A Semiparametric Effect Size Index

Effect size indices are useful tools in study design and reporting because they are unitless measures of association strength that do not depend on sample size. Existing effect size indices are developed for particular parametric models or population parameters. Here, we propose a semiparametric effect size index based on M-estimators. The M-estimation approach makes the effect size index widely generalizable, yielding an index that is unitless across a wide range of models. We demonstrate that the new index is a function of Cohen's $d$, $R^2$, and standardized log odds ratio when each of the parametric models is correctly specified. We provide simple formulas to compute power and sample size. Because the new index is invariant across models, it has the potential to make communication and comprehension of effect size uniform across the behavioral sciences.