This article presents a new asymmetric version of Cohen's w for analyzing contingency tables. As an extension of this established effect size measure, the proposed index quantifies the effect of one variable on another, providing a valuable complement to null hypothesis significance testing. While specific procedures exist for assessing these directional relationships, they exhibit significant limitations in certain scenarios. Furthermore, we introduce a normalization process that constrains the coefficient to a 0, 1 range, enhancing interpretability for both researchers and practitioners. Finally, we present an asymmetric chi-square coefficient that aligns naturally with the proposed effect size, ensuring full conceptual coherence between hypothesis testing and effect size estimation. This coefficient also avoids the interpretability pitfalls that commonly arise when the traditional chi-square test is applied to inherently asymmetric relationships.
Luis D’Angelo (Thu,) studied this question.