Computing Multivariate Effect Sizes and Their Sampling Covariance Matrices With Structural Equation Modeling: Theory, Examples, and Computer Simulations

Frontiers in Psychology
Mike W-L Cheung

Abstract

In the social and behavioral sciences, it is recommended that effect sizes and their sampling variances be reported. Formulas for common effect sizes such as standardized and raw mean differences, correlation coefficients, and odds ratios are well known and have been well studied. However, the statistical properties of multivariate effect sizes have received less attention in the literature. This study shows how structural equation modeling (SEM) can be used to compute multivariate effect sizes and their sampling covariance matrices. We focus on the standardized mean difference (multiple-treatment and multiple-endpoint studies) with or without the assumption of the homogeneity of variances (or covariance matrices) in this study. Empirical examples were used to illustrate the procedures in R. Two computer simulation studies were used to evaluate the empirical performance of the SEM approach. The findings suggest that in multiple-treatment and multiple-endpoint studies, when the assumption of the homogeneity of variances (or covariance matrices) is questionable, it is preferable not to impose this assumption when estimating the effect sizes. Implications and further directions are discussed.

References

Jul 11, 2003·Statistics in Medicine·In-Sun NamPaul Garthwaite
Dec 11, 2003·Psychological Methods·Charles F BondF Dan Richard
Apr 7, 2005·Psychological Methods·Mike W-L Cheung, Wai Chan
Jan 27, 2011·Statistics in Medicine·Dan JacksonIan R White
May 2, 2012·Psychological Methods·Ken Kelley, Kristopher J Preacher
Nov 14, 2013·Psychological Science·Geoff Cumming
Jan 21, 2015·Frontiers in Psychology·Mike W-L Cheung
Jun 9, 2015·Research Synthesis Methods·Christopher Glen Thompson, Betsy Jane Becker
Mar 31, 2010·Multivariate Behavioral Research·Rae-Seon Kim, Betsy Jane Becker

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Citations

Aug 26, 2019·Neuropsychology Review·Mike W-L Cheung
Jul 1, 2021·Alcohol and Alcoholism : International Journal of the Medical Council on Alcoholism·Mike W-L Cheung

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Software Mentioned

Verbal
SEM
R
R Core
smdMES
Math
R Development Core
metaSEM
smdMTS

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