![[PDF]](/pb-assets/Icons/adobe-pdf-icon-1498649896243.png){kind=icon}
Abstract
This article explains a decision rule that uses Bayesian posterior distributions as the basis for accepting or rejecting null values of parameters. This decision rule focuses on the range of plausible values indicated by the highest density interval of the posterior distribution and the relation between this range and a region of practical equivalence (ROPE) around the null value. The article also discusses considerations for setting the limits of a ROPE and emphasizes that analogous considerations apply to setting the decision thresholds for p values and Bayes factors.
References
|
Adjerid, I., Kelley, K. (2018). Big data in psychology: A framework for research advancement. American Psychologist. Advance online publication. doi:10.1037/amp0000190 Google Scholar | |
|
Bayes, T., Price, R. (1763). An essay towards solving a problem in the doctrine of chances. By the late Rev. Mr. Bayes, F. R. S. Communicated by Mr. Price, in a letter to John Canton, A. M. F. R. S. Philosophical Transactions, 53, 370–418. doi:10.1098/rstl.1763.0053 Google Scholar | |
|
Benjamin, D. J., Berger, J. O., Johannesson, M., Nosek, B. A., Wagenmakers, E.-J., Berk, R., . . . Johnson, V. E (2018). Redefine statistical significance. Nature Human Behavior, 2, 6–10. doi:10.1038/s41562-017-0189-z Google Scholar | |
|
Bertotti, B., Iess, L., Tortora, P. (2003). A test of general relativity using radio links with the Cassini spacecraft. Nature, 425, 374–376. doi:10.1038/nature01997 Google Scholar | |
|
Carlin, B. P., Louis, T. A. (2009). Bayesian methods for data analysis (3rd ed.). Boca Raton, FL: CRC Press. Google Scholar | |
|
Cohen, J. (1988). Statistical power analysis for the behavioral sciences (2nd ed.). Hillsdale, NJ: Erlbaum. Google Scholar | |
|
Cox, D. R. (2006). Principles of statistical inference. Cambridge, England: Cambridge University Press. Google Scholar | |
|
Cumming, G. (2014). The new statistics: Why and how. Psychological Science, 25, 7–29. Google Scholar | SAGE Journals | ISI | |
|
Denwood, M. J. (2016). runjags: An R package providing interface utilities, model templates, parallel computing methods and additional distributions for MCMC models in JAGS. Journal of Statistical Software, 71(9), 1–25. doi:10.18637/jss.v071.i09 Google Scholar | |
|
Dienes, Z. (2016). How Bayes factors change scientific practice. Journal of Mathematical Psychology, 72, 78–89. doi:10.1016/j.jmp.2015.10.003 Google Scholar | ISI | |
|
Freedman, L. S., Lowe, D., Macaskill, P. (1984). Stopping rules for clinical trials incorporating clinical opinion. Biometrics, 40, 575–586. Google Scholar | ISI | |
|
Hobbs, B. P., Carlin, B. P. (2008). Practical Bayesian design and analysis for drug and device clinical trials. Journal of Biopharmaceutical Statistics, 18, 54–80. Google Scholar | |
|
Jeffreys, H. (1961). Theory of probability (3rd ed.). Oxford, England: Oxford University Press. Google Scholar | |
|
Kappel, F., Fisher-Fleming, R., Hogue, E. J. (1995). Ideal pear sensory attributes and fruit characteristics. HortScience, 30, 988–993. Google Scholar | |
|
Kappel, F., Fisher-Fleming, R., Hogue, E. J. (1996). Fruit characteristics and sensory attributes of an ideal sweet cherry. HortScience, 31, 443–446. Google Scholar | |
|
Kass, R. E., Raftery, A. E. (1995). Bayes factors. Journal of the American Statistical Association, 90, 773–795. Google Scholar | ISI | |
|
Kruschke, J. K. (2010). Bayesian data analysis. Wiley Interdisciplinary Reviews: Cognitive Science, 1, 658–676. doi:10.1002/wcs.72 Google Scholar | ISI | |
|
