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

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

Subject |
st: RE: Re: Binomial confidence intervals |

Date |
Wed, 8 Sep 2004 14:42:16 +0100 |

A small tweak to Joseph's useful program. It feeds on a given sample size and population proportion, but irrespective of the latter 0.5 is wired in to a crucial line. So I suggest return scalar `method'_covered = (`pi' >= r(lb)) & (`pi' <= r(ub)) -inrange(`pi', r(lb), r(ub))- is a another way of doing it. Nick n.j.cox@durham.ac.uk Joseph Coveney > 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. > > -------------------------------------------------------------- > > 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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