Bayesian inference for psychology. Part I: Theoretical advantages and practical ramifications

. 2018 Feb ; 25 (1) : 35-57.

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Perzistentní odkaz   https://www.medvik.cz/link/pmid28779455
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PubMed 28779455
PubMed Central PMC5862936
DOI 10.3758/s13423-017-1343-3
PII: 10.3758/s13423-017-1343-3
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Bayesian parameter estimation and Bayesian hypothesis testing present attractive alternatives to classical inference using confidence intervals and p values. In part I of this series we outline ten prominent advantages of the Bayesian approach. Many of these advantages translate to concrete opportunities for pragmatic researchers. For instance, Bayesian hypothesis testing allows researchers to quantify evidence and monitor its progression as data come in, without needing to know the intention with which the data were collected. We end by countering several objections to Bayesian hypothesis testing. Part II of this series discusses JASP, a free and open source software program that makes it easy to conduct Bayesian estimation and testing for a range of popular statistical scenarios (Wagenmakers et al. this issue).

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Albert J. Bayesian computation with R. New York: Springer; 2007.

Alcock J. Afterword: An analysis of psychic sleuths’ claims. In: Nickell J, editor. Psychic sleuths: ESP and sensational cases. Buffalo, NY: Prometheus Books; 1994. pp. 172–190.

Andraszewicz S, Scheibehenne B, Rieskamp J, Grasman RPPP, Verhagen AJ, Wagenmakers EJ. An introduction to Bayesian hypothesis testing for management research. Journal of Management. 2015;41:521–543. doi: 10.1177/0149206314560412. DOI

Anscombe FJ. Sequential medical trials. Journal of the American Statistical Association. 1963;58:365–383. doi: 10.1080/01621459.1963.10500851. DOI

Anscombe FJ. Graphs in statistical analysis. The American Statistician. 1973;27:17–21.

Bargh JA, Shalev I. The substitutability of physical and social warmth in daily life. Emotion. 2012;12:154–162. doi: 10.1037/a0023527. PubMed DOI PMC

Bayarri MJ, Benjamin DJ, Berger JO, Sellke TM. Rejection odds and rejection ratios: A proposal for statistical practice in testing hypotheses. Journal of Mathematical Psychology. 2016;72:90–103. doi: 10.1016/j.jmp.2015.12.007. PubMed DOI PMC

Begley CG, Ellis LM. Raise standards for preclinical cancer research. Nature. 2012;483:531–533. doi: 10.1038/483531a. PubMed DOI

Bem DJ. Feeling the future: Experimental evidence for anomalous retroactive influences on cognition and affect. Journal of Personality and Social Psychology. 2011;100:407–425. doi: 10.1037/a0021524. PubMed DOI

Bem DJ, Utts J, Johnson WO. Must psychologists change the way they analyze their data? Journal of Personality and Social Psychology. 2011;101:716–719. doi: 10.1037/a0024777. PubMed DOI

Berger J. The case for objective Bayesian analysis. Bayesian Analysis. 2004;1:1–17.

Berger JO. Statistical decision theory and Bayesian analysis. 2nd edn. New York: Springer; 1985.

Berger JO. Bayes factors. In: Kotz S, Balakrishnan N, Read C, Vidakovic B, Johnson N L, editors. Encyclopedia of statistical sciences, Vol. 1. Hoboken, NJ: Wiley; 2006. pp. 378–386.

Berger JO, Berry DA. Statistical analysis and the illusion of objectivity. American Scientist. 1988;76:159–165.

Berger JO, Delampady M. Testing precise hypotheses. Statistical Science. 1987;2:317–352. doi: 10.1214/ss/1177013238. DOI

Berger JO, Mortera J. Default Bayes factors for nonnested hypothesis testing. Journal of the American Statistical Association. 1999;94:542–554. doi: 10.1080/01621459.1999.10474149. DOI

Berger JO, Pericchi LR. Objective Bayesian methods for model selection: Introduction and comparison (with discussion) In: Lahiri P, editor. Model selection, Vol. 38. Beachwood, OH: Institute of Mathematical Statistics Lecture Notes—Monograph Series; 2001. pp. 135–207.

Berger JO, Wolpert RL. The likelihood principle. 2nd edn. Hayward (CA): Institute of Mathematical Statistics; 1988.

Bernardo JM, Smith AFM. Bayesian theory. New York: Wiley; 1994.

Botella J, Ximénez C, Revuelta J, Suero M. Optimization of sample size in controlled experiments: The CLAST rule. Behavior Research Methods. 2006;38:65–76. doi: 10.3758/BF03192751. PubMed DOI

Bové DS, Held L. Hyper–g priors for generalized linear models. Bayesian Analysis. 2011;6:387–410.

