Re: [R] proportions confidence intervals

From: Marc Schwartz <MSchwartz_at_medanalytics.com>
Date: Tue 13 Jul 2004 - 04:58:25 EST

FWIW, if the exact intervals are what is desired here, as another poster has already suggested, binom.test() will get you there:

> binom.test(1, 10)$conf.int

[1] 0.002528579 0.445016117
attr(,"conf.level")
[1] 0.95

> binom.test(10, 100)$conf.int

[1] 0.04900469 0.17622260
attr(,"conf.level")
[1] 0.95

HTH, Marc Schwartz

On Mon, 2004-07-12 at 13:19, Chuck Cleland wrote:
> Darren also might consider binconf() in library(Hmisc).
>
> > library(Hmisc)
>
> > binconf(1, 10, method="all")
> PointEst Lower Upper
> Exact 0.1 0.002528579 0.4450161
> Wilson 0.1 0.005129329 0.4041500
> Asymptotic 0.1 -0.085938510 0.2859385
>
> > binconf(10, 100, method="all")
> PointEst Lower Upper
> Exact 0.1 0.04900469 0.1762226
> Wilson 0.1 0.05522914 0.1743657
> Asymptotic 0.1 0.04120108 0.1587989
>
> Spencer Graves wrote:
> > Please see:
> > Brown, Cai and DasGupta (2001) Statistical Science, 16: 101-133
> > and (2002) Annals of Statistics, 30: 160-2001
> > They show that the actual coverage probability of the standard
> > approximate confidence intervals for a binomial proportion are quite
> > poor, while the standard asymptotic theory applied to logits produces
> > rather better answers.
> > I would expect "confint.glm" in library(MASS) to give decent
> > results, possibly the best available without a very careful study of
> > this particular question. Consider the following:
> > library(MASS)# needed for confint.glm
> > library(boot)# needed for inv.logit
> > DF10 <- data.frame(y=.1, size=10)
> > DF100 <- data.frame(y=.1, size=100)
> > fit10 <- glm(y~1, family=binomial, data=DF10, weights=size)
> > fit100 <- glm(y~1, family=binomial, data=DF100, weights=size)
> > inv.logit(coef(fit10))
> >
> > (CI10 <- confint(fit10))
> > (CI100 <- confint(fit100))
> >
> > inv.logit(CI10)
> > inv.logit(CI100)
> >
> > In R 1.9.1, Windows 2000, I got the following:
> >
> >> inv.logit(coef(fit10))
> >
> > (Intercept)
> > 0.1
> >
> >>
> >> (CI10 <- confint(fit10))
> >
> > Waiting for profiling to be done...
> > 2.5 % 97.5 %
> > -5.1122123 -0.5258854
> >
> >> (CI100 <- confint(fit100))
> >
> > Waiting for profiling to be done...
> > 2.5 % 97.5 %
> > -2.915193 -1.594401
> >
> >>
> >> inv.logit(CI10)
> >
> > 2.5 % 97.5 %
> > 0.005986688 0.371477058
> >
> >> inv.logit(CI100)
> >
> > 2.5 % 97.5 %
> > 0.0514076 0.1687655
> >
> >>
> >> (naiveCI10 <- .1+c(-2, 2)*sqrt(.1*.9/10))
> >
> > [1] -0.08973666 0.28973666
> >
> >> (naiveCI100 <- .1+c(-2, 2)*sqrt(.1*.9/100))
> >
> > [1] 0.04 0.16



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https://www.stat.math.ethz.ch/mailman/listinfo/r-help PLEASE do read the posting guide! http://www.R-project.org/posting-guide.html Received on Tue Jul 13 05:06:13 2004

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