Marín-Martínez F, Sánchez-Meca J
Departamento de Psicología Básica y Metodología, Facultad de Psicología, Universidad de Murcia, Campus de Espinardo, Apdo 4021, 30080 Murcia, Spain.
Span J Psychol. 1999 May;2(1):32-8. doi: 10.1017/s1138741600005436.
When a primary study includes several indicators of the same construct, the usual strategy to meta-analytically integrate the multiple effect sizes is to average them within the study. In this paper, the numerical and conceptual differences among three procedures for averaging dependent effect sizes are shown. The procedures are the simple arithmetic mean, the Hedges and Olkin (1985) procedure, and the Rosenthal and Rubin (1986) procedure. Whereas the simple arithmetic mean ignores the dependence among effect sizes, both the procedures by Hedges and Olkin and Rosenthal and Rubin take into account the correlational structure of the effect sizes, although in a different way. Rosenthal and Rubin's procedure provides the effect size for a single composite variable made up of the multiple effect sizes, whereas Hedges and Olkin's procedure presents an effect size estimate of the standard variable. The three procedures were applied to 54 conditions, where the magnitude and homogeneity of both effect sizes and correlation matrix among effect sizes were manipulated. Rosenthal and Rubin's procedure showed the highest estimates, followed by the simple mean, and the Hedges and Olkin procedure, this last having the lowest estimates. These differences are not trivial in a meta-analysis, where the aims must guide the selection of one of the procedures.
当一项主要研究包含同一结构的多个指标时，元分析整合多个效应量的常用策略是在研究内部对它们求平均值。本文展示了三种对相关效应量求平均值的方法在数值和概念上的差异。这些方法分别是简单算术平均数法、赫奇斯和奥尔金（1985年）的方法以及罗森塔尔和鲁宾（1986年）的方法。简单算术平均数法忽略了效应量之间的相关性，而赫奇斯和奥尔金以及罗森塔尔和鲁宾的方法都考虑了效应量的相关结构，不过方式有所不同。罗森塔尔和鲁宾的方法提供了由多个效应量组成的单个复合变量的效应量，而赫奇斯和奥尔金的方法给出的是标准变量的效应量估计值。这三种方法被应用于54种情况，其中效应量的大小和同质性以及效应量之间的相关矩阵都受到了操控。罗森塔尔和鲁宾的方法显示出最高的估计值，其次是简单平均数法，赫奇斯和奥尔金的方法估计值最低。在元分析中，这些差异并非微不足道，因为目的必须指导其中一种方法的选择。
