# binom.confint: Binomial confidence intervals In binom: Binomial Confidence Intervals For Several Parameterizations

## Description

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

## Usage

 `1` ```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`.

## 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`.

## Value

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

## Author(s)

Sundar Dorai-Raj ([email protected])

## 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"`
 `1` ```binom.confint(x = c(2, 4), n = 100, tol = 1e-8) ```