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Multisite cluster randomized trials (MCRTs), in which, the intermediate-level clusters (e.g., classrooms) are randomly assigned to the treatment or control condition within each site (e.g., school), are among the most commonly used experimental designs across a broad range of disciplines. MCRTs often align with the theory that programs are delivered at a cluster-level (e.g., teacher professional development) and provide opportunities to explore treatment effect heterogeneity across sites. In designing experimental studies, a critical step is the statistical power analysis and sample size determination. However, the statistical tools for power analysis of moderator effects in three-level MCRTs are not available. In this study, we derived formulas for calculating the statistical power and the minimum detectable effect size difference (MDESD) with confidence intervals for investigating the effects of various moderators in three-level MCRTs. We considered the levels of the moderators (level-1, −2, and −3), the scales of the moderators (binary and continuous), and random and nonrandomly varying slopes of the (moderated) treatment effects. We validated our formulas through Monte Carlo simulations. Finally, we conclude with directions for future work. [ABSTRACT FROM AUTHOR]

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 develops power computation formulas and statistical software to help researchers plan two- and three-level CRCETs. We illustrate the application of our formulas and software for the designs of CRCETs and discuss the influence of sample size, nesting effects, covariates, and the covariance between cost and effectiveness measures on the statistical power of cost-effectiveness estimates. [ABSTRACT FROM AUTHOR]

As a result of the evidence-based decision-making movement, the number of randomized trials evaluating educational programs and curricula has increased dramatically over the past 20 years. Policy makers and practitioners are encouraged to use the results of these trials to inform their decision making in schools and school districts. At the same time, however, little is known about the schools taking part in these randomized trials, both regarding how and why they were recruited and how they compare to populations in need of research. In this article, we report on a study of 37 cluster randomized trials funded by the Institute of Education Sciences between 2011 and 2015. Principal investigators of these grants were interviewed regarding the recruitment process and practices. Additionally, data on the schools included in 34 of these studies were analyzed to determine the general demographics of schools included in funded research, as well as how these samples compare to important policy relevant populations. We show that the types of schools included in research differ in a variety of ways from these populations. Large schools from large school districts in urban areas were overrepresented, whereas schools from small school districts in rural areas and towns are underrepresented. The article concludes with a discussion of how recruitment practices might be improved in order to meet the goals of the evidence-based decision-making movement. [ABSTRACT FROM AUTHOR]

Over the past 15 years, we have seen an increase in the use of cluster randomized trials (CRTs) to test the efficacy of educational interventions. These studies are often designed with the goal of determining whether a program works, or answering the what works question. Recently, the goals of these studies expanded to include for whom and under what conditions an intervention is effective. In this study, we examine the capacity of a set of CRTs to provide rigorous evidence about for whom and under what conditions an intervention is effective. The findings suggest that studies are more likely to be designed with the capacity to detect potentially meaningful individual-level moderator effects, for example, gender, than cluster-level moderator effects, for example, school type. [ABSTRACT FROM AUTHOR]

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 circumstances an intervention works. Furthermore, the researchers are interested in understanding and interpreting variability in treatment effects through moderation analysis as an approach to exploring the sources of the treatment effect variability. This study develops formulas for power analyses to detect the moderator effects in designing three-level cluster randomized trials (CRTs). We develop the statistical formulas for calculating statistical power, minimum detectable effect size difference, and 95% confidence intervals for cluster or cross-level moderation, nonrandomly varying or random slopes, binary or continuous moderators, and designs with or without covariates. We demonstrate how the calculations can be used in the planning phase of three-level CRTs using the software PowerUp!-Moderator. [ABSTRACT FROM AUTHOR]

We develop a theoretical and empirical basis for the design of teacher professional development studies. We build on previous work by (a) developing estimates of intraclass correlation coefficients for teacher outcomes using two- and three-level data structures, (b) developing estimates of the variance explained by covariates, and (c) modifying the conventional optimal design framework to include differential covariate costs so as to capture the point at which the cost of collecting a covariate overtakes the reduction in variance it supplies. We illustrate the use of these estimates to explore the absolute and relative sensitivity of multilevel designs in teacher professional development studies. The results from these analyses are intended to guide researchers in making more-informed decisions about the tradeoffs and considerations involved in selecting study designs for assessing the impacts of professional development programs. [ABSTRACT FROM PUBLISHER]

Recently, there has been an increase in the number of cluster randomized trials (CRTs) to evaluate the impact of educational programs and interventions. These studies are often powered for the main effect of treatment to address the “what works” question. However, program effects may vary by individual characteristics or by context, making it important to also consider power to detect moderator effects. This article presents a framework for calculating statistical power for moderator effects at all levels for two- and three-level CRTs. Annotated R code is included to make the calculations accessible to researchers and increase the regularity in which a priori power analyses for moderator effects in CRTs are conducted. [ABSTRACT FROM AUTHOR]

This article examines the statistical precision of cluster randomized trials (CRTs) funded by the Institute of Education Sciences (IES). Specifically, it compares the total number of clusters randomized and the minimum detectable effect size (MDES) of two sets of studies, those funded in the early years of IES (2002–2004) and those funded in the recent years (2011–2013). Overall, the average precision in terms of MDES of studies in the recent cohort was more than double that of the early cohort (i.e. 0.48 compared to 0.23). The findings suggest a consistent and substantial increase in the precision of CRTs funded by IES in the past decade which is a critical step towards designing studies that have the potential to yield high-quality evidence about the effectiveness of educational interventions. [ABSTRACT FROM PUBLISHER]