How the Maximal Evidence of P-Values Against Point Null Hypotheses Depends on Sample Size

References

• Bayarri, M. J., Benjamin, D. J., Berger, J. O., and Sellke, T. M. (2016), “Rejection Odds and Rejection Ratios: A Proposal for Statistical Practice in Testing Hypotheses,” Journal of Mathematical Psychology, 72, 90–103.
   PubMed Web of Science ®Google Scholar
• Berger, J. O., and Sellke, T. (1987), “Testing a Point Null Hypothesis: The Irreconcilability of P Values and Evidence” (with discussion), Journal of the American Statistical Association, 82, 112–139.
   Web of Science ®Google Scholar
• Bernardo, J. M., and Smith, A. F. M. (2000), Bayesian Theory, Wiley Series in Probability and Statistics, Chichester: Wiley.
   Google Scholar
• Copas, J. B. (1983), “Regression, Prediction and Shrinkage,” Journal of the Royal Statistical Society, Series B, 45, 311–354.
   Google Scholar
• Edwards, W., Lindman, H., and Savage, L. J. (1963), “Bayesian Statistical Inference in Psychological Research,” Psychological Review, 70, 193–242.
   Web of Science ®Google Scholar
• Freeman, P. R. (1993), “The Role of p-values in Analysing Trial Results,” Statistics in Medicine, 12, 1443–1452.
   PubMed Web of Science ®Google Scholar
• Goodman, S. N. (1992), “A Comment on Replication, P-values and Evidence,” Statistics in Medicine, 11, 875–879.
   PubMed Web of Science ®Google Scholar
• ——— (1999a), “Towards Evidence-Based Medical Statistics. 1.: The P value Fallacy,” Annals of Internal Medicine, 130, 995–1004.
   PubMed Web of Science ®Google Scholar
• ——— (1999b), “Towards Evidence-based Medical Statistics. 2.: The Bayes Factor,” Annals of Internal Medicine, 130, 1005–1013.
   PubMed Web of Science ®Google Scholar
• ——— (2001), “Of P-values and Bayes: A Modest Proposal,” Epidemiology, 12, 295–297.
   PubMed Web of Science ®Google Scholar
• Greenland, S. (2006), “Bayesian Perspectives for Epidemiological Research: I. Foundations and Basic Methods,” International Journal of Epidemiology, 35, 765–775.
   PubMed Web of Science ®Google Scholar
• ——— (2011), “Null Misinterpretation in Statistical Testing and its Impact on Health Risk Assessment,” Preventive Medicine, 53, 225–228.
   PubMed Web of Science ®Google Scholar
• Greenland, S., and Poole, C. (2013), “Living with p Values: Resurrecting a Bayesian Perspective on Frequentist Statistics,” Epidemiology, 24, 62–68.
   PubMed Web of Science ®Google Scholar
• Held, L. (2010), “A Nomogram for P Values,” BMC Medical Research Methodology, 10, 21.
   PubMed Web of Science ®Google Scholar
• ——— (2013), “Reverse-Bayes Analysis of Two Common Misinterpretations of Significance Tests,” Clinical Trials, 10, 236–242.
   PubMed Web of Science ®Google Scholar
• Held, L., Sabanés Bové, D., and Gravestock, I. (2015), “Approximate Bayesian Model Selection with the Deviance Statistic,” Statistical Science, 30, 242–257.
   Web of Science ®Google Scholar
• Hu, J., and Johnson, V. E. (2009), “Bayesian Model Selection Using Test Statistics,” Journal of the Royal Statistical Society, Series B, 71, 143–158.
   Google Scholar
• Johnson, V. E. (2005), “Bayes Factors Based on Test Statistics,” Journal of the Royal Statistical Society, Series B, 67, 689–701.
   Google Scholar
• ——— (2008), “Properties of Bayes Factors Based on Test Statistics,” Scandinavian Journal of Statistics, 35, 354–368.
   Web of Science ®Google Scholar
• ——— (2013), “Revised Standards for Statistical Evidence,” Proceedings of the National Academy of Sciences, 110, 19313–19317.
   PubMed Web of Science ®Google Scholar
• Kass, R., and Raftery, A. (1995), “Bayes Factors,” Journal of the American Statistical Association, 90, 773–795.
   Web of Science ®Google Scholar
• Kass, R. E., and Wasserman, L. (1995), “A Reference Bayesian Test for Nested Hypotheses and its Relationship to the Schwarz Criterion,” Journal of the American Statistical Association, 90, 928–934.
   Web of Science ®Google Scholar
• Liang, F., Paulo, R., Molina, G., Clyde, M. A., and Berger, J. O. (2008), “Mixtures of g Priors for Bayesian Variable Selection,” Journal of the American Statistical Association, 103, 410–423.
   Web of Science ®Google Scholar
• Matthews, R. (2001), “Methods for Assessing the Credibility of Clinical Trial Outcomes,” Drug Information Journal, 35, 1469–1478.
   Google Scholar
• Royall, R. M. (1986), “The Effect of Sample Size on the Meaning of Significance Tests,” The American Statistician, 40, 313–315.
   Web of Science ®Google Scholar
• Sabanés Bové, D., and Held, L. (2011), “Hyper-g Priors for Generalized Linear Models,” Bayesian Analysis, 6, 387–410.
   Web of Science ®Google Scholar
• Sellke, T., Bayarri, M. J., and Berger, J. O. (2001), “Calibration of p Values for Testing Precise Null Hypotheses,” The American Statistician, 55, 62–71.
   Web of Science ®Google Scholar
• Spiegelhalter, D. J., Abrams, K. R., and Myles, J. P. (2004), Bayesian Approaches to Clinical Trials and Health-Care Evaluation. New York: Wiley.
   Google Scholar
• Vovk, V. G. (1993), “A Logic of Probability, with Application to the Foundations of Statistics” (with Discussion and a Reply by the Author), Journal Royal Statistical Society, Series B, 55, 317–351.
   Google Scholar
• Wagenmakers, E.-J. (2007), “A Practical Solution to the Pervasive Problems of p Values,” Psychonomic Bulletin & Review, 14, 779–804.
   PubMed Web of Science ®Google Scholar
• Wasserstein, R. L., and Lazar, N. A. (2016), “The ASA’s Statement on p-values: Context, Process, and Purpose,” The American Statistician, 70, 129–133.
   Web of Science ®Google Scholar
• Zellner, A. (1986), “On Assessing Prior Distributions and Bayesian Regression Analysis with g-prior Distributions,” in Bayesian Inference and Decision Techniques: Essays in Honor of Bruno de Finetti, Vol. 6 of Studies in Bayesian Econometrics and Statistics, eds. P. K. Goel and A. Zellner, chap. 5, pp. 233–243. Amsterdam: North-Holland.
   Google Scholar