An evaluation of a difference between effect sizes from two dependent variables in a single study is likely to be based on differences between standard scores if raw scores on those variables are not scaled in comparable units of measurement. The standardization used for this purpose is usually sample-based rather than population-based, but the consequences of this distinction for the construction of confidence intervals on differential effects have not been systematically examined. In this article I show that differential effect confidence intervals (CIs) constructed from differences between the standard scores produced by sample-based standardization can be too narrow when those effects are large and dependent variables are highly correlated, particularly in within-subjects designs. I propose a new approach to the construction of differential effect CIs based on differences between adjusted sample-based standard scores that allow conventional CI procedures to produce Bonett-type CIs (Bonett, 2008) on individual effects. Computer simulations show that differential effect CIs constructed from adjusted standard scores can provide much better coverage probabilities than CIs constructed from unadjusted standard scores.

中文翻译：

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改进了标准化效应大小之间差异的置信区间。

如果这些变量的原始分数没有以可比较的测量单位进行缩放，则对单个研究中两个因变量的效应大小差异的评估可能基于标准分数之间的差异。用于此目的的标准化通常是基于样本而不是基于人口的，但这种区分对构建差异效应置信区间的影响尚未得到系统检查。在本文中，我表明，当这些影响很大且因变量高度相关时，由基于样本的标准化产生的标准分数之间的差异构建的差异效应置信区间 (CI) 可能太窄，尤其是在受试者内部设计中。我提出了一种基于调整后的基于样本的标准分数之间的差异来构建差异效应 CI 的新方法，该方法允许传统的 CI 程序产生关于个体效应的 Bonett 型 CI (Bonett, 2008)。计算机模拟表明，由调整后的标准分数构建的差异效应 CI 可以提供比由未调整的标准分数构建的 CI 更好的覆盖概率。