A Priori Justification for Effect Measures in Single-Case Experimental Designs

Springer Science and Business Media LLC - Tập 45 - Trang 153-186 - 2021
Rumen Manolov1, Mariola Moeyaert2, Joelle E. Fingerhut2
1Department de Psicologia Social i Psicologia Quantitativa, Universitat de Barcelona, Barcelona, Spain
2State University of New York at Albany, Albany, USA

Tóm tắt

Due to the complex nature of single-case experimental design data, numerous effect measures are available to quantify and evaluate the effectiveness of an intervention. An inappropriate choice of the effect measure can result in a misrepresentation of the intervention effectiveness and this can have far-reaching implications for theory, practice, and policymaking. As guidelines for reporting appropriate justification for selecting an effect measure are missing, the first aim is to identify the relevant dimensions for effect measure selection and justification prior to data gathering. The second aim is to use these dimensions to construct a user-friendly flowchart or decision tree guiding applied researchers in this process. The use of the flowchart is illustrated in the context of a preregistered protocol. This is the first study that attempts to propose reporting guidelines to justify the effect measure choice, before collecting the data, to avoid selective reporting of the largest quantifications of an effect. A proper justification, less prone to confirmation bias, and transparent and explicit reporting can enhance the credibility of the single-case design study findings.

Tài liệu tham khảo

Baek, E., Beretvas, S. N., Van den Noortgate, W., & Ferron, J. M. (2020). Brief research report: Bayesian versus REML estimations with noninformative priors in multilevel single-case data. Journal of Experimental Education, 88(4), 698–710. https://doi.org/10.1080/00220973.2018.1527280. Baek, E. K., Petit-Bois, M., Van den Noortgate, W., Beretvas, S. N., & Ferron, J. M. (2016). Using visual analysis to evaluate and refine multilevel models of single-case studies. The Journal of Special Education, 50(1), 18–26. https://doi.org/10.1177/0022466914565367. Barker, J., McCarthy, P., Jones, M., & Moran, A. (2011). Single case research methods in sport and exercise psychology. Routledge. Barnard-Brak, L., Richman, D. M., & Watkins, L. (2020). Treatment burst data points and single case design studies: A Bayesian N-of-1 analysis for estimating treatment effect size. Perspectives on Behavior Science, 43(2), 285–301. https://doi.org/10.1007/s40614-020-00258-8. Barton, E. E., Meadan, H., & Fettig, A. (2019). Comparison of visual analysis, non-overlap methods, and effect sizes in the evaluation of parent implemented functional assessment based interventions. Research in Developmental Disabilities, 85, 31–41. https://doi.org/10.1016/j.ridd.2018.11.001. Beckers, L. W., Stal, R. A., Smeets, R. J., Onghena, P., & Bastiaenen, C. H. (2020). Single-case design studies in children with cerebral palsy: A scoping review. Developmental Neurorehabilitation, 23(2), 73–105. https://doi.org/10.1080/17518423.2019.1645226. Borckardt, J. J., Nash, M. R., Murphy, M. D., Moore, M., Shaw, D., & O’Neil, P. (2008). Clinical practice as natural laboratory for psychotherapy research: A guide to case-based time-series analysis. American Psychologist, 63(2), 77–95. https://doi.org/10.1037/0003-066X.63.2.77. Brogan, K. M., Rapp, J. T., & Sturdivant, B. R. (2019). Transition states in single case experimental designs. Behavior Modification. Advance online publication. https://doi.org/10.1177/0145445519839213. Brossart, D. F., Laird, V. C., & Armstrong, T. W. (2018). Interpreting Kendall’s Tau and Tau-U for single-case experimental designs. Cogent Psychology, 5(1), Article 1518687. https://doi.org/10.1080/23311908.2018.1518687. Brossart, D. F., Parker, R. I., Olson, E. A., & Mahadevan, L. (2006). The relationship between visual analysis and five statistical analyses in a simple AB single-case research design. Behavior Modification, 30(5), 531–563. https://doi.org/10.1177/0145445503261167. Busk, P. L., & Serlin, R. C. (1992). Meta-analysis for single-case research. In T. R. Kratochwill & J. R. Levin (Eds.), Single-case research designs and analysis: New directions for psychology and education (pp. 187−212). Lawrence Erlbaum Associates. Busse, R. T., McGill, R. J., & Kennedy, K. S. (2015). Methods for assessing single-case school-based intervention outcomes. Contemporary School Psychology, 19(3), 136–144. https://doi.org/10.1007/s40688-014-0025-7. Byun, T. M., Hitchcock, E. R., & Ferron, J. (2017). Masked visual analysis: Minimizing Type I error in visually guided single-case design for communication disorders. Journal of Speech, Language, & Hearing Research, 60(6), 1455–1466. https://doi.org/10.1044/2017_JSLHR-S-16-0344. Campbell, J. M. (2004). Statistical comparison of four effect sizes for single-subject designs. Behavior Modification, 28(2), 234–246. https://doi.org/10.1177/0145445503259264. Carlin, M. T., & Costello, M. S. (2018). Development of a distance-based effect size metric for single-case research: Ratio of distances. Behavior Therapy, 49(6), 981–994. https://doi.org/10.1016/j.beth.2018.02.005. Caron, E., & Dozier, M. (2019). Effects of fidelity-focused consultation on clinicians’ implementation: An exploratory multiple baseline design. Administration & Policy in Mental Health 7 Mental Health Services Research, 46(4), 445–457. https://doi.org/10.1007/s10488-019-00924-3. Carter, M. (2013). Reconsidering overlap-based measures for quantitative synthesis of single-subject data: What they tell us and what they don’t. Behavior Modification, 37(3), 378–390. https://doi.org/10.1177/0145445513476609. Center, B. A., Skiba, R. J., & Casey, A. (1985). A methodology for the quantitative synthesis of intra-subject design research. Journal of Special Education, 19(4), 387−400. https://doi.org/10.1177/002246698501900404. Chen, L.