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:
d_prop(p1, p2, n1, n2, a = 0.05)d.prop(p1, p2, n1, n2, a = 0.05)
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.
Proportion for group one (between 0 and 1).
Proportion for group two (between 0 and 1).
Sample size for group one.
Sample size for group two.
Significance level used for confidence intervals. Defaults to 0.05.
$$d = \frac{p_1 - p_2}{s_{\mathrm{pooled}}}$$
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.
d_prop(p1 = .25, p2 = .35, n1 = 100, n2 = 100, a = .05)
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