6,695
Views
17
CrossRef citations to date
0
Altmetric
Supplementing or Replacing p

Blending Bayesian and Classical Tools to Define Optimal Sample-Size-Dependent Significance Levels

, &
Pages 213-222 | Received 13 Mar 2018, Accepted 23 Aug 2018, Published online: 20 Mar 2019

References

  • Bartlett, M. (1957), “A Comment on D. V. Lindley’s Statistical Paradox,” Biometrika, 44, 533–534. DOI:10.1093/biomet/44.3-4.533.
  • Benjamin, D. J., Berger, J. O., Johannesson, M., Nosek, B. A., Wagenmakers, E. J., Berk, R., Bollen, K. A., Brembs, B., Brown, L., Camerer, C., Cesarini, D., Chambers, C. D., Clyde, M., Cook, T. D., De Boeck, P., Dienes, Z., Dreber, A., Easwaran, K., Efferson, C., Fehr, E., Fidler, F., Field, A. P., Forster, M., George, E. I., Gonzalez, R., Goodman, S., Green, E., Green, D. P., Greenwald, A. G., Hadfield, J. D., Hedges, L. V., Held, L., Hua Ho, T., Hoijtink, H., Hruschka, D. J., Imai, K., Imbens, G., Ioannidis, J. P. A., Jeon, M., Jones, J. H., Kirchler, M., Laibson, D., List, J., Little, R., Lupia, A., Machery, E., Maxwell, S. E., McCarthy, M., Moore, D. A., Morgan, S. L., Munafó, M., Nakagawa, S., Nyhan, B., Parker, T. H., Pericchi, L., Perugini, M., Rouder, J., Rousseau, J., Savalei, V., Schönbrodt, F. D., Sellke, T., Sinclair, B., Tingley, D., Van Zandt, T., Vazire, S., Watts, D. J., Winship, C., Wolpert, R. L., Xie, Y., Young, C., Zinman, J., and Johnson, V. E. (2018), “Redefine Statistical Significance,” Nature Human Behaviour, 2, 6–10. DOI:10.1038/s41562-017-0189-z.
  • Berger, J., and Wolpert, R. (1988), The Likelihood Principle, (2nd ed.), Haywood, CA: The Institute of Mathematical Statistics, available at https://projecteuclid.org/euclid.lnms/1215466210
  • Berger, J. O., and Delampady, M. (1987), “Testing Precise Hypotheses,” Statistical Science, 2, 317–335. DOI:10.1214/ss/1177013238.
  • Birnbaum, A. (1962), “On the Foundations of Statistical Inference,” Journal of the American Statistical Association, 57, 269–306. DOI:10.1080/01621459.1962.10480660.
  • Cohen, J. (1994), “The Earth is round (p <.05),” American Psychologist, 49, 997–1003.
  • Cornfield, J. (1966), “Sequential Trials, Sequential Analysis and the Likelihood Principle,” The American Statistician, 20, 18–23. DOI:10.1080/00031305.1966.10479786.
  • DeGroot, M. (1986), Probability and Statistics, Addison-Wesley Series in Statistics, Reading, MA, USA: Addison-Wesley Publishing Company. DOI:10.1086/ahr/80.1.64.
  • Evans, M. (2013), “What does the Proof of Birnbaum’s Theorem Prove?” Electronic Journal Statistics, 7, 2645–2655. DOI:10.1214/13-EJS857.
  • Gandenberger, G. (2015), “A New Proof of the Likelihood Principle,” The British Journal for the Philosophy of Science, 66, 475–503. DOI:10.1093/bjps/axt039.
  • Gelman, A. and Rubin, D. B. (1995), “Avoiding Model Selection in Bayesian Social Research,” Sociological Methodology, 25, 165–173. DOI:10.2307/271064.
  • Hardy, G. H. (1908), “Mendelian Proportions in a Mixed Population,” Science, 28, 49–50. DOI:10.1126/science.28.706.49.
  • Hartl, D. L. and Clark, A. G. (1989), Principles of Population Genetics, (2nd ed.), Sunderland, Mass.: Sinauer Associates.
