Volume 4, Issue 4
Original Article

A standardized mean difference effect size for multiple baseline designs across individuals

Larry V. Hedges

Statistics, Northwestern University, Chicago, USA

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James E. Pustejovsky

Corresponding Author

Statistics, Northwestern University, Chicago, USA

Correspondence to: James E. Pustejovsky, Statistics, Northwestern University, Chicago, USA.

E‐mail: pusto@u.northwestern.edu

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William R. Shadish

Psychological Sciences, University of California, Merced, USA

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First published: 23 August 2013
Citations: 83

Abstract

Single‐case designs are a class of research methods for evaluating treatment effects by measuring outcomes repeatedly over time while systematically introducing different condition (e.g., treatment and control) to the same individual. The designs are used across fields such as behavior analysis, clinical psychology, special education, and medicine. Emerging standards for single‐case designs have focused attention on methods for summarizing and meta‐analyzing findings and on the need for effect sizes indices that are comparable to those used in between‐subjects designs. In the previous work, we discussed how to define and estimate an effect size that is directly comparable to the standardized mean difference often used in between‐subjects research based on the data from a particular type of single‐case design, the treatment reversal or (AB)k design. This paper extends the effect size measure to another type of single‐case study, the multiple baseline design. We propose estimation methods for the effect size and its variance, study the estimators using simulation, and demonstrate the approach in two applications. Copyright © 2013 John Wiley & Sons, Ltd.

