Cautions when normalizing the dependent variable in a regression as a z‐score
指出将因变量标准化为标准正态分布会导致处理效应被系统性地向零衰减且幅度有界，并提出一种替代标准化方法（除以组内变异平方根）来修正此问题，该方法在线性回归中得到的效应估计与Cohen's d数值相同。
Abstract It is common in empirical analysis to facilitate inference by transforming the dependent variable to follow a standard normal distribution. In this paper, I show that using this transformation results in the estimated treatment effects being systematically attenuated toward zero and bounded in magnitude. The level of attenuation can be empirically relevant. I propose an alternative normalization wherein the dependent variable is divided by the square root of its within variation, which corrects these issues. I show that, in a simple linear regression, the method produces an estimated treatment effect that is numerically identical to Cohen's d .