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From |
Steve Samuels <sjsamuels@gmail.com> |

To |
statalist@hsphsun2.harvard.edu |

Subject |
Re: st: manually calculating confidence interval for a proportion |

Date |
Fri, 12 Jul 2013 16:58:10 -0700 |

I've noted the discrepancy between the results of . cii 484 157 and . di invbinomial(484, 157, .975) . di invbinomial(484, 157, .025) The lower tail for -cii- seems to be in error: . cii 484 157 . di invbinomial(484, 157, r(lb)) I've reported this to Stata support. Steve Binomial CIs of the form Estimate +/- Bound are based on the central limit theorem and so use normal percentiles. . scalar calculated_95ub_bin= 157/484 + invnormal(0.025)*(sqrt((1/484)*(157/484)*(1-(157/484)))) . scalar calculated_95lb_bin= 157/484 - invnormal(0.025)*(sqrt((1/484)*(157/484)*(1-(157/484)))) ** Note use of 0.025 . dis calculated_95ub_bin . dis calculated_95lb_bin . cii 484 157 ** The exact CIs are calculated as follows: . di invbinomial(484, 157, .975) . di invbinomial(484, 157, .025) In the absence of the invbinomial() function, the exact CIs can be calculated in terms of the F distribution or the beta distribution. See the Wikipedia entry http://en.wikipedia.org/wiki/Binomial_proportion_confidence_interval Steve sjsamuels@gmail.com On Jul 12, 2013, at 2:49 PM, Wood, Mollie Elizabeth wrote: I am putting together a teaching example for a beginning programming lab, in which I ask students to manually calculate the upper and lower confidence limits for a variety of point estimates, and compare their results to the stata commands (ci, cii). However, I haven't had much look making it work myself! > I used this code to obtain 90% CIs for a mean: scalar calculated_90ub = r(mean) + invttail(_N - 1,0.05)*LOS_se scalar calculated_90lb = r(mean) - invttail(_N - 1,0.05)*LOS_se dis calculated_90ub dis calculated_90lb > Which worked well, and matched the output of Stata's command, ci [var], level(90) > However, when I tried the below command for the 95% CI around a proportion, the results are quite different the stata command, cii N K, level(95) > scalar calculated_95ub_bin= 157/484 + invbinomial(484,157,.05)*(sqrt((1/484)*(157/484)*(1-(157/484)))) scalar calculated_95lb_bin= 157/484 - invbinomial(484,157,.05)*(sqrt((1/484)*(157/484)*(1-(157/484)))) > dis calculated_95ub_bin dis calculated_95lb_bin > I did experiment with several other related functions (invbinomialtail, etc), none of which accurately reproduced the output from cii. > If anyone has a suggestion as to how I'm going wrong, I'd appreciate it very much! * * 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/ * * 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/

**References**:**st: manually calculating confidence interval for a proportion***From:*"Wood, Mollie Elizabeth" <MollieElizabeth.Wood@umassmed.edu>

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