University of Amsterdam, Amsterdam, Netherlands.
University of Turin, Turin, Italy.
Psychon Bull Rev. 2023 Apr;30(2):516-533. doi: 10.3758/s13423-022-02069-1. Epub 2022 Aug 15.
A tradition that goes back to Sir Karl R. Popper assesses the value of a statistical test primarily by its severity: was there an honest and stringent attempt to prove the tested hypothesis wrong? For "error statisticians" such as Mayo (1996, 2018), and frequentists more generally, severity is a key virtue in hypothesis tests. Conversely, failure to incorporate severity into statistical inference, as allegedly happens in Bayesian inference, counts as a major methodological shortcoming. Our paper pursues a double goal: First, we argue that the error-statistical explication of severity has substantive drawbacks; specifically, the neglect of research context and the specificity of the predictions of the hypothesis. Second, we argue that severity matters for Bayesian inference via the value of specific, risky predictions: severity boosts the expected evidential value of a Bayesian hypothesis test. We illustrate severity-based reasoning in Bayesian statistics by means of a practical example and discuss its advantages and potential drawbacks.
一种可以追溯到卡尔·R·波普尔爵士的传统，主要通过其严格程度来评估统计检验的价值：是否有诚实而严格的尝试来证明经过检验的假设是错误的？对于梅奥（1996、2018）等“错误统计学家”以及更普遍的频率主义者来说，严格程度是假设检验的一个关键美德。相反，正如贝叶斯推理中据称的那样，未能将严格程度纳入统计推断被认为是一个主要的方法学缺陷。我们的论文有两个目标：首先，我们认为严格程度的错误统计解释存在实质性的缺陷；具体来说，就是忽视了研究背景和假设预测的特异性。其次，我们认为严格程度通过特定、有风险的预测对贝叶斯推理很重要：严格程度提高了贝叶斯假设检验的预期证据价值。我们通过一个实际例子来说明贝叶斯统计学中的基于严格程度的推理，并讨论了它的优点和潜在的缺点。