  • Jeffreys, H. (1935), “Some Tests of Significance, Treated by the Theory of Probability,” Mathematical Proceedings of the Cambridge Philosophical Society, 31, 203–222. DOI:10.1017/S030500410001330X.
  • Jeffreys, H. (1939), The Theory of Probability, Oxford: The Clarendon Press.
  • Kass, R. E., and Raftery, A. E. (1995), “Bayes Factors,” Journal of the American Statistical Association, 90, 773–795. DOI:10.1080/01621459.1995.10476572.
  • Levine, T. R., Weber, R., Hullett, C., Park, H. S., and Lindsey, L. L. M. (2008), “A Critical Assessment of Null Hypothesis Significance Testing in Quantitative Communication Research,” Human Communication Research, 34, 171–187. DOI:10.1111/j.1468-2958.2008.00317.x.
  • Lindley, D. V. (1957), “A Statistical Paradox,” Biometrika, 44, 187–192. DOI:10.1093/biomet/44.1-2.187.
  • Lindley, D. V., and Phillips, L. D. (1976), “Inference for a Bernoulli Process (a Bayesian View),” The American Statistician, 30, 112–119. DOI:10.2307/2683855.
  • Mayo, D. G. (2014), “On the Birnbaum Argument for the Strong Likelihood Principle,” Statistical Science, 29, 227–239. DOI:10.1214/13-STS457.
  • Montoya-Delgado, L. E., Irony, T. Z., Pereira, C. A. B., and Whittle, M. R. (2001), “An Unconditional Exact Test for the Hardy-Weinberg Equilibrium Law: Sample-Space Ordering Using the Bayes Factor,” Genetics, 158, 875–883.
  • Neyman, J., and 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, Containing Papers of a Mathematical or Physical Character, 231, 289–337. DOI:10.1098/rsta.1933.0009.
  • Pereira, C. A. d. B., Nakano, E. Y., Fossaluza, V., Esteves, L. G., Gannon, M. A., and Polpo, A. (2017), “Hypothesis Tests for Bernoulli Experiments: Ordering the Sample Space by Bayes Factors and Using Adaptive Significance Levels for Decisions,” Entropy, 19, 696. DOI:10.3390/e19120696.
  • Pereira, C. A. d. B., and Wechsler, S. (1993), “On the Concept of p-value,” Revista Brasileira de Probabilidade e Estatística, 7, 159–177.
  • Pericchi, L., and Pereira, C. (2016), “Adaptative Significance Levels using Optimal Decision Rules: Balancing by Weighting the error Probabilities,” Brazilian Journal of. Probability and Statistics, 30, 70–90. DOI:10.1214/14-BJPS257.
  • Schervish, M. (2012), Theory of Statistics, Springer Series in Statistics, New York: Springer.
  • Trafimow, D., and Marks, M. (2015), “Editorial,” Basic and Applied Social Psychology, 37, 1–2. DOI:10.1080/01973533.2015.1012991.
  • Tukey, J. W. (1969), “Analyzing Data: Sanctification or Detective Work?” American Psychologist, 24, 83–91. DOI:10.1037/h0027108.
  • Wasserstein, R. L., and 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.
  • Weakliem, D. L. (1999), “A Critique of the Bayesian Information Criterion for Model Selection,” Sociological Methods & Research, 27, 359–397. DOI:10.1177/0049124199027003002.
  • Wechsler, S., Pereira, C. A. d. B., and Marques F., P. C. (2008), “Birnbaum’s Theorem Redux,” in Bayesian Inference and Maximum Entropy Methods in Science and Engineering: Proceedings of the 28th International Workshop, eds. de Souza Lauretto, M., de Bragança Pereira, C. A., and Stern, J. M., American Inst. of Physics, pp. 96–102.
  • Weinberg, W. (1908), “Über den Nachweis der Vererbung beim Menschen,” Jahreshefte des Vereins für vaterländische Naturkunde in Württemberg, 64, 369–382.