-T., Feng, Y., Wu, P.-J., & Peng, C.-Y. J. (2020). Dealing with missing data by EM in single-case studies. Behavior Research Methods, 52(1), 131–150. https://doi.org/10.3758/s13428-019-01210-8. Chen, M., Hyppa-Martin, J. K., Reichle, J. E., & Symons, F. J. (2016). Comparing single case design overlap-based effect size metrics from studies examining speech generating device interventions. American Journal on Intellectual & Developmental Disabilities, 121(3), 169–193. https://doi.org/10.1352/1944-7558-121.3.169. Chen, L.-T., Peng, C.-Y. J., & Chen, M.-E. (2015). Computing tools for implementing standards for single-case designs. Behavior Modification, 39(6), 835–869. https://doi.org/10.1177/0145445515603706. Chiu, M. M., & Roberts, C. A. (2018). Improved analyses of single cases: Dynamic multilevel analysis. Developmental Neurorehabilitation, 21(4), 253–265. https://doi.org/10.3109/17518423.2015.1119904. Clanchy, K. M., Tweedy, S. M., Tate, R. L., Sterling, M., Day, M. A., Nikles, J., & Ritchie, C. (2019). Evaluation of a novel intervention to improve physical activity for adults with whiplash associated disorders: Protocol for a multiple-baseline, single case experimental study. Contemporary Clinical Trials Communications, 16, 100455. https://doi.org/10.1016/j.conctc.2019.100455. Connell, P. J., & Thompson, C. K. (1986). Flexibility of single-subject experimental designs. Part III: Using flexibility to design or modify experiments. Journal of Speech & Hearing Disorders, 51(3), 214–225. https://doi.org/10.1044/jshd.5103.214. Cook, B. G., Buysse, V., Klingner, J., Landrum, T. J., McWilliam, R. A., Tankersley, M., & Test, D. W. (2015). CEC’s standards for classifying the evidence base of practices in special education. Remedial & Special Education, 36(4), 220–234. https://doi.org/10.1177/0741932514557271. Cook, K. B. & Snyder, S. M. (2020). Minimizing and reporting momentary time-sampling measurement error in single-case research. Behavior Analysis in Practice, 13(1), 247–252. https://doi.org/10.1007/s40617-018-00325-2. Craig, A. R., & Fisher, W. W. (2019). Randomization tests as alternative analysis methods for behavior-analytic data. Journal of the Experimental Analysis of Behavior, 111(2), 309–328. https://doi.org/10.1002/jeab.500. De, T. K., Michiels, B., Tanious, R., Onghena, P. (2020). Handling missing data in randomization tests for single-case experiments: A simulation study. Behavior Research Methods, 52(3), 1355–1370. https://doi.org/10.3758/s13428-019-01320-3. De Young, K. P., & Bottera, A. R. (2018). A summary of reporting guidelines and evaluation domains for using single-case experimental designs and recommendations for the study of eating disorders. International Journal of Eating Disorders, 51(7), 617–628. https://doi.org/10.1002/eat.22887. Declercq, L., Cools, W., Beretvas, S. N., Moeyaert, M., Ferron, J. M., & Van den Noortgate, W. (2020). MultiSCED: A tool for (meta-)analyzing single-case experimental data with multilevel modeling. Behavior Research Methods, 52(1), 177–192. https://doi.org/10.3758/s13428-019-01216-2. Declercq, L., Jamshidi, L., Fernández-Castilla, B., Beretvas, S. N., Moeyaert, M., Ferron, J. M., & Van den Noortgate, W. (2019). Analysis of single-case experimental count data using the linear mixed effects model: A simulation study. Behavior Research Methods, 51(6), 2477–2497. https://doi.org/10.3758/s13428-018-1091-y. Dedrick, R. F., Ferron, J. M., Hess, M. R., Hogarty, K. Y., Kromrey, J. D., Lang, T. R., Niles, J. D., & Lee, R. S. (2009). Multilevel modeling: A review of methodological issues and applications. Review of Educational Research, 79(1), 69–102. https://doi.org/10.3102/0034654308325581. Ferron, J. M., Bell, B. A., Hess, M. R., Rendina-Gobioff, G., & Hibbard, S. T. (2009). Making treatment effect inferences from multiple-baseline data: The utility of multilevel modeling approaches. Behavior Research Methods, 41(2), 372–384. https://doi.org/10.3758/BRM.41.2.372. Ferron, J. M., Goldstein, H., Olszewski, A., & Rohrer, L. (2020). Indexing effects in single-case experimental designs by estimating the percent of goal obtained. Evidence-Based Communication Assessment & Intervention, 14(1–2), 6–27. https://doi.org/10.1080/17489539.2020.1732024. Ferron, J. M., Hogarty, K. Y., Dedrick, R. F., Hess, M. R., Niles, J. D., & Kromrey, J. D. (2008). Reporting results from multilevel analyses. In A. A. O’Connell & D. B. McCoach (Eds.), Multilevel modeling of educational data (pp. 391–426). Information Age Publishing. Ferron, J. M., Joo, S.