Number of times cited according to CrossRef: 83

  • A primer for using multilevel models to meta‐analyze single case design data with AB phases, Journal of Applied Behavior Analysis, 10.1002/jaba.698, 53, 3, (1799-1821), (2020).
  • Using Bayesian methods to test mediators of intervention outcomes in single-case experimental designs, Evidence-Based Communication Assessment and Intervention, 10.1080/17489539.2020.1732029, (1-17), (2020).
  • A Multiple-Baseline Evaluation of Acceptance and Commitment Therapy Focused on Repetitive Negative Thinking for Comorbid Generalized Anxiety Disorder and Depression, Frontiers in Psychology, 10.3389/fpsyg.2020.00356, 11, (2020).
  • Efficacy of a Virtual Reality Biofeedback Game (DEEP) to Reduce Anxiety and Disruptive Classroom Behavior: Single-Case Study, JMIR Mental Health, 10.2196/16066, 7, 3, (e16066), (2020).
  • Multitiered Systems of Support in Preschool Settings: A Review and Meta-Analysis of Single-Case Research, Topics in Early Childhood Special Education, 10.1177/0271121419899720, (027112141989972), (2020).
  • Fast talkers? Investigating the influence of self-talk on mental toughness and finish times in 800-meter runners, Journal of Applied Sport Psychology, 10.1080/10413200.2020.1735574, (1-19), (2020).
  • Assessing consistency of effects when applying multilevel models to single-case data, Behavior Research Methods, 10.3758/s13428-020-01417-0, (2020).
  • Investigating immediacy in multiple-phase-change single-case experimental designs using a Bayesian unknown change-points model, Behavior Research Methods, 10.3758/s13428-020-01345-z, (2020).
  • Acceptance and Commitment Therapy Focused on Repetitive Negative Thinking for Child Depression: A Randomized Multiple-Baseline Evaluation, The Psychological Record, 10.1007/s40732-019-00362-5, (2020).
  • Effects of a Multifaceted Classroom Intervention on Racial Disproportionality, School Psychology Review, 10.1080/2372966X.2020.1788906, (1-17), (2020).
  • Multilevel Meta-Analysis of Individual Participant Data of Single-Case Experimental Designs: One-Stage versus Two-Stage Methods, Multivariate Behavioral Research, 10.1080/00273171.2020.1822148, (1-20), (2020).
  • A meta-analysis on the effectiveness of phonics instruction for teaching decoding skills to students with intellectual disability, Educational Research Review, 10.1016/j.edurev.2019.01.001, (2019).
  • A multiple randomization testing procedure for level, trend, variability, overlap, immediacy, and consistency in single-case phase designs, Behaviour Research and Therapy, 10.1016/j.brat.2019.103414, (103414), (2019).
  • Fitting Bayesian Models for Single-Case Experimental Designs, Methodology, 10.1027/1614-2241/a000180, 15, 4, (147-156), (2019).
  • Peer tutoring and mathematics in secondary education: literature review, effect sizes, moderators, and implications for practice, Heliyon, 10.1016/j.heliyon.2019.e02491, 5, 9, (e02491), (2019).
  • Reprint of “The Single-Case Reporting Guideline In BEhavioural Interventions (SCRIBE) 2016: Explanation and Elaboration”, Pratiques Psychologiques, 10.1016/j.prps.2019.03.001, (2019).
  • Effects of a brief mindfulness-infused behavioral parent training for mothers of children with autism spectrum disorder, Journal of Contextual Behavioral Science, 10.1016/j.jcbs.2019.05.001, (2019).
  • Application of a Single-Case Intervention Procedure To Assess the Replicability of a Two-Component Instructional Strategy, Contemporary Educational Psychology, 10.1016/j.cedpsych.2018.10.006, (2019).
  • The use of touch devices for enhancing academic achievement: A meta‐analysis, Psychology in the Schools, 10.1002/pits.22225, 56, 7, (1187-1206), (2019).
  • Teacher-Delivered Strategies to Increase Students’ Opportunities to Respond: A Systematic Methodological Review, Behavioral Disorders, 10.1177/0198742919828310, (019874291982831), (2019).
  • Social Studies Content Knowledge Interventions for Students With Emotional and Behavioral Disorders: A Meta-Analysis, Behavior Modification, 10.1177/0145445519834622, (014544551983462), (2019).
  • Evaluation of a Home-Based Behavioral Treatment Model for Children With Tube Dependency, Journal of Pediatric Psychology, 10.1093/jpepsy/jsz014, (2019).
  • Transition States in Single Case Experimental Designs, Behavior Modification, 10.1177/0145445519839213, (014544551983921), (2019).
  • A Meta-Analysis of Single-Case Research Using Mathematics Manipulatives With Students At Risk or Identified With a Disability, The Journal of Special Education, 10.1177/0022466919844516, (002246691984451), (2019).
  • A Systematic Review of the Evidence Base for Active Supervision in PK–12 Settings, Behavioral Disorders, 10.1177/0198742919837646, (019874291983764), (2019).
  • Bias Adjustment in Multilevel Meta-Analysis of Standardized Single-Case Experimental Data, The Journal of Experimental Education, 10.1080/00220973.2019.1658568, (1-18), (2019).
  • Game-Based Self-Management: Addressing Inattention during Independent Reading and Written Response, Journal of Applied School Psychology, 10.1080/15377903.2019.1660748, (1-24), (2019).
  • The Impact of Coaching on Teacher-Delivered Behavior-Specific Praise in Pre-K-12 Settings: A Systematic Review, Behavioral Disorders, 10.1177/0198742919839221, (019874291983922), (2019).
