Regression models and effect size measures for single case designs.

A regression modelling approach for the analysis of single case designs (SCDs) is described in this paper. The approach presented addresses two key issues in the analysis of SCDs. The first issue is that of serial dependence among the observations in SCDs. The second issue is that of an effect size measure appropriate for SCDs. As with traditional between-subjects experimental designs, effect size measures are critical in assessing the impact of interventions in SCDs. Although effect size measures when there is level change without trend are straightforward to obtain and have been well studied, the situation is different when there are changes in both level and trend. An effect size measure that combines changes in levels and slopes and that is comparable to the d-type effect size measure obtained in between-subjects designs is presented. Finally, an inferential procedure for assessing the effect of the intervention based on the effect size measure is provided and illustrated.

Single-case intervention research design standards: Additional proposed upgrades and future directions.

Single-case intervention research design standards have evolved considerably over the past decade. These standards serve the dual role of assisting in single-case design (SCD) intervention research methodology and as guidelines for literature syntheses within a particular research domain. In a recent article (Kratochwill et al., 2021), we argued for a need to clarify key features of these standards. In this article we offer additional recommendations for SCD research and synthesis standards that have been either underdeveloped or missing in the conduct of research and in literature syntheses. Our recommendations are organized into three categories: expanding design standards, expanding evidence standards, and expanding the applications and consistency of SCDs. The recommendations we advance are for consideration for future standards, research design training, and they are especially important to guide the reporting of SCD intervention investigations as they enter the literature-synthesis phase of evidence-based practice initiatives.

Honoring Uncontrolled Events: Commentary on Slocum et al.

In this special section of Perspectives on Behavior Science, Slocum et al. (2022) provide a summary of the logic and protocol for the construction, implementation, and analysis of single-case multiple-baseline designs. A major contribution of this article is a reassessment of the nonconcurrent multiple baseline design as a credible approach to documenting experimental control. In this commentary we provide considerations for readers as they approach the Slocum et al. article and suggest that although the resurrection of nonconcurrent multiple-baseline designs to a higher status is warranted, researchers will find more control for threats to internal validity in concurrent multiple-baseline designs, and the concurrent format should remain the preferred option.

Advancing the Application and Use of Single-Case Research Designs: Reflections on Articles from the Special Issue.

This special issue of Perspective on Behavior Science is a productive contribution to current advances in the use and documentation of single-case research designs. We focus in this article on major themes emphasized by the articles in this issue and suggest directions for improving professional standards focused on the design, analysis, and dissemination of single-case research.

Single-case design standards: An update and proposed upgrades.

In this paper, we provide a critique focused on the What Works Clearinghouse (WWC) Standards for Single-Case Research Design (Standards 4.1). Specifically, we (a) recommend the use of visual-analysis to verify a single-case intervention study's design standards and to examine the study's operational issues, (b) identify limitations of the design-comparable effect-size measure and discuss related statistical matters, (c) review the applicability and practicality of Standards 4.1 to single-case designs (SCDs), and (d) recommend inclusion of content pertaining to diversity, equity, and inclusion in future standards. Within the historical context of the WWC Pilot Standards for Single-Case Design (1.0), we suggest that Standards 4.1 may best serve as standards for meta-analyses of SCDs but will need to make clear distinctions among the various types of SCD studies that are included in any research synthesis. In this regard, we argue for transparency in SCD studies that meet design standards and those that do not meet design standards in any meta-analysis emanating from the WWC. The intent of these recommendations is to advance the science of SCD research both in research synthesis and in promoting evidence-based practices.

The Marriage of Policy, Practices, and Data to Achieve Educational Reform.

The policy decisions of state, district and school educators affect the extent to which students have access to high-quality practices. This is especially relevant for students with disabilities and their families. This article summarizes a presentation made at the 2019 AAIDD conference and proposes an operational role for policy makers. Two frequently cited advances in education are (a) the commitment to adopt "evidence-based practices," and (b) the impact of information technology and data systems on the active "use of data for decision making" in schools. This article reviews the integrative role that policy decisions make in transforming effective practices and good data systems into practical outcomes for children and families.

Implementing Effective Educational Practices at Scales of Social Importance.

