Bayesian hypothesis testing for single-subject designs

Psychological Methods

Volumn 18, Issue 2, 2013, Pages 165-185

  de Vries, Rivka M ^a   Morey, Richard D ^a  

^a UNIVERSITY OF GRONINGEN   (Netherlands)

Author keywords

Bayes factor; Bayesian estimation; Intervention effect; Single subject; Trend difference

Indexed keywords

ARTICLE; BAYES THEOREM; HUMAN; METHODOLOGY; PSYCHOLOGY; SAMPLE SIZE; STATISTICAL ANALYSIS; STATISTICAL DISTRIBUTION; STATISTICAL MODEL; STATISTICS; TIME;

BAYES THEOREM; DATA INTERPRETATION, STATISTICAL; HUMANS; LIKELIHOOD FUNCTIONS; MODELS, STATISTICAL; PSYCHOLOGY; RESEARCH DESIGN; SAMPLE SIZE; STATISTICAL DISTRIBUTIONS; TIME FACTORS;

EID: 84879512136     PISSN: 1082989X     EISSN: None     Source Type: Journal    
DOI: 10.1037/a0031037     Document Type: Article

References (58)

1. Abramowitz, M., & Stegun, I. A. (1965). Handbook of mathematical functions: With formulas, graphs, and mathematical tables. New York, NY: Dover.
2. Beeson, P. M., & Robey, R. R. (2006). Evaluating single-subject treatment research: Lessons learned from the aphasia literature. Neuropsychology Review, 16, 161-169. doi:10.1007/s11065-006-9013-7
3. Berger, J. O., & Berry, D. A. (1988). Statistical analysis and the illusion of objectivity. American Scientist, 76, 159-165.
4. Berger, J. O., & Sellke, T. (1987). Testing a point null hypothesis: The irreconcilability of p values and evidence. Journal of the American Statistical Association, 82, 112-122. Retrieved from http://www.jstor.org/stable/2289131
5. Bisconer, S. W., Green, M., Mallon-Czajka, J., & Johnson, J. S. (2006). Managing aggression in a psychiatric hospital using a behaviour plan: A case study. Journal of Psychiatric and Mental Health Nursing, 13, 515-521. doi:10.1111/j.1365-2850.2006.00973.x
6. Bulté, I., & Onghena, P. (2008). An R package for single-case randomization tests. Behavior Research Methods, 40, 467-478. doi:10.3758/BRM.40.2.467
7. Bulté, I., & Onghena, P. (2009). Randomization tests for multiple-baseline designs: An extension of the SCRT-R package. Behavior Research Methods, 41, 477-485. doi:10.3758/BRM.41.2.477
8. Busk, P. L., & Marascuilo, L. A. (1988). Autocorrelation in single-subject research: A counterargument to the myth of no autocorrelation. Behavioral Assessment, 10, 229-242.
9. Casella, G., & Berger, R. L. (2002). Statistical inference. Pacific Grove, CA: Duxbury.
10. Cleveland, W. S. (1981). LOWESS: A program for smoothing scatterplots by robust locally weighted regression. The American Statistician, 35, 54. doi:10.2307/2683591
11. Cohen, J. (1992). A power primer. Psychological Bulletin, 112, 155-159. doi:10.1037/0033-2909.112.1.155
12. Cohen, J. (1994). The earth is round (p < .05). American Psychologist, 49, 997-1003. doi:10.1037/0003-066X.49.12.997
13. Dickey, J. M., & Lientz, B. P. (1970). The weighted likelihood ratio, sharp hypotheses about chances, the order of a Markov chain. The Annals of Mathematical Statistics, 41, 214-226. doi:10.1214/aoms/1177697203
14. Edwards, W., Lindman, H., & Savage, L. J. (1963). Bayesian statistical inference for psychological research. Psychological Review, 70, 193- 242. doi:10.1037/h0044139
15. Ferron, J., & Foster-Johnson, L. (1998). Analyzing single-case data with visually guided randomization tests. Behavior Research Methods, 30, 698-706.
16. Fox, J. (2008). Applied regression analysis and generalized linear models (2nd ed.). Los Angeles, CA: Sage.
17. Gelfand, A., & Smith, A. F. M. (1990). Sampling based approaches to calculating marginal densities. Journal of the American Statistical Association, 85, 398-409. doi:10.1080/01621459.1990.10476213
