A robust effect size measure Aw for Manova with non-normal and non-homogenous data
Bibliographic Data
| ID | 4563754 |
|---|---|
| Authors | Johnson Ching-Hong Li (0000-0002-2553-117X, University of Manitoba, corresponding author), Marcello Nesca (0000-0003-4938-6939, University of Manitoba), Rory Michael Waisman (0000-0003-2608-169X, University of Alberta), Yongtian Cheng (0009-0000-9569-6263, University of Manitoba), Virginia M C Tze (0000-0001-5580-4872, University of Manitoba) |
| Year | 2021 |
| Volume | 14 |
| Issue | 3 |
| Publication date | 2021-09-01 |
| Open Access | Yes |
| Type | ARTICLE |
| Venue | Methodological Innovations (JOURNAL) |
| Journal identifiers | ISSN: 2059-7991 • E-ISSN: 2059-7991 |
| Publisher | SAGE Publications Inc (PUBLISHER) |
| DOI | 10.1177/20597991211055949 |
| OpenAlex | W3217053192 |
| Language | EN |
| References cited | 25 |
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 [Formula: see text], generalized omega squared [Formula: see text]), 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 ( Aw) for MANOVA. The new ES is developed on the basis of the non-parametric A in ANOVA. To test Aw we conducted a Monte-Carlo simulation. The results showed that Aw 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 Aw, particularly when key assumptions are violated. Implications of the proposed Aw for psychological research and other disciplines are also discussed
Covariance · Econometrics · Multivariate analysis of variance · Multivariate statistics · Normality · Null hypothesis · Parametric statistics · Sample size determination · Statistical hypothesis testing · Statistics · Advanced Statistical Methods and Models · Advanced Statistical Modeling Techniques · Mathematics · Optimal Experimental Design Methods
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| Highly cited | No |
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