A Robust Effect Size Index
A Robust Effect Size Index
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DOI：
10.1007/s11336-020-09698-2
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发表时间：
2020-03-30
期刊：
影响因子：
3
通讯作者：
Blume, Jeffrey
中科院分区：
文献类型：
--
作者：
Vandekar, Simon;Tao, Ran;Blume, Jeffrey
效应大小指数在研究设计和报告中是有用的工具，因为它们是不依赖于样本量的关联强度的无单位测量。现有的效应大小指数是针对特定的参数模型或总体参数而开发的。在这里，我们提出了一个基于M-估计的稳健效应大小指标。这种方法产生了一个非常通用的指数，因为它在广泛的模型中是无单位的。我们证明了当每个参数模型被正确指定时，新的指数是Cohen的d、R2和标准化对数赔率比的函数。我们证明了当参数模型不正确时(例如，在未知的异方差下)，现有的效应大小估计是有偏差的。我们给出了计算幂和样本量的简单公式，并使用模拟来评估有限样本下效应量估计量的偏差和标准误差。由于新的指数在不同的模型中是不变的，它有可能使行为科学中对效应大小的沟通和理解统一。
Effect size indices are useful tools in study design and reporting because they are unitless measures of association strength that do not depend on sample size. Existing effect size indices are developed for particular parametric models or population parameters. Here, we propose a robust effect size index based on M-estimators. This approach yields an index that is very generalizable because it is unitless across a wide range of models. We demonstrate that the new index is a function of Cohen's d, R2, and standardized log odds ratio when each of the parametric models is correctly specified. We show that existing effect size estimators are biased when the parametric models are incorrect (e.g., under unknown heteroskedasticity). We provide simple formulas to compute power and sample size and use simulations to assess the bias and standard error of the effect size estimator in finite samples. Because the new index is invariant across models, it has the potential to make communication and comprehension of effect size uniform across the behavioral sciences.