Abstract
BackgroundP values are the most commonly used tool to measure evidence against a hypothesis. Several attempts have been made to transform P values to minimum Bayes factors and minimum posterior probabilities of the hypothesis under consideration. However, the acceptance of such calibrations in clinical fields is low due to inexperience in interpreting Bayes factors and the need to specify a prior probability to derive a lower bound on the posterior probability.MethodsI propose a graphical approach which easily translates any prior probability and P value to minimum posterior probabilities. The approach allows to visually inspect the dependence of the minimum posterior probability on the prior probability of the null hypothesis. Likewise, the tool can be used to read off, for fixed posterior probability, the maximum prior probability compatible with a given P value. The maximum P value compatible with a given prior and posterior probability is also available.ResultsUse of the nomogram is illustrated based on results from a randomized trial for lung cancer patients comparing a new radiotherapy technique with conventional radiotherapy.ConclusionThe graphical device proposed in this paper will enhance the understanding of P values as measures of evidence among non-specialists.
Highlights
P values are the most commonly used tool to measure evidence against a hypothesis
Within a Bayesian framework, the posterior probability is a function of the prior probability and the so-called Bayes factor, which summarizes the evidence against the null hypothesis
The proposed nomogram can be used in three different ways, as will be illustrated by the following example
Summary
P values are the most commonly used tool to measure evidence against a hypothesis. Several attempts have been made to transform P values to minimum Bayes factors and minimum posterior probabilities of the hypothesis under consideration. The P value is defined as the probability, under the assumption of no effect (the null hypothesis H0), of obtaining a result equal to or more extreme than what was observed. The complexity of this definition has led to widespread misinterpretations and criticisms [2,3,4,5]. P values are often misinterpreted (a) as the probability of obtaining the observed data under the assumption of no real effect, (b) as an “observed” type-I error rate, (c) as the false discovery rate, i.e. the probability that a significant finding is “false positive”, and (d) as the (posterior) probability of the null hypothesis [6]. Within a Bayesian framework, the posterior probability is a function of the prior probability and the so-called Bayes factor, which summarizes the evidence against the null hypothesis
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