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Theory and Method

Testing a Point Null Hypothesis: The Irreconcilability of P Values and Evidence

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Pages 112-122 | Received 01 Jan 1985, Published online: 12 Mar 2012

References

  • Berger , J. 1985 . Statistical Decision Theory and Bayesian Analysis , New York : Springer-Verlag .
  • Berger , J. and Berliner , L. M. 1986 . “Robust Bayes and Empirical Bayes Analysis with ε-Contaminated Priors,” . The Annals of Statistics , 14 : 461 – 486 .
  • Berkson , J. 1938 . “Some Difficulties of Interpretation Encountered in the Application of the Chi-Square Test,” . Journal of the American Statistical Association , 33 : 526 – 542 .
  • Berkson , J. 1942 . “Tests of Significance Considered as Evidence,” . Journal of the American Statistical Association , 37 : 325 – 335 .
  • Cressie , N. and Read , T. R. C. 1984 . “Multinomial Goodness-Of-Fit Tests,” . Journal of the Royal Statistical Society, Ser. B , 46 : 440 – 464 .
  • DeGroot , M. H. 1973 . “Doing What Comes Naturally: Interpreting a Tail Area as a Posterior Probability or as a Likelihood Ratio,” . Journal of the American Statistical Association , 68 : 966 – 969 .
  • Dempster , A. P. “The Direct Use of Likelihood for Significance Testing,” . Proceedings of the Conference on Foundational Questions in Statistical Inference . Edited by: Barndorff-Nielsen , O. pp. 335 – 352 . University of Aarhus, Dept. of Theoretical Statistics .
  • Diamond , G. A. and Forrester , J. S. 1983 . “Clinical Trials and Statistical Verdicts: Probable Grounds for Appeal,” . Annals of Internal Medicine , 98 : 385 – 394 .
  • Dickey , J. M. 1971 . “The Weighted Likelihood Ratio, Linear Hypotheses on Normal Location Parameters,” . Annals of Mathematical Statistics , 42 : 204 – 223 .
  • Dickey , J. M. 1973 . “Scientific Reporting,” . Journal of the Royal Statistical Society, Ser. B , 35 : 285 – 305 .
  • Dickey , J. M. 1974 . “Bayesian Alternatives to the F-Test and Least Squares Estimate in the Normal Linear Model,” . In Studies in Bayesian Econometrics and Statistics , Edited by: Fienberg , S. E. and Zellner , A. 515 – 554 . Amsterdam : North-Holland .
  • Dickey , J. M. 1977 . “Is the Tail Area Useful as an Approximate Bayes Factor?,” . Journal of the American Statistical Association , 72 : 138 – 142 .
  • Dickey , J. M. 1980 . “Approximate Coherence for Regression Models With a New Analysis of Fisher's Broadback Wheatfield Example,” . In Bayesian Analysis in Econometrics and Statistics: Essays in Honor of Harold Jeffreys , Edited by: Zellner , A. 333 – 354 . Amsterdam : North-Holland .
  • Dickey , J. M. and Lientz , B. P. 1970 . “The Weighted Likelihood Ratio, Sharp Hypotheses About Chances, the Order of a Markov Chain,” . Annals of Mathematical Statistics , 41 : 214 – 226 .
  • Edwards , A. W. F. 1972 . Likelihood , Cambridge , , U.K. : Cambridge University Press .
  • Edwards , W. , Lindman , H. and Savage , L. J. 1963 . “Bayesian Statistical Inference for Psychological Research,” . Psychological Review , 70 : 193 – 242 . [Reprinted in Robustness of Bayesian Analyses, 1984: eds. Kadane, J., Amsterdam: North-Holland.]
  • Feller , W. 1968 . An Introduction to Probability Theory and Its Applications, , 3rd ed. , Vol. 1 , New York : John Wiley .
  • Good , I. J. 1950 . Probability and the Weighing of Evidence , London : Charles W. Griffin .
  • Good , I. J. 1958 . “Significance Tests in Parallel and in Series,” . Journal of the American Statistical Association , 53 : 799 – 813 .
  • Good , I. J. 1965 . The Estimation of Probabilities: An Essay on Modern Bayesian Methods , Cambridge , MA : MIT Press .
