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A typical rule that has been used for the endorsement of new medications by the Food and Drug Administration is to have two trials, each convincing on its own, demonstrating effectiveness. “Convincing” may be subjectively interpreted, but the use of p-values and the focus on statistical significance (in particular with  p  < .05 being coined significant) is pervasive in clinical research. Therefore, in this paper, we calculate with simulations what it means to have exactly two trials, each with  p  < .05, in terms of the actual strength of evidence quantified by Bayes factors. Our results show that different cases where two trials have a  p -value below .05 have wildly differing Bayes factors. Bayes factors of at least 20 in favor of the alternative hypothesis are not necessarily achieved and they fail to be reached in a large proportion of cases, in particular when the true effect size is small (0.2 standard deviations) or zero. In a non-trivial number of cases, evidence actually points to the null hypothesis, in particular when the true effect size is zero, when the number of trials is large, and when the number of participants in both groups is low. We recommend use of Bayes factors as a routine tool to assess endorsement of new medications, because Bayes factors consistently quantify strength of evidence. Use of  p -values may lead to paradoxical and spurious decision-making regarding the use of new medications.

A simulation study of the strength of evidence in the recommendation of medications based on two trials with statistically significant results