es_from_fisher_z function

Convert a Fisher's z (r-to-z transformation) to several effect size measures

es_from_fisher_z(
  fisher_z,
  n_sample,
  unit_type = "raw_scale",
  n_exp,
  n_nexp,
  cor_to_smd = "viechtbauer",
  sd_iv,
  unit_increase_iv,
  reverse_fisher_z
)

Arguments

• fisher_z: a Fisher's r-to-z transformed correlation coefficient
• n_sample: the total number of participants
• unit_type: the type of unit for the unit_increase_iv argument. Must be either "sd" or "value"
• n_exp: number of the experimental/exposed group
• n_nexp: number of the non-experimental/non-exposed group
• cor_to_smd: formula used to convert a pearson_r or fisher_z value into a SMD.
• sd_iv: the standard deviation of the independent variable
• unit_increase_iv: a value of the independent variable that will be used to estimate the Cohen's d (see details).
• reverse_fisher_z: a logical value indicating whether the direction of the generated effect sizes should be flipped.

Returns

This function estimates and converts between several effect size measures.

natural effect size measure	R + Z
converted effect size measure	D + G + OR
required input data	See 'Section 4. Pearson's r or Fisher's z'
	https://metaconvert.org/input.html

Details

This function converts estimates the standard error of the Fisher's z and performs the z-to-r Fisher's transformation.

Last, it converts this r value into a Cohen's d and OR (see details in es_from_pearson_r()).

Examples

es_from_fisher_z(
  fisher_z = .21, n_sample = 44,
)

References

Cooper, H., Hedges, L.V., & Valentine, J.C. (Eds.). (2019). The handbook of research synthesis and meta-analysis. Russell Sage Foundation.

Mathur, M. B., & VanderWeele, T. J. (2020). A Simple, Interpretable Conversion from Pearson's Correlation to Cohen's for d Continuous Exposures. Epidemiology (Cambridge, Mass.), 31(2), e16–e18. https://doi.org/10.1097/EDE.0000000000001105

Viechtbauer W (2010). “Conducting meta-analyses in R with the metafor package.” Journal of Statistical Software, 36(3), 1–48. doi:10.18637/jss.v036.i03.