binom (version 1.1-1.1)

# binom.confint: Binomial confidence intervals

## Description

Uses eight different methods to obtain a confidence interval on the binomial probability.

## Usage

`binom.confint(x, n, conf.level = 0.95, methods = "all", ...)`

## Arguments

x

Vector of number of successes in the 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.

methods

Which method to use to construct the interval. Any combination of ```c("exact", "ac", "asymptotic", "wilson", "prop.test", "bayes", "logit", "cloglog", "probit")``` is allowed. Default is `"all"`.

Additional arguments to be passed to `binom.bayes`.

## Value

A `data.frame` containing the observed proportions and the lower and upper bounds of the confidence interval for all the methods in `"methods"`.

## Details

Nine methods are allowed for constructing the confidence interval(s):

• `exact` - Pearson-Klopper method. See also `binom.test`.

• `asymptotic` - the text-book definition for confidence limits on a single proportion using the Central Limit Theorem.

• `agresti-coull` - Agresti-Coull method. For a 95% confidence interval, this method does not use the concept of "adding 2 successes and 2 failures," but rather uses the formulas explicitly described in the following link: http://en.wikipedia.org/wiki/Binomial_proportion_confidence_interval#Agresti-Coull_Interval.

• `wilson` - Wilson method.

• `prop.test` - equivalent to ```prop.test(x = x, n = n, conf.level = conf.level)\$conf.int```.

• `bayes` - see `binom.bayes`.

• `logit` - see `binom.logit`.

• `cloglog` - see `binom.cloglog`.

• `probit` - see `binom.probit`.

• `profile` - see `binom.profile`.

By default all eight are estimated for each value of `x` and/or `n`. For the "logit", "cloglog", "probit", and "profile" methods, the cases where `x == 0` or `x == n` are treated separately. Specifically, the lower bound is replaced by `(alpha/2)^n` and the upper bound is replaced by `(1-alpha/2)^n`.

## References

A. Agresti and B.A. Coull (1998), Approximate is better than "exact" for interval estimation of binomial proportions, American Statistician, 52:119-126.

R.G. Newcombe, Logit confidence intervals and the inverse sinh transformation (2001), American Statistician, 55:200-202.

L.D. Brown, T.T. Cai and A. DasGupta (2001), Interval estimation for a binomial proportion (with discussion), Statistical Science, 16:101-133.

Gelman, A., Carlin, J. B., Stern, H. S., and Rubin, D. B. (1997) Bayesian Data Analysis, London, U.K.: Chapman and Hall.

`binom.bayes`, `binom.logit`, `binom.probit`, `binom.cloglog`, `binom.coverage`, `prop.test`, `binom.test` for comparison to method `"exact"`
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