As Joe Coveney notes this is the McNemar test situation. Thus, one is
really computing the sample size to detect a difference from 0.5 for a
single sample using only the discordant parts of the 2x2 table.
+ -
+ a b
- c d
The test is given by X2=(b-c)2/(b+c) - it's easy to show this is the
binomial test. Where we get hung up is that we don't know how many
discordant pairs there will be. I wrote a paper on this in 1992 in
Statistics in Medicine (p. 1521) that isn't the last word on it. I just
observed that the numbers b and c were bounded by the number of discordant
pairs and 0 and you could do some playing with it. So Stata will compute
the sample size for a one sample test against p=0.5, but you then need to
figure out what proportion of discordant pairs you expect.
Peter A. Lachenbruch, Ph. D.
Director, Division of Biostatistics
OBE/CBER/FDA
Phone (301) 827-3320
FAX (301) 827-5218
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