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Functions for transforming between standard errors of different effect size measures.

Usage

se_d2se_logOR(se_d, logOR)

se_d2se_r(se_d, d)

se_r2se_d(se_r, r)

se_logOR2se_d(se_logOR, logOR)

se_d2se_z(se_d, d)

se_r2se_z(se_r, r)

se_r2se_logOR(se_r, r)

se_logOR2se_r(se_logOR, logOR)

se_logOR2se_z(se_logOR, logOR)

se_z2se_d(se_z, z)

se_z2se_r(se_z, z)

se_z2se_logOR(se_z, z)

Arguments

se_d

standard error of Cohen's d

logOR

log(odds ratios)

d

Cohen's d

se_r

standard error of correlation coefficient

r

correlation coefficient

se_logOR

standard error of log(odds ratios)

se_z

standard error of Fisher's z

z

Fisher's z

Details

Transformations for Cohen's d, Fisher's z, and log(OR) are based on borenstein2011introductionRoBMA. Calculations for correlation coefficient were modified to make the standard error corresponding to the computed on Fisher's z scale under the same sample size (in order to make all other transformations consistent). In case that a direct transformation is not available, the transformations are chained to provide the effect size of interest.

It is important to keep in mind that the transformations are only approximations to the true values. From our experience, se_d2se_z works well for values of se(Cohen's d) < 0.5. Do not forget that the effect sizes are standardized and variance of Cohen's d = 1. Therefore, a standard error of study cannot be larger unless the participants provided negative information (of course, the variance is dependent on the effect size as well, and, can therefore be larger).

When setting prior distributions, do NOT attempt to transform a standard normal distribution on Cohen's d (mean = 0, sd = 1) to a normal distribution on Fisher's z with mean 0 and sd = se_d2se_z(0, 1). The approximation does NOT work well in this range of values. Instead, approximate the sd of distribution on Fisher's z using samples in this way: sd(d2z(rnorm(10000, 0, 1))) or, specify the distribution on Cohen's d directly.

References