Bayes factor in one-sample tests of means with a sensitivity analysis: A discussion of separate prior distributions

Due to some widely known critiques of traditional hypothesis testing, Bayesian hypothesis testing using the Bayes factor has been considered as a better alternative. Previous research about the influence of the prior focuses on the prior for the effect size and there is a debate about how to specify the prior. Thus, the focus of this paper is to explore the impact of different priors on the population mean and variance separately (separate priors) on the Bayes factor, and compare the separate priors with the priors on the effect size. Our simulation results show that both the prior distributions on mean and variance have a considerable influence on the Bayes factor, and different types of priors (different separate priors and priors on the effect size) have different influence patterns. We also find that regardless of separate priors or priors on the effect size, and shapes and centers of the priors, different priors could yield similar Bayes factors. Because noninformative prior distributions bias the Bayes factor in support of the null hypothesis, and very informative priors could be risky, we suggest that researchers use weakly informative priors as reasonable priors and they are expected to provide similar conclusions across different shapes and centers of prior distributions. Conducting sensitivity analysis is helpful in examining the influence of prior distributions and specifying reasonable prior distributions for the Bayes factor. A real data example is used to illustrate how to choose reasonable priors by a sensitivity analysis. We hope our results will help researchers choose prior distributions when conducting Bayesian hypothesis testing.