[R] R function which finds confidence interval for binomial variance

Robert A LaBudde ral at lcfltd.com
Fri Sep 26 08:26:11 CEST 2008

Thanks Ralph, Moshe and ctu at bigred.unl.edu for you helpful comments.

Using bootstrap (e.g., 'boot' + boot.ci()) for the confidence 
interval on the variance is not very accurate in coverage, because 
the sampling distribution is extremely skewed. In fact, the 'BCa' 
method returns the same result as the Efron 'percent' method.

Moshe's idea of treating the confidence interval for the binomial 
variance as a transform of the confidence interval for the binomial 
proportion is elegant (Doh! Why didn't I think of that?), except that 
the transform is bivalued, although monotonic on each branch, with 
the branch point singularity at p=0.5.

The bootstrap method does not have much coverage accuracy for any 
proportion, for n=6, 12 and 20, and the proportion method works great 
for n=6, 12, 20 and 50, except near p = 0.5, where it fails to 
achieve reasonable coverage.

So I'm still looking for a reliable method for all p and for reasonable n.

The proportion-based method is the best I've found, so far.
Robert A. LaBudde, PhD, PAS, Dpl. ACAFS  e-mail: ral at lcfltd.com
Least Cost Formulations, Ltd.            URL: http://lcfltd.com/
824 Timberlake Drive                     Tel: 757-467-0954
Virginia Beach, VA 23464-3239            Fax: 757-467-2947

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