Paired design [Power / Sample Size]

posted by ElMaestro  – Denmark, 2014-10-02 16:25 (4278 d 19:45 ago) – Posting: # 13646
Views: 15,368

Hi Hötzi,

thanks for your input.
I am ok with the fixed effects, they are not really what is behind the question.
Let us take the long way around my question:

I consider a 222BE study a paired design - it just has the added complexity of some fixed factors which are constants in a model. Fixed factors are just constants, no bother.
That's is the reason why (to perspectivise a little):
  1. Your can omit the anova and linear model and just apply the simple t-test formulae as given by Chow & Liu 2009 eqn 3.3.9. Yes, looks funny under the sq.root sign but that's just because of the presence of the two sequence which affect the way we calculate the reidual. We could just as well work with one sequence (before and after) and 3.3.9 would in that case be re-written and look more appealing.
  2. Linear model and mixed models for 222BE give the same results as long as you only look at the pairs.
  3. Potvin and Karalis and even the nutcase Fuglsang can get away with simulating differences of pairs when they look at power in 222BE without spending as much as a tenth of a second's thought on sequence or period interference in the muddle, as long as we keep in mind they steal a little df?
Basically shouldn't hence the Proc Power approach alluded to above give the same as powerTOST at corr=0 possibly with the single little difference that fair comparison sould necessitate the df allocation n-2 and not n-1 as we'd do with uncomplicated pairwise comparison?

Pass or fail!
ElMaestro

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