Toward evidence-based medical statistics. 2: The Bayes factor

Bayesian inference is usually presented as a method for determining how sci entific belief should be modified by data. Although Bayesian methodology ha s been one of the most active areas of statistical development in the past 20 years, medical researchers have been reluctant to embrace what they perc eive as a subjective approach to data analysis. It is little understood tha t Bayesian methods have a data-based core, which can be used as a calculus of evidence. This core is the Bayes factor, which in its simplest form is a lso called a likelihood ratio. The minimum Bayes factor is objective and ca n be used in lieu of the P value as a measure of the evidential strength. U nlike P values, Bayes factors have a sound theoretical foundation and an in terpretation that allows their use in both inference and decision making. B ayes factors show that P values greatly overstate the evidence against the null hypothesis. Most important, Bayes factors require the addition of back ground knowledge to be transformed into inferences-probabilities that a giv en conclusion is right or wrong. They make the distinction clear between ex perimental evidence and inferential conclusions while providing a framework in which to combine prior with current evidence.