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Re: st: svy proportion - confidence intervals


From   jpitblado@stata.com (Jeff Pitblado, StataCorp LP)
To   statalist@hsphsun2.harvard.edu
Subject   Re: st: svy proportion - confidence intervals
Date   Thu, 06 Sep 2007 09:51:52 -0500

Yesterday I posted a reply to Hillel Alpert's question about 'Binomial Wald'
confidence intervals.  I then recieved a private email (from someone else)
that pointed out that I made an incorrect assertion about the standard errors
of the sample proportion, sehat(phat), produced by -proportion- and -ci,
binomial wald-.

While the formula used by -ci, binomial wald- is

	sehat(phat) = sqrt(phat(1-phat)/N)			(1)

-proportion-s formula is essential the same as

	sehat(phat) = sqrt(phat(1-phat)/(N-1))			(2)

The methodological distinction here is that formula (1) is derived using
maximum likelihood, while formula (2) is the same as the standard formulas for
the standard error of the sample mean, which uses the sample variance
calculation (an unbiased estimate of the sample variance of the measurement).

--Jeff
jpitblado@stata.com
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