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:
h_prop(p1, p2, n1, n2, a = 0.05)h.prop(p1, p2, n1, n2, a = 0.05)
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.
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.
$$h = 2 \arcsin \sqrt{p_1} - 2 \arcsin \sqrt{p_2}$$
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.
h_prop(p1 = .25, p2 = .35, n1 = 100, n2 = 100, a = .05)
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