binomCI {MKinfer}

Confidence Intervals for Binomial Proportions

Description

This function can be used to compute confidence intervals for binomial proportions.

Usage

binomCI(x, n, conf.level = 0.95, method = "wilson", rand = 123, 
        R = 9999, bootci.type = "all", 
        alternative = c("two.sided", "less", "greater"), ...)

Arguments

x

number of successes

n

number of trials

conf.level

confidence level

method

character string specifing which method to use; see details.

rand

seed for random number generator; see details.

R

number of bootstrap replicates.

bootci.type

type of bootstrap interval; see boot.ci.

alternative

a character string specifying one- or two-sided confidence intervals. Must be one of "two.sided" (default), "greater" or "less" (one-sided intervals). You can specify just the initial letter.

...

further arguments passed to function boot, e.g. for parallel computing.

Details

The Wald interval is obtained by inverting the acceptance region of the Wald large-sample normal test. There is also a Wald interval with continuity correction ("wald-cc").

The Wilson interval, which is the default, was introduced by Wilson (1927) and is the inversion of the CLT approximation to the family of equal tail tests of p = p0. The Wilson interval is recommended by Agresti and Coull (1998) as well as by Brown et al (2001).

The Agresti-Coull interval was proposed by Agresti and Coull (1998) and is a slight modification of the Wilson interval. The Agresti-Coull intervals are never shorter than the Wilson intervals; cf. Brown et al (2001).

The Jeffreys interval is an implementation of the equal-tailed Jeffreys prior interval as given in Brown et al (2001).

The modified Wilson interval is a modification of the Wilson interval for x close to 0 or n as proposed by Brown et al (2001).

The modified Jeffreys interval is a modification of the Jeffreys interval for x == 0 | x == 1 and x == n-1 | x == n as proposed by Brown et al (2001).

The Clopper-Pearson interval is based on quantiles of corresponding beta distributions. This is sometimes also called exact interval.

The arcsine interval is based on the variance stabilizing distribution for the binomial distribution.

The logit interval is obtained by inverting the Wald type interval for the log odds.

The Witting interval (cf. Beispiel 2.106 in Witting (1985)) uses randomization to obtain uniformly optimal lower and upper confidence bounds (cf. Satz 2.105 in Witting (1985)) for binomial proportions.

The bootstrap interval is calculated by using function boot.ci.

For more details we refer to Brown et al (2001) as well as Witting (1985).

Value

A list with class "confint" containing the following components:

estimate

the estimated probability of success.

conf.int

a confidence interval for the probability of success.

Note

A first version of this function appeared in R package SLmisc.

Author(s)

Matthias Kohl [e-mail]

References

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

L.D. Brown, T.T. Cai and A. Dasgupta (2001). Interval estimation for a binomial proportion. Statistical Science, 16(2), 101-133.

H. Witting (1985). Mathematische Statistik I. Stuttgart: Teubner.

See Also

binom.test

Examples

binomCI(x = 42, n = 43, method = "wald")
binomCI(x = 42, n = 43, method = "wald-cc")
binomCI(x = 42, n = 43, method = "wilson")
binomCI(x = 42, n = 43, method = "agresti-coull")
binomCI(x = 42, n = 43, method = "jeffreys")
binomCI(x = 42, n = 43, method = "modified wilson")
binomCI(x = 42, n = 43, method = "modified jeffreys")
binomCI(x = 42, n = 43, method = "clopper-pearson")
binomCI(x = 42, n = 43, method = "arcsine")
binomCI(x = 42, n = 43, method = "logit")
binomCI(x = 42, n = 43, method = "witting")
## bootstrap intervals (R = 999 to reduce computation time for R checks)
binomCI(x = 42, n = 43, method = "boot", R = 999) # may generate values > 1!

## the confidence interval computed by binom.test
## corresponds to the Clopper-Pearson interval
binomCI(x = 42, n = 43, method = "clopper-pearson")$conf.int
binom.test(x = 42, n = 43)$conf.int

## one-sided intervals
binomCI(x = 10, n = 43, alternative = "less")
binomCI(x = 10, n = 43, alternative = "less", method = "boot", 
        bootci.type = "bca", R = 999)
binomCI(x = 10, n = 43, alternative = "greater", method = "boot", 
        bootci.type = "perc", R = 999)
        

## parallel computing for bootstrap
binomCI(x = 10, n = 43, method = "boot", R = 9999, 
        parallel = "multicore", ncpus = 2)