Cluster randomized trials (CRTs) are commonly used to evaluate the causal effects of educational interventions, where the entire clusters (e.g., schools) are randomly assigned to treatment or control conditions. This study introduces statistical methods for designing and analyzing two-level (e.g., students nested within schools) and three-level…

Background: Education scientists are increasingly interested in constructing interventions that are adaptive over time to suit the evolving needs of students, classrooms, or schools. Such "adaptive interventions" (also referred to as dynamic treatment regimens or dynamic instructional regimes) determine which treatment should be offered…

Traditionally, cluster randomized controlled trials are analyzed with the average intervention effect of interest. However, in populations that contain higher degrees of heterogeneity or variation may differ across different values of a covariate, which may not be optimal. Within education and social science contexts, exploring the variation in…

Cluster randomized control trials often incorporate a longitudinal component where, for example, students are followed over time and student outcomes are measured repeatedly. Besides examining how intervention effects induce changes in outcomes, researchers are sometimes also interested in exploring whether intervention effects on outcomes are…

This study investigated the power of two-level hierarchical linear modeling (HLM) to explain variability in intervention effectiveness between participants in context of single-case experimental design (SCED) research. HLM is a flexible technique that allows the inclusion of participant characteristics (e.g., age, gender, and disability types) as…

This study introduces an innovative meta-analytic approach, two-stage multilevel meta-analysis that considers the hierarchical structure of single-case experimental design (SCED) data. This approach is unique as it is suitable to include moderators at the intervention level, participant level, and study level, and is therefore especially…

Multilevel meta-analysis is an innovative synthesis technique used for the quantitative integration of effect size estimates across participants and across studies. The quantitative summary allows for objective, evidence-based, and informed decisions in research, practice, and policy. Based on previous methodological work, the technique results in…

Researchers are often interested in whether the effects of an intervention differ conditional on individual- or group-moderator variables such as children's characteristics (e.g., gender), teacher's background (e.g., years of teaching), and school's characteristics (e.g., urbanity); that is, the researchers seek to examine for whom and under what…

To plan cluster-randomized trials with sufficient statistical power to detect intervention effects on student achievement, researchers need multilevel design parameters, including measures of between-classroom and between-school differences and the amounts of variance explained by covariates at the student, classroom, and school level. Previous…

Researchers designing multisite and cluster randomized trials of educational interventions will usually conduct a power analysis in the planning stage of the study. To conduct the power analysis, researchers often use estimates of intracluster correlation coefficients and effect sizes derived from an analysis of survey data. When there is…

This article reports on a Monte Carlo simulation study, evaluating two approaches for testing the intervention effect in replicated randomized AB designs: two-level hierarchical linear modeling (HLM) and using the additive method to combine randomization test "p" values (RTcombiP). Four factors were manipulated: mean intervention effect,…

A multilevel logistic model for estimating a nonlinear trajectory in a multiple-baseline design is introduced. The model is applied to data from a real multiple-baseline design study to demonstrate interpretation of relevant parameters. A simple change-in-levels (?"Levels") model and a model involving a quadratic function…

The purpose of this study was to explain the variability in data collected from a single-case design study and to identify predictors of communicative outcomes for children with developmental delays or disabilities (n = 4). Using SAS® University Edition, we fit multilevel models with time nested within children. Children's level of baseline…

Questions regarding the generalizability of results from educational experiments have been at the forefront of methods development over the past five years. This work has focused on methods for estimating the effect of an intervention in a well-defined inference population (e.g., Tipton, 2013; O'Muircheartaigh and Hedges, 2014); methods for…

Single-case designs (SCDs) are often used to examine the impact of an intervention over brief periods of time (Kratochwill & Stoiber, 2002; Segool, Brinkman, & Carlson, 2007). The majority of SCDs are inspected using visual analysis (Kromrey & Foster-Johnson, 1996; Morgan & Morgan, 2009). Although the single-case literature…