Thanks for your helpful clarification, Stephen. Is it not the case, however, that the reason it is best to use the "flexible factorial" design for this case is that it can use partitioned errors, as opposed to the "full factorial" design, which pools errors?
Jason
On Oct 23, 2010, at 8:19 AM, Stephen J. Fromm wrote:
> I think the dof is correct:
> 19*4 = 76 observations
> 19 subject effects
> 1 main effect of drug/placebo
> 1 main effect pre/post
> 1 interaction
> Gives
> 76 - 19 - 1 - 1 - 1 = 54 available dof
>
> ImCalc: you create the interaction at the subject level; there are 19 of them, so you get a t-test with 19 -1 = 18 dof, I think.
>
> The fundamental reason for the differences between the models is, I think, that the flexible factorial model uses a so-called "pooled error," whereas the ImCalc method is using a "partitioned error." There's some discussion of this in the archives, though the main SPM reference is the admittedly quite technical manuscript "ANOVAs and SPM," at
> http://www.fil.ion.ucl.ac.uk/~wpenny/publications/rik_anova.pdf
>
> The pooled error method seems standard within the SPM community, but the partitioned error method is the "textbook" method.
>
> The difference between the two methods: the pooled method sticks the data into one big model, with one error term. The partitioned method divides the data among a few models, one for each traditional effect. For a 2x2 ANOVA like yours, where both factors are within subject, there are three effects: main effect of drug/placebo, main effect of pre/post, and the interaction. In that case there are three models.
>
> "Pooled" vs "partitioned" refers to the error terms; in the pooled model, the error is all together in one term; in the partitioned method, the error is partitioned among the different effects.
>
> It's not clear which method is more liberal; depends on the data. Pooled tends to be more liberal in that it has a higher dof. Partitioned tends to be more liberal in that the error term in each model is smaller than the pooled error. Since these two push in opposite directions, you cannot make an _a priori_ conclusion as to which setup is more liberal.
>
> One thing of note: for 2x2, there's no issue of nonsphericity for the partitioned model, since there's only 1 dof. Not true, I think, for the pooled model.
>
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