"
(the error df's will be 4*N-(4+N), rather than N-1, as in the above case).
This is not invalid; it is just less conventional.
For further information, please consult:
http://www.fil.ion.ucl.ac.uk/~wpenny/publications/rik_anova.pdf
Rik
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