A robust effect size measure for MANOVA with non-normal and non-homogenous data

A common research question in psychology entails examining whether significant group differences (e.g. male and female) can be found in a list of numeric variables that measure the same underlying construct (e.g. intelligence). Researchers often use a multivariate analysis of variance (MANOVA), whic...

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Autores principales:	Johnson Ching-Hong Li, Marcello Nesca, Rory Michael Waisman, Yongtian Cheng, Virginia Man Chung Tze
Formato:	article
Lenguaje:	EN
Publicado:	SAGE Publishing 2021
Materias:	Social Sciences H
Acceso en línea:	https://doaj.org/article/0d3925886a4c42d98ec4bf18b6922983
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spelling	oai:doaj.org-article:0d3925886a4c42d98ec4bf18b69229832021-11-30T23:36:02ZA robust effect size measure for MANOVA with non-normal and non-homogenous data2059-799110.1177/20597991211055949https://doaj.org/article/0d3925886a4c42d98ec4bf18b69229832021-11-01T00:00:00Zhttps://doi.org/10.1177/20597991211055949https://doaj.org/toc/2059-7991A common research question in psychology entails examining whether significant group differences (e.g. male and female) can be found in a list of numeric variables that measure the same underlying construct (e.g. intelligence). Researchers often use a multivariate analysis of variance (MANOVA), which is based on conventional null-hypothesis significance testing (NHST). Recently, a number of quantitative researchers have suggested reporting an effect size measure (ES) in this research scenario because of the perceived shortcomings of NHST. Thus, a number of MANOVA ESs have been proposed (e.g. generalized eta squared η Λ 2 , generalized omega squared ω Λ 2 ), but they rely on two key assumptions—multivariate normality and homogeneity of covariance matrices—which are frequently violated in psychological research. To solve this problem we propose a non-parametric (or assumptions-free) ES ( A w ) for MANOVA. The new ES is developed on the basis of the non-parametric A in ANOVA. To test A w we conducted a Monte-Carlo simulation. The results showed that A w was accurate (robust) across different manipulated conditions—including non-normal distributions, unequal covariance matrices between groups, total sample sizes, sample size ratios, true ES values, and numbers of dependent variables—thereby providing empirical evidence supporting the use of A w , particularly when key assumptions are violated. Implications of the proposed A w for psychological research and other disciplines are also discussed.Johnson Ching-Hong LiMarcello NescaRory Michael WaismanYongtian ChengVirginia Man Chung TzeSAGE PublishingarticleSocial SciencesHENMethodological Innovations, Vol 14 (2021)
institution	DOAJ
collection	DOAJ
language	EN
topic	Social Sciences H
spellingShingle	Social Sciences H Johnson Ching-Hong Li Marcello Nesca Rory Michael Waisman Yongtian Cheng Virginia Man Chung Tze A robust effect size measure for MANOVA with non-normal and non-homogenous data
description	A common research question in psychology entails examining whether significant group differences (e.g. male and female) can be found in a list of numeric variables that measure the same underlying construct (e.g. intelligence). Researchers often use a multivariate analysis of variance (MANOVA), which is based on conventional null-hypothesis significance testing (NHST). Recently, a number of quantitative researchers have suggested reporting an effect size measure (ES) in this research scenario because of the perceived shortcomings of NHST. Thus, a number of MANOVA ESs have been proposed (e.g. generalized eta squared η Λ 2 , generalized omega squared ω Λ 2 ), but they rely on two key assumptions—multivariate normality and homogeneity of covariance matrices—which are frequently violated in psychological research. To solve this problem we propose a non-parametric (or assumptions-free) ES ( A w ) for MANOVA. The new ES is developed on the basis of the non-parametric A in ANOVA. To test A w we conducted a Monte-Carlo simulation. The results showed that A w was accurate (robust) across different manipulated conditions—including non-normal distributions, unequal covariance matrices between groups, total sample sizes, sample size ratios, true ES values, and numbers of dependent variables—thereby providing empirical evidence supporting the use of A w , particularly when key assumptions are violated. Implications of the proposed A w for psychological research and other disciplines are also discussed.
format	article
author	Johnson Ching-Hong Li Marcello Nesca Rory Michael Waisman Yongtian Cheng Virginia Man Chung Tze
author_facet	Johnson Ching-Hong Li Marcello Nesca Rory Michael Waisman Yongtian Cheng Virginia Man Chung Tze
author_sort	Johnson Ching-Hong Li
title	A robust effect size measure for MANOVA with non-normal and non-homogenous data
title_short	A robust effect size measure for MANOVA with non-normal and non-homogenous data
title_full	A robust effect size measure for MANOVA with non-normal and non-homogenous data
title_fullStr	A robust effect size measure for MANOVA with non-normal and non-homogenous data
title_full_unstemmed	A robust effect size measure for MANOVA with non-normal and non-homogenous data
title_sort	robust effect size measure for manova with non-normal and non-homogenous data
publisher	SAGE Publishing
publishDate	2021
url	https://doaj.org/article/0d3925886a4c42d98ec4bf18b6922983
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A robust effect size measure for MANOVA with non-normal and non-homogenous data

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