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The Adaptive Baumgartner-Type Test Statistics for Two-Sample Independent Problem
Estadísticas de prueba tipo Baumgartner adaptativas para el problema de dos muestras independientes
DOI:
https://doi.org/10.15446/rce.v49n1.118494Keywords:
Nonparametric tests, Baumgartner-type statistics, Location-scale shift, Relative ranking, Simulations (en)Cambio de ubicación-escala, Estadísticas tipo Baumgartner, Pruebas no paramétricas, Ranking relativo, Simulaciones (es)
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The two-sample independent problem remains a persistent challenge in statistical analysis. Parametric tests, such as Student's t-test and Welch's t-test, are commonly employed to assess the significance of differences between the means of two groups. However, these methods rely on the assumption of normally distributed populations. When this assumption is violated, nonparametric alternatives like the Wilcoxon-Mann-Whitney, Yuen-Welch, Brunner-Munzel, and Baumgartner tests offer robust solutions. This study introduces an adaptive framework for nonparametric two-sample tests, building upon the foundation of Baumgartner-type tests. To enhance statistical power, we incorporate a recently proposed relative rank transformation method that is more resilient to scale differences between the two samples. The adaptive tests are suitable for both location and scale comparisons. Through extensive Monte Carlo simulations, we evaluate the power performance of our adaptive tests under diverse distributional scenarios. Our results demonstrate that adaptive tests offer a substantial advantage over traditional nonparametric methods. To illustrate the practical application of our approaches, we apply the adaptive tests along their competitors to six real-world biomedical datasets. These examples highlight the reliability and effectiveness of the proposed methodology in addressing the two-sample independent location-scale testing problem.
El problema de dos muestras independientes sigue siendo un desafío persistente en el análisis estadístico. Las pruebas paramétricas, como la prueba t de Student y la prueba t de Welch, se emplean comúnmente para evaluar la significancia de las diferencias entre las medias de dos grupos. Sin embargo, estos métodos se basan en el supuesto de poblaciones distribuidas normalmente. Cuando este supuesto se viola, alternativas no paramétricas como las pruebas de Wilcoxon-Mann-Whitney, Yuen-Welch, Brunner-Munzel y Baumgartner ofrecen soluciones robustas. Este estudio introduce un marco adaptativo para pruebas no paramétricas de dos muestras, basado en pruebas tipo Baumgartner. Para mejorar la potencia estadística, se incorpora un método de transformación de rangos relativos recientemente propuesto, el cual es más resistente a las diferencias de escala entre las dos muestras. Las pruebas adaptativas son adecuadas tanto para comparaciones de ubicación como de escala. A través de extensas simulaciones de Monte Carlo, se evalúa el desempeño en potencia de las pruebas adaptativas bajo diversos escenarios distribucionales. Los resultados demuestran que las pruebas adaptativas ofrecen una ventaja sustancial frente a los métodos no paramétricos tradicionales. Para ilustrar la aplicación práctica de los enfoques propuestos, se aplican las pruebas adaptativas junto con sus competidores a seis conjuntos de datos biomédicos reales, destacando la confiabilidad y efectividad de la metodología propuesta para abordar el problema de pruebas de ubicación-escala en dos muestras independientes.
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