Implementing evidence-based practices is becoming both a goal and standard across medicine, psychology, and education. Initial successes, however, are now leading to questions about how successful demonstrations may be expanded to scales of social importance. In this paper, we review lessons learned about scaling up evidence-based practices gleaned from our experience implementing school-wide positive behavioral interventions and supports (PBIS) across more than 23,000 schools in the USA. We draw heavily from the work of Flay et al. (Prev Sci 6:151-175, 2005. doi: 10.1007/s11121-005-5553-y ) related to defining evidence-based practices, the significant contributions from the emerging "implementation science" movement (Fixsen et al. in Implementation research: a synthesis of the literature, University of South Florida, Louis de la Parte Florida Mental Health Institute, The National Implementation Research Network (FMHI Publication #231), Tampa 2005), and guidance we have received from teachers, family members, students, and administrators who have adopted PBIS.

Generalized reduction of problem behavior of young children with autism: building trans-situational interventions.

The effects of functional communication training on the generalized reduction of problem behavior with three 4- to 5-year-old children with autism and problem behavior were evaluated. Participants were assessed in primary teaching settings and in three secondary, generalization settings. Through baseline analysis, lower effort interventions in the secondary settings were documented as ineffective when implemented alone. Higher effort interventions incorporating functional communication training were documented within a multiple baseline design to reduce problem behavior in the primary setting, but not in secondary settings until the lower effort interventions were re-introduced. Results demonstrate the need for trans-situational interventions based on a common functional assessment hypothesis across settings and including intensive interventions that enhance the effects of lower intensity interventions.

School-wide PBIS: An Example of Applied Behavior Analysis Implemented at a Scale of Social Importance.

School-wide Positive Behavioral Interventions and Supports (PBIS) is an example of applied behavior analysis implemented at a scale of social importance. In this paper, PBIS is defined and the contributions of behavior analysis in shaping both the content and implementation of PBIS are reviewed. Specific lessons learned from implementation of PBIS over the past 20 years are summarized.

Problem behavior interventions for young children with autism: a research synthesis.

This paper provides a summary of research on behavioral interventions for children with autism 8 years of age or younger published between 1996 and 2000. The analysis is divided into four sections: (1) emerging themes in the technology of behavior support, (2) a review of existing research syntheses focusing on behavioral interventions, (3) a new literature review of current pertinent research, and (4) an evaluative discussion of the synthesis results and the field's future needs to develop effective behavioral interventions for young children with autism. The authors offer recommendations for strengthening the existing research base and advancing behavioral technology to meet the needs of the defined target population.

Validating the Construct of Coercion in Family Routines: Expanding the Unit of Analysis in Behavioral Assessment with Families of Children with Developmental Disabilities.

We conducted an observational study of parent-child interaction in home activity settings (routines) of families raising young children with developmental disabilities and problem behavior. Our aim was to empirically investigate the construct validity of coercion in typical but unsuccessful family routines. The long-term goal was to develop an expanded ecological unit of analysis that may contribute to sustainable behavioral family intervention. Ten children with autism and/or mental retardation and their families participated. Videotaped observations were conducted in typical but unsuccessful home routines. Parent-child interaction in routines was coded in real time and sequential analyses were conducted to test hypotheses about coercive processes. Following observation, families were interviewed about the social validity of the construct. Results confirmed the presence of statistically significant, attention-driven coercive processes in routines in which parents were occupied with non-child centered tasks. Results partially confirmed the presence of escape-driven coercive processes in routines in which parent demands are common. Additional analysis revealed an alternative pattern with greater magnitude. Family perspectives suggested the social validity of the construct. Results are discussed in terms of preliminary, partial evidence for coercive processes in routines of families of children with developmental disabilities. Implications for behavioral assessment and intervention design are discussed.

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

This article describes a linear modeling approach for the analysis of single-case designs (SCDs). Effect size measures in SCDs have been defined and studied for the situation where there is a level change without a time trend. However, when there are level and trend changes, effect size measures are either defined in terms of changes in R(2) or defined separately for changes in slopes and intercept coefficients. We propose an alternate effect size measure that takes into account changes in slopes and intercepts in the presence of serial dependence and provides an integrated procedure for the analysis of SCDs through estimation and inference based directly on the effect size measure. A Bayesian procedure is described to analyze the data and draw inferences in SCDs. A multilevel model that is appropriate when several subjects are available is integrated into the Bayesian procedure to provide a standardized effect size measure comparable to effect size measures in a between-subjects design. The applicability of the Bayesian approach for the analysis of SCDs is demonstrated through an example.

Decreasing bullying behaviors in middle school: expect respect.

