  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 robust effect size index
based on M-estimators. This approach yields an index that is very generalizable
because it 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 show that
existing effect size estimators are biased when the parametric models are
incorrect (e.g. under unknown heteroskedasticity). We provide simple formulas
to compute power and sample size and use simulations to assess the bias and
variance of the effect size estimator in finite samples. 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.