  • Good , I. J. 1967 . “A Bayesian Significance Test for Multinomial Distributions,” . Journal of the Royal Statistical Society, Ser. B , 29 : 399 – 431 .
  • Good , I. J. 1983 . “Good Thinking: The Foundations of Probability and Its Applications,” , Minneapolis : University of Minnesota Press .
  • Good , I. J. 1984 . Notes C140, C144, C199, C200, and C201 . Journal of Statistical Computation and Simulation , : 19
  • Hill , B. 1982 . Comment on “Lindley's Paradox,” by Glenn Shafer . Journal of the American Statistical Association , 77 : 344 – 347 .
  • Hildreth , C. 1963 . “Bayesian Statisticians and Remote Clients,” . Econometrika , 31 : 422 – 438 .
  • Hodges , J. L. Jr. and Lehmann , E. L. 1954 . “Testing the Approximate Validity of Statistical Hypotheses,” . Journal of the Royal Statistical Society, Ser. B , 16 : 261 – 268 .
  • Jeffreys , H. 1957 . Scientific Inference , Cambridge , , U.K. : Cambridge University Press .
  • Jeffreys , H. 1961 . Theory of Probability, , 3rd ed. , Oxford , , U.K. : Oxford University Press .
  • Jeffreys , H. 1980 . “Some General Points in Probability Theory,” . In Bayesian Analysis in Econometrics and Statistics , Edited by: Zellner , A. 451 – 454 . Amsterdam : North-Holland .
  • Kiefer , J. 1977 . “Conditional Confidence Statements and Confidence Estimators” (with discussion) . Journal of the American Statistical Association , 72 : 789 – 827 .
  • Learner , E. E. 1978 . Specification Searches: Ad Hoc Inference With Nonexperimental Data , New York : John Wiley .
  • Lempers , F. B. 1971 . Posterior Probabilities of Alternative Linear Models , Rotterdam : University of Rotterdam Press .
  • Lindley , D. V. 1957 . “A Statistical Paradox,” . Biometrika , 44 : 187 – 192 .
  • Lindley , D. V. “The Use of Prior Probability Distributions in Statistical Inference and Decision,” . Proceedings of the Fourth Berkeley Symposium on Mathematical Statistics and Probability . pp. 453 – 468 . Berkeley : University of California Press .
  • Lindley , D. V. 1965 . Introduction to Probability and Statistics From A Bayesian Viewpoint , Cambridge , , U.K. : Cambridge University Press . (Parts 1 and 2)
  • Lindley , D. V. 1977 . “A Problem in Forensic Science,” . Biometrika , 64 : 207 – 213 .
  • Pratt , J. W. 1965 . “Bayesian Interpretation of Standard Inference Statements” (with discussion) . Journal of the Royal Statistical Society, Ser. B , 27 : 169 – 203 .
  • Raiffa , H. and Schlaifer , R. 1961 . Applied Statistical Decision Theory , Harvard University, Division of Research, Graduate School of Business Administration .
  • Shafer , G. 1982 . “Lindley's Paradox,” . Journal of the American Statistical Association , 77 : 325 – 351 .
  • Smith , A. F. M. and Spiegelhalter , D. J. 1980 . “Bayes Factors and Choice Criteria for Linear Models,” . Journal of the Royal Statistical Society, Ser. B , 42 : 213 – 220 .
  • Smith , C. A. B. 1965 . “Personal Probability and Statistical Analysis,” . Journal of the Royal Statistical Society, Ser. A , 128 : 469 – 499 .
  • Solo , V. 1984 . “An Alternative to Significance Tests,” , Purdue University, Dept. of Statistics . Technical Report 84–14
  • Zellner , A. 1971 . An Introduction to Bayesian Inference in Econometrics , New York : John Wiley .
  • Zellner , A. 1984 . “Posterior Odds Ratios for Regression Hypotheses: General Considerations and Some Specific Results,” . In Basic Issues in Econometrics , 275 – 305 . Chicago : University of Chicago Press .
  • Zellner , A. and Siow , A. 1980 . “Posterior Odds Ratios for Selected Regression Hypotheses,” . In Bayesian Statistics , Edited by: Bernardo , J. M. , DeGroot , M. H. , Lindley , D. V. and Smith , A. F. M. 586 – 603 . Valencia : University Press .

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