Data_Sheet_4_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，且已有深入研究。然而，在文献中，对多元效应量的统计特性关注较少。本研究展示了如何利用结构方程模型（SEM）计算多元效应量及其抽样协方差矩阵。本研究聚焦于标准化均值差异（包括多处理和多终点研究），并探讨在假设方差（或协方差矩阵）齐次性或不齐次性时的适用性。通过R语言中的实证示例来说明计算过程。此外，通过两项计算机模拟研究评估了SEM方法的经验性能。研究发现，在多处理和多终点研究中，当方差（或协方差矩阵）齐次性的假设存在疑问时，在估计效应量时不宜强制施加这一假设。本研究还讨论了其影响及未来的研究方向。