Confidence Interval for a Single Proportion

The Wilson (1927) score interval for a binomial proportion, the package's default for proportion inference: unlike the textbook Wald interval it cannot escape [0, 1], behaves sensibly at 0 and 1 counts, and holds close to nominal coverage at small n (Brown, Cai, & DasGupta, 2001, recommend it for general use). The Wald interval is available for instruction and comparison.

Usage

ci_proportion(successes, n, conf_level = 0.95, method = c("wilson", "wald"))

Arguments

successes: Number of successes, a single non-negative integer.
n: Number of trials, a single positive integer at least successes.
conf_level: Confidence level. Defaults to 0.95.
method: "wilson" (default) or "wald".

Value

A data.frame (class dmar_tbl) with rows lower_limit, proportion, upper_limit, successes, and n, so the point estimate sits between its confidence limits.

References

Brown, L. D., Cai, T. T., & DasGupta, A. (2001). Interval estimation for a binomial proportion. Statistical Science, 16(2), 101–133. doi:10.1214/ss/1009213286

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

Author

Ken Kelley kkelley@nd.edu

Examples

ci_proportion(successes = 17, n = 50)
#>  term        value
#>  lower_limit 0.224
#>  proportion  0.34 
#>  upper_limit 0.478
#>  successes   17   
#>  n           50   
#> 
#> Confidence level: 95%

# The Wilson interval stays inside [0, 1] even at the boundary.
ci_proportion(successes = 0, n = 20)
#>  term        value   
#>  lower_limit 1.39e-17
#>  proportion  0       
#>  upper_limit 0.161   
#>  successes   0       
#>  n           20      
#> 
#> Confidence level: 95%