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Abstract
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 language | English |
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Pages (from-to) | 148-151 |
Number of pages | 4 |
Journal | American Statistician |
Volume | 73 |
Issue number | sup1 |
Early online date | 20 Mar 2019 |
DOIs | |
Publication status | Published - 29 Mar 2019 |
Keywords
- Embedding model
- Exponential tilting
- Generalized Likelihood Ratio (GLR)