Averaging correlations: Expected values and bias in combined Pearson rs and Fisher's z transformations
Averaging correlations: Expected values and bias in combined Pearson rs and Fisher's z transformations
复制标题
DOI：
10.1080/00221309809595548
复制
发表时间：
1998-07-01
影响因子：
2.5
通讯作者：
Burke, MJ
中科院分区：
文献类型：
--
作者：
Corey, DM;Dunlap, WP;Burke, MJ
R.A.Fisher的z(z‘；1958)本质上正规化了皮尔逊r的抽样分布，因此可以用来获得受抽样分布偏斜影响较小的平均相关性，这意味着统计量的偏差较小。然而，分析公式表明，平均r的预期偏差小于平均z‘反向转换为平均r的预期偏差。在很大程度上由于这一事实，J.E.Hunter和F.L.Schmidt(1990)认为平均r比平均r更可取。在本研究中，对平均r和平均r的偏差进行了经验性检验。当矩阵的相关性被平均时，z‘的使用减少了偏差。对于独立相关性，与分析预期相反，平均r(z‘)通常也是较无偏倚的统计量。得出的结论是：(A)平均r(z‘)是对总体相关性的无偏估计，并且(B)当对少量相关性进行平均时，期望值公式不能充分地预测平均r的偏差。
R.A. Fisher's z (z'; 1958) essentially normalizes the sampling distribution of Pearson r and can thus be used to obtain an average correlation that is less affected by sampling distribution skew, suggesting a less biased statistic. Analytical formulae, however, indicate less expected bias in average r than in average z' back-converted to average r,. In large part because of this fact, J. E. Hunter and F L. Schmidt (1990) have argued that average r is preferable to average r,. In the present study, bias in average r and average r, was empirically examined. When correlations from a matrix were averaged, the use of z' decreased bias. For independent correlations, contrary to analytical expectations, average r(z') was also generally the less biased statistic. It is concluded that (a) average r(z') is a less biased estimate of the population correlation than average r and (b) expected values formulae do not adequately predict bias in average r, when a small number of correlations are averaged.