题目：A new definition of standardized mean difference allowing for unequal variances
汇报人： 童铁军
会议时间：2025年4月21日(周一) 14：00
地点：综合楼615会议室
报告人简介：
童铁军，香港浸会大学数学系教授。2005 年博士毕业于美国加州大学圣巴巴拉分校，2005-2007 年在美国耶鲁大学从事博士后研究，2007-2010 年在美国科罗拉多大学博尔德分校担任助理教授，2010 年至今任职于香港浸会大学数学系。主要科研方向包括非参数回归模型、高维数据分析、Meta 分析和循证医学。已在国际知名的学术期刊 JASA、Biometrika、Statistical Science、JMLR、Nature Communications 等发表学术论文 100 余篇，包括数篇 ESI 热点论文和ESI 高被引论文，单篇论文最高被引用 8500 余次。
摘要：
The standardized mean difference (SMD) is a commonly used effect size to quantify the mean difference between the case and control groups with continuous outcomes. Under the equal variance assumption, the SMD can be naturally defined as the mean difference divided by the common standard deviation. In clinical practice, however, the equal variance assumption may be too restrictive. To allow for unequal variances, the common approach in the literature is to take an arithmetic mean of the two variances, yet by doing so, the resulting SMD cannot be unbiasedly estimated. Inspired by this, we propose a geometric approach for averaging the two variances, which subsequently yields a new and novel measure for standardizing the mean difference allowing for unequal variances. We further propose the Cohen-type and Hedges type estimators for the new SMD, and moreover derive their statistical properties together with the confidence intervals. Simulation results show that the Hedges-type estimator performs best under a wide range of settings in terms of the bias and coverage probability, and a real data example also demonstrates that our new SMD and its estimator bring new insights to the existing literature and can also be highly recommended for practical use.