Brown L. The conditional level of Student’s t test. The Annals of Mathematical Statistics. 1967;38:1068–1071. doi: 10.1214/aoms/1177698776. DOI

Buehler RJ, Fedderson AP. Note on a conditional property of Student’s t. The Annals of Mathematical Statistics. 1963;34:1098–1100. doi: 10.1214/aoms/1177704034. DOI

Button KS, Ioannidis JPA, Mokrysz C, Nosek BA, Flint J, Robinson ESJ, Munafò MR. Power failure: Why small sample size undermines the reliability of neuroscience. Nature Reviews Neuroscience. 2013;14:1–12. PubMed

Cornfield J. The Bayesian outlook and its application. Biometrics. 1969;25:617–657. doi: 10.2307/2528565. PubMed DOI

Chambers CD. Registered Reports: A new publishing initiative at Cortex. Cortex. 2013;49:609–610. doi: 10.1016/j.cortex.2012.12.016. PubMed DOI

Cox DR. Some problems connected with statistical inference. The Annals of Mathematical Statistics. 1958;29:357–372. doi: 10.1214/aoms/1177706618. DOI

Cumming G. Replication and p intervals: p values predict the future only vaguely, but confidence intervals do much better. Perspectives on Psychological Science. 2008;3:286–300. doi: 10.1111/j.1745-6924.2008.00079.x. PubMed DOI

Cumming G. The new statistics: Why and how. Psychological Science. 2014;25:7–29. doi: 10.1177/0956797613504966. PubMed DOI

Dawid AP. Statistical theory: The prequential approach. Journal of the Royal Statistical Society A. 1984;147:278–292. doi: 10.2307/2981683. DOI

Dawid AP. Comment on “the philosophy of statistics” by D. V. Lindley. The Statistician. 2000;49:325–326.

Dawid AP. Statistics on trial. Significance. 2005;2:6–8. doi: 10.1111/j.1740-9713.2005.00075.x. DOI

de Finetti B. Theory of probability, Vol. 1 and 2. New York: Wiley; 1974.

De Groot, A. D. (1956/2014). The meaning of “significance” for different types of research. Translated and annotated by Eric-Jan Wagenmakers, Denny Borsboom, Josine Verhagen, Rogier Kievit, Marjan Bakker, Angelique Cramer, Dora Matzke, Don Mellenbergh, and Han L. J. van der Maas. Acta Psychologica, 148, 188–194. PubMed

Dienes Z. Understanding psychology as a science: An introduction to scientific and statistical inference. New York: Palgrave MacMillan; 2008.

Dienes Z. Bayesian versus orthodox statistics: Which side are you on? Perspectives on Psychological Science. 2011;6:274–290. doi: 10.1177/1745691611406920. PubMed DOI

Dienes Z. Using Bayes to get the most out of non-significant results. Frontiers in Psycholology. 2014;5:781. PubMed PMC

Donnellan MB, Lucas RE, Cesario J. On the association between loneliness and bathing habits: Nine replications of Bargh and Shalev (2012) Study 1. Emotion. 2015;15:109–119. doi: 10.1037/a0036079. PubMed DOI

Eagle, A. (Ed.) (2011). Philosophy of probability: Contemporary readings. New York: Routledge.

Edwards AWF. Likelihood. Baltimore, MD: The Johns Hopkins University Press; 1992.

Edwards W. Tactical note on the relation between scientific and statistical hypotheses. Psychological Bulletin. 1965;63:400–402. doi: 10.1037/h0021967. PubMed DOI

Edwards W, Lindman H, Savage LJ. Bayesian statistical inference for psychological research. Psychological Review. 1963;70:193–242. doi: 10.1037/h0044139. DOI

Estes WK. The problem of inference from curves based on group data. Psychological Bulletin. 1956;53:134–140. doi: 10.1037/h0045156. PubMed DOI

Etz, A., & Wagenmakers, E. J. (2016). J. B. S. Haldane’s contribution to the Bayes factor hypothesis test. Manuscript submitted for publication and uploaded to ArXiv.

Etz, A., Gronau, Q.F., Dablander, F., Edelsbrunner, P.A., & Baribault, B. (this issue). How to become a Bayesian in eight easy steps: An annotated reading list. PubMed

Fisher RA. Statistical methods and scientific inference. 2nd edn. New York: Hafner; 1959.

