{"title":"Waldian t tests: Sequential Bayesian t tests with controlled error probabilities.","authors":"Martin Schnuerch, Daniel W Heck, Edgar Erdfelder","doi":"10.1037/met0000492","DOIUrl":null,"url":null,"abstract":"<p><p>Bayesian <i>t</i> tests have become increasingly popular alternatives to null-hypothesis significance testing (NHST) in psychological research. In contrast to NHST, they allow for the quantification of evidence in favor of the null hypothesis and for optional stopping. A major drawback of Bayesian <i>t</i> tests, however, is that error probabilities of statistical decisions remain uncontrolled. Previous approaches in the literature to remedy this problem require time-consuming simulations to calibrate decision thresholds. In this article, we propose a sequential probability ratio test that combines Bayesian <i>t</i> tests with simple decision criteria developed by Abraham Wald in 1947. We discuss this sequential procedure, which we call Waldian <i>t</i> test, in the context of three recently proposed specifications of Bayesian <i>t</i> tests. Waldian <i>t</i> tests preserve the key idea of Bayesian t tests by assuming a distribution for the effect size under the alternative hypothesis. At the same time, they control expected frequentist error probabilities, with the nominal Type I and Type II error probabilities serving as upper bounds to the actual expected error rates under the specified statistical models. Thus, Waldian <i>t</i> tests are fully justified from both a Bayesian and a frequentist point of view. We highlight the relationship between Bayesian and frequentist error probabilities and critically discuss the implications of conventional stopping criteria for sequential Bayesian <i>t</i> tests. Finally, we provide a user-friendly web application that implements the proposed procedure for interested researchers. (PsycInfo Database Record (c) 2024 APA, all rights reserved).</p>","PeriodicalId":20782,"journal":{"name":"Psychological methods","volume":" ","pages":"99-116"},"PeriodicalIF":7.6000,"publicationDate":"2024-02-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Psychological methods","FirstCategoryId":"102","ListUrlMain":"https://doi.org/10.1037/met0000492","RegionNum":1,"RegionCategory":"心理学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"2022/4/14 0:00:00","PubModel":"Epub","JCR":"Q1","JCRName":"PSYCHOLOGY, MULTIDISCIPLINARY","Score":null,"Total":0}
引用次数: 0
Abstract
Bayesian t tests have become increasingly popular alternatives to null-hypothesis significance testing (NHST) in psychological research. In contrast to NHST, they allow for the quantification of evidence in favor of the null hypothesis and for optional stopping. A major drawback of Bayesian t tests, however, is that error probabilities of statistical decisions remain uncontrolled. Previous approaches in the literature to remedy this problem require time-consuming simulations to calibrate decision thresholds. In this article, we propose a sequential probability ratio test that combines Bayesian t tests with simple decision criteria developed by Abraham Wald in 1947. We discuss this sequential procedure, which we call Waldian t test, in the context of three recently proposed specifications of Bayesian t tests. Waldian t tests preserve the key idea of Bayesian t tests by assuming a distribution for the effect size under the alternative hypothesis. At the same time, they control expected frequentist error probabilities, with the nominal Type I and Type II error probabilities serving as upper bounds to the actual expected error rates under the specified statistical models. Thus, Waldian t tests are fully justified from both a Bayesian and a frequentist point of view. We highlight the relationship between Bayesian and frequentist error probabilities and critically discuss the implications of conventional stopping criteria for sequential Bayesian t tests. Finally, we provide a user-friendly web application that implements the proposed procedure for interested researchers. (PsycInfo Database Record (c) 2024 APA, all rights reserved).
在心理学研究中,贝叶斯 t 检验已逐渐成为零假设显著性检验(NHST)的替代方法。与 NHST 不同的是,贝叶斯 t 检验允许对支持零假设的证据进行量化,并可选择停止。然而,贝叶斯 t 检验的一个主要缺点是统计决策的误差概率仍然不受控制。以往文献中弥补这一问题的方法需要耗时的模拟来校准决策阈值。在本文中,我们提出了一种顺序概率比检验,它将贝叶斯 t 检验与亚伯拉罕-沃尔德(Abraham Wald)于 1947 年提出的简单决策标准相结合。我们将结合最近提出的三种贝叶斯 t 检验规范来讨论这种序列程序,我们称之为 Waldian t 检验。Waldian t 检验保留了贝叶斯 t 检验的主要思想,即假设备选假设下效应大小的分布。同时,它们控制了预期的频数误差概率,名义 I 型和 II 型误差概率是指定统计模型下实际预期误差率的上限。因此,从贝叶斯和频繁主义的角度来看,Waldian t 检验都是完全合理的。我们强调了贝叶斯误差概率与频数误差概率之间的关系,并批判性地讨论了传统停止标准对序列贝叶斯 t 检验的影响。最后,我们为感兴趣的研究人员提供了一个用户友好型网络应用程序,以实现所建议的程序。(PsycInfo Database Record (c) 2022 APA, 版权所有)。
期刊介绍:
Psychological Methods is devoted to the development and dissemination of methods for collecting, analyzing, understanding, and interpreting psychological data. Its purpose is the dissemination of innovations in research design, measurement, methodology, and quantitative and qualitative analysis to the psychological community; its further purpose is to promote effective communication about related substantive and methodological issues. The audience is expected to be diverse and to include those who develop new procedures, those who are responsible for undergraduate and graduate training in design, measurement, and statistics, as well as those who employ those procedures in research.