Table 1.

Definitions of effect size measures and pathways between them as well as transformation formulas are given and effect sizes derived from Cohen´s benchmark values: SMD = 0.2 (small), 0.5 (medium‐sized), and 0.8 (large) for relevance of a difference

Effect size measures with relationships
Robust/assumption free
Magnitude	MW	MWD	MWodds	RDaverage
Small	0.444	–0.113	0.798	–0.056
Medium	0.362	–0.276	0.567	–0.138
Large	0.286	–0.428	0.400	–0.214

Measures with distribution assumption
	Normal distribution	Proportional odds	Lehmann alternative
	Cohen's δ	Odds ratio β	Hazard rate ratio γ
Parameters	$\delta =-{\mathrm{\Phi }}^{-1}(\mathrm{MW})•\sqrt{2}$	β = Numerical solution of $\text{MW}={\displaystyle \frac{\beta \text{*}(\beta -1-\ln \left(\beta \right))}{{\left(\beta -1\right)}^2}}$	$\gamma ={\displaystyle \frac{\mathrm{MW}}{1-\mathrm{MW}}}$
	0.200	0.713	0.798
	0.500	0.428	0.567
	0.800	0.256	0.400
Odds ratio extreme	${\left({\displaystyle \frac{\mathrm{\Phi }(-\delta /2)}{\mathrm{\Phi }(+\delta /2)}}\right)}^2$	Constant = β	From γ→0
	0.727	0.713	0.798
	0.450	0.428	0.567
	0.277	0.256	0.400
Risk difference extreme	$\mathrm{\Phi }\left({\displaystyle \frac{-\delta }{2}}\right)-\mathrm{\Phi }\left({\displaystyle \frac{+\delta }{2}}\right)$	${\displaystyle \frac{\sqrt{\beta }-1}{\sqrt{\beta }+1}}$	$\sqrt[(1-\gamma )\phantom{\frac{1}{2}}]{\gamma }\left(1-{\displaystyle \frac{1}{\gamma }}\right)$
	–0.080	–0.085	–0.083
	–0.197	–0.209	–0.206
	–0.311	–0.329	–0.326

Remark: the direction of the effect size measures could also be reversed: SMD could be minus instead of plus; MW, reflected around 0.5; OR, larger than 1 or reciprocal. The direction of superiority, however, must be defined.