ci_p_wilson: Wilson confidence interval for Binomial proportion

In fhernanb/stests: Package with useful statistical tests

Wilson confidence interval for Binomial proportion

Description

This function calculates the confidence interval for a proportion. It is vectorized, allowing users to evaluate it using either single values or vectors.

Usage

ci_p_wilson(x, n, conf.level = 0.95)

Arguments

x	a number or a vector with the number of successes.
n	a number or a vector with the number of trials.
conf.level	confidence level for the returned confidence interval. By default is 0.95.

Details

The expression to obtain the confidence interval is given below:

\frac{\hat{p}+ \frac{z_{\alpha/2}^2}{2n}}{\widetilde{n}} \pm \frac{z_{\alpha/2}^2}{\widetilde{n}} \sqrt{ (\hat{p}(1 - \hat{p}) + \frac{z_{\alpha/2}^2}{4n} )/n},

where \hat{p}=\frac{x}{n} is the sample proportion, \widetilde{n}=1 + \frac{ z_{\alpha/2}^2}{n}, x the number of observed successes in the sample with size n. The value z_{\alpha/2} is the 1-\alpha/2 percentile of the standard normal distribution (e.g., z_{0.025}=1.96 for a 95% confidence interval).

Value

A matrix with the lower and upper limits.

Author(s)

Victor David Usuga, [e-mail]

References

Wilson, E. B. (1927). Probable inference, the law of succession, and statistical inference. Journal of the American Statistical Association, 22(158), 209-212.

See Also

ci_p.

Examples

ci_p_wilson(x= 0, n=50, conf.level=0.95)
ci_p_wilson(x=15, n=50, conf.level=0.95)
ci_p_wilson(x=50, n=50, conf.level=0.95)

fhernanb/stests documentation built on March 29, 2025, 10:36 a.m.