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Is the p-value a good measure of evidence? Asymptotic consistency criteria

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  • Grendár, M.

Abstract

What are the criteria that a measure of statistical evidence should satisfy? It is argued that a measure of evidence should be consistent. Consistency is an asymptotic criterion: the probability that, if a measure of evidence in data strongly testifies against a hypothesis H, then H is indeed not true, should go to 1 as more and more data appear. The p-value is not consistent, while the ratio of likelihoods is. The same holds also with respect to the unconditional consistency criterion.

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  • Grendár, M., 2012. "Is the p-value a good measure of evidence? Asymptotic consistency criteria," Statistics & Probability Letters, Elsevier, vol. 82(6), pages 1116-1119.
    • Handle: RePEc:eee:stapro:v:82:y:2012:i:6:p:1116-1119
    DOI: 10.1016/j.spl.2012.02.018
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    1. Sellke T. & Bayarri M. J. & Berger J. O., 2001. "Calibration of rho Values for Testing Precise Null Hypotheses," The American Statistician, American Statistical Association, vol. 55, pages 62-71, February.
    2. Mudholkar, Govind S. & Chaubey, Yogendra P., 2009. "On defining P-values," Statistics & Probability Letters, Elsevier, vol. 79(18), pages 1963-1971, September.
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