-H., & Levin, J. R. (2017). A Monte Carlo evaluation of masked visual analysis in response-guided versus fixed-criteria multiple-baseline designs. Journal of Applied Behavior Analysis, 50(4), 701–716. https://doi.org/10.1002/jaba.410. Ferron, J. M., Moeyaert, M., Van den Noortgate, W., & Beretvas, S. N. (2014). Estimating causal effects from multiple-baseline studies: Implications for design and analysis. Psychological Methods, 19(4), 493–510. https://doi.org/10.1037/a0037038. Ferron, J., Rohrer, L. L., & Levin, J. R. (2019). Randomization procedures for changing criterion designs. Behavior Modification. Advance online publication. https://doi.org/10.1177/0145445519847627. Ferron, J. M., & Ware, W. (1995). Analyzing single-case data: The power of randomization tests. Journal of Experimental Education, 63(2), 167–178. https://doi.org/10.1080/00220973.1995.9943820. Fingerhut, J., Moeyaert, M., & Manolov, R. (2020). Literature review of single-case quantitative analysis techniques. https://psyarxiv.com/7yt4g. Fisher, W. W., & Lerman, D. C. (2014). It has been said that, “There are three degrees of falsehoods: Lies, damn lies, and statistics”. Journal of School Psychology, 52(2), 243–248. https://doi.org/10.1016/j.jsp.2014.01.001. Gage, N. A., & Lewis, T. J. (2013). Analysis of effect for single-case design research Journal of Applied Sport Psychology, 25(1), 46–60. https://doi.org/10.1080/10413200.2012.660673. Ganz, J. B., & Ayres, K. M. (2018). Methodological standards in single-case experimental design: Raising the bar. Research in Developmental Disabilities, 79(1), 3–9. https://doi.org/10.1016/j.ridd.2018.03.003. Garwood, J. D., Werts, M. G., Mason, L. H., Harris, B., Austin, M. B., Ciullo, S., Magner, K., Koppenhaver, D. A., & Shin, M. (2019). Improving persuasive science writing for secondary students with emotional and behavioral disorders educated in residential treatment facilities. Behavioral Disorders, 44(4), 227–240. https://doi.org/10.1177/0198742918809341. Gertler, P., & Tate, R. L. (2021). Behavioural activation therapy to improve participation in adults with depression following brain injury: A single-case experimental design study. Neuropsychological Rehabilitation, 31(3), 369–391. https://doi.org/10.1080/09602011.2019.1696212. Ginns, D. S., & Begeny, J.C. (2019). Effects of performance feedback on treatment integrity of a class-wide level system for secondary students with emotional disturbance. Behavioral Disorders, 44(3), 175–189. https://doi.org/10.1177/0198742918795884. Gonzales, J. E., & Cunningham, C. A. (2015). The promise of pre-registration in psychological research. Psychological Science Agenda, 29(8). https://www.apa.org/science/about/psa/2015/08/pre-registration. Good, K. E. (2019). The pen or the cursor: A single-subject comparison of a paper-based graphic organizer and a computer-based graphic organizer to support the persuasive writing of students with emotional and behavioral disorders or mild autism (Publication No. 13864282.) [Doctoral dissertation, George Mason University]. ProQuest Dissertations. Hales, A. H., Wesselmann, E. D., & Hilgard, J. (2019). Improving psychological science through transparency and openness: An overview. Perspectives on Behavior Science, 42(1), 13–31. https://doi.org/10.1007/s40614-018-00186-8. Hantula, D. A. (2019). Editorial: Replication and reliability in behavior science and behavior analysis: A call for a conversation. Perspectives on Behavior Science, 42(1), 1–11. https://doi.org/10.1007/s40614-019-00194-2. Hayes, S. C. (1981). Single case experimental design and empirical clinical practice. Journal of Consulting & Clinical Psychology, 49(2), 193–211. https://doi.org/10.1037/0022-006X.49.2.193. Hedges, L. V, Pustejovsky, J. E., & Shadish, W. R. (2012). A standardized mean difference effect size for single case designs. Research Synthesis Methods, 3(3), 224–239. https://doi.org/10.1002/jrsm.1052. Hedges, L. V, Pustejovsky, J. E., & Shadish, W. R. (2013). A standardized mean difference effect size for multiple-baseline designs across individuals. Research Synthesis Methods, 4(4), 324–341. https://doi.org/10.1002/jrsm.1086. Hembry, I., Bunuan, R., Beretvas, S. N., Ferron, J. M., & Van den Noortgate, W. (2015). Estimation of a nonlinear intervention phase trajectory for multiple-baseline design data. The Journal of Experimental Education, 83(4), 514–546. https://doi.org/10.1080/00220973.2014.907231. Heyvaert, M., & Onghena, P. (2014a). Analysis of single-case data: Randomisation tests for measures of effect size. Neuropsychological Rehabilitation, 24(3–4), 507–527. https://doi.org/10.1080/09602011.2013.818564. Heyvaert, M., & Onghena, P. (2014b). Randomization tests for single-case experiments: State of the art, state of the science, and state of the application. Journal of Contextual Behavioral Science, 3(1), 51–64. https://doi.org/10.1016/j.jcbs.2013.10.002. Horner, R. H., Carr, E. G., Halle, J., McGee, G., Odom, S., & Wolery, M. (2005). The use of single-subject research to identify evidence-based practice in special education. Exceptional Children, 71(2), 165–179. https://doi.org/10.1177/001440290507100203. Hox, J. (2020). Important yet unheeded: Some small sample issues that are often overlooked. In R. van de Schoot & M. Miočević (Eds.), Small sample size solutions: A guide for applied researchers and practitioners (pp. 254–265). Routledge. Institute of Education Sciences. (2020). Standards for