Fitts DA. Improved stopping rules for the design of efficient small–sample experiments in biomedical and biobehavioral research. Behavior Research Methods. 2010;42:3–22. doi: 10.3758/BRM.42.1.3. PubMed DOI

Frick RW. A better stopping rule for conventional statistical tests. Behavior Research Methods, Instruments, and Computers. 1998;30:690–697. doi: 10.3758/BF03209488. DOI

Gallistel CR. The importance of proving the null. Psychological Review. 2009;116:439–453. doi: 10.1037/a0015251. PubMed DOI PMC

Gelfand AE, Smith AFM. Sampling–based approaches to calculating marginal densities. Journal of the American Statistical Association. 1990;85:398–409. doi: 10.1080/01621459.1990.10476213. DOI

Gelman A, Carlin JB, Stern HS, Dunson DB, Vehtari A, Rubin DB. Bayesian data analysis. 3rd edn. Boca Raton: Chapman & Hall/CRC; 2014.

Gelman A, Hill J. Data analysis using regression and multilevel/hierarchical models. Cambridge: Cambridge University Press; 2007.

Gigerenzer G. Mindless statistics. The Journal of Socio–Economics. 2004;33:587–606. doi: 10.1016/j.socec.2004.09.033. DOI

Gigerenzer G, Krauss S, Vitouch O. The null ritual: What you always wanted to know about significance testing but were afraid to ask. In: Kaplan D, editor. The sage handbook of quantitative methodology for the social sciences. Thousand Oaks, CA: Sage; 2004. pp. 391–408.

Gilks WR, Richardson S, Spiegelhalter DJ. Markov chain Monte Carlo in practice. Chapman & Hall/CRC: Boca Raton, FL; 1996.

Gillispie CC. Pierre–Simon Laplace 1749–1827: A life in exact science. Princeton, NJ: Princeton University Press; 1997.

Gleser LJ. Setting confidence intervals for bounded parameters: Comment. Statistical Science. 2002;17:161–163.

Goldstein M. Subjective Bayesian analysis: Principles and practice. Bayesian Analysis. 2006;1:403–420. doi: 10.1214/06-BA116. DOI

Goldstein NJ, Cialdini RB, Griskevicius V. A room with a viewpoint: Using social norms to motivate environmental conservation in hotels. Journal of Consumer Research. 2008;35:472–482. doi: 10.1086/586910. DOI

Grant DA. Testing the null hypothesis and the strategy and tactics of investigating theoretical models. Psychological Review. 1962;69:54–61. doi: 10.1037/h0038813. PubMed DOI

Greenland, S., Senn, S. J., Rothman, K. J., Carlin, J. B., Poole, C., Goodman, S. N., & Altman, D. G. (in press). Statistical tests, p–values, confidence intervals, and power: A guide to misinterpretations. The American Statistician. PubMed PMC

Haldane JBS. A note on inverse probability. Mathematical Proceedings of the Cambridge Philosophical Society. 1932;28:55–61. doi: 10.1017/S0305004100010495. DOI

Halsey LG, Curran-Everett D, Vowler SL, Drummond GB. The fickle P value generates irreproducible results. Nature Methods. 2015;12:179–185. doi: 10.1038/nmeth.3288. PubMed DOI

Hartshorne C, Weiss P. Collected papers of Charles Sanders Peirce: Volume II: Elements of logic. Cambridge: Harvard University Press; 1932.

Heathcote A, Brown S, Mewhort DJK. The power law repealed: The case for an exponential law of practice. Psychonomic Bulletin & Review. 2000;7:185–207. doi: 10.3758/BF03212979. PubMed DOI

Heathcote A, Brown SD, Wagenmakers EJ. An introduction to good practices in cognitive modeling. In: Forstmann B U, Wagenmakers E J, editors. An introduction to model–based cognitive neuroscience. New York: Springer; 2015. pp. 25–48.

Hill R. Reflections on the cot death cases. Significance. 2005;2:13–15. doi: 10.1111/j.1740-9713.2005.00077.x. PubMed DOI

Hoekstra R, Morey RD, Rouder JN, Wagenmakers EJ. Robust misinterpretation of confidence intervals. Psychonomic Bulletin & Review. 2014;21:1157–1164. doi: 10.3758/s13423-013-0572-3. PubMed DOI

Hoijtink H. Informative hypotheses: Theory and practice for behavioral and social scientists. Boca Raton: Chapman & Hall/CRC; 2011.

Hoijtink H, Klugkist I, Boelen P. Bayesian evaluation of informative hypotheses. New York: Springer; 2008.

Huelsenbeck JP, Ronquist F. MRBAYES: Bayesian inference of phylogenetic trees. Bioinformatics. 2001;17:754–755. doi: 10.1093/bioinformatics/17.8.754. PubMed DOI

Ioannidis JPA. Why most published research findings are false. PLoS Medicine. 2005;2:696–701. PubMed PMC

JASP Team (2016). JASP (Version 0.8)[computer software]. Retrieved from https://jasp-stats.org/.

