Simulation data for the analysis of Bayesian posterior significance and effect size indices for the two-sample t-test to
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BMC Research Notes Open Access
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Simulation data for the analysis of Bayesian posterior significance and effect size indices for the two‑sample t‑test to support reproducible medical research Riko Kelter*
Abstract Objectives: The data presented herein represents the simulated datasets of a recently conducted larger study which investigated the behaviour of Bayesian indices of significance and effect size as alternatives to traditional p-values. The study considered the setting of Student’s and Welch’s two-sample t-test often used in medical research. It investigated the influence of the sample size, noise, the selected prior hyperparameters and the sensitivity to type I errors. The posterior indices used included the Bayes factor, the region of practical equivalence, the probability of direction, the MAP-based p-value and the e-value in the Full Bayesian Significance Test. The simulation study was conducted in the statistical programming language R. Data description: The R script files for simulation of the datasets used in the study are presented in this article. These script files can both simulate the raw datasets and run the analyses. As researchers may be faced with different effect sizes, noise levels or priors in their domain than the ones studied in the original paper, the scripts extend the original results by allowing to recreate all analyses of interest in different contexts. Therefore, they should be relevant to other researchers. Keywords: Bayesian significance and effect measures, Bayesian hypothesis testing, Student’s two-sample t-test, Welch’s two-sample t-test, Bayesian Biostatistics Objective The problems of p-values have been discussed in countless papers [1, 2], but for clinical research, only a few attractive alternatives have been proposed [3, 4]. Bayesian methods are one of the preferred solutions [5, 6]. This paper presents replication scripts which extend the results of a simulation study which investigated the behaviour of Bayesian posterior indices for the two-sample t-test. Indices were compared for their sensitivity to prior elicitation, sample size, error rates and noise.
*Correspondence: riko.kelter@uni‑siegen.de Department of Mathematics, University of Siegen, Siegen, Germany
Results showed that indices differed substantially in their ability to control type I error rates and to detect an existing effect. Based on these results, the Bayes factor [7] and the ROPE [5] were isolated as suitable for the twosample t-test. The simulation data is generated by the provided replication scripts in the statistical programming language R [8] and should be relevant to other researchers. The original paper considered only four fixed effect sizes, and via the provided scripts the results of the original paper can be extended to different context. For example, if researchers expect effect sizes from δ = 0.4 to δ = 0.6 , they can obtain the error rates, influence of noise and robustness to prior selection for different posterior indices
© The Author(s) 2020. This article is licensed
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