I have recently run a study in which I would like to analyse the data as a
factorial 3x2 repeated measures ANOVA (using the two-stage partitioned error
approach), but have a question about the analysis of the main effects and
their interaction at the group level.
For the 3 level factor there are 2 differential effects (similarly, for the
interaction there are two differential effects) that must be modelled at the
group level. According to Rik Henson's SPM paper, you create a one-way
ANOVA with n levels (n is the number of differential effects / columns in
the design matrix, for my example that's two) and assess the overall effect
with the F-contrast 'eye(n)'.
Now this works OK, except that the degrees of freedom seem to be severely
inflated for any effect that has more than 1 differential effect. For
example, with my 19 subjects, one would expect the DF to be [2,18] when
assessing a 3-level factor, but the two-stage partitioned error approach
gives a DF of [2,36], and hence an inflated p value. Is this a problem?
How does one work around this? The problem would seem to be even worse when
using a pooled error ANOVA since then your DF would be inflated by a factor
equal to the number of conditions you have!
Am I missing something?
Thank you in advance for any insights!