Les P-values comme votes d'experts

Guy Morel

ESAIM: Probability and Statistics (2010)

  • Volume: 4, page 191-204
  • ISSN: 1292-8100

Abstract

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The p-values are often implicitly used as a measure of evidence for the hypotheses of the tests. This practice has been analyzed with different approaches. It is generally accepted for the one-sided hypothesis problem, but it is often criticized for the two-sided hypothesis problem. We analyze this practice with a new approach to statistical inference. First we select good decision rules without using a loss function, we call them experts. Then we define a probability distribution on the space of experts. The measure of evidence for a hypothesis is the inductive probability of experts that decide this hypothesis.

How to cite

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Morel, Guy. "Les P-values comme votes d'experts." ESAIM: Probability and Statistics 4 (2010): 191-204. <http://eudml.org/doc/197743>.

@article{Morel2010,
abstract = { The p-values are often implicitly used as a measure of evidence for the hypotheses of the tests. This practice has been analyzed with different approaches. It is generally accepted for the one-sided hypothesis problem, but it is often criticized for the two-sided hypothesis problem. We analyze this practice with a new approach to statistical inference. First we select good decision rules without using a loss function, we call them experts. Then we define a probability distribution on the space of experts. The measure of evidence for a hypothesis is the inductive probability of experts that decide this hypothesis. },
author = {Morel, Guy},
journal = {ESAIM: Probability and Statistics},
keywords = {Théorie de la décision; tests; p-values; seuils minimum de rejet; hypothèses unilatérales et bilatérales.; unilateral hypothesis; bilateral hypothesis},
language = {eng},
month = {3},
pages = {191-204},
publisher = {EDP Sciences},
title = {Les P-values comme votes d'experts},
url = {http://eudml.org/doc/197743},
volume = {4},
year = {2010},
}

TY - JOUR
AU - Morel, Guy
TI - Les P-values comme votes d'experts
JO - ESAIM: Probability and Statistics
DA - 2010/3//
PB - EDP Sciences
VL - 4
SP - 191
EP - 204
AB - The p-values are often implicitly used as a measure of evidence for the hypotheses of the tests. This practice has been analyzed with different approaches. It is generally accepted for the one-sided hypothesis problem, but it is often criticized for the two-sided hypothesis problem. We analyze this practice with a new approach to statistical inference. First we select good decision rules without using a loss function, we call them experts. Then we define a probability distribution on the space of experts. The measure of evidence for a hypothesis is the inductive probability of experts that decide this hypothesis.
LA - eng
KW - Théorie de la décision; tests; p-values; seuils minimum de rejet; hypothèses unilatérales et bilatérales.; unilateral hypothesis; bilateral hypothesis
UR - http://eudml.org/doc/197743
ER -

References

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  1. J.R. Barra, Notions fondamentales de statistique mathématique. Dunod, Paris (1971).  Zbl0257.62004
  2. J.O. Berger, Statistical decision theory and Bayesian analysis, second edition. Springer-Verlag, New York (1985).  
  3. J.O. Berger et T. Sellke, Testing a point null hypothesis: The irreconcilability of p-values and evidence. J. Amer. Statist. Assoc.82 (1987) 112-122.  Zbl0612.62022
  4. R.J. Buehler, Fiducial inference, An appreciation, edited by R.A. Fisher. Springer-Verlag, New York, Lecture Notes in Statistics (1980) 109-118.  
  5. G. Casella et R.L. Berger, Reconciling Bayesian and frequentist evidence in the one-sided testing problem. J. Amer. Statist. Assoc.82 (1987) 106-111.  Zbl0612.62021
  6. J.M. Dickey, Three multidimensional-integral identities with bayesian applications. Ann. Math. Statist.39 (1968) 1615-1628.  Zbl0169.50505
  7. R.A. Fisher, The fiducial argument in statistical inference. Annals of Eugenics6 (1935) 391-398.  
  8. K.R. Gabriel, Simultaneous test procedures — some theory of multiple comparisons. Ann. Math. Statist.40 (1969) 224-250.  Zbl0198.23602
  9. H.M.J. Hung, R.T. O'Neill, P. Bauer et K. Köhne, The behavior of the p-value when the alternative hypothesis is true. Biometrics53 (1997) 11-22.  Zbl0876.62015
  10. J.T. Hwang, G. Casella, C. Robert, M.T. Wells et R.H. Farrell, Estimation of accuracy in testing. Ann. Statist.20 (1992) 490-509.  Zbl0761.62022
  11. S. Karlin, Decision theory for Pólya type distributions. Case of two actions, I, in Proc. Third Berkeley Symposium on Math. Statist. and Prob. Univ. of Calif. Press 1 (1955) 115-128.  
  12. A.H. Kroese, E.A. van der Meulen, K. Poortema et W. Schaafsma, Distributional inference. Statistica Neerlandica49 (1995) 63-82.  
  13. E.L. Lehmann, Testing statistical hypotheses, second edition. Wiley, New York (1986).  Zbl0608.62020
  14. E.A. van der Meulen et W. Schaafsma, Assessing weights of evidence for discussing classical statistical hypotheses. Statistics & Decisions11 (1993) 201-220.  Zbl0804.62022
  15. A. Monfort, Cours de statistique mathématique. Économica, Paris (1982).  
  16. G. Morel, Expertises : procédures statistiques d'aide à la décision, Pré-publication. LAST-Université de Tours (1997) 182.  
  17. G. Morel, Probabiliser l'espace des décisions, Pub. Sém. 97 : Bru Huber Prum, Paris V (1998) 71-98.  
  18. C. Robert, L'analyse statistique bayésienne. Économica, Paris (1992).  
  19. D. Salomé, Statistical inference via fiducial methods, Ph.D. Thesis, Rijksuniversiteit Groningen (1998).  
  20. W. Schaafsma, J. Tolboom et B. van der Meulen, Discussing truth and falsity by computing a Q-value, in Statistical Data Analysis and Inference, edited by Y. Dodge. North-Holland, Amsterdam (1989) 85-100.  Zbl0735.62002
  21. H. Scheffé, The analysis of variance, sixième édition. Wiley, New York (1970).  
  22. M.J. Schervish, P-values: What they are and what they are not. Amer. Statist.50 (1996) 203-206.  
  23. P. Thompson, Improving the admissibility screen: Evaluating test statistics on the basis of p-values rather than power. Comm. Statist. Theory Methods25 (1996) 537-553.  Zbl0875.62043
  24. * Recherche réalisée dans le cadre du LAST et du CNRS UPRES-A 6083 de Tours..  

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