Chan Wai, Chan Daniel W-L
Department of Psychology, The Chinese University of Hong Kong, Shatin, Hong Kong.
Psychol Methods. 2004 Sep;9(3):369-85. doi: 10.1037/1082-989X.9.3.369.
The standard Pearson correlation coefficient is a biased estimator of the true population correlation, rho, when the predictor and the criterion are range restricted. To correct the bias, the correlation corrected for range restriction, rc, has been recommended, and a standard formula based on asymptotic results for estimating its standard error is also available. In the present study, the bootstrap standard-error estimate is proposed as an alternative. Monte Carlo simulation studies involving both normal and nonnormal data were conducted to examine the empirical performance of the proposed procedure under different levels of rho, selection ratio, sample size, and truncation types. Results indicated that, with normal data, the bootstrap standard-error estimate is more accurate than the traditional estimate, particularly with small sample size. With nonnormal data, performance of both estimates depends critically on the distribution type. Furthermore, the bootstrap bias-corrected and accelerated interval consistently provided the most accurate coverage probability for rho.
当预测变量和标准变量存在范围限制时,标准皮尔逊相关系数是对总体真实相关系数ρ的有偏估计。为了校正偏差,有人推荐使用经范围限制校正的相关系数rc,并且还有一个基于渐近结果来估计其标准误差的标准公式。在本研究中,我们提出了自助法标准误差估计作为一种替代方法。我们进行了涉及正态和非正态数据的蒙特卡罗模拟研究,以检验所提出的程序在不同水平的ρ、选择比率、样本量和截断类型下的实证表现。结果表明,对于正态数据,自助法标准误差估计比传统估计更准确,尤其是在小样本量的情况下。对于非正态数据,两种估计的表现都严重依赖于分布类型。此外,自助偏差校正和加速区间始终为ρ提供最准确的覆盖概率。