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…

The purpose of this two-part study is to evaluate methods for multiple group analysis when the comparison group is at the within level with multilevel data, using a multilevel factor mixture model (ML FMM) and a multilevel multiple-indicators multiple-causes (ML MIMIC) model. The performance of these methods was evaluated integrally by a series of…

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…

The Bayesian information criterion (BIC) can be useful for model selection within multilevel modeling studies. However, the formula for BIC requires a value for N, which is unclear in multilevel models, since N is observed in at least two levels. The present study uses simulated data to evaluate the rate of false positives and power when using a…

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…

Education experiments frequently assign students to treatment or control conditions within schools. Longitudinal components added in these studies (e.g., students followed over time) allow researchers to assess treatment effects in average rates of change (e.g., linear or quadratic). We provide methods for a priori power analysis in three-level…

The use of advanced quantitative methods within mixed methods research has been investigated in a limited capacity. In particular, hierarchical linear models are a popular approach to account for multilevel data, such as students within schools, but its use and value as the quantitative strand in a mixed methods study remains unknown. This article…

Multilevel data are a reality for many disciplines. Currently, although multiple options exist for the treatment of multilevel data, most disciplines strictly adhere to one method for multilevel data regardless of the specific research design circumstances. The purpose of this Monte Carlo simulation study is to compare several methods for the…

In multilevel multiple-indicator multiple-cause (MIMIC) models, covariates can interact at the within level, at the between level, or across levels. This study examines the performance of multilevel MIMIC models in estimating and detecting the interaction effect of two covariates through a simulation and provides an empirical demonstration of…

An important concern when planning research studies is to obtain maximum precision of an estimate of a treatment effect given a budget constraint. When research designs have a "multilevel" or "hierarchical" structure changes in sample size at different levels of the design will impact precision differently. Furthermore, there…

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…

The hierarchical network model (HNM) is a framework introduced by Sweet, Thomas, and Junker for modeling interventions and other covariate effects on ensembles of social networks, such as what would be found in randomized controlled trials in education research. In this article, we develop calculations for the power to detect an intervention…