Fig 1.
Valid statements based on p-values and Bayes factors.
The p-value and the Bayes factor allow fundamentally different statements concerning the null hypothesis. The p-value can be used to make a discrete decision: reject or retain the null hypothesis. The Bayes factor grades the evidence that the data provide for and against the null hypothesis.
Fig 2.
Relation between p-values and Bayes factors.
P-values and Bayes factors in favor of the null hypothesis for 43 null results from the 2015 volume of NEJM. All Bayes factors indicate support in favor of the null hypothesis, and most Bayes factors do so in a compelling fashion. At the same time, the support in favor of the null hypothesis is highly variable. The p-value only explains 8.39% of the variance in the log Bayes factors (r = 0.29).
Fig 3.
Relation between sample size and Bayes factors.
Among the 43 null results from the 2015 volume of NEJM, large samples are more likely to yield compelling evidence in favor of the null hypothesis than small samples (r = 0.72).