A Note on the Connection between Likelihood Inference, Bayes Factors, and P-Values

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The p-value is widely used for quantifying evidence in a statistical hypothesis testing problem. A major criticism, however, is that the p-value does not satisfy the likelihood principle. In this paper, we show that a p-value assessment of evidence can indeed be defined within the likelihood inference framework. Included within this framework is a link between a p-value and the likelihood ratio statistic. Thus, a link between a p-value and the Bayes factor can also be highlighted. The connection between p-values and likelihood based measures of evidence broaden the use of the p-value and deepen our understanding of statistical hypothesis testing.