excellence in education research. https://ies.ed.gov/seer/index.asp. Janosky, J. E., Leininger, S. L., Hoerger, M. P., & Libkuman, T. M. (2009). Single subject designs in biomedicine. Springer. Johnson, A. H., & Cook, B. G. (2019). Preregistration in single-case design research. Exceptional Children, 86(1), 95–112. https://doi.org/10.1177/0014402919868529. Jonas, K. J., & Cesario, J. (2016). How can preregistration contribute to research in our field? Comprehensive Results in Social Psychology, 1(1–3), 1–7. https://doi.org/10.1080/23743603.2015.1070611. Joo, S. H., & Ferron, J. M. (2019). Application of the within-and between-series estimators to non-normal multiple-baseline data: Maximum likelihood and Bayesian approaches. Multivariate Behavioral Research, 54(5), 666–689. https://doi.org/10.1080/00273171.2018.1564877. Joo, S. H., Ferron, J. M., Beretvas, S. N., Moeyaert, M., & Van den Noortgate, W. (2018). The impact of response-guided baseline phase extensions on treatment effect estimates. Research in Developmental Disabilities, 79, 77–87. https://doi.org/10.1016/j.ridd.2017.12.018. Kazdin, A. E. (2019). Single-case experimental designs. Evaluating interventions in research and clinical practice. Behaviour Research & Therapy, 117, 3–17. https://doi.org/10.1016/j.brat.2018.11.015. Kennedy, C. H. (2005). Single-case designs for educational research. Pearson. Kipfmiller, K. J., Brodhead, M. T., Wolfe, K., LaLonde, K., Sipila, E. S., Bak, M. S., & Fisher, M. H. (2019). Training front-line employees to conduct visual analysis using a clinical decision-making model. Journal of Behavioral Education, 28(3), 301–322. https://doi.org/10.1007/s10864-018-09318-1. Krasny-Pacini, A., & Evans, J. (2018). Single-case experimental designs to assess intervention effectiveness in rehabilitation: A practical guide. Annals of Physical & Rehabilitation Medicine, 61(3), 164–179. https://doi.org/10.1016/j.rehab.2017.12.002. Kratochwill, T. R., Hitchcock, J., Horner, R. H., Levin, J. R., Odom, S. L., Rindskopf, D. M. & Shadish, W. R. (2010). Single-case designs technical documentation. What Works Clearinghouse. https://ies.ed.gov/ncee/wwc/Docs/ReferenceResources/wwc_scd.pdf. Kratochwill, T. R., Hitchcock, J. H., Horner, R. H., Levin, J. R., Odom, S. L., Rindskopf, D. M., & Shadish, W. R. (2013). Single-case intervention research design standards. Remedial and Special Education, 34(1), 26−38. https://doi.org/10.1177/0741932512452794. Kratochwill, T. R., & Levin, J. R. (2010). Enhancing the scientific credibility of single-case intervention research: Randomization to the rescue. Psychological Methods, 15(2), 124–144. https://doi.org/10.1037/a0017736. Kratochwill, T. R., Levin, J. R., & Horner, R. H. (2018). Negative results: Conceptual and methodological dimensions in single-case intervention research. Remedial & Special Education, 34(1), 26–38. https://doi.org/10.1177/0741932512452794. Krypotos, A.-M., Klugkist, I., Mertens, G., & Engelhard, I. M. (2019). A step-by-step guide on preregistration and effective data sharing for psychopathology research. Journal of Abnormal Psychology, 128(6), 517–527. https://doi.org/10.1037/abn0000424. Kubina, R. M., Kostewicz, D. E., Brennan, K. M., & King, S. A. (2017). A critical review of line graphs in behavior analytic journals. Educational Psychology Review, 29(3), 583–598. https://doi.org/10.1007/s10648-015-9339-x. Kwasnicka, D., & Naughton, F. (2020). N-of-1 methods: A practical guide to exploring trajectories of behaviour change and designing precision behaviour change interventions. Psychology of Sport & Exercise, 47, 101570. https://doi.org/10.1016/j.psychsport.2019.101570. Lane, J. D., & Gast, D. L. (2014). Visual analysis in single case experimental design studies: Brief review and guidelines. Neuropsychological Rehabilitation, 24(3–4), 445–463. https://doi.org/10.1080/09602011.2013.815636. Lanovaz, M. J., Turgeon, S., Cardinal, P., & Wheatley, T. L. (2019). Using single-case designs in practical settings: Is within-subject replication always necessary? Perspectives on Behavior Science, 42(1), 153–162. https://doi.org/10.1007/s40614-018-0138-9. Ledford, J. R., Ayres, K. M., Lane, J. D., & Lam, M. F. (2015). Identifying issues and concerns with the use of interval-based systems in single case research using a pilot simulation study. Journal of Special Education, 49(2), 104–117. https://doi.org/10.1177/0022466915568975. Ledford, J. R., Barton, E. E., Severini, K. E., & Zimmerman, K. N. (2019). A primer on single-case research designs: Contemporary use and analysis. American Journal on Intellectual & Developmental Disabilities, 124(1), 35–56. https://doi.org/10.1352/1944-7558-124.1.35. Levin, J. R., Ferron, J. M., & Gafurov, B. S. (2017). Additional comparisons of randomization-test procedures for single-case multiple-baseline designs: Alternative effect types. Journal of School Psychology, 63, 13–34. https://doi.org/10.1016/j.jsp.2017.02.003. Levin, J. R., Ferron, J. M., & Gafurov, B. S. (2018). Comparison of randomization-test procedures for single-case multiple-baseline designs. Developmental Neurorehabilitation, 21(5), 290–311. https://doi.org/10.1080/17518423.2016.1197708. Levin, J. R., Ferron, J. M., & Gafurov, B. S. (2020). Investigation of single-case multiple-baseline randomization tests of