From p.dalgaard at biostat.ku.dk  Sat Apr 19 00:13:03 2003
From: p.dalgaard at biostat.ku.dk (Peter Dalgaard BSA)
Date: Fri Apr 18 23:11:10 2003
Subject: [Rd] prop.test  confidence intervals (PR#2794)
In-Reply-To: <200304181701.h3IH15pD022324@pubhealth.ku.dk>
References: <200304181701.h3IH15pD022324@pubhealth.ku.dk>
Message-ID: <x2he8v4ihs.fsf@biostat.ku.dk>

rbaer@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
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[Rd] prop.test confidence intervals (PR#2794)
Peter Dalgaard BSA