d_prop: Cohen's d (SMD) for Independent Proportions (Binary Outcomes)

In MOTE: Effect Size and Confidence Interval Calculator

Cohen's d (SMD) for Independent Proportions (Binary Outcomes)

Description

This function computes a standardized mean difference effect size for two independent proportions by treating each as the mean of a Bernoulli (0/1) variable and computing a standardized mean difference (SMD) directly using the pooled Bernoulli standard deviation. This follows the same logic as Cohen's d for continuous variables, but applied to binary outcomes:

Usage

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

d.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

d = \frac{p_1 - p_2}{s_{\mathrm{pooled}}}

where

s_{\mathrm{pooled}} = \sqrt{\frac{(n_1 - 1)p_1(1 - p_1) + (n_2 - 1)p_2(1 - p_2)} {n_1 + n_2 - 2}}

This replaces the original z‐based formulation used in older versions of MOTE. The SMD effect size is directly comparable to all other d‐type effect sizes in the package.

Value

A list with the same structure as [d_ind_t()], containing the standardized mean difference and its confidence interval, along with auxiliary statistics. The list is augmented with explicit entries 'p1', 'p2', 'p1_value', and 'p2_value' to emphasize that the original inputs were proportions.

Examples

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

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