binom.coverage
Probability coverage for binomial confidence intervals
Determines the probability coverage for a binomial confidence interval.
Usage
binom.coverage(p, n, conf.level = 0.95, method = "all", ...)
Arguments
 p
 The (true) probability of success in a binomial experiment.
 n
 Vector of number of independent trials in the binomial experiment.
 conf.level
 The level of confidence to be used in the confidence interval.
 method
 Either a character string to be passed to
binom.confint
or a function that computes the upper and lower confidence bound for a binomial proportion. If a function is supplied, the first three arguments must be the same asbinom.confint
and the return value of the function must be adata.frame
with column headers"method"
,"lower"
, and"upper"
. Seebinom.confint
for available methods. Default is"all"
.  ...
 Additional parameters to be passed to
binom.confint
. Only used when method is either"bayes"
or"profile"
Details
Derivations are based on the results given in the references. Methods
whose coverage probabilities are consistently closer to 0.95 are more
desireable. Thus, Wilson's, logit, and cloglog appear to be good for
this sample size, while Jeffreys, asymptotic, and prop.test are
poor. Jeffreys is a variation of Bayes using prior shape parameters of
0.5 and having equal probabilities in the tail. The Jeffreys'
equaltailed interval was created using binom.bayes using (0.5,0.5) as
the prior shape parameters and type = "central"
.
Value

A
data.frame
containing the "method"
used, "n"
, "p"
,
and the coverage probability, C(p,n)
.
References
L.D. Brown, T.T. Cai and A. DasGupta (2001), Interval estimation for a binomial proportion (with discussion), Statistical Science, 16:101133. L.D. Brown, T.T. Cai and A. DasGupta (2002), Confidence Intervals for a Binomial Proportion and Asymptotic Expansions, Annals of Statistics, 30:160201.
See Also
Examples
binom.coverage(p = 0.5, n = 50)