h_prop: Cohen's h for Independent Proportions

In MOTE: Effect Size and Confidence Interval Calculator

Cohen's h for Independent Proportions

Description

This function computes Cohen's h effect size for the difference between two independent proportions. Cohen's h is defined as a difference between arcsine-transformed proportions:

Usage

h_prop(p1, p2, n1, n2, a = 0.05)

h.prop(p1, p2, n1, n2, a = 0.05)

Arguments

p1	Proportion for group one (between 0 and 1).
p2	Proportion for group two (between 0 and 1).
n1	Sample size for group one.
n2	Sample size for group two.
a	Significance level used for confidence intervals. Defaults to 0.05.

Details

h = 2 \arcsin \sqrt{p_1} - 2 \arcsin \sqrt{p_2}

where p_1 and p_2 are proportions for groups 1 and 2, respectively.

Using a simple large-sample approximation (via the delta method), the standard error of h can be taken as:

\mathrm{SE}(h) \approx \sqrt{1 / n_1 + 1 / n_2}

,

which leads to a (1 - \alpha) confidence interval for h:

h \pm z_{1 - \alpha/2} \, \mathrm{SE}(h).

This effect size is commonly recommended for differences in proportions (Cohen, 1988) and is particularly useful for power analysis and meta-analysis when working directly with proportions.

Value

A list containing Cohen's h effect size and related statistics:

• ‘h' – Cohen’s h.

• 'hlow', 'hhigh' – lower and upper confidence interval limits.

• 'h_lower_limit', 'h_upper_limit' – snake_case aliases for the confidence limits.

• 'p1', 'p2' – input proportions for each group.

• 'n1', 'n2' – sample sizes for each group, with snake_case aliases 'sample_size_1', 'sample_size_2'.

• 'z', 'p' – z statistic and p value for the difference in proportions using a pooled-proportion standard error.

• 'z_value', 'p_value' – snake_case aliases for the z statistic and p value.

• 'estimate' – APA-style formatted string for Cohen's h and its confidence interval.

• 'statistic' – APA-style formatted string for the z test of the difference in proportions.

Examples

h_prop(p1 = .25, p2 = .35, n1 = 100, n2 = 100, a = .05)

MOTE documentation built on Dec. 15, 2025, 9:06 a.m.