  • Teaching academic skills to students with significant intellectual disabilities: A systematic review of the single-case design literature, Journal of Intellectual Disabilities, 10.1177/1744629519895387, (174462951989538), (2019).
  • Tailoring Cognitive Behavioral Therapy for Depression and Anxiety Symptoms in Mexican Terminal Cancer Patients: A Multiple Baseline Study, Journal of Clinical Psychology in Medical Settings, 10.1007/s10880-019-09620-8, (2019).
  • Evaluating the effectiveness of therapeutic horse riding for children and young people experiencing disability: a single-case experimental design study, Disability and Rehabilitation, 10.1080/09638288.2019.1610083, (1-10), (2019).
  • Comparing Visual and Statistical Analysis of Multiple Baseline Design Graphs, Behavior Modification, 10.1177/0145445518768723, 43, 3, (361-388), (2018).
  • Evaluating Tau-U With Oral Reading Fluency Data and the Impact of Measurement Error, Behavior Modification, 10.1177/0145445518760174, 43, 3, (413-438), (2018).
  • A Systematic Review of Teacher-Delivered Behavior-Specific Praise on K–12 Student Performance, Remedial and Special Education, 10.1177/0741932517751054, 40, 2, (112-128), (2018).
  • A meta‐analytic review of the evidence for check‐in check‐out, Psychology in the Schools, 10.1002/pits.22195, 56, 3, (393-412), (2018).
  • A multiple-baseline evaluation of a brief acceptance and commitment therapy protocol focused on repetitive negative thinking for moderate emotional disorders, Journal of Contextual Behavioral Science, 10.1016/j.jcbs.2018.04.004, 9, (1-14), (2018).
  • Efficacy of Video Modeling and Brief Coaching on Teacher Implementation of an Evidence-Based Practice for Students With Severe Disabilities, Journal of Special Education Technology, 10.1177/0162643418770639, 33, 4, (259-269), (2018).
  • Review of Single Subject Research Examining the Effectiveness of Interventions for At‐Risk English Learners, Learning Disabilities Research & Practice, 10.1111/ldrp.12160, 33, 2, (64-74), (2018).
  • The effectiveness of the Pathways and Resources for Engagement and Participation (PREP) intervention: improving participation of adolescents with physical disabilities, Developmental Medicine & Child Neurology, 10.1111/dmcn.13682, 60, 5, (513-519), (2018).
  • Between-case standardized effect size analysis of single case designs: Examination of the two methods, Research in Developmental Disabilities, 10.1016/j.ridd.2018.05.009, 79, (88-96), (2018).
  • A Gradual Effects Model for Single-Case Designs, Multivariate Behavioral Research, 10.1080/00273171.2018.1466681, 53, 4, (574-593), (2018).
  • Special Issue on Advances in Single-Case Research Design and Analysis, Developmental Neurorehabilitation, 10.1080/17518423.2018.1468600, 21, 4, (209-211), (2018).
  • Systematic Review of High Probability Requests in K-12 Settings: Examining the Evidence Base, Behavioral Disorders, 10.1177/0198742918800029, (019874291880002), (2018).
  • Nonparametric meta-analysis for single-case research: Confidence intervals for combined effect sizes, Behavior Research Methods, 10.3758/s13428-018-1044-5, (2018).
  • Efficacy and Safety of Budesonide in the Treatment of Eosinophilic Esophagitis: Updated Systematic Review and Meta-Analysis of Randomized and Non-Randomized Studies, Drugs in R&D, 10.1007/s40268-018-0253-9, (2018).
  • The effectiveness of visual activity schedules for individuals with intellectual disabilities: A meta-analysis, Journal of Intellectual & Developmental Disability, 10.3109/13668250.2018.1431761, (1-12), (2018).
  • Response Cards to Increase Engagement and Active Participation of Middle School Students With EBD, Remedial and Special Education, 10.1177/0741932518800807, (074193251880080), (2018).
  • Efficacy of metacognitive therapy in improving mental health: A meta‐analysis of single‐case studies, Journal of Clinical Psychology, 10.1002/jclp.22567, 74, 6, (896-915), (2017).
  • A Review of the Pyramidal Training Approach for Practitioners Working With Individuals With Disabilities, Behavior Modification, 10.1177/0145445517692952, 41, 4, (558-580), (2017).
  • A Meta-Analysis of School-Based Group Contingency Interventions for Students With Challenging Behavior: An Update, Remedial and Special Education, 10.1177/0741932517716900, 38, 6, (353-370), (2017).
  • Findings Across Practitioner Training Studies in Special Education: A Comprehensive Review and Meta-Analysis, Exceptional Children, 10.1177/0014402917698008, 84, 1, (7-26), (2017).
  • A Meta-Analysis of Class-Wide Interventions for Supporting Student Behavior, School Psychology Review, 10.17105/SPR-2017-0015.V46-2, 46, 2, (149-164), (2017).
  • Introduction to the Special Issue on Single-Case Systematic Reviews and Meta-Analyses, Remedial and Special Education, 10.1177/0741932517717043, 38, 6, (323-330), (2017).
  • Functional Assessment–Based Interventions for Students With or At-Risk for High-Incidence Disabilities: Field Testing Single-Case Synthesis Methods, Remedial and Special Education, 10.1177/0741932517693320, 38, 6, (331-352), (2017).
