ci_prop_diff_jp: Jeffreys-Perks Confidence Interval for Difference in...

In cicalc: Calculate Confidence Intervals

Jeffreys-Perks Confidence Interval for Difference in Proportions

Description

Jeffreys-Perks Confidence Interval for Difference in Proportions

Usage

ci_prop_diff_jp(x, by, conf.level = 0.95, 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
data	(data.frame) Optional data frame containing the variables specified in x and by.

Details

The confidence interval is calculated by \theta^* \pm w where:

\theta^* = \frac{(\hat{p}_1 - \hat{p}_2) + z^2v(1-2\hat{\psi})}{1+z^2u}

where

w = \frac{z}{1+z^2u}\sqrt{u\{4\hat{\psi}(1-\hat{\psi})-(\hat{p}_1 - \hat{p}_2)^2\}+2v(1-2\hat{\psi})(\hat{p}_1-\hat{p}_2) +4z^2v^2(1-2\hat{\psi})^2 }

\hat{\psi} = \frac{1}{2}\left(\frac{x_1 + 1/2}{n_1+1}+\frac{x_2 + 1/2}{n_2+1}\right)

u = \frac{1/n_1 + 1/n_2}{4}

v = \frac{1/n_1 - 1/n_2}{4}

Value

An object containing the following components:

n	The number of responses for each group
N	The total number in each group
estimate	The point estimate of the difference in proportions (theta*)
conf.low	Lower bound of the confidence interval
conf.high	Upper bound of the confidence interval
conf.level	The confidence level used
method	Jeffreys-Perks Confidence Interval

References

Constructing Confidence Intervals for the Differences of Binomial Proportions in SAS

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_jp(x = responses, by = arm)

cicalc documentation built on Aug. 8, 2025, 7 p.m.