Motivated by the recent replication and reproducibility crisis, Gelman and Carlin (2014, Perspect. Psychol. Sci., 9, 641) advocated focusing on controlling for Type S/M errors, instead of the classic Type I/II errors, when conducting hypothesis testing. In this paper, we aim to fill several theoretical gaps in the methodology proposed by Gelman and Carlin (2014, Perspect. Psychol. Sci., 9, 641). In particular, we derive the closed‐form expression for the expected Type M error, and study the mathematical properties of the probability of Type S error as well as the expected Type M error, such as monotonicity. We demonstrate the advantages of our results through numerical and empirical examples.

中文翻译：

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假设检验中有关S / M型错误的注释。

通过最近的复制和再现危机的推动下，盖尔曼和卡林（2014，Perspect。心理学，科学，9，641）倡导注重在控制型S / M的错误，而不是经典的I / II类型的错误，在导通时的假设测试。在本文中，我们的目标是填写由吉尔曼和卡林（2014年，提出的方法的几个理论间隙Perspect。心理学。科学。，9，641）。特别是，我们推导了预期的M型错误的闭式表达式，并研究了S型错误的概率以及预期的M型错误（例如单调性）的数学属性。我们通过数值和经验示例来证明我们的结果的优势。