# [R] proportions confidence intervals

Spencer Graves spencer.graves at pdf.com
Mon Jul 12 19:44:25 CEST 2004

```      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

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))
 -0.08973666  0.28973666
>   (naiveCI100 <- .1+c(-2, 2)*sqrt(.1*.9/100))
 0.04 0.16

hope this helps.  spencer graves

Darren Shaw wrote:

> Dear R users
>
> this may be a simple question - but i would appreciate any thoughts
>
> does anyone know how you would get one lower and one upper confidence
> interval for a set of data that consists of proportions.  i.e. taking
> a usual confidence interval for normal data would result in the lower
> confidence interval being negative - which is not possible given the
> data (which is constrained between 0 and 1)
>
> i can see how you calculate a upper and lower confidence interval for
> a single proportion, but not for a set of proportions
>
> many thanks
>
>
> Darren Shaw
>
>
>
> -----------------------------------------------------------------
> Dr Darren J Shaw
> Centre for Tropical Veterinary Medicine (CTVM)
> The University of Edinburgh
> Scotland, EH25 9RG, UK
>
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