# [Rd] prop.test confidence intervals (PR#2794)

Peter Dalgaard BSA p.dalgaard at biostat.ku.dk
Sat Apr 19 00:13:03 MEST 2003

```rbaer at kcom.edu writes:

> As an example, I include x=6 and n=42 which has a mean proportion of 0.115.

...n=52...

> When I calculate the 95% CI using the normal approximation by hand (and no
> continuity correction) I get (0.028, 0.202).  The exact binomial CI from
> binom.test() is (0.044, 0.234).  With correct=FALSE prop.test produces CI95 =
> (0.05396969, 0.22971664) which is neither of these.  With correct=TRUE it
> produces  (0.04778925, 0.2412937) This seems reasonably like a normal
> approximation 95% CI (which I presume is what is used by prop.test()) of the
> true binomial but I did not actually check it by hand.
>
> BUG summary.  The prop.test() calculation of 95% CI of sample proportions is
> improperly calculated when continuity correction is turned off.

Uhm... Basically, we know the correct answer from binom.test, and R's
intervals are considerably closer to that than the textbook p+-2*se(p)
formula. So R has a bug because it isn't inaccurate enough??

This might enlighten you:

prop.test(6,52,p=.05396969,alt="g",correct=F)
prop.test(6,52,p=.22971664,alt="l",correct=F)

also, consider the case x=0.

--
O__  ---- Peter Dalgaard             Blegdamsvej 3
c/ /'_ --- Dept. of Biostatistics     2200 Cph. N
(*) \(*) -- University of Copenhagen   Denmark      Ph: (+45) 35327918
~~~~~~~~~~ - (p.dalgaard at biostat.ku.dk)             FAX: (+45) 35327907

```