TITLE:
A Note on the Connection between Likelihood Inference, Bayes Factors, and P-Values
AUTHORS:
Andrew A. Neath
KEYWORDS:
Hypothesis Testing, Likelihood Principle, Statistical Evidence
JOURNAL NAME:
Open Access Library Journal,
Vol.4 No.1,
January
4,
2017
ABSTRACT: 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.