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From |
Ronan Conroy <rconroy@rcsi.ie> |

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

Subject |
st: why don't confidence intervals from -proportion- use the same formula as -ci-? |

Date |
Fri, 11 Jan 2013 11:44:42 +0000 |

I have a real problem with the confidence intervals produced by the -proportion- command. . input outcome freq outcome freq 1. 0 21 2. 1 2 3. end Here is the confidence interval which is most probably closest the the nominal coverage according to - Brown L, Cai T, DasGupta A. Interval estimation for a binomial proportion. Statistical Science. 2001;16(2):101–17. . ci outcome [fw=freq], bin wil ------ Wilson ------ Variable | Obs Mean Std. Err. [95% Conf. Interval] -------------+--------------------------------------------------------------- outcome | 23 .0869565 .0587534 .02418 .2679598 Now here is what -proportion- does. . proportion outcome [fw=freq] Proportion estimation Number of obs = 23 -------------------------------------------------------------- | Proportion Std. Err. [95% Conf. Interval] -------------+------------------------------------------------ outcome | 0 | .9130435 .0600739 .7884579 1.037629 1 | .0869565 .0600739 -.037629 .2115421 -------------------------------------------------------------- . end of do-file According to the manual: "Methods and formulas proportion is implemented as an ado-file. Proportions are means of indicator variables; see [R] mean." Is anyone prepared to defend this approach as the only formula implemented by -proportion-? Or indeed to tell me that they have managed to publish a paper that included confidence intervals such as the one above? I myself find this bizarre. Consider the example above. The confidence interval includes a value that is impossible - zero. With two observed successes, the success rate cannot be zero. And it includes probabilities that have no definition: negative probabilities. While I am prepared to accept that physicists have now produced temperatures that are lower than absolute zero, I cannot bring myself to persuade anyone that a confidence interval for a probability can extend beyond the interval 0-1. I believe it would be good if Stata's -proportion- command allowed the choice of some more believable methods. Ronán Conroy rconroy@rcsi.ie Associate Professor Division of Population Health Sciences Royal College of Surgeons in Ireland Beaux Lane House Dublin 2 * * For searches and help try: * http://www.stata.com/help.cgi?search * http://www.stata.com/support/faqs/resources/statalist-faq/ * http://www.ats.ucla.edu/stat/stata/

**Follow-Ups**:**st: RE: why don't confidence intervals from -proportion- use the same formula as -ci-?***From:*"Lachenbruch, Peter" <Peter.Lachenbruch@oregonstate.edu>

**Re: st: why don't confidence intervals from -proportion- use the same formula as -ci-?***From:*Austin Nichols <austinnichols@gmail.com>

**Re: st: why don't confidence intervals from -proportion- use the same formula as -ci-?***From:*"JVerkuilen (Gmail)" <jvverkuilen@gmail.com>

**Re: st: why don't confidence intervals from -proportion- use the same formula as -ci-?***From:*Marcello Pagano <pagano@hsph.harvard.edu>

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