The common approach to meta-analysis is overwhelmingly dominant in practice but suffers from a major limitation: It is suitable for analyzing only a single effect of interest. However, contemporary psychological research studies—and thus meta-analyses of them—typically feature multiple dependent effects of interest. In this paper, we introduce novel meta-analytic methodology that (a) accommodates an arbitrary number of effects—specifically, contrasts of means—and (b) yields results in standard deviation units in order to adjust for differences in the measurement scales used for the dependent measure across studies. Importantly, when all studies follow the same two-condition study design and interest centers on the simple contrast between the two conditions as measured on the standardized mean difference (or Cohen’s d) scale, our approach is equivalent to the common approach. Consequently, our approach generalizes the common approach to accommodate an arbitrary number of contrasts. As we illustrate and elaborate on across three extensive case studies, our approach has several advantages relative to the common approach. To facilitate the use of our approach, we provide a website that implements it.

中文翻译：

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具有多重对比和测量尺度差异的研究的荟萃分析

Meta 分析的常用方法在实践中占绝对优势，但存在一个主要限制：它仅适用于分析感兴趣的单一效应。然而，当代心理学研究——以及对它们的荟萃分析——通常具有多种相关的兴趣效应。在本文中，我们介绍了新的元分析方法，该方法 (a) 适应任意数量的效应——特别是均值的对比——和 (b) 以标准差单位产生结果，以便调整用于测量尺度的差异跨研究的依赖测量。重要的是，当所有研究都遵循相同的双条件研究设计时，兴趣集中在两个条件之间的简单对比上，如标准化均值差（或 Cohen's d) 规模，我们的方法相当于普通的方法。因此，我们的方法概括了通用方法以适应任意数量的对比。正如我们在三个广泛的案例研究中说明和阐述的那样，我们的方法相对于常用方法具有几个优点。为了便于使用我们的方法，我们提供了一个实施它的网站。