When two independent means μ1 and μ2 are compared, H0 : μ1 = μ2, H1 : μ1≠μ2, and H2 : μ1 > μ2 are the hypotheses of interest. This paper introduces the package , which can be used to determine the sample size needed to evaluate these hypotheses using the approximate adjusted fractional Bayes factor (AAFBF) implemented in the package . Both the Bayesian t test and the Bayesian Welch’s test are available in this package. The sample size required will be calculated such that the probability that the Bayes factor is larger than a threshold value is at least η if either the null or alternative hypothesis is true. Using the package and/or the tables provided in this paper, psychological researchers can easily determine the required sample size for their experiments.

The last 25 years have shown a steady increase in attention for the Bayes factor as a tool for hypothesis evaluation and model selection. The present review highlights the potential of the Bayes factor in psychological research. We discuss six types of applications: Bayesian evaluation of point null, interval, and informative hypotheses, Bayesian evidence synthesis, Bayesian variable selection and model Daniel W. Heck https://orcid.

The last 25 years have shown a steady increase in attention for the Bayes factor as a tool for hypothesis evaluation and model selection. The present review highlights the potential of the Bayes factor in psychological research. We discuss six types of applications: Bayesian evaluation of point null, interval, and informative hypotheses, Bayesian evidence synthesis, Bayesian variable selection and model averaging, and Bayesian evaluation of cognitive models. We elaborate what each application entails, give illustrative examples, and provide an overview of key references and software with links to other applications. The paper is concluded with a discussion of the opportunities and pitfalls of Bayes factor applications and a sketch of corresponding future research lines.

When two independent means 1 and 2 are compared, 0 : 1 = 2 , 1 : 1 ≠ 2 , and 2 : 1 > 2 are the hypotheses of interest. This paper introduces the R package SSDbain, which can be used to determine the sample size needed to evaluate these hypotheses using the Approximate Adjusted Fractional Bayes Factor (AAFBF) implemented in the R package bain.Both the Bayesian t-test and the Bayesian Welch's test are available in this R package. The sample size required will be calculated such that the probability that the Bayes factor is larger than a threshold value is at least if either the null or alternative hypothesis is true. Using the R package SSDbain and/or the tables provided in this paper, psychological researchers can easily determine the required sample size for their experiments. SSDbain SAMPLE SIZE DETERMINATION 3 Sample Size Determination for the Bayesian t-test and Welch's test Using the Approximate Adjusted Fractional Bayes Factor1− , for a one-sided alternative hypothesis (Gigerenzer, 1993(Gigerenzer, , 2004. Statistical power is the probability of finding an effect when it exists in the population, that is, the probability of rejecting the null hypothesis when the alternative is true. Power analysis for Neyman-Pearson hypothesis testing has been studied for more than 50 years. Cohen (1988, 1992) played a pioneering role in the development of effect sizes and power analysis, and he provided mathematical equations for the relation between effect size, sample size, Type I error rate and power. For example, if one aims for a power of 80%, the minimum sample size per group should be 394, 64 and 26 for small ( = 0.2), medium ( = 0.5) and large ( = 0.8) effect sizes, respectively for an independent samples two-sided t-test at Type I error rate = .05, where Cohen's is the standardized difference between two means. To perform statistical power analyses for various tests, the

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