A decision-theoretic formulation of fisher's approach to testing

American Statistician

Volumn 64, Issue 4, 2010, Pages 345-349

  Rice, Kenneth ^a  

^a UNIVERSITY OF WASHINGTON   (United States)

Author keywords

Bayesian inference; Decision theory; Testing

Indexed keywords

EID: 79960973338     PISSN: 00031305     EISSN: None     Source Type: Journal    
DOI: 10.1198/tast.2010.09060     Document Type: Article

References (25)

1. Berger, J. O. (2003), "Could Fisher, Jeffreys and Neyman Have Agreed on Testing?" Statistical Science, 18 (1), 1-32.
2. 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, 112-122, 123-133, 135-139, 1201.
3. Casella, G., Hwang, J. T. G., and Robert, C. (1993), "A Paradox in Decision-Theoretic Interval Estimation," Statistica Sinica, 3, 141-155.
4. Christensen, R. (2005), "Testing Fisher, Neyman, Pearson, and Bayes," The American Statistician, 59 (2), 121-126.
5. Cox, D. R., and Hinkley, D. V. (2000), Theoretical Statistics, Boca Ratou, FL: Chapman & Hall.
6. Datta, S., and Datta, S. (2005), "Empirical Bayes Screening of Many p-Values With Applications to Microarray Studies," Bioinformatics, 21 (9), 1987-1994.
7. Garthwaite, P. H., and Dickey, J. M. (1992), "Elicitation of Prior Distributions for Variable-Selection Problems in Regression," The Annals of Statistics, 20, 1697-1719.
8. Guo, M., and Heitjan, D. F. (2010), "Multiplicity-Calibrated Bayesian Hypothesis Tests," Biostatistics, 11, 473-483.
9. Hubbard, R., and Armstrong, J. (2006), "Why We Don't Really Know What Statistical Significance Means: A Major Educational Failure," Journal of Marketing Education, 28, 114-120.
10. Hubbard, R., and Bayarri, M. J. (2003), "Confusion Over Measures of Evidence (p's) versus Errors (?'s) in Classical Statistical Testing," The American Statistician, 57 (3), 171-178.
11. Hurlbert, S., and Lombardi, C. (2009), "Final Collapse of the Neyman-Pearson Decision Theoretic Framework and Rise of the neoFisherian," Annales Zoologici Fennici, 46 (5), 311-349.
12. Lavine, M., and Schervish, M. J. (1999), "Bayes Factors: What They Are and What They Are Not," The American Statistician, 53, 119-122.
13. Lindley, D. (1957), "A Statistical Paradox," Biometrika, 44, 187-192.
14. Madruga, M. R., Esteves, L. G., Esteves, L. G., and Wechsler, S. (2001), "On the Bayesianity of Pereira-Stern Tests," Test (Madrid), 10 (2), 291-299.
15. Mayo, D., and Cox, D. (2006), "Frequentist Statistics as a Theory of Inductive Inference," in Optimality: The Second Erich L. Lehmann Symposiums. IMS Lecture Notes-Monograph Series, Vol. 49, ed. J. Rojo, Beachwood, OH: Institute of Mathematical Statistics, pp. 77-97.
16. Moreno, E., and Girón, F. J. (2006), "On the Frequentist and Bayesian Approaches to Hypothesis Testing," Statistics and Operations Research Transactions, 30, 3-28.
17. Murdoch, D. J., Tsai, Y.-L., and Adcock, J. (2008), "P -Values Are Random Variables," The American Statistician, 62 (3), 242-245.
18. Pearson, T., and Manolio, T. (2008), "How to Interpret a Genome-Wide Association Study," Journal of the American Medical Association, 299 (11), 1335-1344.
19. Pereira, C. A. d. B., Stern, J. M., and Wechslerz, S. (2008), "Can a Signicance Test Be Genuinely Bayesian?" Bayesian Analysis, 3 (1), 79-100.
20. Sackrowitz, H., and Samuel-Cahn, E. (1999), "p Values as Random Variables-Expected p Values," The American Statistician, 53, 326-331.
21. Schervish, M. J. (1996), "P Values: What They Are and What They Are Not," The American Statistician, 50, 203-206.
22. Schmidt, F. L. (1996), "Statistical Significance Testing and Cumulative Knowledge in Psychology: Implications for Training of Researchers," Psychological Methods, 1 (2), 115-129.
23. van der Vaart, A. (2000), Asymptotic Statistics. Cambridge Series in Statistical and Probabilistic Mathematics, Cambridge: Cambridge University Press.
24. Wakefield, J. (2009), "Bayes Factors for Genome-Wide Association Studies: Comparison With p-Values," Genetic Epidemiology, 33, 79-86.
25. Weir, B. (1996), Genetic Data Analysis II, Sunderland, MA: Sinauer Associates.