Jaynes ET. Confidence intervals vs Bayesian intervals. In: Harper W L, Hooker C A, editors. Foundations of probability theory, statistical inference, and statistical theories of science, Vol. II. Dordrecht: D. Reidel Publishing Company; 1976. pp. 175–257.

Jaynes ET. Probability theory: The logic of science. Cambridge: Cambridge University Press; 2003.

Jeffreys H. Some tests of significance, treated by the theory of probability. Proceedings of the Cambridge Philosophy Society. 1935;31:203–222. doi: 10.1017/S030500410001330X. DOI

Jeffreys H. Theory of probability. 3rd edn. Oxford: Oxford University Press; 1961.

Jeffreys H. Review of “the foundations of statistical inference”. Technometrics. 1963;3:407–410. doi: 10.2307/1266347. DOI

Jeffreys H. Scientific inference. 3rd edn. Cambridge: Cambridge University Press; 1973.

Jeffreys H. Some general points in probability theory. In: Zellner A, editor. Bayesian analysis in econometrics and statistics: Essays in honor of Harold Jeffreys. Amsterdam: North-Holland Publishing Company; 1980. pp. 451–453.

Jefferys WH, Berger JO. Ockham’s razor and Bayesian analysis. American Scientist. 1992;80:64–72.

John LK, Loewenstein G, Prelec D. Measuring the prevalence of questionable research practices with incentives for truth–telling. Psychological Science. 2012;23:524–532. doi: 10.1177/0956797611430953. PubMed DOI

Johnson VE. Revised standards for statistical evidence. Proceedings of the National Academy of Sciences of the United States of America. 2013;110:19313–19317. doi: 10.1073/pnas.1313476110. PubMed DOI PMC

Joyce JM. A non–pragmatic vindication of probabilism. Philosophy of Science. 1998;65:575–603. doi: 10.1086/392661. DOI

Kass RE, Raftery AE. Bayes factors. Journal of the American Statistical Association. 1995;90:773–795. doi: 10.1080/01621459.1995.10476572. DOI

Klugkist I, Laudy O, Hoijtink H. Inequality constrained analysis of variance: A Bayesian approach. Psychological Methods. 2005;10:477–493. doi: 10.1037/1082-989X.10.4.477. PubMed DOI

Kruschke, J. K. (2010a). Doing Bayesian data analysis: A tutorial introduction with R and BUGS Burlington. MA: Academic Press.

Kruschke, J. K. (2010b). What to believe: Bayesian methods for data analysis. Trends in Cognitive Sciences, 14, 293–300. PubMed

Kruschke JK. Bayesian assessment of null values via parameter estimation and model comparison. Perspectives on Psychological Science. 2011;6:299–312. doi: 10.1177/1745691611406925. PubMed DOI

Lakens D, Evers ERK. Sailing from the seas of chaos into the corridor of stability: Practical recommendations to increase the informational value of studies. Perspectives on Psychological Science. 2014;9:278–292. doi: 10.1177/1745691614528520. PubMed DOI

Lee MD. Three case studies in the Bayesian analysis of cognitive models. Psychonomic Bulletin & Review. 2008;15:1–15. doi: 10.3758/PBR.15.1.1. PubMed DOI

Lee MD. How cognitive modeling can benefit from hierarchical Bayesian models. Journal of Mathematical Psychology. 2011;55:1–7. doi: 10.1016/j.jmp.2010.08.013. DOI

Lee, M. D., & Wagenmakers, E. J. (2013). Bayesian cognitive modeling: A practical course. Cambridge University Press.

Lee MD, Fuss I, Navarro D. A Bayesian approach to diffusion models of decision–making and response time. In: Schölkopf B, Platt J, Hoffman T, editors. Advances in neural information processing systems, Vol. 19. Cambridge: MIT Press; 2006. pp. 809–815.

Lewis SM, Raftery AE. Estimating Bayes factors via posterior simulation with the Laplace–Metropolis estimator. Journal of the American Statistical Association. 1997;92:648–655.

Liang F, Paulo R, Molina G, Clyde MA, Berger JO. Mixtures of g priors for Bayesian variable selection. Journal of the American Statistical Association. 2008;103:410–423. doi: 10.1198/016214507000001337. DOI

Lindley DV. Introduction to probability & statistics from a Bayesian viewpoint. Part 2 Inference. Cambridge: Cambridge University Press; 1965.

Lindley DV. Jeffreys’s contribution to modern statistical thought. In: Zellner A, editor. Bayesian analysis in econometrics and statistics: Essays in honor of Harold Jeffreys. Amsterdam: North-Holland Publishing Company; 1980. pp. 35–39.

Lindley DV. Making decisions. 2nd edn. London: Wiley; 1985.

Lindley DV. Comment on “tests of significance in theory and practice” by D. J. Johnstone. Journal of the Royal Statistical Society, Series D (The Statistician) 1986;35:502–504.