  • Technology-Aided Instruction and Intervention for Students With ASD: A Meta-Analysis Using Novel Methods of Estimating Effect Sizes for Single-Case Research, Remedial and Special Education, 10.1177/0741932517729508, 38, 6, (371-386), (2017).
  • Recommendations for Choosing Single-Case Data Analytical Techniques, Behavior Therapy, 10.1016/j.beth.2016.04.008, 48, 1, (97-114), (2017).
  • The use of a smartwatch as a prompting device for people with acquired brain injury: a single case experimental design study, Neuropsychological Rehabilitation, 10.1080/09602011.2017.1310658, (1-21), (2017).
  • Reducing anger outbursts after a severe TBI: a single-case study, Neuropsychological Rehabilitation, 10.1080/09602011.2016.1270837, 29, 1, (107-130), (2016).
  • Quantifying differences between conditions in single-case designs: Possible analysis and meta-analysis, Developmental Neurorehabilitation, 10.3109/17518423.2015.1100688, 21, 4, (238-252), (2016).
  • 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, 10.3109/17518423.2015.1100690, 21, 4, (266-278), (2016).
  • How Can Single-Case Data Be Analyzed? Software Resources, Tutorial, and Reflections on Analysis, Behavior Modification, 10.1177/0145445516664307, 41, 2, (179-228), (2016).
  • Effects of a Summarizing Strategy on Written Summaries of Children With Emotional and Behavioral Disorders, Remedial and Special Education, 10.1177/0741932516669051, 38, 2, (87-97), (2016).
  • EFFECTS OF MINDFULNESS‐BASED INTERVENTIONS ON DISRUPTIVE BEHAVIOR: A META‐ANALYSIS OF SINGLE‐CASE RESEARCH, Psychology in the Schools, 10.1002/pits.21982, 54, 1, (70-87), (2016).
  • A survey of publication practices of single‐case design researchers when treatments have small or large effects, Journal of Applied Behavior Analysis, 10.1002/jaba.308, 49, 3, (656-673), (2016).
  • Does a pre-intervention functional assessment increase intervention effectiveness? A meta-analysis of within-subject interrupted time-series studies, Clinical Psychology Review, 10.1016/j.cpr.2016.05.003, 47, (71-84), (2016).
  • Seeing red: Relearning to read in a case of Balint’s Syndrome, NeuroRehabilitation, 10.3233/NRE-161342, 39, 1, (111-117), (2016).
  • Between‐case standardized mean difference effect sizes for single‐case designs: a primer and tutorial using the scdhlm web application, Campbell Systematic Reviews, 10.4073/cmdp.2016.1, 12, 1, (1-31), (2016).
  • The consequences of modeling autocorrelation when synthesizing single-case studies using a three-level model, Behavior Research Methods, 10.3758/s13428-015-0612-1, 48, 2, (803-812), (2015).
  • Meta‐Analysis, Emerging Trends in the Social and Behavioral Sciences, 10.1002/9781118900772, (1-16), (2015).
  • Computing Tools for Implementing Standards for Single-Case Designs, Behavior Modification, 10.1177/0145445515603706, 39, 6, (835-869), (2015).
  • Further developments in summarising and meta-analysing single-case data: An illustration with neurobehavioural interventions in acquired brain injury, Neuropsychological Rehabilitation, 10.1080/09602011.2015.1064452, 25, 5, (637-662), (2015).
  • Interactive augmented reality using Scratch 2.0 to improve physical activities for children with developmental disabilities, Research in Developmental Disabilities, 10.1016/j.ridd.2014.10.016, 37, (1-8), (2015).
  • Probability and Visual Aids for Assessing Intervention Effectiveness in Single-Case Designs, Behavior Modification, 10.1177/0145445515593512, 39, 5, (691-720), (2015).
  • Throwing the baby out with the bathwater: pitfalls of misrepresenting single-case experimental designs, Aphasiology, 10.1080/02687038.2014.987045, 29, 5, (583-587), (2014).
  • The Effectiveness of Collaborative/Therapeutic Assessment for Psychotherapy Consultation: A Pragmatic Replicated Single-Case Study, Journal of Personality Assessment, 10.1080/00223891.2014.955917, 97, 3, (261-270), (2014).
  • An effect size measure and Bayesian analysis of single-case designs, Journal of School Psychology, 10.1016/j.jsp.2013.12.002, 52, 2, (213-230), (2014).
  • undefined, 2014 9th International Conference on Computer Science & Education, 10.1109/ICCSE.2014.6926474, (298-302), (2014).
  • Assessing Functional Relations in Single-Case Designs, Behavior Modification, 10.1177/0145445514545679, 38, 6, (878-913), (2014).
  • Analysis and meta-analysis of single-case designs with a standardized mean difference statistic: A primer and applications, Journal of School Psychology, 10.1016/j.jsp.2013.11.005, 52, 2, (123-147), (2014).
  • Analysis and meta-analysis of single-case designs: An introduction, Journal of School Psychology, 10.1016/j.jsp.2013.11.009, 52, 2, (109-122), (2014).
  • Design-Comparable Effect Sizes in Multiple Baseline Designs, Journal of Educational and Behavioral Statistics, 10.3102/1076998614547577, 39, 5, (368-393), (2014).
  • Statistical Analyses of Single-Case Designs, Current Directions in Psychological Science, 10.1177/0963721414524773, 23, 2, (139-146), (2014).
  • Increase in physical activities in kindergarten children with cerebral palsy by employing MaKey–MaKey-based task systems, Research in Developmental Disabilities, 10.1016/j.ridd.2014.04.028, 35, 9, (1963-1969), (2014).

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