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From |
"Nick Cox" <n.j.cox@durham.ac.uk> |

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

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

Date |
Tue, 11 Mar 2008 18:28:23 -0000 |

There is a superb review paper at Brown, L.D., Cai, T.T., DasGupta, A. 2001. Interval estimation for a binomial proportion. Statistical Science 16: 101-133. This should be accessible to many, if not all, Statalist members at <http://projecteuclid.org/DPubS/Repository/1.0/Disseminate?handle=euclid .ss/1009213286&view=body&content-type=pdf_1> Nick n.j.cox@durham.ac.uk Maarten buis Actually, exact confidence intervals are not as exact as the name suggests, especially in the case of small proportions. These confidence interval tends to be conservative, see: (Agresti 2002, pp. 18-19) and the simulation below. If the exact method where truely exact in all regards, than the proportion of 95% confidence intervals containing the true proportion should be .95. In actual fact the proportion is higher, this is what I mean with the interval being conservative. *--------------- begin example ---------------------------- set more off capture program drop sim program define sim, rclass drop _all set obs 1000 gen x = uniform()<.99 ci x, binomial return scalar correct = r(lb)<.99 & r(ub)>.99 end simulate correct=r(correct), reps(10000): sim sum correct *------------------- end example -------------------------- (For more on how to use examples I sent to the Statalist, see http://home.fsw.vu.nl/m.buis/stata/exampleFAQ.html ) The reference you seem to refer to is: Agresti, A. and B.C. Coull (1998) "Approximate is better than exact for interval estimation of binomial parameters" The American Statistician, pp. 119--126. Alan Agresti (2002) "Categorical Data Analysis", 2nd edition, Wiley. Hope this helps, Maarten --- "Lachenbruch, Peter" <Peter.Lachenbruch@oregonstate.edu> wrote: > 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). Nick Cox > 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/

**References**:**st: RE: RE: Confidence Interval for Proportion***From:*"Lachenbruch, Peter" <Peter.Lachenbruch@oregonstate.edu>

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

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