Non-normal Data in Repeated Measures ANOVA: Impact on Type I Error and Power.

IF 3.5 2区心理学 Q1 PSYCHOLOGY, MULTIDISCIPLINARY Psicothema Pub Date : 2023-02-01 DOI:10.7334/psicothema2022.292

María J Blanca, Jaume Arnau, F J García-Castro, Rafael Alarcón, Roser Bono

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引用次数: 12

Abstract

Background: Repeated measures designs are commonly used in health and social sciences research. Although there are other, more advanced, statistical analyses, the F-statistic of repeated measures analysis of variance (RM-ANOVA) remains the most widely used procedure for analyzing differences in means. The impact of the violation of normality has been extensively studied for between-subjects ANOVA, but this is not the case for RM-ANOVA. Therefore, studies that extensively and systematically analyze the robustness of RM-ANOVA under the violation of normality are needed. This paper reports the results of two simulation studies aimed at analyzing the Type I error and power of RM-ANOVA when the normality assumption is violated but sphericity is fulfilled.

Method: Study 1 considered 20 distributions, both known and unknown, and we manipulated the number of repeated measures (3, 4, 6, and 8) and sample size (from 10 to 300). Study 2 involved unequal distributions in each repeated measure. The distributions analyzed represent slight, moderate, and severe deviation from normality.

Results: Overall, the results show that the Type I error and power of the F-statistic are not altered by the violation of normality.

Conclusions: RM-ANOVA is generally robust to non-normality when the sphericity assumption is met.

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重复测量方差分析中的非正态数据:对I型误差和功率的影响。

背景:重复测量设计常用于卫生和社会科学研究。虽然有其他更先进的统计分析，但重复测量方差分析(RM-ANOVA)的f统计量仍然是分析均值差异最广泛使用的方法。违反正态性的影响已经被广泛地研究了受试者之间的方差分析，但对于rm -方差分析却不是这样。因此，需要广泛而系统地分析RM-ANOVA在违反正态性下的稳健性的研究。本文报道了两项模拟研究的结果，旨在分析RM-ANOVA在违反正态性假设但满足球性假设时的I型误差和功率。方法:研究1考虑了20种已知和未知的分布，我们对重复测量的数量(3,4,6和8)和样本量(从10到300)进行了调整。研究2涉及每个重复测量的不均匀分布。分析的分布有轻微、中度和严重偏离正态的情况。结果:总体而言，结果表明f统计量的I型误差和功率不会因违反正态性而改变。结论:当球形假设满足时，RM-ANOVA对非正态性一般是稳健的。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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来源期刊

Psicothema PSYCHOLOGY, MULTIDISCIPLINARY-

CiteScore

6.50

自引率

16.70%

发文量

审稿时长

24 weeks

期刊介绍： La revista Psicothema fue fundada en Asturias en 1989 y está editada conjuntamente por la Facultad y el Departamento de Psicología de la Universidad de Oviedo y el Colegio Oficial de Psicólogos del Principado de Asturias. Publica cuatro números al año. Se admiten trabajos tanto de investigación básica como aplicada, pertenecientes a cualquier ámbito de la Psicología, que previamente a su publicación son evaluados anónimamente por revisores externos. Psicothema está incluida en las bases de datos nacionales e internacionales más relevantes, entre las que cabe destacar Psychological Abstracts, Current Contents y MEDLINE/Index Medicus, entre otras. Además, figura en las listas de Factor de Impacto del Journal Citation Reports. Psicothema es una revista abierta a cualquier enfoque u orientación psicológica que venga avalada por la fuerza de los datos y los argumentos, y en la que encuentran acomodo todos los autores que sean capaces de convencer a los revisores de que sus manuscritos tienen la calidad para ser publicados. Psicothema es una revista de acceso abierto lo que significa que todo el contenido está a disposición de cualquier usuario o institución sin cargo alguno. Los usuarios pueden leer, descargar, copiar, distribuir, imprimir, buscar, o realizar enlaces a los textos completos de esta revista sin pedir permiso previo al editor o al autor, siempre y cuando la fuente original sea referenciada. Para acervos y repositorios, se prefiere que la cobertura se realice mediante enlaces a la propia web de Psicothema. Nos parece que una apuesta decidida por la calidad es el mejor modo de servir a nuestros lectores, cuyas sugerencias siempre serán bienvenidas.