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Re: Factorial Design w/ Partitioned Error, are DFs incorrect?

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Wed, 4 Nov 2009 09:35:55 +0000

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 ```Conor - > 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! > I am not sure why you think the F df's for a main effect across 3 levels, with 19 subjects, should be [2,18]. I would have thought they should be [2,36], ie [(m-1),(m-1)x(n-1)], where m=3 and n=19? Am I missing something? For a pooled error, the df's are not "inflated"; they are correct for a model where only a single error term is used. The question is not whether the df's are "correct", but how (and whether) you want to partition that error into different components for each ANOVA effect (with each component having different df's). Best wishes Rik -- -------------------------------------------------------                  Dr Richard Henson          MRC Cognition & Brain Sciences Unit                  15 Chaucer Road                    Cambridge                   CB2 7EF, UK            Office: +44 (0)1223 355 294 x522               Mob: +44 (0)794 1377 345               Fax: +44 (0)1223 359 062 http://www.mrc-cbu.cam.ac.uk/people/rik.henson/personal ------------------------------------------------------- ```