Kennet-Cohen Tamar, Kleper Dvir, Turvall Elliot
National Institute for Testing and Evaluation, Jerusalem, Israel.
Br J Math Stat Psychol. 2018 Feb;71(1):39-59. doi: 10.1111/bmsp.12105. Epub 2017 Jun 20.
A frequent topic of psychological research is the estimation of the correlation between two variables from a sample that underwent a selection process based on a third variable. Due to indirect range restriction, the sample correlation is a biased estimator of the population correlation, and a correction formula is used. In the past, bootstrap standard error and confidence intervals for the corrected correlations were examined with normal data. The present study proposes a large-sample estimate (an analytic method) for the standard error, and a corresponding confidence interval for the corrected correlation. Monte Carlo simulation studies involving both normal and non-normal data were conducted to examine the empirical performance of the bootstrap and analytic methods. Results indicated that with both normal and non-normal data, the bootstrap standard error and confidence interval were generally accurate across simulation conditions (restricted sample size, selection ratio, and population correlations) and outperformed estimates of the analytic method. However, with certain combinations of distribution type and model conditions, the analytic method has an advantage, offering reasonable estimates of the standard error and confidence interval without resorting to the bootstrap procedure's computer-intensive approach. We provide SAS code for the simulation studies.
心理学研究中一个常见的主题是，根据基于第三个变量进行了选择过程的样本，来估计两个变量之间的相关性。由于间接范围限制，样本相关性是总体相关性的有偏估计量，因此要使用校正公式。过去，针对校正后的相关性，人们用正态数据检验了自助法标准误差和置信区间。本研究提出了一种用于标准误差的大样本估计（一种解析方法），以及针对校正相关性的相应置信区间。进行了涉及正态和非正态数据的蒙特卡罗模拟研究，以检验自助法和解析方法的实证表现。结果表明，对于正态和非正态数据，在各种模拟条件（受限样本量、选择比率和总体相关性）下，自助法标准误差和置信区间总体上都是准确的，并且优于解析方法的估计。然而，在分布类型和模型条件的某些组合下，解析方法具有优势，无需采用自助法过程中计算量大的方法，就能提供合理的标准误差和置信区间估计。我们提供了模拟研究的SAS代码。