Lindley DV. The analysis of experimental data: The appreciation of tea and wine. Teaching Statistics. 1993;15:22–25. doi: 10.1111/j.1467-9639.1993.tb00252.x. DOI

Lindley DV. The philosophy of statistics. The Statistician. 2000;49:293–337.

Lindley DV. That wretched prior. Significance. 2004;1:85–87. doi: 10.1111/j.1740-9713.2004.026.x. DOI

Lindley DV. Understanding uncertainty. Hoboken: Wiley; 2006.

Lindsay DS. Replication in psychological science. Psychological Science. 2015;26:1827–1832. doi: 10.1177/0956797615616374. PubMed DOI

Lunn D, Jackson C, Best N, Thomas A, Spiegelhalter D. The BUGS book: A practical introduction to Bayesian analysis. Chapman & Hall/CRC: Boca Raton, FL; 2012.

Ly, A., Verhagen, A. J., & Wagenmakers, E. J. (2016a). An evaluation of alternative methods for testing hypotheses, from the perspective of Harold Jeffreys. Journal of Mathematical Psychology, 72, 43– 55.

Ly, A., Verhagen, A. J., & Wagenmakers, E. J. (2016b). Harold Jeffreys’s default Bayes factor hypothesis tests: Explanation, extension, and application in psychology. Journal of Mathematical Psychology, 72, 19–32.

Marin JM, Robert CP. Bayesian core: A practical approach to computational Bayesian statistics. New York: Springer; 2007.

Marsman, M., & Wagenmakers, E. J. (in press). Three insights from a bayesian interpretation of the one–sided p value. Educational and Psychological Measurement. PubMed PMC

Maruyama Y, George EI. Fully Bayes factors with a generalized g–prior. The Annals of Statistics. 2011;39:2740–2765. doi: 10.1214/11-AOS917. DOI

Masson MEJ. A tutorial on a practical Bayesian alternative to null–hypothesis significance testing. Behavior Research Methods. 2011;43:679–690. doi: 10.3758/s13428-010-0049-5. PubMed DOI

Morey RD, Rouder JN. Bayes factor approaches for testing interval null hypotheses. Psychological Methods. 2011;16:406–419. doi: 10.1037/a0024377. PubMed DOI

Morey RD, Rouder JN, Speckman PL. A statistical model for discriminating between subliminal and near–liminal performance. Journal of Mathematical Psychology. 2008;52:21–36. doi: 10.1016/j.jmp.2007.09.007. DOI

Morey RD, Romeijn J, Rouder JN. The humble Bayesian: Model checking from a fully Bayesian perspective. British Journal of Mathematical and Statistical Psychology. 2013;66:68–75. doi: 10.1111/j.2044-8317.2012.02067.x. PubMed DOI

Morey RD, Rouder JN, Verhagen AJ, Wagenmakers EJ. Why hypothesis tests are essential for psychological science: A comment on Cumming. Psychological Science. 2014;25:1289–1290. doi: 10.1177/0956797614525969. PubMed DOI

Morey RD, Hoekstra R, Rouder JN, Lee MD, Wagenmakers EJ. The fallacy of placing confidence in confidence intervals. Psychonomic Bulletin & Review. 2016;23:103–123. doi: 10.3758/s13423-015-0947-8. PubMed DOI PMC

Morey, R. D., Wagenmakers, E J., & Rouder, J. N. (in press). Calibrated Bayes factors should not be used: A reply to Hoijtink, Van Kooten, and Hulsker. Multivariate Behavioral Research. PubMed

Morrison DE, Henkel RE. The significance test controversy. New Brunswick: Transaction Publishers; 1970.

Mulaik S, Steiger J. What if there were no significance tests. Mahwah: Erlbaum; 1997.

Mulder J, Klugkist I, van de Schoot R, Meeus WHJ, Selfhout M, Hoijtink H. Bayesian model selection of informative hypotheses for repeated measurements. Journal of Mathematical Psychology. 2009;53:530–546. doi: 10.1016/j.jmp.2009.09.003. DOI

Myung IJ. Tutorial on maximum likelihood estimation. Journal of Mathematical Psychology. 2003;47:90–100. doi: 10.1016/S0022-2496(02)00028-7. DOI

Myung IJ, Pitt MA. Applying Occam’s razor in modeling cognition: A Bayesian approach. Psychonomic Bulletin & Review. 1997;4:79–95. doi: 10.3758/BF03210778. DOI

Myung, I. J., Forster, M. R., & Browne, M. W. (2000). Model selection [Special issue]. Journal of Mathematical Psychology, 44(1–2). PubMed

