# st: paired samples proportions

 From "Lachenbruch, Peter" To "statalist (E-mail)" Subject st: paired samples proportions Date Wed, 27 Aug 2003 09:10:06 -0400

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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