A nonconcurrent multiple baseline across 3 middle schools was used to assess the impact that teaching all students to follow the Bullying and Harassment Prevention in Positive Behavior Support: Expect Respect intervention had on bullying behaviors. The 3 schools were using School-Wide Positive Behavioral Interventions and Supports and as part of this effort all students in each school had been taught to discriminate "respectful" versus "nonrespectful" behavior. The Expect Respect intervention included, 3 1-hr lessons over a 6-month period to learn (a) how to signal "stop" when encountering nonrespectful behavior, (b) how to follow a "stopping routine" when asked to stop, (c) how to utilize the "bystander routine" when you are a witness to disrespectful behavior that does not stop even after the perpetrator has been asked to, and (d) how to recruit adult support if bullying behaviors endured. Before intervention implementation, 8 students from each school were engaged in focus groups to define the perceived need for bully prevention, and the bully prevention routines that best fit the social culture of their school. Data assessing the fidelity of intervention implementation indicate that the program was used with high fidelity and that in each of the 3 schools a reduction of verbal or physical aggression in the cafeteria was documented via direct observation. No consistent patterns were found with respect to the conditional probabilities that bystanders or recipients of bullying would use the bully prevention routines. No consistent changes were reported in student pre-post rating of school climate.

Measurement invariance of an instrument assessing sustainability of school-based universal behavior practices.

The purpose of the study was to examine the extent to which the School-Wide Universal Behavior Sustainability Index: School Teams (SUBSIST; McIntosh, Doolittle, Vincent, Horner, & Ervin, 2009), a measure of school and district contextual factors that promote the sustainability of school practices, demonstrated measurement invariance across groups of schools that differed in length of time implementing school-wide Positive Behavioral Interventions and Supports (PBIS; Sugai & Horner, 2009), student ethnic composition, and student socioeconomic status (SES). School PBIS team members and district coaches representing 860 schools in 14 U.S. states completed the SUBSIST. Findings supported strong measurement invariance, for all items except 1, of a model with two school-level factors (School Priority and Team Use of Data) and 2 district-level factors (District Priority and Capacity Building) across groups of schools at initial implementation, institutionalization, and sustainability phases of PBIS implementation. Schools in the sustainability phase were rated significantly higher on School Priority and Team Use of Data than schools in initial implementation. Strong measurement invariance held across groups of schools that differed in student ethnicity and SES. The findings regarding measurement invariance are important for future longitudinal investigations of factors that may promote the sustained implementation of school practices.

A randomized wait-list controlled analysis of the implementation integrity of team-initiated problem solving processes.

Members of Positive Behavior Interventions and Supports (PBIS) teams from 34 elementary schools participated in a Team-Initiated Problem Solving (TIPS) Workshop and follow-up technical assistance. Within the context of a randomized wait-list controlled trial, team members who were the first recipients of the TIPS intervention demonstrated greater implementation integrity in using the problem-solving processes during their team meetings than did members of PBIS Teams in the Wait-List Control group. The success of TIPS at improving implementation integrity of the problem-solving processes is encouraging and suggests the value of conducting additional research focused on determining whether there is a functional relation between use of these problem-solving processes and actual resolution of targeted student academic and social problems.

A generalized least squares regression approach for computing effect sizes in single-case research: application examples.

A new method for deriving effect sizes from single-case designs is proposed. The strategy is applicable to small-sample time-series data with autoregressive errors. The method uses Generalized Least Squares (GLS) to model the autocorrelation of the data and estimate regression parameters to produce an effect size that represents the magnitude of treatment effect from baseline to treatment phases in standard deviation units. In this paper, the method is applied to two published examples using common single case designs (i.e., withdrawal and multiple-baseline). The results from these studies are described, and the method is compared to ten desirable criteria for single-case effect sizes. Based on the results of this application, we conclude with observations about the use of GLS as a support to visual analysis, provide recommendations for future research, and describe implications for practice.

Bully prevention in positive behavior support.

Bullying behaviors are a growing concern in U.S. schools. We present here a behavioral approach to bully prevention utilizing a schoolwide intervention. Bully prevention in positive behavior support (BP-PBS) teaches students to withhold the social rewards hypothesized to maintain bullying. A single-subject multiple baseline design across 6 students and three elementary schools was implemented in an empirical evaluation of the intervention's effectiveness. Results indicated that implementation was functionally related to decreased incidents of bullying for all 6 students observed. In addition, we observed a decrease in the social responses from victims and bystanders. Finally, school staff implemented the program with a high degree of fidelity and rated the program as effective and efficient. Limitations and implications of these results are discussed.