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
[email protected]
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