Wald Confidence Interval for Difference in Proportions

Calculates the Wald interval by following the usual textbook definition for a difference in proportions confidence interval using the normal approximation.

Usage

ci_prop_diff_wald(x, by, conf.level = 0.95, correct = FALSE, data = NULL)

Arguments

x

(binary/numeric/logical)
vector of a binary values, i.e. a logical vector, or numeric with values c(0, 1)

by

(string)
A character or factor vector with exactly two unique levels identifying the two groups to compare. Can also be a column name if a data frame provided in the data argument.

conf.level

(scalar numeric)
a scalar in (0,1) indicating the confidence level. Default is 0.95

correct

(logical)
apply continuity correction.

data

(data.frame)
Optional data frame containing the variables specified in x and by.

Value

A list containing the following components:

estimate

The point estimate of the difference in proportions (p_x - p_y)

conf.low

Lower bound of the confidence interval

conf.high

Upper bound of the confidence interval

conf.level

The confidence level used

Details

$$(\hat{p}_1 - \hat{p}_2) \pm z_{\alpha/2} \sqrt{\frac{\hat{p}_1(1 - \hat{p}_1)}{n_1}+\frac{\hat{p}_2(1 - \hat{p}_2)}{n_2}}$$

Examples

responses <- expand(c(9, 3), c(10, 10))
arm <- rep(c("treat", "control"), times = c(10, 10))

# Calculate 95% confidence interval for difference in proportions
ci_prop_diff_wald(x = responses, by = arm)
#> 
#> ── Wald Confidence Interval without Continuity Correction ──────────────────────
#> • 9/10 - 3/10
#> • Estimate: 0.6
#> • 95% Confidence Interval:
#>   (0.2605, 0.9395)