trend and variability. Educational Psychology Review. Advance online publication. https://doi.org/10.1007/s10648-020-09549-7. Levin, J. R., Ferron, J. M., & Kratochwill, T. R. (2012). Nonparametric statistical tests for single-case systematic and randomized ABAB . . . AB and alternating treatment intervention designs: New developments, new directions. Journal of School Psychology, 50(5), 599–624. https://doi.org/10.1016/j.jsp.2012.05.001. Lieberman, R. G., Yoder, P. J., Reichow, B., & Wolery, M. (2010). Visual analysis of multiple baseline across participants graphs when change is delayed. School Psychology Quarterly, 25(1), 28–44. https://doi.org/10.1037/a0018600. Lindsay, D. S. (2015). Replication in psychological science. Psychological Science, 26(12), 1827–1832. https://doi.org/10.1177/0956797615616374. Lobo, M. A., Moeyaert, M., Cunha, A. B., & Babik, I. (2017). Single-case design, analysis, and quality assessment for intervention research. Journal of Neurologic Physical Therapy, 41(3), 187–197. https://doi.org/10.1097/NPT.0000000000000187. Ma, H. H. (2006). An alternative method for quantitative synthesis of single-subject research: Percentage of data points exceeding the median. Behavior Modification, 30(5), 598–617. https://doi.org/10.1177/0145445504272974. Maggin, D. M., Briesch, A. M., Chafouleas, S. M., Ferguson, T. D., & Clark, C. (2014). A comparison of rubrics for identifying empirically supported practices with single-case research. Journal of Behavioral Education, 23(2), 287–311. https://doi.org/10.1007/s10864-013-9187-z. Maggin, D. M., Cook, B. G., & Cook, L. (2018). Using single-case research designs to examine the effects of interventions in special education. Learning Disabilities Research & Practice, 33(4), 182–191. https://doi.org/10.1111/ldrp.12184. Maggin, D. M., Robertson, R. E., & Cook, B. G. (2020). Introduction to the special series on results-blind peer review: An experimental analysis on editorial recommendations and manuscript evaluations. Behavioral Disorders, 45(4), 195–206. https://doi.org/10.1177/0198742920936619. Maggin, D. M., Swaminathan, H., Rogers, H. J., O’Keefe, 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(3), 301–321. https://doi.org/10.1016/j.jsp.2011.03.004. Manolov, R. (2018). Linear trend in single-case visual and quantitative analyses. Behavior Modification, 42(5), 684–706. https://doi.org/10.1177/0145445517726301. Manolov, R. (2019). A simulation study on two analytical techniques for alternating treatments designs. Behavior Modification, 43(4), 544–563. https://doi.org/10.1177/0145445518777875. Manolov, R., Gast, D. L., Perdices, M., & Evans, J. J. (2014). Single-case experimental designs: Reflections on conduct and analysis. Neuropsychological Rehabilitation, 24(3-4), 634–660. https://doi.org/10.1080/09602011.2014.903199. Manolov, R., & Moeyaert, M. (2017a). How can single-case data be analyzed? Software resources, tutorial, and reflections on analysis. Behavior Modification, 41(2), 179–228. https://doi.org/10.1177/0145445516664307. Manolov, R., & Moeyaert, M. (2017b). Recommendations for choosing single-case data analytical techniques. Behavior Therapy, 48(1), 97–114. https://doi.org/10.1016/j.beth.2016.04.008. Manolov, R., & Onghena, P. (2018). Analyzing data from single-case alternating treatments designs. Psychological Methods, 23(3), 480–504. https://doi.org/10.1037/met0000133. Manolov, R., & Solanas, A. (2013). A comparison of mean phase difference and generalized least squares for analyzing single-case data. Journal of School Psychology, 51(2), 201–215. https://doi.org/10.1016/j.jsp.2012.12.005. Manolov, R., Solanas, A., & Sierra, V. (2019). Extrapolating baseline trend in single-case data: Problems and tentative solutions. Behavior Research Methods, 51(6), 2847–2869. https://doi.org/10.3758/s13428-018-1165-x. Manolov, R., Solanas, A., & Sierra, V. (2020). Changing criterion designs: Integrating methodological and data analysis recommendations. Journal of Experimental Education, 88(2), 335–350. https://doi.org/10.1080/00220973.2018.1553838. McDougall, D. (2005). The range-bound changing criterion design. Behavioral Interventions, 20(2), 129–137. https://doi.org/10.1002/bin.189. Michiels, B., Heyvaert, M., Meulders, A., & Onghena, P. (2017). Confidence intervals for single-case effect size measures based on randomization test inversion. Behavior Research Methods, 49(1), 363–381. https://doi.org/10.3758/s13428-016-0714-4. Michiels, B., & Onghena, P. (2019). Randomized single-case AB phase designs: Prospects and pitfalls. Behavior Research Methods, 51(6), 2454–2476. https://doi.org/10.3758/s13428-018-1084-x. Michiels, B., Tanious, R., De, T. K., & Onghena, P. (2020). A randomization test wrapper for synthesizing single-case experiments using multilevel models: A Monte Carlo simulation study. Behavior Research Methods, 52(2), 654–666. https://doi.org/10.3758/s13428-019-01266-6. Moeyaert, M., Akhmedjanova, D., Ferron, J., Beretvas, S. N., & Van den Noortgate, W. (2020). Effect size estimation for combined single-case experimental designs. Evidence-Based Communication Assessment and Intervention, 14(1–2), 28–51. https://doi.org/10.1080/17489539.2020.1747146. Moeyaert, M., Ferron, J., Beretvas, S., & Van den Noortgate, W. (2014a). From a single-level analysis to