ci_p_wald_bs: Wald with Blyth and Still approximation Binomial Score...

In fhernanb/stests: Package with useful statistical tests

Wald with Blyth and Still approximation Binomial Score confidence interval for Binomial proportion

Description

This function calculates the Wald Binomial Score confidence interval for a Binomial proportion. It is vectorized, allowing the evaluation of single values or vectors.

Usage

ci_p_wald_bs(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, it is 0.95.

Details

The Wald Binomial Score confidence interval is an adjusted version of the Wald interval, designed to improve accuracy in small samples and near the boundaries of the parameter space.

The estimated proportion is given by:

\hat{p} = \frac{x}{n}

,

and its complement is:

\hat{q} = 1 - \hat{p}

.

The Wald Binomial Score interval incorporates adjustments for the sample size and confidence level:

\text{wn\_z} = \sqrt{n - z^2 - \frac{2z}{\sqrt{n}} - \frac{1}{n}}

,

where z is the quantile of the standard normal distribution corresponding to the confidence level. The final confidence interval is given by:

\text{Lower} = \hat{p} - \frac{z \sqrt{\hat{p}\hat{q} + \frac{1}{2n}}}{\text{wn\_z}},

\text{Upper} = \hat{p} + \frac{z \sqrt{\hat{p}\hat{q} + \frac{1}{2n}}}{\text{wn\_z}}.

This interval is particularly useful when n is small or when the proportion \hat{p} is close to 0 or 1.

Value

A vector with the lower and upper limits of the confidence interval.

Author(s)

David Esteban Cartagena Mejía, [e-mail]

References

Blyth, C.R. and Still, H.A. (1983). Binomial confidence intervals, Journal of the American Statistical Association, 78, 108–116.

See Also

ci_p.

Examples

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

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