Deciding on Null Hypotheses using P-values or Bayesian alternatives: A simulation study

The p-value is currently one of the key elements for testing statistical hypothesis despite its critics. Bayesian statistics and Bayes Factors have been proposed as alternatives to improve the scientific decision making when testing a hypothesis. This study compares the performance of two Bayes Factor estimations (the BIC-based Bayes Factor and the Vovk-Sellke p-value calibration) with the p-value when the null hypothesis holds.

A million pairs of independent data sets were simulated. All simulated data came from a normal population and different sample sizes were considered. Exact p-values for comparing sample means were recorded for each sample pair as well as Bayesian alternatives.

Bayes factors exhibit better performance than the p-value, favouring the null hypothesis over the alternative. The BIC-based Bayes Factor is more accurate than the p-value calibration under the simulation conditions and this behaviour improves as the sample size grows.

Our results show that Bayesian factors are good complements for testing a hypothesis. The use of the Bayesian alternatives we have tested could help researchers avoid claiming false statistical discoveries. We suggest using classical and Bayesian statistics together instead of rejecting either of them.