In two-level designs, the total sample is a function of both the number of Level 2 clusters and the average number of Level 1 units per cluster. Traditional multilevel power calculations rely on either the arithmetic average or the harmonic mean when estimating the average number of Level 1 units across clusters of unbalanced size. The current…

In cluster randomized evaluations, a treatment or intervention is randomly assigned to a set of clusters each with constituent individual units of observations (e.g., student units that attend schools, which are assigned to treatment). One consideration of these designs is how many units are needed per cluster to achieve adequate statistical…

In cluster randomized evaluations, a treatment or intervention is randomly assigned to a set of clusters each with constituent individual units of observations (e.g., student units that attend schools, which are assigned to treatment). One consideration of these designs is how many units are needed per cluster to achieve adequate statistical…

Power in multilevel models remains an area of interest to both methodologists and substantive researchers. In two-level designs, the total sample is a function of both the number of level-2 (e.g., schools) clusters and the average number of level-1 (e.g., classrooms) units per cluster. Traditional multilevel power calculations rely on either the…

Multilevel modeling (MLM) is a statistical technique for analyzing clustered data. Despite its long history, the technique and accompanying computer programs are rapidly evolving. Given the complexity of multilevel models, it is crucial for researchers to provide complete and transparent descriptions of the data, statistical analyses, and results.…

Multivariate analysis of variance (MANOVA) is a statistical method used to examine group differences on multiple outcomes. This article reports results of a review of MANOVA in gifted education journals between 2011 and 2017 (N = 56). Findings suggest a number of conceptual and procedural misunderstandings about the nature of MANOVA and its…

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…

Multilevel models are an increasingly popular method to analyze data that originate from a clustered or hierarchical structure. To effectively utilize multilevel models, one must have an adequately large number of clusters; otherwise, some model parameters will be estimated with bias. The goals for this paper are to (1) raise awareness of the…

Field experiments in education frequently assign entire groups such as schools to treatment or control conditions. These experiments incorporate sometimes a longitudinal component where for example students are followed over time to assess differences in the average rate of linear change, or rate of acceleration. In this study, we provide methods…

Recent publications have drawn attention to the idea of utilizing prior information about the correlation structure to improve statistical power in cluster randomized experiments. Because power in cluster randomized designs is a function of many different parameters, it has been difficult for applied researchers to discern a simple rule explaining…

Meta-analyses often include studies that report multiple effect sizes based on a common pool of subjects or that report effect sizes from several samples that were treated with very similar research protocols. The inclusion of such studies introduces dependence among the effect size estimates. When the number of studies is large, robust variance…

The Institute of Education Sciences has funded more than 100 experiments to evaluate educational interventions in an effort to generate scientific evidence of program effectiveness on which to base education policy and practice. In general, these studies are designed with the goal of having adequate statistical power to detect the average…

In this article, a 2-way multigroup common factor model (MG-CFM) is presented. The MG-CFM can be used to estimate interaction effects between 2 grouping variables on 1 or more hypothesized latent variables. For testing the significance of such interactions, a likelihood ratio test is presented. In a simulation study, the robustness of the…

In some instances, intentionally or not, study designs are such that there is clustering in one group but not in the other. This paper describes methods for computing effect size estimates and their variances when there is clustering in only one group and the analysis has not taken that clustering into account. The authors provide the effect size…

With research indicating substantial differences among teachers in terms of their effectiveness (Nye, Konstantopoulous, & Hedges, 2004), a major focus of recent research in education has been on improving teacher quality through professional development (Desimone, 2009; Institute of Educations Sciences [IES], 2012; Measures of Effective…