Anderson-Hauck Confidence Interval for Difference in Proportions

Usage

ci_prop_diff_ha(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.

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
conf.low: Lower bound of the confidence interval
conf.high: Upper bound of the confidence interval
conf.level: The confidence level used
method: Anderson-Hauck Confidence Interval

Details

The confidence interval is given by:

$$(\hat{p}_1 - \hat{p}_2) \pm \left[ \frac{1}{2 \min(n_1, n_2)} + z \sqrt{ \frac{\hat{p}_1 (1 - \hat{p}_1)}{n_1 - 1} + \frac{\hat{p}_2 (1 - \hat{p}_2)}{n_2 - 1} } \right]$$.

References

Hauck WW, Anderson S. (1986) A comparison of large-sample confidence interval methods for the difference of two binomial probabilities The American Statistician 40(4). p.318-322. 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_ha(x = responses, by = arm)
#> 
#> ── Anderson-Hauck Confidence Interval ──────────────────────────────────────────
#> • 9/10 - 3/10
#> • Estimate: 0.6
#> • 95% Confidence Interval:
#>   (0.1922, 1)