Confidence intervals for binomial probability of success.

Uses one of three methods to compute a confidence interval for the probability of success (p) in a binomial distribution.

binCI(
  x,
  n,
  conf.level = 0.95,
  type = c("wilson", "exact", "asymptotic"),
  verbose = FALSE
)

Arguments

x	A single or vector of numbers that contains the number of observed successes.
n	A single or vector of numbers that contains the sample size.
conf.level	A single number that indicates the level of confidence (default is `0.95`).
type	A string that identifies the type of method to use for the calculations. See details.
verbose	A logical that indicates whether `x`, `n`, and `x/n` should be included in the returned matrix (`=TRUE`) or not (`=FALSE`; DEFAULT).

Value

A #x2 matrix that contains the lower and upper confidence interval bounds as columns and, if verbose=TRUE x, n, and x/n .

Details

This function will compute confidence interval for three possible methods chosen with the type argument.

`type="wilson"`	Wilson's (Journal of the American Statistical Association, 1927) confidence interval for a proportion. This is the score CI, based on inverting the asymptotic normal test using the null standard error.
`type="exact"`	Computes the Clopper/Pearson exact CI for a binomial success probability.
`type="asymptotic"`	This uses the normal distribution approximation.

Note that Agresti and Coull (2000) suggest that the Wilson interval is the preferred method and is, thus, the default type.

References

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

Author

Derek H. Ogle, derek@derekogle.com, though this is largely based on binom.exact, binom.wilson, and binom.approx from the old epitools package.

Examples

## All types at once
binCI(7,20)
#>              95% LCI   95% UCI
#> Exact      0.1539092 0.5921885
#> Wilson     0.1811918 0.5671457
#> Asymptotic 0.1409627 0.5590373

## Individual types
binCI(7,20,type="wilson")
#>    95% LCI   95% UCI
#>  0.1811918 0.5671457
binCI(7,20,type="exact")
#>    95% LCI   95% UCI
#>  0.1539092 0.5921885
binCI(7,20,type="asymptotic")
#>    95% LCI   95% UCI
#>  0.1409627 0.5590373
binCI(7,20,type="asymptotic",verbose=TRUE)
#>            x  n proportion   95% LCI   95% UCI
#> Asymptotic 7 20       0.35 0.1409627 0.5590373

## Multiple types
binCI(7,20,type=c("exact","asymptotic"))
#>              95% LCI   95% UCI
#> Exact      0.1539092 0.5921885
#> Asymptotic 0.1409627 0.5590373
binCI(7,20,type=c("exact","asymptotic"),verbose=TRUE)
#>            x  n proportion   95% LCI   95% UCI
#> Exact      7 20       0.35 0.1539092 0.5921885
#> Asymptotic 7 20       0.35 0.1409627 0.5590373

## Use with multiple inputs
binCI(c(7,10),c(20,30),type="wilson")
#>    95% LCI   95% UCI
#>  0.1811918 0.5671457
#>  0.1923050 0.5121995
binCI(c(7,10),c(20,30),type="wilson",verbose=TRUE)
#>       x  n proportion   95% LCI   95% UCI
#> [1,]  7 20  0.3500000 0.1811918 0.5671457
#> [2,] 10 30  0.3333333 0.1923050 0.5121995