An effect size measure and Bayesian analysis of single-case designs

Journal of School Psychology

Volumn 52, Issue 2, 2014, Pages 213-230

  Swaminathan, Hariharan ^a   Rogers, H Jane ^a   Horner, Robert H ^b  

^a UNIVERSITY OF CONNECTICUT   (United States)

^b UNIVERSITY OF OREGON   (United States)

Author keywords

Autocorrelation; Bayesian analysis; Standardized effect size

Indexed keywords

BAYES THEOREM; HUMAN; METHODOLOGY; STANDARDS; STATISTICAL ANALYSIS; STATISTICAL MODEL;

BAYES THEOREM; DATA INTERPRETATION, STATISTICAL; HUMANS; LINEAR MODELS; RESEARCH DESIGN;

EID: 84897633823     PISSN: 00224405     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.jsp.2013.12.002     Document Type: Article

References (60)

1. Algina J., Swaminathan H. Alternatives to Simonton's analyses of the interrupted and multiple group time-series designs. Psychological Bulletin 1979, 86:919-926.
2. Allison D., Gorman B. Calculating effect sizes for meta-analysis: The case of the single case. Behavior Research and Therapy 1993, 31:621-641.
3. Beach C.M., MacKinnon J.G. A maximum likelihood procedure with autocorrelated errors. Econometrica 1978, 46:51-58.
4. Beretvas S.N., Chung H. A review of meta-analyses of single-subject experimental designs: Methodological issues and practice. Evidence-Based Communication Assessment and Intervention 2008, 2(3):129-141. 10.1080/17489530802446302.
5. 2-change effect-size indices for single-subject experimental designs. Evidence-Based Communication Assessment and Intervention 2008, 2(3):120-128.
6. Bloom H.S. Estimating program impacts on student achievement using "short" interrupted time series. Paper presented at the annual American Educational Research Association meeting, Montreal, Canada 1999, April.
7. Box G.E.P., Jenkins G. Time series analysis: Forecasting and control 1970, Holden-Day, San Francisco, CA.
8. Box G.E.P., Tiao G.C. Bayesian inference in statistical analysis 1973, Addison-Wesley, Reading, MA.
9. Brossart D.F., Parker R.I., Olson E.A., Mahadevan L. The relationship between five statistical analyses in a simple AB single-case research design. Behavior Modification 2006, 30:531-563.
10. Browne W.J., Draper D. A comparison of Bayesian and likelihood-based methods for fitting multilevel models. Bayesian Analysis 2006, 1:473-514.
11. Campbell D.T., Stanley J.C. Experimental and quasi-experimental designs for research 1966, Rand McNally, Boston, MA.
12. Center B.A., Skiba R.J., Casey A. A methodology for quantitative synthesis of intra-subject design research. Journal of Special Education 1985-1986, 19(4):387-400.
13. Cochran D., Orcutt G.H. Application of least squares regression to relationships containing autocorrelated error terms. Journal of the American Statistical Association 1949, 44:32-61.
14. Gelman A. Prior distributions for variance parameters in hierarchical models. Bayesian Analysis 2006, 1:515-533.
15. Gelman A., Carlin J.B., Stern H.S., Rubin D.B. Bayesian data analysis 2004, Chapman & Hall/CRC, Boca Raton, FL. 2nd ed.
16. Glass G.V., Willson V.L., Gottman L.M. Design and analysis of time-series experiments 1975, Colorado Associated University Press, Boulder, CO.
17. Goldberger A.S. Best linear unbiased prediction in the generalized linear regression model. Journal of the American Statistical Association 1962, 57:369-375.
18. Gorsuch R.L. Three methods for analyzing limited time series (N of 1) data. Behavioral Assessment 1983, 5:141-154.
19. Harrop J.W., Velicer W.F. A comparison of three alternative methods of time series model identification. Multivariate Behavioral Research 1985, 20:27-74.
20. Hedges L.V. Meta-analysis. The handbook of statistics 2007, 919-954. Elsevier, Amsterdam. C.R. Rao, S. Sinharay (Eds.).
21. Hedges L.V., Pustejovsky J.E., Shadish W.R. A standardized mean difference effect size for single case designs. Research Synthesis Methods 2012, 3:224-239. 10.1002/jrsm.1052.
22. Hedges L.V., Pustejovsky J.E., Shadish W.R. A standardized mean difference effect size for multiple baseline designs across individuals. Research Synthesis Methods 2013, 10.1002/jrsm.1086.
23. Hersen M., Barlow D.H. Single-case experimental designs: Strategies for studying behavior 1976, Pergamon Press, New York, NY.
24. Horner R.H., Carr E.G., Halle J., McGee G., Odom S., Wolery M. The use of single-subject research to identify evidence-based practice in special education. Exceptional Children 2005, 71:165-180.
25. Horner R.H., Swaminathan H., Sugai G., Smolkowski K. Expanding analysis and use of single-case research. Education and Treatment of Children 2012, 35:269-290.
26. Huitema B. Autocorrelation in applied behavior analysis: A myth. Behavioral Assessment 1985, 7:107-118.
27. Huitema B., McKean J. Design specification issues in time-series intervention models. Educational and Psychological Measurement 2000, 60:38-58.
28. Kang W., Shin D.W., Lee Y. Biases of the restricted maximum likelihood estimators for ARMA processes with polynomial time trend. Journal of Statistical Planning and Inference 2003, 116:163-176.
