Expected length for binomial confidence intervals
Determines the expected length for a binomial confidence interval.
binom.length(p, n, conf.level = 0.95, method = "all", ...)
- The (true) probability of success in a binomial experiment.
- Vector of number of independent trials in the binomial experiment.
- The level of confidence to be used in the confidence interval.
- Either a character string to be passed to
binom.confintor 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 as
binom.confintand the return value of the function must be a
data.framewith column headers
binom.confintfor available methods. Default is
- Additional parameters to be passed to
binom.confint. Only used when method is either
Derivations are based on the results given in the references. Methods
whose length 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'
equal-tailed interval was created using binom.bayes using (0.5,0.5) as
the prior shape parameters and
type = "central".
"p", and the average length,
L.D. Brown, T.T. Cai and A. DasGupta (2001), Interval estimation for a binomial proportion (with discussion), Statistical Science, 16:101-133. L.D. Brown, T.T. Cai and A. DasGupta (2002), Confidence Intervals for a Binomial Proportion and Asymptotic Expansions, Annals of Statistics, 30:160-201.
binom.length(p = 0.5, n = 50)