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.
Cite this paper
Neath, A. A. (2017). A Note on the Connection between Likelihood Inference, Bayes Factors, and P-Values. Open Access Library Journal, 4, e3292. doi: http://dx.doi.org/10.4236/oalib.1103292.
Wasserstein, R. and Lazar,
N. (2016) The ASA’s Statement on p-Values: Context, Process, and Purpose. The American Statistician, 70, 129-133. https://doi.org/10.1080/00031305.2016.1154108
Berger, J. and
Wolpert, R. (1988) The Likelihood Principle: A Review, Generalizations, and
Statistical Implications. Institute of Mathematical Statistics, Hayward, CA.
Sellke, T., Bayarri, M. and Berger, J. (2001) Calibration
of p-Values for Testing Precise Null Hypotheses. The American Statistician, 55, 62-71. https://doi.org/10.1198/000313001300339950