Berry K J, Mielke P W
Department of Sociology, Colorado State University, Fort Collins, CO 80523-1784, USA.
Psychol Rep. 2000 Dec;87(3 Pt 2):1101-14. doi: 10.2466/pr0.2000.87.3f.1101.
The Fisher transformation of the sample correlation coefficient r (1915, 1921) and two related techniques by Gayen (1951) and Jeyaratnam (1992) are examined for robustness to nonnormality. Monte Carlo analyses compare combinations of sample sizes and population parameters for seven bivariate distributions. The Fisher, Gayen, and Jeyaratnam approaches are shown to provide useful results for a bivariate normal distribution with any population correlation coefficient rho and for nonnormal bivariate distributions when rho = 0. In contrast, the techniques are virtually useless for nonnormal bivariate distributions when rho not equal to 0.0. Surprisingly, small samples are found to provide better estimates than large samples for skewed and symmetric heavy-tailed bivariate distributions.
对样本相关系数r的费希尔变换（1915年、1921年）以及盖恩（1951年）和杰亚拉特纳姆（1992年）提出的两种相关技术进行了非正态性稳健性检验。蒙特卡罗分析比较了七种双变量分布的样本量和总体参数的组合。结果表明，对于任何总体相关系数rho的双变量正态分布以及rho = 0时的非正态双变量分布，费希尔、盖恩和杰亚拉特纳姆方法都能提供有用的结果。相比之下，当rho不等于0.0时，这些技术对于非正态双变量分布几乎毫无用处。令人惊讶的是，对于偏态和对称重尾双变量分布，发现小样本比大样本能提供更好的估计。
