A nomogram for P values
Biostatistics Unit, Institute of Social and Preventive Medicine, University of Zurich, Hirschengraben 84, 8001 Zurich, Switzerland
BMC Medical Research Methodology 2010, 10:21 doi:10.1186/1471-2288-10-21Published: 16 March 2010
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. 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.
I 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.
Use of the nomogram is illustrated based on results from a randomized trial for lung cancer patients comparing a new radiotherapy technique with conventional radiotherapy.
The graphical device proposed in this paper will enhance the understanding of P values as measures of evidence among non-specialists.