Cohen's d (i.e., standardized mean difference) value.
n_exp
number of participants in the experimental/exposed group.
n_nexp
number of participants in the non-experimental/non-exposed group.
smd_to_cor
formula used to convert the cohen_d value into a coefficient correlation (see details).
reverse_d
a logical value indicating whether the direction of generated effect sizes should be flipped.
Details
This function estimates the standard error of a Cohen's d value and computes a Hedges' g (G).
Odds ratio (OR) and correlation coefficients (R/Z) are then converted from the Cohen's d.
To estimate the standard error of Cohen's d, the following formula is used (formula 12.13 in Cooper):
B. To estimate the correlation coefficient according to Cooper et al. (2019) (formulas 12.40-42)
and Borenstein et al. (2009) (formulas 54-56),
the following formulas are used (smd_to_cor="lipsey_cooper"):
p=n_exp+n_nexpn_exp
R=cohen_d2+1/(p∗(1−p))cohen_d
a=(n_exp∗n_nexp)(n_exp+n_nexp)2
var_R=(cohen_d2+a)3a2∗cohen_d_se2
R_se=R_var
R_ci_lo=R−qt(.975,n_exp+n_nexp−2)∗R_se
R_ci_up=R+qt(.975,n_exp+n_nexp−2)∗R_se
Z=atanh(R)
Z_var=cohen_d_se2+(1/p∗(1−p))cohen_d_se2
Z_se=Z_var
Z_ci_lo=Z−qnorm(.975)∗Z_se
Z_ci_up=Z+qnorm(.975)∗Z_se
Value
This function estimates and converts between several effect size measures.
natural effect size measure
D + G
converted effect size measure
OR + R + Z
required input data
See 'Section 1. Cohen's d or Hedges' g'
https://metaconvert.org/html/input.html
References
Cooper, H., Hedges, L.V., & Valentine, J.C. (Eds.). (2019). The handbook of research synthesis and meta-analysis. Russell Sage Foundation.
Borenstein, M., Hedges, L. V., Higgins, J. P., & Rothstein, H. R. (2021). Introduction to meta-analysis. John Wiley & Sons.
Hedges LV (1981): Distribution theory for Glass’s estimator of effect size and related estimators. Journal of Educational and Behavioral Statistics, 6, 107–28
Jacobs, P., & Viechtbauer, W. (2017). Estimation of the biserial correlation and its sampling variance for use in meta-analysis. Research synthesis methods, 8(2), 161–180.