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st: RE: Binomial confidence intervals


From   "Nick Cox" <n.j.cox@durham.ac.uk>
To   <statalist@hsphsun2.harvard.edu>
Subject   st: RE: Binomial confidence intervals
Date   Tue, 7 Sep 2004 18:55:13 +0100

-exact- is something of a propaganda term. It just 
means the method due to Clopper and E.S. Pearson
from 1934 or thereabouts. Even then a method 
due to E.B. Wilson in 1927 was available 
which (we know now) has generally better coverage 
properties. And the Jeffreys method, which 
although it has a Bayesian frisson to it, is 
interpretable as a continuity-corrected variant 
of the exact method. The Jeffreys method requires
you to know -invibeta()- and is thus not congenial for 
hand calculation, but a doddle with current Stata. 

If you download -cij- and -ciw- from SSC 
you won't get any extra functionality (well, 
you will, but it's not documented), but you 
will get sets of references on the topic embedded
in the help files. 

Above all, go straight to the paper by Brown, 
Cai and DasGupta in Statistical Science in 
2001. This was the avalanche that started 
the stone rolling that led eventually to these changes
to -ci-, added since the initial release of Stata 8. 

My reading of the literature, and some practical 
experience, is that especially for proportions near 0 
or 1 the -exact- method can perform distinctly 
poorly while -jeffreys- and -wilson- can be 
relied on to give much more plausible answers. 

Turning this around, if the methods disagree the 
problem is thereby flagged as more difficult. 

It's arguable that we have here a bizarre situation, 
namely: many statistics texts have recommended 
the Clopper-Pearson method for decades and 
all along at least one better method was 
already available. 

Nick 
n.j.cox@durham.ac.uk 

> -----Original Message-----
> From: owner-statalist@hsphsun2.harvard.edu
> [mailto:owner-statalist@hsphsun2.harvard.edu]On Behalf Of Richard
> Williams
> Sent: 07 September 2004 18:25
> To: statalist@hsphsun2.harvard.edu
> Subject: st: Binomial confidence intervals
> 
> 
> The -ci- command includes several options for computing 
> binomial confidence 
> intervals: exact (the default), wilson, agresti and jeffreys. 
>  Just so I am 
> clear on these, is "exact" really really really exact?  Am I 
> correct in 
> guessing that "exact" can be the most difficult to do by 
> hand, and the 
> others are therefore approximations that are somewhat easier 
> to calculate 
> if you don't have a computer?  Is there any reason I would 
> not want to use 
> "exact", other than perhaps to replicate a calculation done 
> using one of 
> the other methods? Thanks for any insights.
> 
> 
> -------------------------------------------
> Richard Williams, Notre Dame Dept of Sociology
> OFFICE: (574)631-6668, (574)631-6463
> FAX:    (574)288-4373
> HOME:   (574)289-5227
> EMAIL:  Richard.A.Williams.5@ND.Edu
> WWW (personal):    http://www.nd.edu/~rwilliam
> WWW (department):    http://www.nd.edu/~soc
> 
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