Right: texts say you can't use the pooled method unless certain interaction terms disappear (ie, are not significant), I think. Though it would be interesting to see exactly why it's wrong if you use the pooled variance when textbooks say you can't. I can't recall seeing a precise exposition on that, other than that you have a larger error term but also more dof's, which work in different directions.
Your second point: I'd have to think about it. :-)
Cheers,
Stephen J. Fromm, PhD
Contractor, NIMH/MAP
(301) 451--9265
________________________________________
From: [log in to unmask] [[log in to unmask]]
Sent: Tuesday, January 04, 2011 5:12 AM
To: Fromm, Stephen (NIH/NIMH) [C]
Cc: [log in to unmask]
Subject: Re: Design matrix for each or all subject(s)?
...
> Part of my reluctance is related to my disagreement with the way
> repeated measures are handled by SPM, which is a separate topic. As
> outlined in "ANOVAs and SPM"
> link http://www.fil.ion.ucl.ac.uk/~wpenny/publications/rik_anova.pdf
> there's the partitioned variance method and pooled variance method.
> IMHO the pooled variance method (the one commonly used by the SPM
> community) is incorrect (because it gets df counting wrong), though
> that appears to be a minority opinion.
Well this is an interesting point, but one that would also apply to F
tests conducted in analogous designs in textbook univariate
situations. I'd expect there should be something on this in that
well-researched (indeed by now dated) literature.
> On the other hand, if I recall correctly, there was a thread on the
> listserv devoted to the topic of the main effect of group which
> implicitly showed that the pooled variance method was indeed faulty.
One thing I'd like to know, where was ever shown that the smoothness
of F maps can be estimated from residuals? That is, irrespective of
the numerator df's? That does not seem intuitive to me. Given that
residuals are good to estimate smoothness of t maps (numerator df =
1), it does not follow they are good for higher df's. When I look at F
maps, they seem different from t maps. This seems relevant to the
pooled error idea, which relies on F testing.
Best wishes,
Roberto Viviani
Dept. of Psychiatry, University of Ulm, Germany
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