On Wed, 10 Apr 2013, rfro...@jbu.edu went:

I think the problem is in the use of the term "power" as synonymous
with sample size.

I agree.  The Buttons et al. paper never seemed to say anything about
within-subject designs (even though a lot of fMRI studies probably use
such designs).  And that's one place where power and sample size
decouple.  If you tested five different doses of a drug, including
placebo, in a Latin-square design using just five participants (each
receiving all five doses), you'd have plenty of power--more than you'd
have if you used a between-groups design with 25 participants (each
receiving one of the five doses).  But with your five-person Latin
square, you'd be more vulnerable to nonreplicability due to
idiosyncrasies of your sample, which is what Buttons et al. are
concerned about.

At least, that's my thinking.  Someone set me straight if need be.

--David Epstein
  da...@neverdave.com





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