均值回归效应在教育干预研究中的识别与校正：一种混合贝叶斯模型

摘要

均值回归在数据分析中普遍存在，教育研究者却常把它误当作真实变化的证据，把随机波动错误地归因于处理效应。作为一种极端值在重复施测后自然向平均值靠拢的统计现象，均值回归在采用前测—后测设计或纵向设计的教育研究中尤其容易被误读：观察到的变化即便只是统计假象，也往往被认定为处理的效果。本文借助一个假想案例与两项真实研究，考察均值回归带来的技术难题，并提出一种混合贝叶斯模型；与多重基线校正、公式化校正等常规做法相比，该模型能更有效地削弱均值回归的影响。具体而言，该混合贝叶斯模型依靠多次基线测量把前测阶段与均值回归相关的失真降到最低，并利用标准差、总体均值等先验知识来细化后测数据的校正。由此，该模型为教育研究者准确评估干预效果、提升各类研究驱动的教育政策与实践的有效性，提供了一件新的工具。

Abstract

Although regression to the mean is pervasive in data analysis, educational researchers often misconstrue it as evidence of genuine change and mistakenly attribute random changes to treatment effects. A statistical phenomenon where extreme values naturally move closer to the average after repeated treatment, regression to the mean is especially susceptible to misinterpretations in educational studies with pretest-posttest or longitudinal designs. In such studies, observed changes are frequently assumed to be the effects of treatment, even in cases where the changes are statistical artifacts. Using a hypothetical case and two real-world studies, this paper investigates the technical challenges that regression to the mean poses and introduces a hybrid Bayesian model that mitigates its effects more effectively than conventional approaches, such as multiple baseline adjustments and formulaic corrections. In particular, the hybrid Bayesian model relies on multiple baseline measurements to minimize distortions associated with regression to the mean during the pretest phase and leverages prior knowledge (such as standard deviations and population means) to refine post-test data adjustments. It follows that the model provides educational researchers with an innovative tool for accurately evaluating interventions and enhancing the effectiveness of various research-driven educational policies and practices.