Using Bayes Factors to Test Hypotheses in Developmental Research

REFERENCES

• Bem, D. J. (2011). Feeling the future: Experimental evidence for anomalous retroactive influences on cognition and affect. Journal of Personality and Social Psychology, 100(3), 407–425. doi:10.1037/a0021524
   PubMed Web of Science ®Google Scholar
• Brose, A., Schmiedek, F., Lövdén, M., Molenaar, P. C. M., & Lindenberger, U. (2010). Adult age differences in covariation of motivation and working memory performance: Contrasting between-person and within-person findings. Research in Human Development, 7(1), 61–78. doi:10.1080/15427600903578177
   Web of Science ®Google Scholar
• Budescu, D. V., Broomell, S., & Por, H.-H. (2009). Improving communication of uncertainty in the reports of the intergovernmental panel on climate change. Psychological Science, 20(3), 299–308. doi:10.1111/j.1467-9280.2009.02284.x
   PubMed Web of Science ®Google Scholar
• Carpenter, B., Gelman, A., Hoffman, M., Lee, D., Goodrich, B., Betancourt, M., … Riddell, A. (in press). Stan: A probabilistic programming language. Journal of Statistical Software. Retrieved from http://www.stat.columbia.edu/~gelman/research/published/stan-paper-revision-feb2015.pdf
   Web of Science ®Google Scholar
• Cohen, J. (1988). Statistical power analysis for the behavioral sciences (2nd ed.). Hillsdale, NJ: Erlbaum.
   Google Scholar
• Cohen, J. (1994). The earth is round (p < .05). American Psychologist, 49(12), 997–1003. doi:10.1037/0003-066X.49.12.997
   Web of Science ®Google Scholar
• Etz, A., & Wagenmakers, E.-J. (2015). J. B. S. Haldane’s contribution to the Bayes factor hypothesis test (arXiv preprint No. 1511.08180). Retrieved from https://arxiv.org/abs/1511.08180
   Google Scholar
• Ferguson, C. J., & Heene, M. (2012). A vast graveyard of undead theories: Publication bias and psychological science’s aversion to the null. Perspectives on Psychological Science, 7(6), 555–561. doi:10.1177/1745691612459059
   Web of Science ®Google Scholar
• Gelman, A. (2012). Ethics and statistics: Ethics and the statistical use of prior information. Chance, 25(4), 52–54. doi:10.1080/09332480.2012.752294
   Google Scholar
• Gigerenzer, G., Krauss, S., & Vitouch, O. (2004). The null ritual: What you always wanted to know about significance testing but were afraid to ask. In D. Kaplan (Ed.), The Sage handbook of quantitative methodology for the social sciences (pp. 391–408). Thousand Oaks, CA: Sage.
   Google Scholar
• Gigerenzer, G., & Marewski, J. N. (2015). Surrogate science: The idol of a universal method for scientific inference. Journal of Management, 41(2), 421–440. doi:10.1177/0149206314547522
   Web of Science ®Google Scholar
• Glover, S., & Dixon, P. (2004). Likelihood ratios: A simple and flexible statistic for empirical psychologists. Psychonomic Bulletin & Review, 11(5), 791–806. doi:10.3758/BF03196706
   PubMed Web of Science ®Google Scholar
• Grange, J. A., Kowalczyk, A. W., & O’Loughlin, R. (2016). The effect of episodic retrieval on inhibition in task switching (SSRN Scholarly Paper No. ID 2695998). Retrieved from https://papers.ssrn.com/abstract=2695998
   Google Scholar
• Hager, W. (2013). The statistical theories of Fisher and of Neyman and Pearson: A methodological perspective. Theory & Psychology, 23(2), 251–270. doi:10.1177/0959354312465483
   Web of Science ®Google Scholar
• Haller, H., & Krauss, S. (2002). Misinterpretations of significance: A problem students share with their teachers? Methods of Psychological Research Online, 7(1). Retrieved from https://pdfs.semanticscholar.org/a77b/e62627ff35f08469b56d08fc776bad512e94.pdf
   Google Scholar
• Hubbard, R., & Bayarri, M. J. (2003). Confusion over measures of evidence (p’s) versus errors (α’s) in classical statistical testing. The American Statistician, 57(3), 171–178. doi:10.1198/0003130031856
   Web of Science ®Google Scholar
• JASP Team. (2016). JASP (Version 0.8.0.0). Retrieved from https://jasp-stats.org
   Google Scholar
• Jeffreys, H. (1961). The theory of probability. Oxford, England: Oxford University Press.