18. Geman, S., & Geman, D. (1984). Stochastic relaxation, Gibbs distribution, and the Bayesian restoration of images. IEEE Transactions on Pattern Analysis and Machine Intelligence, PAMI- 6, 721-741. doi:10.1109/TPAMI.1984.4767596
19. Glover, S., & Dixon, P. (2004). Likelihood ratios: A simple and flexible statistic for empirical psychologists. Psychonomic Bulletin & Review, 11, 791-806. doi:10.3758/BF03196706
20. Good, I. J. (1985). Weight of evidence: A brief survey. In J. M. Bernardo, M. H. DeGroot, D. V. Lindley, & A. F. M. Smith (Eds.), Bayesian statistics 2 (pp. 249-270). North-Holland, the Netherlands: Elsevier Science Publishers.
21. Hacking, I. (1965). Logic of statistical inference. Cambridge, England: Cambridge University Press.
22. Jacobson, N. S., & Truax, P. (1991). Clinical significance: A statistical approach to defining meaningful change in psychotherapy research. Journal of Consulting and Clinical Psychology, 59, 12-19. doi:10.1037/0022-006X.59.1.12
23. Jaynes, E. (1986). Bayesian methods: General background. In J. Justice (Ed.), Maximum-entropy and Bayesian methods in applied statistics (pp. 1-25). doi:10.1017/CBO9780511569678.003
24. Jaynes, E. (2003). Probability theory: The logic of science. doi:10.1017/CBO9780511790423
25. Jeffreys, H. (1946). An invariant form for the prior probability in estimation problems. Proceedings of the Royal Society of London: Series A: Mathematical, Physical, and Engineering Sciences, 186, 453-461. doi: 10.1098/rspa.1946.0056
26. Jeffreys, H. (1961). Theory of probability (3rd ed.). New York, NY: Oxford University Press.
27. Kinugasa, T., Cerin, E., & Hooper, S. (2004). Single-subject research designs and data analyses for assessing elite athletes' conditioning. Sports Medicine, 34, 1035-1050. doi:10.2165/00007256-200434150-00003
28. Lee, P. M. (2004). Bayesian statistics: An introduction (3rd ed.). New York, NY: Wiley.
29. Lindley, D. V. (1957). A statistical paradox. Biometrika, 44, 187-192.
30. Loftus, G. R. (1996). Psychology will be a much better science when we change the way we analyze data. Current Directions in Psychological Science, 5, 161-171. doi:10.1111/1467-8721.ep11512376
31. Ma, H.-H. (2006). An alternative method for quantitative synthesis of single-subject researchers. Behavior Modification, 30, 598-617. doi: 10.1177/0145445504272974
32. Maggin, D. M., Swaminathan, H., Rogers, H. J., O'Keeffe, B. V., Sugai, G., & Horner, R. H. (2011). A generalized least squares regression approach for computing effect sizes in single-case research: Application examples. Journal of School Psychology, 49, 301-321. doi:10.1016/j.jsp .2011.03.004
33. Manolov, R., & Solanas, A. (2009). Problems of the randomization test for AB designs. Psicológica, 30, 137-154.
34. Mastropieri, M., & Scruggs, T. (1985). Early intervention for socially withdrawn children. The Journal of Special Education, 19, 429-441. doi:10.1177/002246698501900407
35. Matyas, T. A., & Greenwood, K. M. (1997). Serial dependency in singlecase time series. In R. D. Franklin, D. B. Allison, & B. S. Gorman (Eds.), Design and analysis of single-case research (pp. 215-243). Mahwah, NJ: Erlbaum.
36. McDowall, D., McCleary, R., Meidinger, E. E., & Hay, R. A. (1980). Interrupted time series analysis. In J. L. Sullivan (Series Ed.), Quantitative applications in the social sciences (Vol. 21). Beverly Hills, CA: Sage.
37. Morey, R. D., & Rouder, J. N. (2011). Bayes factor approaches for testing interval null hypotheses. Psychological Methods, 16, 406-419. doi: 10.1037/a0024377
38. Morey, R. D., Rouder, J. N., Pratte, M. S., & Speckman, P. L. (2011). Using MCMC chain outputs to efficiently estimate Bayes factors. Journal of Mathematical Psychology, 55, 368-378. doi:10.1016/j.jmp.2011.06.004
39. Morgan, D. L., & Morgan, R. K. (2009). Single-case research methods for the behavioral and health sciences. Los Angeles, CA: Sage.
