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From |
"JVerkuilen (Gmail)" <jvverkuilen@gmail.com> |

To |
statalist@hsphsun2.harvard.edu |

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

Date |
Fri, 11 Jan 2013 10:13:57 -0500 |

On Fri, Jan 11, 2013 at 6:44 AM, Ronan Conroy <rconroy@rcsi.ie> wrote: > 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.> This is a common issue with Wald confidence intervals for proportions or other bounded quantities such as Poisson rates. Notice that the confidence interval for 0 also exceeds 1. . expand freq (21 observations created) . reg outcome ------------------------------------------------------------------------------ outcome | Coef. Std. Err. t P>|t| [95% Conf. Interval] -------------+---------------------------------------------------------------- _cons | .0869565 .0600739 1.45 0.162 -.037629 .2115421 ------------------------------------------------------------------------------ You'll see that the answer is the same, so in this case it's using the unbiased estimate of the sampling variance here. Then there's: . prtest outcome == .1 One-sample test of proportion outcome: Number of obs = 23 ------------------------------------------------------------------------------ Variable | Mean Std. Err. [95% Conf. Interval] -------------+---------------------------------------------------------------- outcome | .0869565 .0587534 -.028198 .202111 ------------------------------------------------------------------------------ p = proportion(outcome) z = -0.2085 Ho: p = 0.1 Ha: p < 0.1 Ha: p != 0.1 Ha: p > 0.1 Pr(Z < z) = 0.4174 Pr(|Z| > |z|) = 0.8348 Pr(Z > z) = 0.5826 In this case the SE is what you'd get from using sqrt(pi*(1-pi)/n)). -margins- uses the delta method and generates a similarly inadmissible confidence interval. This is clearly a not-well-thought through use of the delta method in a small sample where asymptotics don't apply. There are many different ways to make a better estimator, none of which appear to be clear winners, though Agresti and Coull have gone through the options. http://en.wikipedia.org/wiki/Binomial_proportion_confidence_interval Agresti, Alan; Coull, Brent A. (1998). Approximate is better than 'exact' for interval estimation of binomial proportions. The American Statistician 52: 119–126. As to whether I've seen papers published like that... probably. There are some horrible things in journals. Do a meta-analysis sometime if you need proof! * * 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**:**Re: st: why don't confidence intervals from -proportion- use the same formula as -ci-?***From:*"JVerkuilen (Gmail)" <jvverkuilen@gmail.com>

**References**:**st: why don't confidence intervals from -proportion- use the same formula as -ci-?***From:*Ronan Conroy <rconroy@rcsi.ie>

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