Cómo proceder cuando se violan la normalidad y la esfericidad en el ANOVA de medidas repetidas
Agencias de apoyo
- This research was supported by grant PID2020-113191GB-I00, awarded through MCIN/AEI/10.13039/501100011033.
Resumen
Las pruebas F ajustadas se han propuesto como alternativa al estadístico F en el ANOVA de medidas repetidas. A pesar de existir investigación previa, falta evidencia sobre el comportamiento de estos estadísticos en caso de violación simultánea de normalidad y esfericidad. El objetivo del presente trabajo ha sido realizar un examen detallado del error de tipo I y la potencia del estadístico F y los ajustes de Greenhouse-Geisser (F-GG) y Huynh-Feldt (F-HF), manipulando el número de medidas repetidas (3-6), el tamaño de la muestra (10-300), la esfericidad (estimador Greenhouse-Geisser de épsilon, desde su límite inferior al superior), y la forma de la distribución (desde desviaciones leves a extremas de la normalidad). Los resultados muestran que el comportamiento de F-GG y F-HF depende del grado de violación de la normalidad, esfericidad y tamaño muestral. En general, se sugiere utilizar F-GG en caso de violación de la esfericidad y desviaciones leves o moderadas de la normalidad; con desviaciones graves de ambos, F-GG puede utilizarse con un tamaño muestral superior a 10; y con desviaciones extremas, este estadístico puede utilizarse con un tamaño muestral superior a 30. En caso de resultados discrepantes entre F-GG y F-HF, la elección depende del valor epsilon.
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