Evaluating how an effect-size estimate performs between two continuous variables based on the common-language effect size (CLES) has received increasing attention. While Blomqvist (1950; https://doi.org/10.1214/aoms/1177729754) developed a parametric estimator (q') for the CLES, there has been limited progress in further refining CLES. This study: a) extends Blomqvist’s work by providing a mathematical foundation for Bp (a non-parametric version of CLES) and an analytic approach for estimating its standard error; and b) evaluates the performance of the analytic and bootstrap confidence intervals (CIs) for Bp. The simulation shows that the bootstrap bias-corrected-and-accelerated interval (BCaI) has the best protected Type 1 error rate with a slight compromise in Power, whereas the analytic-t CI has the highest overall Power but with a Type 1 error slightly larger than the nominal value. This study also uses a real-world data-set to demonstrate the applicability of the CLES in measuring the relationship between age and sexual compulsivity.

中文翻译：

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共同语言效应大小估计的分析和引导置信区间

基于共同语言效应大小 (CLES) 评估两个连续变量之间的效应大小估计如何受到越来越多的关注。虽然 Blomqvist (1950; https://doi.org/10.1214/aoms/1177729754) 为 CLES 开发了一个参数估计器 (q')，但在进一步完善 CLES 方面进展有限。这项研究： a) 通过为 Bp（CLES 的非参数版本）和估计其标准误差的分析方法提供数学基础，扩展了 Blomqvist 的工作；b) 评估 Bp 的分析和引导置信区间 (CI) 的性能。仿真表明，自举偏置校正和加速间隔 (BCaI) 具有最佳保护的 1 类错误率，功率略有妥协，而分析-t CI 具有最高的总功率，但类型 1 误差略大于标称值。本研究还使用真实世界的数据集来证明 CLES 在测量年龄与性强迫症之间关系方面的适用性。