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Asymmetric Chi-square Test and Cohen’s w in Contingency Tables
Prueba de chi-cuadrado y w de Cohen asimétricas en tablas de contingencia
DOI:
https://doi.org/10.15446/rce.v49n1.118682Keywords:
Asymmetric relationship, Chi-square test, Cohen’s w (en)Prueba de chi-cuadrado, Relación asimétrica, w de Cohen (es)
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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.
Este artículo presenta una nueva versión asimétrica de la w de Cohen para analizar tablas de contingencia. Como una extensión de esta medida de tamaño del efecto ya establecida, el índice propuesto cuantifica el efecto de una variable sobre otra, constituyendo un valioso complemento a las pruebas de significación de hipótesis nula. Si bien existen procedimientos específicos para evaluar estas relaciones direccionales, estos presentan limitaciones significativas en ciertos escenarios. Además, se introduce un proceso de normalización que restringe el coeficiente al rango [0, 1], mejorando su interpretabilidad tanto para investigadores como para profesionales. Finalmente, se presenta un coeficiente de chi-cuadrado asimétrico que se alinea naturalmente con el tamaño del efecto propuesto, garantizando coherencia conceptual entre la prueba de hipótesis y la estimación de la magnitud del efecto, y evitando problemas de interpretación asociados al uso del chi-cuadrado tradicional en relaciones inherentemente asimétricas.
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