Dudgeon Paul
a Melbourne School of Psychological Sciences, The University of Melbourne.
Multivariate Behav Res. 2016 Mar-Jun;51(2-3):139-53. doi: 10.1080/00273171.2015.1121372. Epub 2016 Mar 25.
In linear regression, the most appropriate standardized effect size for individual independent variables having an arbitrary metric remains open to debate, despite researchers typically reporting a standardized regression coefficient. Alternative standardized measures include the semipartial correlation, the improvement in the squared multiple correlation, and the squared partial correlation. No arguments based on either theoretical or statistical grounds for preferring one of these standardized measures have been mounted in the literature. Using a Monte Carlo simulation, the performance of interval estimators for these effect-size measures was compared in a 5-way factorial design. Formal statistical design methods assessed both the accuracy and robustness of the four interval estimators. The coverage probability of a large-sample confidence interval for the semipartial correlation coefficient derived from Aloe and Becker was highly accurate and robust in 98% of instances. It was better in small samples than the Yuan-Chan large-sample confidence interval for a standardized regression coefficient. It was also consistently better than both a bootstrap confidence interval for the improvement in the squared multiple correlation and a noncentral interval for the squared partial correlation.
在线性回归中，对于具有任意度量的单个自变量而言，最合适的标准化效应量仍存在争议，尽管研究人员通常会报告标准化回归系数。替代性的标准化度量包括半偏相关、复相关系数平方的改进量以及偏相关系数平方。文献中尚未基于理论或统计依据提出支持这些标准化度量中某一个的论据。通过蒙特卡罗模拟，在一个五因素析因设计中比较了这些效应量度量的区间估计量的性能。正式的统计设计方法评估了这四种区间估计量的准确性和稳健性。源自阿洛和贝克尔的半偏相关系数的大样本置信区间的覆盖概率在98%的情况下具有高度准确性和稳健性。在小样本中，它比袁 - 钱标准化回归系数的大样本置信区间表现更好。它也始终优于复相关系数平方改进量的自助置信区间和偏相关系数平方的非中心区间。
