Optimal sampling frameworks attempt to identify the most efficient sampling plans to achieve an adequate statistical power. Although such calculations are theoretical in nature, they are critical to the judicious and wise use of funding because they serve as important starting points that guide practical discussions around sampling tradeoffs and…

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…

Cluster randomized trials (CRTs) are commonly used to evaluate educational interventions, particularly their effectiveness. Recently there has been greater emphasis on using these trials to explore cost-effectiveness. However, methods for establishing the power of cluster randomized cost-effectiveness trials (CRCETs) are limited. This study…

When well-implemented, mediation analyses play a critical role in probing theories of action because their results help lay the ground work for the critical development of a treatment and the iterative advancement of theories that are foundational to a discipline. Despite strong interest in designs that incorporate mediation, few studies have…

Conventional optimal design frameworks consider a narrow range of sampling cost structures that thereby constrict their capacity to identify the most powerful and efficient designs. We relax several constraints of previous optimal design frameworks by allowing for variable sampling costs in cluster-randomized trials. The proposed framework…

Researchers face many choices when conducting large-scale multisite individually randomized control trials. One of the most common quantities of interest in multisite RCTs is the overall average effect. Even this quantity is non-trivial to define and estimate. The researcher can target the average effect across individuals or sites. Furthermore,…

Cost-effectiveness analysis is a widely used educational evaluation tool. The randomized controlled trials that aim to evaluate the cost-effectiveness of the treatment are commonly referred to as randomized cost-effectiveness trials (RCETs). This study provides methods of power analysis for two-level multisite RCETs. Power computations take…

Professional development for teachers is regarded as one of the principal pathways through which we can understand and cultivate effective teaching and improve student outcomes. A critical component of studies that seek to improve teaching through professional development is the detailed assessment of the intermediate teacher development processes…

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…

Recent studies show cluster randomized trials may be well powered to detect mediation or indirect effects in multilevel settings. However, literature has rarely provided guidance on designing cluster-randomized trials aim to assess indirect effects. In this study, we developed closed-form expression to estimate the variance of and the statistical…

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…

When a multisite randomized trial reveals between-site variation in program impact, methods are needed for further investigating heterogeneous mediation mechanisms across the sites. We conceptualize and identify a joint distribution of site-specific direct and indirect effects under the potential outcomes framework. A method-of-moments procedure…

Current practice for conducting power analyses in hierarchical trials using survey based ICC and effect size estimates may be misestimating power because ICCs are not being adjusted to account for treatment effect heterogeneity. Results presented in Table 1 show that the necessary adjustments can be quite large or quite small. Furthermore, power…

To assess the direct and indirect effect of an intervention, multilevel 2-1-1 studies with intervention randomized at the upper (class) level and mediator and outcome measured at the lower (student) level are frequently used in educational research. In such studies, the mediation process may flow through the student-level mediator (the within…

Designs that facilitate inferences concerning both the total and indirect effects of a treatment potentially offer a more holistic description of interventions because they can complement "what works" questions with the comprehensive study of the causal connections implied by substantive theories. Mapping the sensitivity of designs to…