Prior research has suggested that clustered regression discontinuity designs are a formidable alternative to cluster randomized designs because they provide targeted treatment assignment while maintaining a high-quality basis for inferences on local treatment effects. However, methods for the design and analysis of clustered regression…

A simulation study was conducted to examine the efficacy of nine frequently-used HOV tests, including Levene's tests with squared residuals and with absolute residuals, Brown and Forsythe (BF) test, Bootstrap BF test, O'Brien test, Z-variance test, Box-Scheffé (BS) test, Bartlett test, and Pseudo jackknife test under comprehensive simulation…

Optimal design of multisite randomized trials leverages sampling costs to optimize sampling ratios and ultimately identify more efficient and powerful designs. Past implementations of the optimal design framework have assumed that costs of sampling units are equal across treatment conditions. In this study, we developed a more flexible optimal…

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…

Single subject (SS) designs are popular in educational and psychological research. There exist several statistical techniques designed to analyze such data and to address the question of whether an intervention has the desired impact. Recently, researchers have suggested that generalized additive models (GAMs) might be useful for modeling…

This article discusses the sample size requirements for the interaction, row, and column effects, respectively, by forming a linear contrast for a 2×2 factorial design for fixed-effects heterogeneous analysis of variance. The proposed method uses the Welch t test and its corresponding degrees of freedom to calculate the final sample size in a…

Structured means analysis is a very useful approach for testing hypotheses about population means on latent constructs. In such models, a z test is most commonly used for testing the statistical significance of the relevant parameter estimates or of the differences between parameter estimates, where a z value is computed based on the asymptotic…

The authors performed a Monte Carlo simulation to empirically investigate the robustness and power of 4 methods in testing mean differences for 2 independent groups under conditions in which 2 populations may not demonstrate the same pattern of nonnormality. The approaches considered were the t test, Wilcoxon rank-sum test, Welch-James test with…

Increasing the correlation between the independent variable and the mediator ("a" coefficient) increases the effect size ("ab") for mediation analysis; however, increasing a by definition increases collinearity in mediation models. As a result, the standard error of product tests increase. The variance inflation caused by…

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…

A multilevel meta-analysis can combine the results of several single-subject experimental design studies. However, the estimated effects are biased if the effect sizes are standardized and the number of measurement occasions is small. In this study, the authors investigated 4 approaches to correct for this bias. First, the standardized effect…

The authors examined 2 approaches for determining the required sample size of Welch's test for detecting equality of means when the greatest difference between any 2 group means is given. It is shown that the actual power obtained with the sample size of the suggested approach is consistently at least as great as the nominal power. However, the…

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…

Formulas to determine the necessary sample sizes for parametric tests of group comparisons are available from several sources and appropriate when population distributions are normal. However, in the context of nonnormal population distributions, researchers recommend Yuen's trimmed mean test, but formulas to determine sample sizes have not been…

There is general agreement that meta-analysis is an important tool for synthesizing study results in quantitative educational research. Yet, a shared feature of many meta-analyses is a failure to report sufficient information for readers to fully judge the reported findings, such as the populations to which generalizations are to be made,…