Abstract
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 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 η 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.
Highlights
In the Neyman–Pearson approach to hypothesis testing (Gigerenzer, 2004) a null and an alternative hypothesis are compared
We focus on the approximate adjusted fractional Bayes factor (AAFBF) in this manuscript because it is available for both the t test and the Welch’s test
The function SSDttest implemented in the R package SSDbain has been developed for sample-size determination for twosided and one-sided hypotheses under a Bayesian t test or Bayesian Welch’s test using the AAFBF as implemented in the R package bain
Summary
In the Neyman–Pearson approach to hypothesis testing (Gigerenzer, 2004) a null and an alternative hypothesis are compared. One-sided alternative hypothesis can effectively reduce the required sample size and it is recommended to be used This manuscript will provide a comprehensive analysis for both two-sided and one-sided alternative hypotheses; (3) the sample size will be calculated such that the probability that the Bayes factor is larger than a user specified threshold is at least η if either the null hypothesis or the alternative hypothesis is true; (4) we use the dichotomy method to compute the sample size very fast. This method is simple and used but with high computation effort, especially for the case when the required sample size is large, e.g., the sample size of 500 will cause several hundreds of iterations, while only 12 iterations are required with our method; (5) the sensitivity of SSD with respect to the specification of the prior will be highlighted This is very important when Bayes factor is used for the hypothesis testing evaluation, because there exists some uncertainty for the required sample size for different prior distributions.
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