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 , $$R^2$$ R 2 , 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.

中文翻译：

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稳健的效应量指数

效应量指数是研究设计和报告中的有用工具，因为它们是关联强度的无单位度量，不依赖于样本量。现有的效应大小指数是为特定的参数模型或总体参数开发的。在这里，我们提出了一个基于 M 估计量的稳健效应量指数。这种方法产生了一个非常通用的索引，因为它在广泛的模型中是无单位的。我们证明，当正确指定每个参数模型时，新指数是 Cohen 的 d 、$$R^2$$R 2 和标准化对数优势比的函数。我们表明，当参数模型不正确时（例如，在未知异方差下），现有的效应大小估计量是有偏差的。我们提供了简单的公式来计算功效和样本量，并使用模拟来评估有限样本中效应量估计量的偏差和标准误差。由于新指数在模型之间是不变的，因此它有可能使行为科学中对效应大小的交流和理解保持一致。