Data_Sheet_5_Computing Multivariate Effect Sizes and Their Sampling Covariance Matrices With Structural Equation Modeling: Theory, Examples, and Computer Simulations.docx

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.

在社会与行为科学领域，学界通常建议报告效应量（effect size）及其抽样方差（sampling variance）。诸如标准化均数差（standardized mean difference）、原始均数差（raw mean difference）、相关系数（correlation coefficient）以及比值比（odds ratio）等常见效应量的计算公式已广为人知且得到充分研究。然而，多变量效应量（multivariate effect size）的统计特性在现有文献中却较少受到关注。本研究阐明了如何利用结构方程模型（structural equation modeling, SEM）计算多变量效应量及其抽样协方差矩阵（sampling covariance matrix），并聚焦于存在或不满足方差（或协方差矩阵）齐性假设场景下的标准化均数差，涵盖多处理、多终点研究情形。本研究借助R语言中的实证示例对上述分析流程进行演示，并通过两项计算机模拟研究对结构方程模型方法的实证表现进行评估。研究结果表明，在多处理、多终点研究中，当方差（或协方差矩阵）齐性假设存疑时，在估计效应量时优先选择不施加该假设。本文还探讨了本研究的启示与未来研究方向。