a multilevel analysis of since-case experimental designs. Journal of School Psychology, 52(2), 191–211. https://doi.org/10.1016/j.jsp.2013.11.003. Moeyaert, M., Rindskopf, D., Onghena, P., & Van den Noortgate, W. (2017). Multilevel modeling of single-case data: A comparison of maximum likelihood and Bayesian estimation. Psychological Methods, 22(4), 760–778. https://doi.org/10.1037/met0000136. Moeyaert, M., Ugille, M., Ferron, J., Beretvas, S. N., & Van den Noortgate, W. (2014b). The influence of the design matrix on treatment effect estimates in the quantitative analyses of single-case experimental designs research. Behavior Modification, 38(5), 665–704. https://doi.org/10.1177/0145445514535243. Moeyaert, M., Zimmerman, K. N., & Ledford, J. R. (2018). Synthesis and meta-analysis of single-case research. In J. R. Ledford & D. L. Gast (Eds.), Single case research methodology. Applications in special education and behavioral sciences (3rd ed.) (pp. 393–416). Routledge. Morley, S. (2018). Single-case methods in clinical psychology: A practical guide. Routledge. Natesan Batley, P., Shukla Mehta, S., & Hitchcock, J. H. (2020). A Bayesian rate ratio effect size to quantify intervention effects for count data in single case experimental research. Behavioral Disorders. Advance online publication. https://doi.org/10.1177/0198742920930704. Nikles, J., & Mitchell, G. (2015). The essential guide to N-of-1 trials in health. Springer. Ninci, J., Vannest, K. J., Willson, V., & Zhang, N. (2015). Interrater agreement between visual analysts of single-case data: A meta-analysis. Behavior Modification, 39(4), 510–541. https://doi.org/10.1177/0145445515581327. Nosek, B. A., Ebersole, C. R., DeHaven, A. C., & Mellor, D. T. (2018). The preregistration revolution. Proceedings of the National Academy of Sciences, 115(11), 2600–2606. https://doi.org/10.1073/pnas.1708274114. Nuzzo, R. (2015). How scientists fool themselves–and how they can stop. Nature News, 526(7572), 182. https://doi.org/10.1038/526182a. Odom, S. L., Barton, E. E., Reichow, B., Swaminathan, H., & Pustejovsky, J. E. (2018). Between-case standardized effect size analysis of single case designs: Examination of the two methods. Research in Developmental Disabilities, 79(1), 88–96. https://doi.org/10.1016/j.ridd.2018.05.009. Olive, M. L., & Smith, B. W. (2005). Effect size calculations and single subject designs. Educational Psychology, 25(2–3), 313–324. https://doi.org/10.1080/0144341042000301238. Onghena, P. (1992). Randomization tests for extensions and variations of ABAB single-case experimental designs: A rejoinder. Behavioral Assessment, 14(2), 153–171. Onghena, P. (2020). One by one: The design and analysis of replicated randomized single-case experiments. In R. van de Schoot & M. Miočević (Eds.), Small sample size solutions: A guide for applied researchers and practitioners (pp. 87–101). Routledge. Onghena, P., & Edgington, E. S. (1994). Randomization tests for restricted alternating treatments designs. Behaviour Research & Therapy, 32(7), 783–786. https://doi.org/10.1016/0005-7967(94)90036-1. Onghena, P., & Edgington, E. S. (2005). Customization of pain treatments: Single-case design and analysis. Clinical Journal of Pain, 21(1), 56–68. https://doi.org/10.1097/00002508-200501000-00007. Onghena, P., Tanious, R., De, T. K., & Michiels, B. (2019). Randomization tests for changing criterion designs. Behaviour Research & Therapy, 117, 18–27. https://doi.org/10.1016/j.brat.2019.01.005. Parker, R. I., Cryer, J., & Byrns, G. (2006). Controlling baseline trend in single-case research. School Psychology Quarterly, 21(4), 418–443. https://doi.org/10.1037/h0084131. Parker, R. I., & Hagan-Burke, S. (2007). Single case research results as clinical outcomes. Journal of School Psychology, 45(6), 637–653. https://doi.org/10.1016/j.jsp.2007.07.004. Parker, R. I., & Vannest, K. J. (2009). An improved effect size for single-case research: Nonoverlap of all pairs. Behavior Therapy, 40(4), 357–367. https://doi.org/10.1016/j.beth.2008.10.006. Parker, R. I., Vannest, K. J., & Brown, L. (2009). The improvement rate difference for single-case research. Exceptional Children, 75(2), 135−150. https://doi.org/10.1177/001440290907500201. Parker, R. I., Vannest, K. J., & Davis, J. L. (2011a). Effect size in single-case research: A review of nine nonoverlap techniques. Behavior Modification, 35(4), 303–322. https://doi.org/10.1177/0145445511399147. Parker, R. I., Vannest, K. J., Davis, J. L., & Sauber, S. B. (2011b). Combining nonoverlap and trend for single-case research: Tau-U. Behavior Therapy, 42(2), 284−299. https://doi.org/10.1016/j.beth.2010.08.006. Peng, C. Y. J., & Chen, L. T. (2018). Handling missing data in single-case studies. Journal of Modern Applied Statistical Methods, 17(1), eP2488. https://doi.org/10.22237/jmasm/1525133280. Perone, M. (1999). Statistical inference in behavior analysis: Experimental control is better. The Behavior Analyst, 22(2), 109–116. https://doi.org/10.1007/BF03391988. Porcino, A. J., Shamseer, L., Chan, A. W., Kravitz, R. L., Orkin, A., Punja, S., Ravaud, P., Schmid, C. H., & Vohra, S. (2020). SPIRIT extension and elaboration for N-of-1 trials: SPENT 2019 checklist. BMJ, 368, m122. https://doi.org/10.1136/bmj.m122. Pustejovsky, J. E. (2018). Using response ratios for