Two- and three-level designs in educational and psychological research can involve entire populations of Level-3 and possibly Level-2 units, such as schools and educational districts nested within a given state, or neighborhoods and counties in a state. Such a design is of increasing relevance in empirical research owing to the growing popularity…

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…

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…

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…

Researchers in the field of early adolescence interested in quantifying the environmental influences on a response variable of interest over time would use cluster sampling (i.e., obtaining repeated measures from students nested within classrooms and/or schools) to obtain the needed sample size. The resulting longitudinal data would be nested at…

Randomized experiments are generally considered to provide the strongest basis for causal inferences about cause and effect. Consequently randomized field trials have been increasingly used to evaluate the effects of education interventions, products, and services. Populations of interest in education are often hierarchically structured (such as…

Numerous studies have suggested that academic stress has negative impact on adolescents' psychological function, few of those studies, however, considered whether and how the impact of stress on adolescents' emotional states is moderated by corresponding regulation. This study aimed to examine the fluctuation of emotional states before and after…

Cluster randomized experiments are ubiquitous in modern education research. Although a variety of modeling approaches are used to analyze these data, perhaps the most common methodology is a normal mixed effects model where some effects, such as the treatment effect, are regarded as fixed, and others, such as the effect of group random assignment…

This article presents 3 standardized effect size measures to use when sharing results of an analysis of mediation of treatment effects for cluster-randomized trials. The authors discuss 3 examples of mediation analysis (upper-level mediation, cross-level mediation, and cross-level mediation with a contextual effect) with demonstration of the…

Mind wandering--mentation unrelated to one's current activity and surroundings--is a ubiquitous phenomenon, but seemingly competing ideas have been proposed regarding its relation to executive cognitive processes. The control-failure hypothesis postulates that executive processes prevent mind wandering, whereas the global availability hypothesis…

Educational researchers commonly use the rule of thumb of "design effect smaller than 2" as the justification of not accounting for the multilevel or clustered structure in their data. The rule, however, has not yet been systematically studied in previous research. In the present study, we generated data from three different models…