# Re: st: RE: Binomial confidence intervals

 From Richard Williams To statalist@hsphsun2.harvard.edu Subject Re: st: RE: Binomial confidence intervals Date Tue, 07 Sep 2004 13:28:13 -0500

```At 06:55 PM 9/7/2004 +0100, Nick Cox wrote:
```
```-exact- is something of a propaganda term. It just
means the method due to Clopper and E.S. Pearson
from 1934 or thereabouts. Even then a method
due to E.B. Wilson in 1927 was available
which (we know now) has generally better coverage
properties. And the Jeffreys method, which
although it has a Bayesian frisson to it, is
interpretable as a continuity-corrected variant
of the exact method. The Jeffreys method requires
you to know -invibeta()- and is thus not congenial for
hand calculation, but a doddle with current Stata.
```
Thanks Nick. Since the 1980s, my course notes have referred to the Wilson CI, although I didn't explicitly label it as such. It is nice to know that I haven't been totally misleading my students for over a decade, at least on this point.

These binomial variables are a bit tricky. Another thing I've taught for years is the normal approximation to the binomial using the correction for continuity (where the correction involves adding or subtracting .5 to the observed number of successes). I've recently learned that this is fairly controversial and that the correction sometimes makes things worse rather than better. Googling across the web, however, I've found plenty of other people teaching the same thing I have, although others have not. Luckily, I believe the -bitest- command gives you exact results (if not, somebody please correct me on this too!)

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Richard Williams, Notre Dame Dept of Sociology
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