Functions for transforming between standard errors of different effect size measures.
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)standard error of Cohen's d
log(odds ratios)
Cohen's d
standard error of correlation coefficient
correlation coefficient
standard error of log(odds ratios)
standard error of Fisher's z
Fisher's z
Transformations for Cohen's d, Fisher's z, and log(OR) are based on (Borenstein et al. 2011) . 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.
Borenstein M, Hedges LV, Higgins JP, Rothstein HR (2011). Introduction to meta-analysis. John Wiley & Sons.