Agresti-Coull confidence interval for a binomial proportion

Agresti-Coull confidence interval for a binomial proportion

Usage

agrestiCoullCI(n1, n0, q)

Arguments

n1

number of successes/ones

n0

number of failures/zeroes

q

quantile for eventual CI (e.g. 0.95 for a 95 percent binomial CI)

Value

the approximate (q x 100) percent confidence interval for (p|n1,n0,q)

Details

\(z_\alpha = \Phi^{-1}(1 - \frac{\alpha}{2})\)

\(\tilde{n} = n_{\text{successes}} + n_{\text{failures}} + z^2_\alpha\)

\(\tilde{p} = \frac{1}{\tilde{n}}(n_{\text{success}} + \frac{z^2_\alpha}{2})\)

\(p \approx \tilde{p} \pm z_\alpha \times \sqrt{\frac{\tilde{p}}{\tilde{n}} \times (1 - \tilde{p})}\)

Examples

agrestiCoullCI(10, 3, 0.95)
#>    conf.est conf.est.lowerCI conf.est.upperCI
#> 1 0.7078205         0.490628        0.9250129