meta-analyzing single-case designs with behavioral outcomes. Journal of School Psychology, 68(June), 99−112. https://doi.org/10.1016/j.jsp.2018.02.003. Pustejovsky, J. E. (2019). Procedural sensitivities of effect sizes for single-case designs with directly observed behavioral outcome measures. Psychological Methods, 24(2), 217−235. https://doi.org/10.1037/met0000179. Pustejovsky, J. E., Hedges, L. V., & Shadish, W. R. (2014). Design-comparable effect sizes in multiple baseline designs: A general modeling framework. Journal of Educational & Behavioral Statistics, 39(5), 368−393. https://doi.org/10.3102/1076998614547577. Pustejovsky, J. E., & Swan, D. M. (2015). Four methods for analyzing partial interval recording data, with application to single-case research. Multivariate Behavioral Research, 50(3), 365−380. https://doi.org/10.1080/00273171.2015.1014879. Pustejovsky, J. E., & Swan, D. M. (2018). Effect size definitions and mathematical details. Retrieved from https://cran.r-project.org/web/packages/SingleCaseES/vignettes/Effect-size-definitions.html. Pustejovsky, J. E., Swan, D. M., & English, K. W. (2019). An examination of measurement procedures and characteristics of baseline outcome data in single-case research. Behavior Modification. Advance online publication. https://doi.org/10.1177/0145445519864264. Raulston, T. J., Zemantic, P. K, Machalicek, W., Hieneman, M., Kurtz-Nelson, E., Barton, H., Hansen, S. G., & Frantz, R. J. (2019). Effects of a brief mindfulness-infused behavioral parent training for mothers of children with autism spectrum disorder. Journal of Contextual Behavioral Science, 13, 42–51. https://doi.org/10.1016/j.jcbs.2019.05.001. Riley-Tillman, T. C., Burns, M. K., & Kilgus, S. P. (2020). Evaluating educational interventions: Single-case design for measuring response to intervention (2nd ed.). Guilford Press. Schlosser, R. W., Lee, D. L., & Wendt, O. (2008). Application of the percentage of non-overlapping data (PND) in systematic reviews and meta-analyses: A systematic review of reporting characteristics. Evidence-Based Communication Assessment & Intervention, 2(3), 163–187. https://doi.org/10.1080/17489530802505412. Shadish, W. R., Hedges, L. V., & Pustejovsky, J. E. (2014a). Analysis and meta-analysis of single-case designs with a standardized mean difference statistic: A primer and applications. Journal of School Psychology, 52(2), 123–147. https://doi.org/10.1016/j.jsp.2013.11.005. Shadish, W. R., Kyse, E. N., & Rindskopf, D. M. (2013). Analyzing data from single-case designs using multilevel models: New applications and some agenda items for future research. Psychological Methods, 18(3), 385–405. https://doi.org/10.1037/a0032964. Shadish, W. R., Zuur, A. F., & Sullivan, K. J. (2014b). Using generalized additive (mixed) models to analyze single case designs. Journal of School Psychology, 52(2), 149–178. https://doi.org/10.1016/j.jsp.2013.11.004. 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. https://doi.org/10.1177/0956797611417632. Smith, J. D. (2012). Single-case experimental designs: A systematic review of published research and current standards. Psychological Methods, 17(4), 510−550. https://doi.org/10.1037/a0029312. Smith, J. D., Borckardt, J. J., & Nash, M. R. (2012). Inferential precision in single-case time-series data streams: How well does the EM procedure perform when missing observations occur in autocorrelated data? Behavior Therapy, 43(3), 679–685. https://doi.org/10.1016/j.beth.2011.10.001. Solanas, A., Manolov, R., & Onghena, P. (2010). Estimating slope and level change in N = 1 designs. Behavior Modification, 34(3), 195–218. https://doi.org/10.1177/0145445510363306. Solmi, F., Onghena, P., Salmaso, L., & Bulté, I. (2014). A permutation solution to test for treatment effects in alternation design single-case experiments. Communications in Statistics—Simulation and Computation, 43(5), 1094–1111. https://doi.org/10.1080/03610918.2012.725295. Solomon, B. G. (2014). Violations of assumptions in school-based single-case data: Implications for the selection and interpretation of effect sizes. Behavior Modification, 38(4), 477–496. https://doi.org/10.1177/0145445513510931. Solomon, B. G., Howard, T. K., & Stein, B. L. (2015). Critical assumptions and distribution features pertaining to contemporary single-case effect sizes. Journal of Behavioral Education, 24(4), 438–458. https://doi.org/10.1007/s10864-015-9221-4. Swaminathan, H., Rogers, H. J., & Horner, R. H. (2014a). An effect size measure and Bayesian analysis of single-case designs. Journal of School Psychology, 52(2), 213–230. https://doi.org/10.1016/j.jsp.2013.12.002. Swaminathan, H., Rogers, H. J., Horner, R., Sugai, G., & Smolkowski, K. (2014b). Regression models for the analysis of single case designs. Neuropsychological Rehabilitation, 24(3–4), 554–571. https://doi.org/10.1080/09602011.2014.887586. Swan, D. M., & Pustejovsky, J. E. (2018). A gradual effects model for single-case designs. Multivariate Behavioral Research, 53(4), 574–593. https://doi.org/10.1080/00273171.2018.1466681. Swan, D. M., Pustejovsky, J. E., & Beretvas, S. N. (2020). The impact of response-guided designs on count outcomes in single-case experimental design baselines. Evidence-Based Communication Assessment & Intervention, 14(1−2), 