A scale to measure a psychological construct is subject to measurement error. When meta-analyzing correlations obtained from scale scores, many researchers recommend correcting for measurement error. I considered three caveats when correcting for measurement error in meta-analysis of correlations: (a) the distribution of true scores can be non-normal, resulting in violation of the normality assumption for raw correlations and Fisher’s z transformed correlations; (b) coefficient alpha is often used as the reliability, but correlations corrected for measurement error using alpha can be inaccurate when some assumptions of alpha (e.g., tau-equivalence) are violated; and (c) item scores are often ordinal, making the disattenuation formula potentially problematic. Via three simulation studies, I examined the performance of two meta-analysis approaches—with raw correlations and z scores. In terms of estimation accuracy and coverage probability of the mean correlation, results showed that (a) considering the true-score distribution alone, estimation of the mean correlation was slightly worse when true scores of the constructs were skewed rather than normal; (b) when the tau-equivalence assumption was violated and coefficient alpha was used for correcting measurement error, the mean correlation estimates can be biased and coverage probabilities can be low; and (c) discretization of continuous items can result in biased estimates and undercoverage of the mean correlations even when tau-equivalence was satisfied. With more categories and/or items on a scale, results can improve whether tau-equivalence was met or not. Based on these findings, I gave recommendations for conducting meta-analyses of correlations.

中文翻译：

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相关系数的荟萃分析：处理测量误差的警示故事。


测量心理结构的量表可能会出现测量误差。当对从量表得分获得的相关性进行荟萃分析时，许多研究人员建议纠正测量误差。在校正相关性荟萃分析中的测量误差时，我考虑了三个警告：(a) 真实得分的分布可能是非正态的，导致违反原始相关性和 Fisher z 变换相关性的正态性假设； (b) 系数 α 通常被用作可靠性，但当违反 α 的某些假设（例如 tau 等价性）时，使用 α 校正测量误差的相关性可能不准确； (c) 项目分数通常是有序的，这使得减衰减公式可能存在问题。通过三项模拟研究，我通过原始相关性和 z 分数检查了两种元分析方法的性能。在平均相关性的估计精度和覆盖概率方面，结果表明：（a）单独考虑真实分数分布时，当构建体的真实分数偏斜而不是正态时，平均相关性的估计稍差； (b) 当违反 tau 等价假设并使用系数 alpha 来校正测量误差时，平均相关估计可能会出现偏差，并且覆盖概率可能较低； (c) 即使满足 tau 等价性，连续项的离散化也会导致估计偏差和平均相关性的覆盖不足。随着规模上的类别和/或项目增多，无论是否满足 tau 等价性，结果都可以改善。根据这些发现，我提出了进行相关性荟萃分析的建议。