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From |
Richard Williams <Richard.A.Williams.5@nd.edu> |

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:

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.-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.

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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**References**:**st: RE: Binomial confidence intervals***From:*"Nick Cox" <n.j.cox@durham.ac.uk>

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