ci_prop_diff_haldane: Haldane Confidence Interval for Difference in Proportions

In cicalc: Calculate Confidence Intervals

Haldane Confidence Interval for Difference in Proportions

Description

Haldane Confidence Interval for Difference in Proportions

Usage

ci_prop_diff_haldane(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{\hat{p}_1 + \hat{p}_2}{2}

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	Haldane 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_haldane(x = responses, by = arm)

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