Data_Sheet_2_Computing Multivariate Effect Sizes and Their Sampling Covariance Matrices With Structural Equation Modeling: Theory, Examples, and Computer Simulations.PDF

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.

在社会和行为科学领域，建议报告效应量及其抽样方差。标准化均值差异、原始均值差异、相关系数和优势比等常见效应量的公式广为人知，且研究深入。然而，多元效应量的统计性质在文献中却受到较少关注。本研究展示了如何运用结构方程模型（SEM）来计算多元效应量及其抽样协方差矩阵。本研究着重于标准化均值差异（多重处理和多重终点研究），考虑或未考虑方差齐性（或协方差矩阵齐性）的假设。通过实证示例，在R语言中展示了计算过程的实现。此外，通过两项计算机模拟研究评估了SEM方法的实证性能。研究结果表明，在多重处理和多重终点研究中，当方差齐性（或协方差矩阵齐性）的假设存在疑问时，在估计效应量时不宜强加此假设。讨论了相关影响及进一步研究方向。