82−107. https://doi.org/10.1080/17489539.2020.1739048. Tanious, R., De, T. K., Michiels, B., Van den Noortgate, W., & Onghena, P. (2020). Assessing consistency in single-case A-B-A-B phase designs. Behavior Modification, 44(4), 518–551. https://doi.org/10.1177/0145445519837726. Tanious, R., De, T. K., & Onghena, P. (2019). A multiple randomization testing procedure for level, trend, variability, overlap, immediacy, and consistency in single-case phase designs. Behaviour Research & Therapy, 119, 103414. https://doi.org/10.1016/j.brat.2019.103414. Tarlow, K. (2017). An improved rank correlation effect size statistic for single-case designs: Baseline corrected Tau. Behavior Modification, 41(4), 427–467. https://doi.org/10.1177/0145445516676750. Tarlow, K. R., & Brossart, D. F. (2018). A comprehensive method of single-case data analysis: Interrupted Time-Series Simulation (ITSSIM). School Psychology Quarterly, 33(4), 590–603. https://doi.org/10.1037/spq0000273. Tate, R. L., & Perdices, M. (2019). Single-case experimental designs for clinical research and neurorehabilitation settings: Planning, conduct, analysis, and reporting. Routledge. Tate, R. L., Perdices, M., Rosenkoetter, U., McDonald, S., Togher, L., …. Wilson, B. (2016). The Single-Case Reporting guideline In BEhavioural interventions (SCRIBE) 2016 statement. Journal of School Psychology, 56, 133−142. https://doi.org/10.1016/j.jsp.2016.04.001. Tate, R. L., Rosenkoetter, U., Wakim, D., Sigmundsdottir, L., Doubleday, J., Togher, L., McDonald, S., & Perdices, M. (2015). The risk-of-bias in N-of-1 trials (RoBiNT) scale: An expanded manual for the critical appraisal of single-case reports. Author. Tincani, M., & Travers, J. (2018). Publishing single-case research design studies that do not demonstrate experimental control. Remedial & Special Education, 39(2), 118–128. https://doi.org/10.1177/0741932517697447. Valentine, J. C., Tanner-Smith, E. E., & Pustejovsky, J. E. (2016). Between-case standardized mean difference effect sizes for single-case designs: A primer and tutorial using the scdhlm web application. The Campbell Collaboration. https://doi.org/10.4073/cmdp.2016.1. Van den Noortgate, W., & Onghena, P. (2003). Hierarchical linear models for the quantitative integration of effect sizes in single-case research. Behavior Research Methods, Instruments, & Computers, 35(1), 1–10. https://doi.org/10.3758/BF03195492. Van den Noortgate, W., & Onghena, P. (2008). A multilevel meta-analysis of single-subject experimental design studies. Evidence-Based Communication Assessment & Intervention, 2(3), 142–151. https://doi.org/10.1080/17489530802505362. Vannest, K. J., & Ninci, J. (2015). Evaluating intervention effects in single-case research designs. Journal of Counseling & Development, 93(4), 403–411. https://doi.org/10.1002/jcad.12038. Vannest, K. J., Parker, R. I., Davis, J. L., Soares, D. A., & Smith, S. L. (2012). The Theil–Sen slope for high-stakes decisions from progress monitoring. Behavioral Disorders, 37(4), 271–280. https://doi.org/10.1177/019874291203700406. Vannest, K. J., Peltier, C., & Haas, A. (2018). Results reporting in single case experiments and single case meta-analysis. Research in Developmental Disabilities, 79, 10–18. https://doi.org/10.1016/j.ridd.2018.04.029. Verboon, P., & Peters, G. J. (2020). Applying the generalized logistic model in single case designs: Modeling treatment-induced shifts. Behavior Modification, 44(1), 27–48. https://doi.org/10.1177/0145445518791255. Wendt, O., & Miller, B. (2012). Quality appraisal of single-subject experimental designs: An overview and comparison of different appraisal tools. Education & Treatment of Children, 35(2), 235–268. https://doi.org/10.1353/etc.2012.0010. What Works Clearinghouse. (2020). What Works Clearinghouse standards handbook, Version 4.1. U.S. Department of Education, Institute of Education Sciences, National Center for Education Evaluation and Regional Assistance. https://ies.ed.gov/ncee/wwc/handbooks. Wiley, R. W., & Rapp, B. (2019). Statistical analysis in small-n designs: Using linear mixed-effects modeling for evaluating intervention effectiveness. Aphasiology, 33(1), 1–30. https://doi.org/10.1080/02687038.2018.1454884. Wolery, M., Busick, M., Reichow, B., & Barton, E. E. (2010). Comparison of overlap methods for quantitatively synthesizing single-subject data. Journal of Special Education, 44(1), 18–29. https://doi.org/10.1177/0022466908328009. Wolfe, K., Seaman, M. A., & Drasgow, E. (2016). Interrater agreement on the visual analysis of individual tiers and functional relations in multiple baseline designs. Behavior Modification, 40(6), 852–873. https://doi.org/10.1177/0145445516644699. Yucesoy-Ozkan, S., Rakap, S., & Gulboy, E. (2020). Evaluation of treatment effect estimates in single-case experimental research: Comparison of twelve overlap methods and visual analysis. British Journal of Special Education, 47(1), 67–87. https://doi.org/10.1111/1467-8578.12294. Zelinsky, N. A. M., & Shadish, W. R. (2018). A demonstration of how to do a meta-analysis that combines single-case designs with between-groups experiments: The effects of choice making on challenging behaviors performed by people with disabilities. Developmental Neurorehabilitation, 21(4), 266–278. https://doi.org/10.3109/17518423.2015.1100690.