40. Parker, R. I., & Brossart, D. F. (2003). Evaluating single-case research data: A comparison of seven statistical methods. Behavior Therapy, 34, 189-211. doi:10.1016/S0005-7894(03)80013-8
41. Parker, R. I., Brossart, D. F., Vannest, K. J., Long, J. R., Garcia de Alba, R., Baugh, F. G., & Sullivan, J. R. (2005). Effect sizes in single case research: How large is large? School Psychology Review, 34, 116-132.
42. Parker, R. I., & Hagan-Burke, S. (2007). Median-based overlap analysis for single case data. Behavior Modification, 31, 919-936. doi:10.1177/0145445507303452
43. Parker, R. I., Hagan-Burke, S., & Vannest, K. (2007). Percentage of all non-overlapping data (PAND): An alternative to PND. Journal of Special Education, 40, 194-204. doi:10.1177/00224669070400040101
44. Parker, R. I., & Vannest, K. (2009). An improved effect size for single-case research: Nonoverlap of all pairs. Behavior Therapy, 40, 357-367. doi:10.1016/j.beth.2008.10.006
45. Rasquin, S. M. C., Van De Sande, P., Praamstra, A. J., & Van Heugten, C. M. (2009). Cognitive-behavioral intervention for depression after stroke: Five single case studies on effects and feasibility. Neuropsychological Rehabilitation, 19, 208-222. doi:10.1080/09602010802091159
46. R Development Core Team. (2009). R: A language and environment for statistical computing. Retrieved from http://www.R-project.org
47. Reichardt, C. S., & Gollob, H. F. (1997). When confidence intervals should be used instead of statistical tests, and vice versa. In L. L. Harlow, S. A. Mulaik, & J. H. Steiger (Eds.), What if there were no significance tests? (pp. 259-284). Mahwah, NJ: Erlbaum.
48. Rouder, J. N., & Morey, R. D. (2005). Relational and arelational confidence intervals: A comment on Fidler et al. Psychological Science, 16, 77-79.
49. 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, 225-237. doi:10.3758/PBR.16.2.225
50. Royall, R. (1997). Statistical evidence: A likelihood paradigm. New York, NY: CRC Press.
51. Schmidt, F. L., & Hunter, J. E. (1997). Eight common but false objections to the discontinuation of significance testing in the analysis of research data. In L. L. Harlow, S. A. Mulaik, & J. H. Steiger (Eds.), What if there were no significance tests? (pp. 37-64). London, England: Erlbaum.
52. Sellke, T., Bayarri, M. J., & Berger, J. O. (2001). Calibration of p values for testing precise null hypotheses. American Statistician, 55, 62-71. doi:10.1198/000313001300339950
53. Shadish, W., Rindskopf, D., & Hedges, L. (2008). The state of the science in the meta-analysis of single-case experimental designs. Evidence- Based Communication Assessment and Intervention, 2, 188-196. doi: 10.1080/17489530802581603
54. Sharpley, C. F., & Alavosius, M. P. (1988). Autocorrelation in behavioral data: An alternative perspective. Behavioral Assessment, 10, 243-251.
55. Solanas, A., Manolov, R., & Sierra, V. (2010). Lag-one autocorrelation in short series: Estimation and hypotheses testing. Psicológica, 31, 357-381.
56. Wagenmakers, E.-J., Lee, M. D., Lodewyckx, T., & Iverson, G. (2008). Bayesian versus frequentist inference. In H. Hoijtink, I. Klugkist, & P. Boelen (Eds.), Practical Bayesian approaches to testing behavioral and social science hypotheses (pp. 181-207). New York, NY: Springer.
57. Wellek, S. (2003). Testing statistical hypotheses of equivalence. Boca Raton, FL: Chapman & Hall/CRC.
58. Zellner, A., & Siow, A. (1980). Posterior odds ratios for selected regression hypotheses. In J. M. Bernardo, M. H. DeGroot, D. V. Lindley, & A. F. M. Smith (Eds.), Bayesian statistics: Proceedings of the First International Meeting held in Valencia (Spain) (pp. 585-603). Valencia, Spain: University of Valencia.