Three Insights from a Bayesian Interpretation of the One-Sided P Value

Educational and Psychological Measurement

Volumn 77, Issue 3, 2017, Pages 529-539

  Marsman, Maarten ^a   Wagenmakers, Eric Jan ^a  

^a UNIVERSITY OF AMSTERDAM   (Netherlands)

Author keywords

Bayesian inference; estimation; hypothesis testing; null hypothesis

Indexed keywords

EID: 85019199861     PISSN: 00131644     EISSN: 15523888     Source Type: Journal    
DOI: 10.1177/0013164416669201     Document Type: Article

References (44)

1. Berger J. O., Delampady M., (1987). Testing precise hypotheses. Statistical Science, 2, 317-352.
2. Berger J. O., Mortera J., (1999). Default Bayes factors for nonnested hypothesis testing. Journal of the American Statistical Association, 94, 542-554.
3. Cano J. A., Carazo C., Salmerón C., (2013). Bayesian model selection approach to the one way analysis of variance under homoscedasticity. Computational Statistics, 28, 919-931.
4. Casella G., Berger R. L., (1987). Reconciling Bayesian and frequentist evidence in the one-sided testing problem. Journal of the American Statistical Association, 82, 106-111.
5. Cohen J., (1990). Things I have learned (thus far). American Psychologist, 45, 1304-1312.
6. 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.
7. Dickey J. M., (1977). Is the tail area useful as an approximate Bayes factor?Journal of the American Statistical Association, 72, 138-142.
8. Dickey J. M., 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.
9. Edwards W., (1965). Tactical note on the relation between scientific and statistical hypotheses. Psychological Bulletin, 63, 400-402.
10. Edwards W., Lindman H., Savage L. J., (1963). Bayesian statistical inference for psychological research. Psychological Review, 70, 193-242.
11. Gelman A., (2013). p values and statistical practice. Epidemiology, 24, 69-72.
12. Girón F. J., Martínez M. L., Moreno E., Torres F., (2006). Objective testing procedures in linear models: Calibration of the p-values. Scandinavian Journal of Statistics, 33, 765-784.
13. Greenland S., Poole C., (2013). Living withP values: Resurrecting a Bayesian perspective on frequentist statistics. Epidemiology, 24, 62-68.
14. Hagen R. L., (1997). In praise of the null hypothesis statistical test. American Psychologist, 52, 15-24.
15. Jeffreys H., (1961). Theory of probability (3rd ed.). Oxford, England: Oxford University Press.
16. Johnson D. H., (1999). The insignificance of statistical significance testing. Journal of Wildlife Management, 63, 763-772.
17. Johnson V. E., (2013). Revised standards for statistical evidence. Proceedings of the National Academy of Sciences of the United States of America, 110, 19313-19317.
18. Kass R. E., Raftery A. E., (1995). Bayes factors. Journal of the American Statistical Association, 90, 773-795.
19. Lee P. M., (2012). Bayesian statistics: An introduction (4th ed.). Chichester, England: Wiley.
20. Leek J. T., Peng R. D., (2015). P values are just the tip of the iceberg. Nature, 520, 612.
21. Lindley D. V., (1957). A statistical paradox. Biometrika, 44, 187-192.
22. Lindley D. V., (1965). Introduction to probability & statistics from a Bayesian viewpoint. Part 2. Inference. Cambridge, England: Cambridge University Press.
23. Ly A., Verhagen A. J., Wagenmakers E.-J., (2016). Harold Jeffreys’s default Bayes factor hypothesis tests: Explanation, extension, and application in psychology. Journal of Mathematical Psychology, 72, 19–32.
24. Marin J.-M., Robert C. P., (2007). Bayesian core: A practical approach to computational Bayesian statistics. New York, NY: Springer.
25. Meehl P. E., (1978). Theoretical risks and tabular asterisks: Sir Karl, Sir Ronald, and the slow progress of soft psychology. Journal of Consulting and Clinical Psychology, 46, 806-834.
26. Morey R. D., Wagenmakers E.-J., (2014). Simple relation between Bayesian order-restricted and point-null hypothesis tests. Statistics and Probability Letters, 92, 121-124.
27. Morrison D. E., Henkel R. E., (1970). The significance test controversy. New Brunswick, NJ: Transaction.
28. Mulaik S., Steiger J., (1997). What if there were no significance tests. Mahwah, NJ: Erlbaum.
29. Nickerson R. S., (2000). Null hypothesis statistical testing: A review of an old and continuing controversy. Psychological Methods, 5, 241-301.
30. O’Hagan A., Forster J., (2004). Kendall’s advanced theory of statistics. Vol. 2B: Bayesian inference (2nd ed.). London, England: Arnold.
31. Pratt J. W., (1965). Bayesian interpretation of standard inference statements. Journal of the Royal Statistical Society B, 27, 169-203.
32. Pratt J. W., Raiffa H., Schlaifer R., (1995). Introduction to statistical decision theory. Cambridge: MIT Press.
33. Rouanet H., (1996). Bayesian methods for assessing importance of effects. Psychological Bulletin, 119, 149-158.
34. Rouder J. N., (2014). Optional stopping: No problem for Bayesians. Psychonomic Bulletin & Review, 21, 301-308.
35. Rouder J. N., Morey R. D., Speckman P. L., Province J. M., (2012). Default Bayes factors for ANOVA designs. Journal of Mathematical Psychology, 56, 356-374.
36. Rozeboom W. W., (1997). Good science is abductive, not hypothetico-deductive. In Mulaik S., Steiger J., (Eds.), What if there were no significance tests (pp. 335-392). Mahwah, NJ: Erlbaum.
37. Sanborn A. N., Hills T. T., (2014). The frequentist implications of optional stopping on Bayesian hypothesis tests. Psychonomic Bulletin & Review, 21, 283-300.
38. Schervish M. J., (1996). P values: What they are and what they are not. The American Statistician, 50, 203-206.
39. Sellke T., Bayarri M. J., Berger J. O., (2001). Calibration of p values for testing precise null hypotheses. The American Statistician, 55, 62-71.
40. Wagenmakers E.-J., (2007). A practical solution to the pervasive problems of p values. Psychonomic Bulletin & Review, 14, 779-804.
41. Wagenmakers E.-J., Lodewyckx T., Kuriyal H., Grasman R., (2010). Bayesian hypothesis testing for psychologists: A tutorial on the Savage–Dickey method. Cognitive Psychology, 60, 158-189.
42. Wainer H., (1999). One cheer for null hypothesis significance testing. Psychological Methods, 4, 212-213.
43. Wetzels R., Grasman R. P. P. P., Wagenmakers E.-J., (2010). An encompassing prior generalization of the Savage–Dickey density ratio test. Computational Statistics & Data Analysis, 54, 2094-2102.
44. Wetzels R., Matzke D., Lee M. D., Rouder J. N., Iverson G. J., Wagenmakers E.-J., (2011). Statistical evidence in experimental psychology: An empirical comparison using 855 t tests. Perspectives on Psychological Science, 6, 291-298.