Kruschke, J. K. (2011a). Bayesian assessment of null values via parameter estimation and model comparison. Perspectives on Psychological Science, 6, 299–312. Google Scholar | SAGE Journals | ISI | |
|
Kruschke, J. K. (2011b). Doing Bayesian data analysis: A tutorial with R and BUGS (1st ed.). Burlington, MA: Academic Press. Google Scholar | |
|
Kruschke, J. K. (2013). Bayesian estimation supersedes the t test. Journal of Experimental Psychology: General, 142, 573–603. doi:10.1037/a0029146 Google Scholar | |
|
Kruschke, J. K. (2015). Doing Bayesian data analysis: A tu-torial with R, JAGS, and Stan (2nd ed.). Burlington, MA: Academic Press. Google Scholar | |
|
Kruschke, J. K., Aguinis, H., Joo, H. (2012). The time has come: Bayesian methods for data analysis in the organizational sciences. Organizational Research Methods, 15, 722–752. doi:10.1177/1094428112457829 Google Scholar | SAGE Journals | ISI | |
|
Kruschke, J. K., Liddell, T. M. (2018a). Bayesian data analysis for newcomers. Psychonomic Bulletin & Review, 25, 155–177. doi:10.3758/s13423-017-1272-1 Google Scholar | |
|
Kruschke, J. K., Liddell, T. M. (2018b). The Bayesian new statistics: Hypothesis testing, estimation, meta-analysis, and power analysis from a Bayesian perspective. Psychonomic Bulletin & Review, 25, 178–206. doi:10.3758/s13423-016-1221-4 Google Scholar | |
|
Kruschke, J. K., Vanpaemel, W. (2015). Bayesian estimation in hierarchical models. In Busemeyer, J. R., Wang, J., Townsend, J. T., Eidels, A. (Eds.), The Oxford handbook of computational and mathematical psychology (pp. 279–299). Oxford, England: Oxford University Press. Google Scholar | |
|
Lakens, D. (2014). Performing high-powered studies efficiently with sequential analyses. European Journal of Social Psychology, 44, 701–710. Google Scholar | |
|
Lakens, D. (2017). Equivalence tests: A practical primer for t tests, correlations, and meta-analyses. Social Psychological & Personality Science, 8, 355–362. Google Scholar | |
|
Lakens, D., Adolfi, F., Albers, C., Anvari, F., Apps, M., Argamon, S., . . . Zwaan, R. (2017). Justify your alpha. Retrieved from https://psyarxiv.com/9s3y6 Google Scholar | |
|
Lazarus, R. S., Eriksen, C. W. (1952). Effects of failure stress upon skilled performance. Journal of Experimental Psychology, 43, 100–105. doi:10.1037/h0056614 Google Scholar | |
|
Lesaffre, E. (2008). Superiority, equivalence, and non-inferiority trials. Bulletin of the NYU Hospital for Joint Diseases, 66, 150–154. Google Scholar | |
|
Little, T. A. (2015). Equivalence testing for comparability. BioPharm International, 28(2), 45–48. Google Scholar | |
|
Maxwell, S. E. (2004). The persistence of underpowered studies in psychological research: Causes, consequences, and remedies. Psychological Methods, 9, 147–163. Google Scholar | ISI | |
|
Meehl, P. E. (1967). Theory-testing in psychology and physics: A methodological paradox. Philosophy of Science, 34, 103–115. Google Scholar | ISI | |
|
Meehl, P. E. (1997). The problem is epistemology, not statistics: Replace significance tests by confidence intervals and quantify accuracy of risky numerical predictions. In Harlow, L. L., Mulaik, S. A., Steiger, J. H. (Eds.), What if there were no significance tests? (pp. 395–425). Mahwah, NJ: Erlbaum. Google Scholar | |
|
Plummer, M. (2003). JAGS: A program for analysis of Bayesian graphical models using Gibbs sampling. In Hornik, K., Leisch, F., Zeileis, A. (Eds.), Proceedings of the 3rd International Workshop on Distributed Statistical Computing (DSC 2003). Retrieved from https://www.r-project.org/conferences/DSC-2003/Proceedings/Plummer.pdf Google Scholar | |
|
Plummer, M. (2017). JAGS Version 4.3.0 user manual. Retrieved from https://sourceforge.net/projects/mcmc-jags/files/Manuals/4.x/jagsusermanual.pdf/download Google Scholar | |
