p-Values, Bayes Factors, and Sufficiency

Jonathan Rougier*

*Corresponding author for this work

Research output: Contribution to journalArticle (Academic Journal)peer-review

5 Citations (Scopus)
260 Downloads (Pure)


Various approaches can be used to construct a model from a null distribution and a test statistic. I prove that one such approach, originating with D. R. Cox, has the property that the p-value is never greater than the Generalized Likelihood Ratio (GLR). When combined with the general result that the GLR is never greater than any Bayes factor, we conclude that, under Cox’s model, the p-value is never greater than any Bayes factor. I also provide a generalization, illustrations for the canonical Normal model, and an alternative approach based on sufficiency. This result is relevant for the ongoing discussion about the evidential value of small p-values, and the movement among statisticians to “redefine statistical significance.”.

Original languageEnglish
Pages (from-to)148-151
Number of pages4
JournalAmerican Statistician
Issue numbersup1
Early online date20 Mar 2019
Publication statusPublished - 29 Mar 2019


  • Embedding model
  • Exponential tilting
  • Generalized Likelihood Ratio (GLR)


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