   Google Scholar
• Jeffreys, H. (1935). Some tests of significance, treated by the theory of probability. In Mathematical Proceedings of the Cambridge Philosophical Society (31, pp. 203–222). Cambridge University Press.
   Google Scholar
• Jeffreys, H. (1980). Some general points in probability theory. In H. Jeffreys & A. Zellner (Eds.), Bayesian analysis in econometrics and statistics: Essays in honor of Harold Jeffreys (pp. 451–453). New York, NY: North-Holland.
   Google Scholar
• Koechlin, E., Dehaene, S., & Mehler, J. (1997). Numerical transformations in five-month-old human infants. Mathematical Cognition, 3(2), 89–104. doi:10.1080/135467997387425
   Google Scholar
• Kruschke, J. K. (2011). Bayesian assessment of null values via parameter estimation and model comparison. Perspectives on Psychological Science, 6(3), 299–312. doi:10.1177/1745691611406925
   Web of Science ®Google Scholar
• Kruschke, J. K. (2013). Bayesian estimation supersedes the t test. Journal of Experimental Psychology: General, 142(2), 573–603. doi:10.1037/a0029146
   PubMed Web of Science ®Google Scholar
• Kruschke, J. K., & Liddell, T. M. (2017). The Bayesian new statistics: Hypothesis testing, estimation, meta-analysis, and power analysis from a Bayesian perspective. Psychonomic Bulletin & Review, 1–29. doi:10.3758/s13423-016-1221-4
   PubMed Web of Science ®Google Scholar
• Lavine, M., & Schervish, M. J. (1999). Bayes factors: What they are and what they are not. American Statistician, 53(2), 119–122. doi:10.1080/00031305.1999.10474443
   Web of Science ®Google Scholar
• Liu, C. C., & Aitkin, M. (2008). Bayes factors: Prior sensitivity and model generalizability. Journal of Mathematical Psychology, 52(6), 362–375. doi:10.1016/j.jmp.2008.03.002
   Web of Science ®Google Scholar
• Loehlin, J. C. (2007). The strange case of c2 = 0: What does it imply for views of human development? Research in Human Development, 4(3/4), 151–162. doi:10.1080/15427600701662959
   Google Scholar
• Ly, A., Verhagen, 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. doi:10.1016/j.jmp.2015.06.004
   Web of Science ®Google Scholar
• Mayo, D. G., & Spanos, A. (2011). Error statistics. In P. S. Bandyopadhyay & M. R. Forster (Eds.), Philosophy of statistics (pp. 153–198). Oxford, England: Elsevier.
   Google Scholar
• Morey, R. D., & Rouder, J. N. (2011). Bayes factor approaches for testing interval null hypotheses. Psychological Methods, 16(4), 406–419. doi:10.1037/a0024377
   PubMed Web of Science ®Google Scholar
• Morey, R. D., Rouder, J. N., & Jamil, T. (2015). Package ‘BayesFactor’. Retrieved from https://cran.r-project.org/web/packages/BayesFactor/
   Google Scholar
• Morey, R. D., Wagenmakers, E.-J., & Rouder, J. N. (2016). Calibrated Bayes factors should not be used: A reply to Hoijtink, van Kooten, and Hulsker. Multivariate Behavioral Research, 51(1), 11–19. doi:10.1080/00273171.2015.1052710
   PubMed Web of Science ®Google Scholar
• Neyman, J., & Pearson, E. S. (1933). On the problem of the most efficient tests of statistical hypotheses. Philosophical Transactions of the Royal Society of London. Series A: Mathematical and Physical Sciences, 231, 289–337. doi:10.1098/rsta.1933.0009
   Google Scholar
• O’Hara, R. B., & Sillanpää, M. J. (2009). A review of Bayesian variable selection methods: What, how and which. Bayesian Analysis, 4(1), 85–117. doi:10.1214/09-BA403
   Web of Science ®Google Scholar
• Perezgonzalez, J. D. (2016). Commentary: How Bayes factors change scientific practice. Frontiers in Psychology, 7. doi:10.3389/fpsyg.2016.01504
   PubMed Web of Science ®Google Scholar
• Peterson, D. (2016). The baby factory: Difficult research objects, disciplinary standards, and the production of statistical significance. Socius: Sociological Research for a Dynamic World, 2, 1–10. doi:10.1177/2378023115625071
   Google Scholar