|
Rindermann, H., Thompson, J. (2011). Cognitive capitalism: The effect of cognitive ability on wealth, as mediated through scientific achievement and economic freedom. Psychological Science, 22, 754–763. Google Scholar | SAGE Journals | ISI | |
|
Rouder, J. N., Morey, R. D., Province, J. M. (2013). A Bayes factor meta-analysis of recent extrasensory perception experiments: Comment on Storm, Tressoldi, and Di Risio (2010). Psychological Bulletin, 139, 241–247. Google Scholar | |
|
Schiff, L. I. (1960). On experimental tests of the general theory of relativity. American Journal of Physics, 28, 340–343. doi:10.1119/1.1935800 Google Scholar | |
|
Schönbrodt, F. D., Wagenmakers, E.-J., Zehetleitner, M., Perugini, M. (2017). Sequential hypothesis testing with Bayes factors: Efficiently testing mean differences. Psychological Methods, 22, 322–339. Google Scholar | |
|
Schuirmann, D. J. (1987). A comparison of the two one-sided tests procedure and the power approach for assessing the equivalence of average bioavailability. Journal of Pharmacokinetics and Biopharmaceutics, 15, 657–680. Google Scholar | |
|
Serlin, R. C., Lapsley, D. K. (1985). Rationality in psychological research: The good-enough principle. American Psychologist, 40, 73–83. Google Scholar | ISI | |
|
Serlin, R. C., Lapsley, D. K. (1993). Rational appraisal of psychological research and the good-enough principle. In Keren, G., Lewis, C. (Eds.), A handbook for data analysis in the behavioral sciences: Methodological issues (pp. 199–228). Mahwah, NJ: Erlbaum. Google Scholar | |
|
Spiegelhalter, D. J., Freedman, L. S., Parmar, M. K. B. (1994). Bayesian approaches to randomized trials. Journal of the Royal Statistical Society: Series A, 157, 357–416. Google Scholar | ISI | |
|
U.S. Food and Drug Administration, Center for Drug Evaluation and Research . (2001). Guidance for industry: Statistical approaches to establishing bioequiva-lence. Retrieved from https://www.fda.gov/downloads/drugs/guidances/ucm070244.pdf Google Scholar | |
|
U.S. Food and Drug Administration, Center for Drug Evaluation and Research and Center for Biologics Evaluation and Research . (2016). Non-inferiority clinical trials to establish effectiveness: Guidance for industry. Retrieved from https://www.fda.gov/downloads/drugs/guidancecomplianceregulatoryinformation/guidances/ucm202140.pdf Google Scholar | |
|
U.S. Food and Drug Administration, Center for Veterinary Medicine . (2016). Guidance for industry: Bioequivalence: Blood level bioequivalence study VICH GL52. Re-trieved from https://www.fda.gov/downloads/AnimalVeterinary/GuidanceComplianceEnforcement/GuidanceforIndustry/UCM415697.pdf Google Scholar | |
|
Walker, E., Nowacki, A. S. (2011). Understanding equivalence and noninferiority testing. Journal of General Internal Medicine, 26, 192–196. Google Scholar | ISI | |
|
Wasserstein, R. L., Lazar, N. A. (2016). The ASA’s statement on p-values: Context, process, and purpose. The American Statistician, 70, 129–133. doi:10.1080/00031305.2016.1154108 Google Scholar | |
|
Westlake, W. J. (1976). Symmetrical confidence intervals for bioequivalence trials. Biometrics, 32, 741–744. Google Scholar | ISI | |
|
Westlake, W. J. (1981). Response to bioequivalence testing—a need to rethink. Biometrics, 37, 591–593. Google Scholar | ISI | |
|
Wiens, B. L. (2002). Choosing an equivalence limit for noninferiority or equivalence studies. Controlled Clinical Trials, 23, 2–14. Google Scholar | |
|
Will, C. M. (2014). The confrontation between general relativity and experiment. Living Reviews in Relativity, 17, Article 4. doi:10.12942/lrr-2014-4 Google Scholar |
