Bayesian methods have been said to solve small sample problems in frequentist methods by reflecting prior knowledge in the prior distribution. However, there are dangers in strongly reflecting prior knowledge or situations where much prior knowledge cannot be used. In order to address the issue, in this article, we considered to apply two Bayesian…

Comprehensive evaluation of treatment effects is aided by considerations for moderated effects. In educational research, the combination of natural hierarchical structures and prevalence of group-administered or shared facilitator treatments often produces three-level partially nested data structures. Literature details planning strategies for a…

Sample size determination in multilevel randomized trials (MRTs) and multilevel regression discontinuity designs (MRDDs) can be complicated due to multilevel structure, monetary restrictions, differing marginal costs per treatment and control units, and range restrictions in sample size at one or more levels. These issues have sparked a set of…

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…

Small samples are common in growth models due to financial and logistical difficulties of following people longitudinally. For similar reasons, longitudinal studies often contain missing data. Though full information maximum likelihood (FIML) is popular to accommodate missing data, the limited number of studies in this area have found that FIML…

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…

Measures of variability are successfully used in predictive modeling in research areas outside of education. This study examined how standard deviations can be used to address research questions not easily addressed using traditional measures such as group means based on index variables. Student survey data were obtained from the Organisation for…

Multilevel modeling has grown in use over the years as a way to deal with the nonindependent nature of observations found in clustered data. However, other alternatives to multilevel modeling are available that can account for observations nested within clusters, including the use of Taylor series linearization for variance estimation, the design…

The authors compared the effects of using the true Multilevel Latent Growth Curve Model (MLGCM) with single-level regular and design-based Latent Growth Curve Models (LGCM) with or without the higher-level predictor on various criterion variables for multilevel longitudinal data. They found that random effect estimates were biased when the…

The design of research studies utilizing binary multilevel models must necessarily incorporate knowledge of multiple factors, including estimation method, variance component size, or number of predictors, in addition to sample sizes. This Monte Carlo study examined the performance of random effect binary outcome multilevel models under varying…

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…