• Plummer, M. (2003). JAGS: A program for analysis of Bayesian graphical models using Gibbs sampling. In Proceedings of the 3rd International Workshop on Distributed Statistical Computing (pp). Retrieved from https://www.r-project.org/conferences/DSC-2003/Drafts/Plummer.pdf
   Google Scholar
• Richard, F. D., Bond, C. F., & Stokes-Zoota, J. J. (2003). One hundred years of social psychology quantitatively described. Review of General Psychology, 7(4), 331–363. doi:10.1037/1089-2680.7.4.331
   Web of Science ®Google Scholar
• Rosnow, R. L., & Rosenthal, R. (1989). Statistical procedures and the justification of knowledge in psychological science. American Psychologist, 44(10), 1276–1284. doi:10.1037/0003-066X.44.10.1276
   Web of Science ®Google Scholar
• Rouder, J. N. (2016, March 21). Roll your own II: Bayes factors with null intervals [Web log post]. Retrieved, from http://jeffrouder.blogspot.com/2016/03/roll-your-own-ii-bayes-factors-with.html
   Google Scholar
• Rouder, J. N., & Morey, R. D. (2012). Default Bayes factors for model selection in regression. Multivariate Behavioral Research, 47(6), 877–903. doi:10.1080/00273171.2012.734737
   PubMed Web of Science ®Google Scholar
• Rouder, J. N., Morey, R. D., Speckman, P. L., & Province, J. M. (2012). Default Bayes factors for ANOVA designs. Journal of Mathematical Psychology, 56(5), 356–374. doi:10.1016/j.jmp.2012.08.001
   Web of Science ®Google Scholar
• Rouder, J. N., Speckman, P. L., Sun, D., Morey, R. D., & Iverson, G. (2009). Bayesian t tests for accepting and rejecting the null hypothesis. Psychonomic Bulletin & Review, 16(2), 225–237. doi:10.3758/PBR.16.2.225
   PubMed Web of Science ®Google Scholar
• Schönbrodt, F. D., Wagenmakers, E.-J., Zehetleitner, M., & Perugini, M. (2015). Sequential hypothesis testing with Bayes factors: Efficiently testing mean differences, 22(2), 322–339. Psychological Methods. doi:10.1037/met0000061
   PubMed Web of Science ®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(6), 657–680. doi:10.1007/BF01068419
   PubMedGoogle Scholar
• Sedlmeier, P., & Gigerenzer, G. (1989). Do studies of statistical power have an effect on the power of studies? Psychological Bulletin, 105(2), 309–316. doi:10.1037/0033-2909.105.2.309
   Web of Science ®Google Scholar
• Simmons, J. P., Nelson, L. D., & Simonsohn, U. (2011). False-positive psychology: Undisclosed flexibility in data collection and analysis allows presenting anything as significant. Psychological Science, 22(11), 1359–1366. doi:10.1177/0956797611417632
   PubMed Web of Science ®Google Scholar
• Tromovitch, P. (2015). The lay public’s misinterpretation of the meaning of ‘significant’: A call for simple yet significant changes in scientific reporting. Journal of Research Practice, 11(1). Retrieved from http://jrp.icaap.org/index.php/jrp/article/view/477
   Web of Science ®Google Scholar
• Wagenmakers, E.-J. (2007). A practical solution to the pervasive problems of p values. Psychonomic Bulletin & Review, 14(5), 779–804. doi:10.3758/BF03194105
   PubMed Web of Science ®Google Scholar
• Wagenmakers, E.-J., Wetzels, R., Borsboom, D., Van Der Maas, H. L. J., & Kievit, R. A. (2012). An agenda for purely confirmatory research. Perspectives on Psychological Science, 7(6), 632–638. doi:10.1177/1745691612463078
   Web of Science ®Google Scholar
• 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(3), 291–298. doi:10.1177/1745691611406923
   Web of Science ®Google Scholar
• Williams, M. N. (2017, April 10). Separating model from hypothesis in the Bayes factor test [Web log post]. Retrieved from http://thepathologicalscience.blogspot.com/2017/04/separating-model-from-hypothesis-in.html
   Google Scholar
• Wynn, K. (1992). Addition and subtraction by human infants. Nature, 358(6389), 749–750. doi:10.1038/358749a0
   PubMed Web of Science ®Google Scholar
• Zondervan-Zwijnenburg, M., Peeters, M., Depaoli, S., & van de Schoot, R. (in press). Where do priors come from? A Bayesian evaluation of a latent growth model with informative priors. Research in Human Development.
   Google Scholar