One important benefit of Bayesian statistics is that you can provide relative support for the null hypothesis. When the null hypothesis is true, p-values will forever randomly wander between 0 and 1, but a Bayes factor has consistency (Rouder, Speckman, Sun, Morey, & Iverson, 2009), which means that as the sample size increases, the Bayes Factor will tell you which of two hypotheses has received more support.
Bayes Factors can express relative evidence for the null hypothesis (H0) compared to the alternative hypothesis (H1), referred to as a BF01, or relative evidence for H1 compared to H0 (a BF10). A BF01 > 3 is sometimes referred to as substantial evidence for H0 (see Wagenmakers, Wetzels, Borsboom, & Van Der Maas, 2011), but what they really mean is substantial evidence for H0 compared to H1.
Table 1 from Wagenmakers et al., 2011, #fixedthatforyou
Since a Bayes Factor provides relative support for one over another hypothesis, the choice for an alternative hypothesis is important. In Neyman-Pearson Frequentist approaches, researchers have to specify the alternative hypothesis to be able to calculate the power of their test. For example, let’s assume a researcher no idea what to expect, and decided to use the average effect size in psychology of d = 0.43 as the expected effect when the alternative hypothesis is true. It then becomes easy to calculate that you need 115 participants in each group of your experiment, if you plan to perform a two-sided independent t-test with an alpha of 0.05, and you want to have 90% power.
When calculating the Bayes Factor, the alternative is specified through the r-scale. This is a scale for the Cauchy prior, which is chosen in such a way that the researcher expects there is a 50% chance of observing an absolute effect larger than the scale value …read more
Source:: r-bloggers.com