Faculty of Behavioral and Social Sciences, University of Groningen, Groningen, the Netherlands.
Psychol Methods. 2011 Dec;16(4):406-19. doi: 10.1037/a0024377. Epub 2011 Jul 25.
Psychological theories are statements of constraint. The role of hypothesis testing in psychology is to test whether specific theoretical constraints hold in data. Bayesian statistics is well suited to the task of finding supporting evidence for constraint, because it allows for comparing evidence for 2 hypotheses against each another. One issue in hypothesis testing is that constraints may hold only approximately rather than exactly, and the reason for small deviations may be trivial or uninteresting. In the large-sample limit, these uninteresting, small deviations lead to the rejection of a useful constraint. In this article, we develop several Bayes factor 1-sample tests for the assessment of approximate equality and ordinal constraints. In these tests, the null hypothesis covers a small interval of non-0 but negligible effect sizes around 0. These Bayes factors are alternatives to previously developed Bayes factors, which do not allow for interval null hypotheses, and may especially prove useful to researchers who use statistical equivalence testing. To facilitate adoption of these Bayes factor tests, we provide easy-to-use software.
心理理论是一种约束性陈述。在心理学中，假设检验的作用是检验特定的理论约束是否适用于数据。贝叶斯统计非常适合寻找约束证据的任务，因为它允许比较两个假设的证据。假设检验中的一个问题是，约束可能只是近似的而不是精确的，并且小偏差的原因可能是微不足道或无趣的。在大样本极限下，这些无趣的小偏差会导致有用约束的被拒绝。在本文中，我们开发了几种贝叶斯因子 1 样本检验方法，用于评估近似相等和有序约束。在这些检验中，零假设涵盖了一个小的非零但可忽略的效应大小区间，围绕着 0。这些贝叶斯因子是之前开发的贝叶斯因子的替代方法，这些因子不允许区间零假设，并且可能特别有助于使用统计等效性检验的研究人员。为了促进这些贝叶斯因子检验的采用，我们提供了易于使用的软件。