29. Kazdin A.E. Single-case research designs: Methods for clinical and applied settings 1982, Oxford University Press, New York, NY.
30. Kennedy C.H. Single case designs for educational research 2005, Allyn and Bacon, Boston, MA.
31. Kratochwill T., Levin J.R. Single case research design and analysis: New directions for psychology and education 1992, Erlbaum, Hillsdale, NJ.
32. Kratochwill T., Stoiber K. Empirically supported interventions and school psychology: Conceptual and practical issues, Part II. School Psychology Quarterly 2000, 15:233-253.
33. Lambert M.C., Cartledge G., Heward W.L., Lo Y. Effects of response cards on disruptive behavior and academic responding during math lessons by fourth-grade urban students. Journal of Positive Behavior Interventions 2006, 8:88-99.
34. Lunn D., Spiegelhalter D., Thomas A., Best N. The BUGS project: Evolution, critique and future directions. Statistics in Medicine 2009, 28(25):3049-3067.
35. Maddala G.S. Econometrics 1977, McGraw Hill, New York, NY.
36. Maggin D., Swaminathan H., Rogers H.J., O'Keefe B., Sugai G., Horner R. A generalized least squares regression approach for computing effect sizes in single- case research: Application examples. Journal of School Psychology 2011, 49:301-321.
37. Manolov R., Solanas A. A comparison of mean phase difference and generalized least squares for analyzing single-case data. Journal of School Psychology 2013, 51:201-215.
38. Odom S.L., Brantlinger E., Gersten R., Horner R.H., Thompson B., Harris K. Research in special education: Scientific methods and evidence-based practices. Exceptional Children 2005, 71:137-148.
39. Parker R., Hagan-Burke S., Vannest K. Percent of all non-overlapping data (PAND): An alternative to PND. Journal of Special Education 2007, 40:194-204.
40. Raudenbush S.W., Bryk A.S., Cheong A.S., Fai Y.F., Congdon R.T., du Toit M. HLM 7: Hierarchical linear and nonlinear modeling 2011, Scientific Software International, Lincolnwood, IL.
41. Rogosa D. Comparing nonparallel regression lines. Psychological Bulletin 1980, 88:307-321.
42. Rubin D.B. Assignment to treatment group on the basis of a covariate. Journal of Educational Statistics 1977, 2:1-26.
43. Shadish W.R., Cook T.D., Campbell D.T. Experimental and quasi-experimental designs for generalized causal inference 2002, Houghton-Mifflin, Boston, MA.
44. Simonton D.K. Cross-sectional time-series experiments: Some suggested statistical analyses. Psychological Bulletin 1977, 84:489-502.
45. Snijders T., Bosker R. Multilevel analysis 1999, Sage Publications, Thousand Oaks, CA.
46. Spiegelhalter D.J., Thomas A., Best N., Gilks W., Lunn D. BUGS: Bayesian inference using Gibbs sampling 2003, MRC Biostatistics Unit, Cambridge, England, (www.mrc-bsu.cam.ac.uk/bugs/).
47. Swaminathan H. Multilevel data analysis. Multilevel analysis of educational data 1989, 277-282. Academic Press, New York, NY. R.D. Bock (Ed.).
48. Swaminathan H., Algina J. Analysis of quasi-experimental time-series designs. Journal of Multivariate Behavioral Research 1977, 12:111-131.
49. Swaminathan H., Horner R.H., Sugai G., Smolkowski K. Application of generalized least squares regression to measure effect size in single-case research: A technical report 2008, Institute for Education Sciences.
50. Swaminathan H., Rogers H.J. Estimation procedures for hierarchical linear models. Multilevel modeling of educational data 2008, 469-519. Information Age Publishing, Charlotte, NC. A.A. O'Connell, D.B. McCoach (Eds.).
51. Todman J., Dugard P. Single-case and small-n experimental designs: A practical guide to randomization tests 2001, Erlbaum, Mahwah, NJ.
52. Van den Noortgate W., Onghena P. Combining single-case experimental data using hierarchical linear models. School Psychology Quarterly 2003, 18:325-346.
53. Velicer W.F., McDonald R.P. Time series analysis without model identification. Multivariate Behavioral Research 1984, 19:33-47.
54. Velicer W.F., McDonald R.P. Cross sectional time series: A general transformation approach. Multivariate Behavioral Research 1991, 26:247-254.
55. Velicer W.F., Molenaar P.C. Time series analysis for psychological research. Handbook of psychology, Volume 2: Research methods in psychology 2012, 628-660. Wiley, Hoboken, NJ. 2nd ed. J.A. Schinka, W.F. Velicer (Eds.).
56. White D.M., Rusch F.R., Kazdin A.E., Hartmann D.P. Applications of meta-analysis in individual subject research. Behavioral Assessment 1989, 11:281-296.
57. Whitehurst G.J. Evidence-based education. PowerPoint presentation http://www.ed.gov/offices/OERI/presentations/evidencebase.ppt.
58. Wong M., Cook T.D., Steiner P.M. No child left behind: An interim evaluation of its effects on learning using two interrupted time series each with its own non-equivalent comparison series. Institute of Policy Research 2011, Northwestern University, (WP-09-11).
59. Wong V.C., Wing C., Steiner P.M., Wong M., Cook T.D. Research designs for program evaluation. Handbook of psychology, Volume 2: Research methods in psychology 2012, 316-341. Wiley, Hoboken, NJ. 2nd ed. J.A. Schinka, W.F. Velicer (Eds.).
60. Zellner A. An introduction to Bayesian inference in econometrics 1971, Wiley, New York, NY.