Hafdahl Adam R
Department of Mathematics, Washington University in St. Louis, Missouri, USA.
Br J Math Stat Psychol. 2009 May;62(Pt 2):233-61. doi: 10.1348/000711008X281633. Epub 2008 Feb 6.
Several authors have studied or used the following estimation strategy for meta-analysing correlations: obtain a point estimate or confidence interval for the mean Fisher z correlation, and transform this estimate to the Pearson r metric. Using the relationship between Fisher z and Pearson r random variables, I demonstrate the potential discrepancy induced by directly z-to-r transforming a mean correlation parameter. Point and interval estimators based on an alternative integral z-to-r transformation are proposed. Analytic expressions for the expectation and variance of certain meta-analytic point estimators are also provided, as are selected moments of correlation parameters; numerical examples are included. In an application of these analytic results, the proposed point estimator outperformed its usual direct z-to-r counterpart and compared favourably with an estimator based on Pearson r correlations. Practical implications, extensions of the proposed estimators, and uses for the analytic results are discussed.
获取平均费希尔z相关性的点估计或置信区间，并将此估计转换为皮尔逊r度量。利用费希尔z和皮尔逊r随机变量之间的关系，我证明了直接对平均相关性参数进行z到r转换所导致的潜在差异。提出了基于替代积分z到r转换的点估计和区间估计。还提供了某些元分析点估计量的期望和方差的解析表达式，以及相关性参数的选定矩；包括数值示例。在这些分析结果的应用中，所提出的点估计量优于其通常的直接z到r对应物，并且与基于皮尔逊r相关性的估计量相比具有优势。讨论了实际意义、所提出估计量的扩展以及分析结果的用途。
