Wald Continuity-Corrected confidence interval for Binomial proportion

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

ci_p_wald_cc(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.

Value

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

Details

The Wald continuity-corrected confidence interval adjusts the standard Wald interval for small sample sizes or when the proportion \(\hat{p}\) is near 0 or 1. It incorporates a continuity correction to improve accuracy.

The estimated proportion is given by:

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

and its complement is:

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

The continuity-corrected interval incorporates the critical value \(z\) from the standard normal distribution:

$$\text{Lower} = \hat{p} - z \sqrt{\frac{\hat{p}\hat{q}}{n}} - \frac{1}{2n},$$ $$\text{Upper} = \hat{p} + z \sqrt{\frac{\hat{p}\hat{q}}{n}} + \frac{1}{2n}.$$

These adjustments ensure that the confidence interval is valid even at the boundaries of the parameter space.

References

Pires, Ana M., and Conceiçao Amado. "Interval estimators for a binomial proportion: Comparison of twenty methods". REVSTAT-Statistical Journal 6.2 (2008): 165-197.

See also

ci_p.

Author

David Esteban Cartagena Mejía, dcartagena@unal.edu.co

Examples

ci_p_wald_cc(x = 15, n = 50, conf.level = 0.95)
#>           [,1]
#> [1,] 0.1629798
#> [2,] 0.4370202
ci_p_wald_cc(x = 0, n = 50, conf.level = 0.95)
#>           [,1]
#> [1,] 0.0000000
#> [2,] 0.9288783
ci_p_wald_cc(x = 50, n = 50, conf.level = 0.95)
#>            [,1]
#> [1,] 0.07112174
#> [2,] 1.00000000