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From |
Joseph Coveney <jcoveney@bigplanet.com> |

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

Subject |
st: Re: Binomial confidence intervals |

Date |
Wed, 08 Sep 2004 21:04:23 +0900 |

Paul Seed wrote: As I don't have access to a decent Stats library here, I tried to obtain the recommended paper (Brown, Cai, & DasGupta. Interval Estimation for a Binomial Proportion. Statistical Science, 2001, 16, pp. 101-133.) over the internet; but it is currently behind a "rolling firewall", until 2005. Would anyone who has seen it hazard a comment on which of the new methods - Wilson, Jeffreys or Agresti they would prefer for small samples. ---------------------------------------------------------------------------- In the absence of access to the article, you can run -simulate- calling a program such as the -exbinci- ditty in the do-file below, and make a choice suitable to your circumstances based on the results. I wrote the do-file below in an attempt to illustrate Bobby Gutierrez's point to the list. In order to run it, you'll need to install Joseph Hilbe's -rnd- suite from SSC. In the do-file below, with 10 trials and a population mean of 50% (these are options in the program that you can change to suit your circumstances), the true parameter lies within the 95% confidence interval 9797 times out of 10000 experiments for each of the methods. This compares with a 95% confidence interval's expectation to contain the parameter 9500 times out of the 10000 experiments. (A 95% confidence interval is supposed to contain the population parameter 95% of the time over the long run.) With more trials (100) in the experiment, the 95% confidence intervals by the Jeffreys, Wilson or Agresti methods are reasonably good: each, 9452 times out of 10000 experiments. At 9652 times out of 10000 experiments, the Clopper-Pearson method is still a just a little conservative in its probability of coverage. Joseph Coveney ---------------------------------------------------------------------------- clear set more off local seed = date("2004-09-08", "ymd") set seed `seed' set seed0 `seed' macro drop seed program define exbinci, rclass version 8.2 syntax , N(integer) Pi(real) rndbin `n' `pi' 1 foreach method in exact wilson jeffreys agresti { ci xb, binomial `method' // you can trap for the possibility that UL or LL is missing here return scalar `method'_covered = (0.5 >= r(lb)) & (0.5 <= r(ub)) } end * population (true) parameter = 0.5; m + n = 10 simulate "exbinci, n(10) pi(0.5)" /// exact_covered = r(exact_covered) /// wilson_covered = r(wilson_covered) /// jeffreys_covered = r(jeffreys_covered) /// agresti_covered = r(agresti_covered), reps(10000) summarize drop _all * population parameter = 0.5; m + n = 100 simulate "exbinci, n(100) pi(0.5)" /// exact_covered = r(exact_covered) /// wilson_covered = r(wilson_covered) /// jeffreys_covered = r(jeffreys_covered) /// agresti_covered = r(agresti_covered), reps(10000) summarize exit * * 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/

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