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Wilson and Clopper-Pearson Confidence Intervals for Binomial Proportions

Source: R/nemsqa_binomial_confint.R
nemsqa_binomial_confint.Rd

[Experimental]

Computes confidence intervals for binomial proportions using either the Wilson or Clopper-Pearson method. This function supports vectorized operations and allows optional correction for continuity. The Wilson interval is computed using stats::prop.test(), while the Clopper-Pearson interval is computed using stats::binom.test().

Usage

nemsqa_binomial_confint(
  data = NULL,
  x,
  n,
  method = c("wilson", "clopper-pearson"),
  conf.level = 0.95,
  correct = TRUE
)

Arguments

data

An optional tibble or data.frame containing the variables x and n. If provided, x and n should be column names.

x

Numeric vector or column name (if data is provided) representing the number of successes.

n

Numeric vector or column name (if data is provided) representing the total number of trials.

method

Character string specifying the confidence interval method. Must be either "wilson" (default) or "clopper-pearson".

conf.level

Numeric value between 0 and 1 indicating the confidence level. Defaults to 0.95 (95% confidence interval).

correct

Logical, indicating whether to apply continuity correction for Wilson intervals. Defaults to TRUE.

Value

A tibble containing the estimated proportion (prop), lower confidence interval (lower_ci), upper confidence interval (upper_ci), and a formatted proportion label (prop_label). If data is provided, these columns are appended to data via dplyr::bind_cols().

Details

The Wilson confidence interval is calculated using stats::prop.test(), which provides an improved approximation to the binomial proportion confidence interval by avoiding the instability of the Wald interval (Wilson, 1927). The Clopper-Pearson interval, computed using stats::binom.test(), is an exact method based on the cumulative probabilities of the binomial distribution (Clopper & Pearson, 1934).

The use of match.arg() within nemsqar::nemsqa_binomial_confint() allows users to specify the method using partial matching, meaning they can enter just "w" instead of "wilson" or "c" instead of "clopper-pearson".

References

Clopper, C. J. & Pearson, E. S. (1934). The use of confidence or fiducial limits illustrated in the case of the binomial. Biometrika, 26, 404–413. doi:10.2307/2331986.

Wilson, E.B. (1927). Probable inference, the law of succession, and statistical inference. Journal of the American Statistical Association, 22, 209–212. doi:10.2307/2276774.

Examples

# Example without a data frame
nemsqa_binomial_confint(data = NULL,
                        x = c(5, 10, 20),
                        n = c(50, 100, 200),
                        method = "wilson"
                        )
#> # A tibble: 3 × 4
#>    prop prop_label lower_ci upper_ci
#>   <dbl> <chr>         <dbl>    <dbl>
#> 1   0.1 10%          0.0374    0.226
#> 2   0.1 10%          0.0516    0.180
#> 3   0.1 10%          0.0637    0.152

# Example with a data.frame
data <- data.frame(successes = c(5, 10, 20), trials = c(50, 100, 200))
nemsqa_binomial_confint(data,
                        x = successes,
                        n = trials,
                        method = "clopper-pearson"
                        )
#>   successes trials prop prop_label   lower_ci  upper_ci
#> 1         5     50  0.1        10% 0.03327509 0.2181354
#> 2        10    100  0.1        10% 0.04900469 0.1762226
#> 3        20    200  0.1        10% 0.06215937 0.1502128