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Effect Size Conversions

Source: vignettes/effect-size-conversions.Rmd
effect-size-conversions.Rmd

Helper functions convert study parameters into effect sizes used by power_compute().

Cohen’s d

d=μ1−μ0σd = \frac{\mu_1 - \mu_0}{\sigma}

effect_size_d(mean_h1 = 15, mean_h0 = 10, sd = 8)
#> [1] 0.625

Cohen’s f from η2\eta^2

f=η21−η2f = \sqrt{\frac{\eta^2}{1-\eta^2}}

effect_size_f(eta2 = 0.06)
#> [1] 0.2526456
eta2_from_f(0.25)
#> [1] 0.05882353

Cohen’s f2f^2 from R2R^2

f2=R21−R2f^2 = \frac{R^2}{1-R^2}

effect_size_f2(r2 = 0.1)
#> [1] 0.1111111
r2_from_f2(0.1111111)
#> [1] 0.09999999

R2R^2 increase

f2=Rfull2−Rreduced21−Rfull2f^2 = \frac{R^2_{\text{full}} - R^2_{\text{reduced}}}{1 - R^2_{\text{full}}}

effect_size_f2_increase(r2_full = 0.2, r2_reduced = 0.1)
#> [1] 0.125

Cohen’s w (chi-square)

w=∑i(p1i−p0i)2p0iw = \sqrt{\sum_i \frac{(p_{1i} - p_{0i})^2}{p_{0i}}}

effect_size_w(p0 = c(0.25, 0.25, 0.25, 0.25), p1 = c(0.4, 0.3, 0.2, 0.1))
#> [1] 0.4472136

Cohen’s h (proportions)

h=2arcsin⁡(p1)−2arcsin⁡(p0)h = 2\arcsin(\sqrt{p_1}) - 2\arcsin(\sqrt{p_0})

effect_size_h(p1 = 0.45, p2 = 0.3)
#> [1] 0.3113494