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From |
"Lachenbruch, Peter" <Peter.Lachenbruch@oregonstate.edu> |

To |
<statalist@hsphsun2.harvard.edu> |

Subject |
st: RE: RE: Confidence Interval for Proportion |

Date |
Tue, 11 Mar 2008 09:42:05 -0700 |

For small proportions, the exact option is useful. It is the standard that the other methods hope to reach. Coverage is exact. Agresti and Coull have a nice paper (I don't remember the attribution, but I think it's American Statistician, somewhere around 2000). Tony Peter A. Lachenbruch Department of Public Health Oregon State University Corvallis, OR 97330 Phone: 541-737-3832 FAX: 541-737-4001 -----Original Message----- From: owner-statalist@hsphsun2.harvard.edu [mailto:owner-statalist@hsphsun2.harvard.edu] On Behalf Of Nick Cox Sent: Tuesday, March 11, 2008 7:05 AM To: statalist@hsphsun2.harvard.edu Subject: st: RE: Confidence Interval for Proportion The "correct" CI for a binomial variable is a matter of dispute. In your case you are looking for a CI around a point estimate of 0.029. A symmetric CI around such a point estimate is likely to include 0 and some negative values unless the sample size is very, very large. Some people just truncate the interval at 0, but a more defensible procedure is to work on a transformed scale and back-transform, or do something approximately equivalent that yields positive endpoints for the CI with about the right coverage. [R] ci has several pointers to the literature. Alternative CIs can be got in this way: . gen rep78_1 = rep78 == 1 . ci rep78_1 if rep78 < ., binomial jeffreys . ci rep78_1 if rep78 < ., binomial Wilson Nick n.j.cox@durham.ac.uk Martin Weiss try this in Stata: ************************ sysuse auto, clear proportion rep78 matrix define A=e(b) matrix define B=e(V) count if rep78!=. *Upper/Lower Bound for proportion of "1" di A[1,1]+invnormal(1-0.05/2)*sqrt(A[1,1]*(1-A[1,1])/`r(N)') di A[1,1]-invnormal(1-0.05/2)*sqrt(A[1,1]*(1-A[1,1])/`r(N)') *Standard Error for "1" *Mistake obviously there... di sqrt(A[1,1]*(1-A[1,1])/`r(N)') ************************ Then let me know: why do I not hit the correct CI for the proportion of "1" in the repair record? Something`s wrong with the standard error, I do not know what, though... * * For searches and help try: * http://www.stata.com/support/faqs/res/findit.html * http://www.stata.com/support/statalist/faq * http://www.ats.ucla.edu/stat/stata/ * * For searches and help try: * http://www.stata.com/support/faqs/res/findit.html * http://www.stata.com/support/statalist/faq * http://www.ats.ucla.edu/stat/stata/

**Follow-Ups**:**Re: st: RE: RE: Confidence Interval for Proportion***From:*Maarten buis <maartenbuis@yahoo.co.uk>

**st: RE: RE: RE: Confidence Interval for Proportion***From:*"Newson, Roger B" <r.newson@imperial.ac.uk>

**References**:**st: Confidence Interval for Proportion***From:*"Martin Weiss" <martin.weiss@uni-tuebingen.de>

**st: RE: Confidence Interval for Proportion***From:*"Nick Cox" <n.j.cox@durham.ac.uk>

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