binom.length: Expected length for binomial confidence intervals

In binom: Binomial Confidence Intervals For Several Parameterizations

Description

Determines the expected length for a binomial confidence interval.

Usage

binom.length(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 as binom.confint and the return value of the function must be a data.frame with column headers "method", "lower" and "upper". See binom.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 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".

Value

A data.frame containing the "method" used, "n", "p", and the average length, L(p,n).

Author(s)

Sundar Dorai-Raj ([e-mail])

References

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.

See Also

binom.confint, binom.coverage

Examples

binom.length(p = 0.5, n = 50)

Example output

          method  n   p    length
1  agresti-coull 50 0.5 0.2647754
2     asymptotic 50 0.5 0.2743657
3          bayes 50 0.5 0.2678533
4        cloglog 50 0.5 0.2701117
5          exact 50 0.5 0.2867770
6          logit 50 0.5 0.2678187
7         probit 50 0.5 0.2690582
8        profile 50 0.5 0.2692184
9            lrt 50 0.5 0.2692274
10     prop.test 50 0.5 0.2810356
11        wilson 50 0.5 0.2645934

binom documentation built on May 2, 2019, 5:16 p.m.