Neyman J. Outline of a theory of statistical estimation based on the classical theory of probability. Philosophical Transactions of the Royal Society of London, Series A, Mathematical and Physical Sciences. 1937;236:333–380. doi: 10.1098/rsta.1937.0005. DOI

Nilsson H, Winman A, Juslin P, Hansson G. Linda is not a bearded lady: Configural weighting and adding as the cause of extension errors. Journal of Experimental Psychology: General. 2009;138:517–534. doi: 10.1037/a0017351. PubMed DOI

Nobles R, Schiff D. Misleading statistics within criminal trials: The Sally Clark case. Significance. 2005;2:17–19. doi: 10.1111/j.1740-9713.2005.00078.x. PubMed DOI

Nosek BA, Bar-Anan Y. Scientific utopia: I. Opening scientific communication. Psychological Inquiry. 2012;23:217–243. doi: 10.1080/1047840X.2012.692215. DOI

Nosek BA, Spies JR, Motyl M. Scientific utopia: II. Restructuring incentives and practices to promote truth over publishability. Perspectives on Psychological Science. 2012;7:615–631. doi: 10.1177/1745691612459058. PubMed DOI PMC

Nosek BA, Alter G, Banks GC, Borsboom D, Bowman SD, Breckler SJ, ... Yarkoni T. Promoting an open research culture. Science. 2015;348:1422–1425. doi: 10.1126/science.aab2374. PubMed DOI PMC

Ntzoufras I. Bayesian modeling using winBUGS. Hoboken: Wiley; 2009.

Ntzoufras I, Dellaportas P, Forster JJ. Bayesian variable and link determination for generalised linear models. Journal of Statistical Planning and Inference. 2003;111:165–180. doi: 10.1016/S0378-3758(02)00298-7. DOI

Nuzzo R. Statistical errors. Nature. 2014;506:150–152. doi: 10.1038/506150a. PubMed DOI

O’Hagan A. Fractional Bayes factors for model comparison. Journal of the Royal Statistical Society B. 1995;57:99–138.

O’Hagan A, Forster J. Kendall’s advanced theory of statistics vol 2B: Bayesian inference. 2nd edn. London: Arnold; 2004.

Overstall AM, Forster JJ. Default Bayesian model determination methods for generalised linear mixed models. Computational Statistics & Data Analysis. 2010;54:3269–3288. doi: 10.1016/j.csda.2010.03.008. DOI

Pashler H, Wagenmakers EJ. Editors’ introduction to the special section on replicability in psychological science: A crisis of confidence? Perspectives on Psychological Science. 2012;7:528–530. doi: 10.1177/1745691612465253. PubMed DOI

Peirce, C. S. (1878a). Deduction, induction, and hypothesis. Popular Science Monthly, 13, 470–482.

Peirce, C. S. (1878b). The probability of induction. Popular Science Monthly, 12, 705–718.

Pierce DA. On some difficulties in a frequency theory of inference. The Annals of Statistics. 1973;1:241–250. doi: 10.1214/aos/1176342362. DOI

Pratt JW. Review of Lehmann, E. L., Testing Statistical Hypotheses. Journal of the American Statistical Association. 1961;56:163–167. doi: 10.2307/2282344. DOI

Pratt JW, Raiffa H, Schlaifer R. Introduction to statistical decision theory. Cambridge: MIT Press; 1995.

Pratte MS, Rouder JN. Assessing the dissociability of recollection and familiarity in recognition memory. Journal of Experimental Psychology: Learning, Memory, and Cognition. 2012;38:1591–1607. PubMed

Raftery AE. Bayes factors and BIC. Sociological Methods & Research. 1999;27:411–427. doi: 10.1177/0049124199027003005. PubMed DOI PMC

Ramsey, F. P. Braithwaite, R. B. (Ed.) (1926). Truth and probability. London: Kegan Paul.

Robert CP. The expected demise of the Bayes factor. Journal of Mathematical Psychology. 2016;72:33–37. doi: 10.1016/j.jmp.2015.08.002. DOI

Rouder JN. Optional stopping: No problem for Bayesians. Psychonomic Bulletin & Review. 2014;21:301–308. doi: 10.3758/s13423-014-0595-4. PubMed DOI

Rouder JN, Morey RD. A Bayes–factor meta analysis of Bem’s ESP claim. Psychonomic Bulletin & Review. 2011;18:682–689. doi: 10.3758/s13423-011-0088-7. PubMed DOI

Rouder JN, Morey RD. Default Bayes factors for model selection in regression. Multivariate Behavioral Research. 2012;47:877–903. doi: 10.1080/00273171.2012.734737. PubMed DOI

Rouder JN, Lu J, Speckman PL, Sun D, Jiang Y. A hierarchical model for estimating response time distributions. Psychonomic Bulletin & Review. 2005;12:195–223. doi: 10.3758/BF03257252. PubMed DOI

