标题： 一种贝叶斯方法在教育研究中估计效应大小 显示英文标题

标题： A Bayesian Approach to Estimating Effect Sizes in Educational Research

摘要： 在教育研究中，对任何心理测量数据进行描述性分析的第一步，是在不同时间点和组间对受试者在测试中的表现进行计算，以得到学习进步和学习成就的相对度量。 对于这些效应量，有来自频率统计的经典方法，如学生氏或韦尔奇的$t$检验，它们各自具有优势和不足。 在本文中，我们提出了一种纯粹的贝叶斯方法，用于分析学习结果中的组内和组间差异，自然地考虑到数据的多层结构，以及不同时间点和组之间的异方差性。 我们使用 R 中的 brms 包进行详细实现，该包作为概率编程语言 Stan 的包装器，通过包含在线补充材料，便于未来研究中实施这些方法。 我们建议，在合并设计中，应计算一个效应量$d_s$，而在配对设计中，应计算两个可能不同的量$d_s$和$d_z$，以校正组内设计中的相关性，并允许在不同研究之间进行比较。 所有这些效应量都基于 2007 年引入的希奇总效应量$\delta_t$的想法。 显示英文摘要

摘要： In educational research, a first step in the descriptive analysis of data from any psychometric measurement of the performance of subjects in tests at different time points and between groups is to compute relative measures of learning gains and learning achievements. For these effect sizes, there are classical approaches coming from frequentistic statistics like Student's or Welch's $t$-test with their own strengths and weaknesses. In this paper, we propose a purely Bayesian approach for analysing within-group and between-group differences in learning outcomes, taking naturally into account the multilevel structure of the data, as well as heterogeneous variances among time points and groups. We provide a detailed implementation using the brms package in R serving as a wrapper for the probabilistic programming language Stan, facilitating the implementation of these methods in future research by including online supplementary material. We recommend that for a pooled design, one computes an effect size $d_s$, and for a paired design, one should compute two possibly different quantities $d_s$ and $d_z$ to correct for correlations in within-group designs and allowing for comparability across different studies. All these effect sizes are based on ideas coming from Hedge's total effect size $\delta_t$ introduced in 2007.