Calculates the Agresti-Coull interval (created by Alan Agresti and Brent Coull) by
(for 95% CI) adding two successes and two failures to the data and then using the Wald formula to construct a CI.
Usage
ci_prop_agresti_coull(x, conf.level = 0.95, data = NULL)
Arguments
- x
(binary/numeric/logical)
vector of a binary values, i.e. a logical vector, or numeric with values c(0, 1)
- conf.level
(scalar numeric)
a scalar in (0,1) indicating the confidence level. Default is 0.95
- data
(data.frame)
Optional data frame containing the variables specified in x and by.
Details
$$
\left( \frac{\tilde{p} + z^2_{\alpha/2}/2}{n + z^2_{\alpha/2}} \pm
z_{\alpha/2} \sqrt{\frac{\tilde{p}(1 - \tilde{p})}{n} +
\frac{z^2_{\alpha/2}}{4n^2}} \right)$$