Rouder JN, Lu J, Sun D, Speckman P, Morey R, Naveh-Benjamin M. Signal detection models with random participant and item effects. Psychometrika. 2007;72:621–642. doi: 10.1007/s11336-005-1350-6. DOI

Rouder JN, Morey RD, Speckman PL, Pratte MP. Detecting chance: A solution to the null sensitivity problem in subliminal priming. Psychonomic Bulletin & Review. 2007;14:597–605. doi: 10.3758/BF03196808. PubMed DOI

Rouder JN, Lu J, Morey RD, Sun D, Speckman PL. A hierarchical process dissociation model. Journal of Experimental Psychology: General. 2008;137:370–389. doi: 10.1037/0096-3445.137.2.370. PubMed DOI

Rouder JN, Speckman PL, Sun D, Morey RD, Iverson G. Bayesian t tests for accepting and rejecting the null hypothesis. Psychonomic Bulletin & Review. 2009;16:225–237. doi: 10.3758/PBR.16.2.225. PubMed DOI

Rouder JN, Morey RD, Speckman PL, Province JM. Default Bayes factors for ANOVA designs. Journal of Mathematical Psychology. 2012;56:356–374. doi: 10.1016/j.jmp.2012.08.001. DOI

Royall RM. Statistical evidence: A likelihood paradigm. London: Chapman & Hall; 1997.

Scheibehenne, B., Jamil, T., & Wagenmakers, E J. (in press). Bayesian evidence synthesis can reconcile seemingly inconsistent results: The case of hotel towel reuse. Psychological Science. PubMed

Schönbrodt, F. D., Wagenmakers, E. J., Zehetleitner, M., & Perugini, M. (in press). Sequential hypothesis testing with Bayes factors: Efficiently testing mean differences. Psychological Methods. PubMed

Sellke T, Bayarri MJ, Berger JO. Calibration of p values for testing precise null hypotheses. The American Statistician. 2001;55:62–71. doi: 10.1198/000313001300339950. DOI

Sharpe D. Why the resistance to statistical innovations? Bridging the communication gap. Psychological Methods. 2013;18:572–582. doi: 10.1037/a0034177. PubMed DOI

Shiffrin RM, Lee MD, Kim W, Wagenmakers EJ. A survey of model evaluation approaches with a tutorial on hierarchical Bayesian methods. Cognitive Science. 2008;32:1248–1284. doi: 10.1080/03640210802414826. PubMed DOI

Simmons JP, Nelson LD, Simonsohn U. False–positive psychology: Undisclosed flexibility in data collection and analysis allows presenting anything as significant. Psychological Science. 2011;22:1359–1366. doi: 10.1177/0956797611417632. PubMed DOI

Simonsohn, U. (2015a). Posterior–hacking: Selective reporting invalidates Bayesian results also. Unpublished manuscript.

Simonsohn, U. (2015b). Small telescopes: Detectability and the evaluation of replication results. Psychological Science, 26, 559–569. PubMed

Stulp G, Buunk AP, Verhulst S, Pollet TV. Tall claims? Sense and nonsense about the importance of height of US presidents. The Leadership Quarterly. 2013;24:159–171. doi: 10.1016/j.leaqua.2012.09.002. DOI

Trafimow D, Marks M. Editorial. Basic And Applied Social Psychology. 2015;37:1–2. doi: 10.1080/01973533.2015.1012991. DOI

Turing, A. M. (1941/2012). The applications of probability to cryptography. UK National Archives, HW 25/37.

Tversky A, Kahneman D. Extensional versus intuitive reasoning: The conjunction fallacy in probability judgment. Psychological Review. 1983;90:293–315. doi: 10.1037/0033-295X.90.4.293. DOI

van Erven T, Grünwald P, de Rooij S. Catching up faster by switching sooner: A predictive approach to adaptive estimation with an application to the AIC–BIC dilemma. Journal of the Royal Statistical Society B. 2012;74:361–417. doi: 10.1111/j.1467-9868.2011.01025.x. DOI

van Ravenzwaaij, D., Cassey, P., & Brown, S. D. (in press). A simple introduction to Markov chain Monte-Carlo sampling. Psychonomic Bulletin & Review. PubMed PMC

Vandekerckhove, J., Matzke, D., & Wagenmakers, E. J. (2015). Model comparison and the principle of parsimony. In Busemeyer, J., Townsend, J., Wang, Z. J., & Eidels, A. (Eds.) Oxford handbook of computational and mathematical psychology (pp. 300319). Oxford University Press.

