Michiels Bart, Heyvaert Mieke, Meulders Ann, Onghena Patrick
Faculty of Psychology and Educational Sciences, KU Leuven - University of Leuven, Leuven, Belgium.
Behav Res Methods. 2017 Feb;49(1):363-381. doi: 10.3758/s13428-016-0714-4.
In the current paper, we present a method to construct nonparametric confidence intervals (CIs) for single-case effect size measures in the context of various single-case designs. We use the relationship between a two-sided statistical hypothesis test at significance level α and a 100 (1 - α) % two-sided CI to construct CIs for any effect size measure θ that contain all point null hypothesis θ values that cannot be rejected by the hypothesis test at significance level α. This method of hypothesis test inversion (HTI) can be employed using a randomization test as the statistical hypothesis test in order to construct a nonparametric CI for θ. We will refer to this procedure as randomization test inversion (RTI). We illustrate RTI in a situation in which θ is the unstandardized and the standardized difference in means between two treatments in a completely randomized single-case design. Additionally, we demonstrate how RTI can be extended to other types of single-case designs. Finally, we discuss a few challenges for RTI as well as possibilities when using the method with other effect size measures, such as rank-based nonoverlap indices. Supplementary to this paper, we provide easy-to-use R code, which allows the user to construct nonparametric CIs according to the proposed method.
在本文中，我们提出了一种方法，用于在各种单病例设计的背景下为单病例效应量度量构建非参数置信区间（CI）。我们利用在显著性水平α下的双侧统计假设检验与100(1 - α)%双侧CI之间的关系，为任何效应量度量θ构建置信区间，该区间包含在显著性水平α下不能被假设检验拒绝的所有点零假设θ值。这种假设检验反演（HTI）方法可以使用随机化检验作为统计假设检验来构建θ的非参数置信区间。我们将此过程称为随机化检验反演（RTI）。我们在完全随机单病例设计中，以θ为两种处理之间均值的未标准化和标准化差异的情况下说明RTI。此外，我们展示了RTI如何扩展到其他类型的单病例设计。最后，我们讨论了RTI面临的一些挑战以及将该方法与其他效应量度量（如基于秩的非重叠指数）一起使用时的可能性。作为本文的补充，我们提供了易于使用的R代码，用户可以根据所提出的方法构建非参数置信区间。