Vanpaemel W. Prior sensitivity in theory testing: An apologia for the Bayes factor. Journal of Mathematical Psychology. 2010;54:491–498. doi: 10.1016/j.jmp.2010.07.003. DOI

Vanpaemel W, Lee MD. Using priors to formalize theory: Optimal attention and the generalized context model. Psychonomic Bulletin & Review. 2012;19:1047–1056. doi: 10.3758/s13423-012-0300-4. PubMed DOI

Verhagen AJ, Wagenmakers EJ. Bayesian tests to quantify the result of a replication attempt. Journal of Experimental Psychology: General. 2014;143:1457–1475. doi: 10.1037/a0036731. PubMed DOI

Wagenmakers EJ. A practical solution to the pervasive problems of p values. Psychonomic Bulletin & Review. 2007;14:779–804. doi: 10.3758/BF03194105. PubMed DOI

Wagenmakers, E. J., & Waldorp, L. (2006). Model selection: Theoretical developments and applications [Special issue]. Journal of Mathematical Psychology, 50(2).

Wagenmakers EJ, Grünwald P, Steyvers M. Accumulative prediction error and the selection of time series models. Journal of Mathematical Psychology. 2006;50:149–166. doi: 10.1016/j.jmp.2006.01.004. DOI

Wagenmakers EJ, Lodewyckx T, Kuriyal H, Grasman R. Bayesian hypothesis testing for psychologists: A tutorial on the Savage–Dickey method. Cognitive Psychology. 2010;60:158–189. doi: 10.1016/j.cogpsych.2009.12.001. PubMed DOI

Wagenmakers EJ, Wetzels R, Borsboom D, van der Maas HLJ. Why psychologists must change the way they analyze their data: The case of psi. Journal of Personality and Social Psychology. 2011;100:426–432. doi: 10.1037/a0022790. PubMed DOI

Wagenmakers EJ, Wetzels R, Borsboom D, van der Maas HLJ, Kievit RA. An agenda for purely confirmatory research. Perspectives on Psychological Science. 2012;7:627–633. doi: 10.1177/1745691612463078. PubMed DOI

Wagenmakers EJ, Verhagen AJ, Ly A, Bakker M, Lee MD, Matzke D, ... Morey RD. A power fallacy. Behavior Research Methods. 2015;47:913–917. doi: 10.3758/s13428-014-0517-4. PubMed DOI

Wagenmakers EJ, Morey RD, Lee MD. Bayesian benefits for the pragmatic researcher. Current Directions in Psychological Science. 2016;25:169–176. doi: 10.1177/0963721416643289. DOI

Wagenmakers EJ, Verhagen AJ, Ly A. How to quantify the evidence for the absence of a correlation. Behavior Research Methods. 2016;48:413–426. doi: 10.3758/s13428-015-0593-0. PubMed DOI PMC

Wagenmakers, E J., Love, J., Marsman, M., Jamil, T., Ly, A., Verhagen, A. J., ..., & Morey, R. D. (this issue). Bayesian statistical inference for psychological science. Part II: Example applications with JASP. Psychonomic Bulletin & Review. PubMed PMC

Wagenmakers, E J., Verhagen, A. J., Ly, A., Matzke, D., Steingroever, H., Rouder, J. N., & Morey, R. D. (in press). The need for Bayesian hypothesis testing in psychological science. In S.O. Lilienfeld, & I. Waldman (Eds.) Psychological science under scrutiny: Recent challenges and proposed solutions. Wiley.

Wald A, Wolfowitz J. Optimal character of the sequential probability ratio test. The Annals of Mathematical Statistics. 1948;19:326–339. doi: 10.1214/aoms/1177730197. DOI

Wetzels R, Wagenmakers EJ. A default Bayesian hypothesis test for correlations and partial correlations. Psychonomic Bulletin & Review. 2012;19:1057–1064. doi: 10.3758/s13423-012-0295-x. PubMed DOI PMC

Wetzels R, Matzke D, Lee MD, Rouder JN, Iverson GJ, Wagenmakers EJ. Statistical evidence in experimental psychology: An empirical comparison using 855 t tests. Perspectives on Psychological Science. 2011;6:291–298. doi: 10.1177/1745691611406923. PubMed DOI

Wrinch D, Jeffreys H. On certain fundamental principles of scientific inquiry. Philosophical Magazine. 1921;42:369–390.

Wrinch D, Jeffreys H. On certain fundamental principles of scientific inquiry. Philosophical Magazine. 1923;45:368–374.

Yonelinas AP. The nature of recollection and familiarity: A review of 30 years of research. Journal of Memory and Language. 2002;46:441–517. doi: 10.1006/jmla.2002.2864. DOI

Zabell S. Commentary on Alan M. Turing: The applications of probability to cryptography. Cryptologia. 2012;36:191–214. doi: 10.1080/01611194.2012.697811. DOI

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