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…

Decomposing variables into between and within components are often required in multilevel analysis. This method of decomposition should not ignore possible unreliability of an observed group mean (i.e., arithmetic mean) that is due to small cluster sizes and can lead to substantially biased estimates. Adjustment procedures that allow unbiased…

Large-scale education data are collected via complex sampling designs that incorporate clustering and unequal probability of selection. Multilevel models are often utilized to account for clustering effects. The probability weighted approach (PWA) has been frequently used to deal with the unequal probability of selection. In this study, we examine…

Lord's Paradox occurs when a continuous covariate is statistically controlled for and the relationship between a continuous outcome and group status indicator changes in both magnitude and direction. This phenomenon poses a challenge to the notion of evidence-based policy, where data are supposed to be self-evident. We examined 50 effect size…

Conventional multilevel modeling works well with purely hierarchical data; however, pure hierarchies rarely exist in real datasets. Applied researchers employ ad hoc procedures to create purely hierarchical data. For example, applied educational researchers either delete mobile participants' data from the analysis or identify the student only with…

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…

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…

Many classroom climate studies suffer from 2 critical problems: They (a) treat climate as a student-level (L1) variable in single-level analyses instead of a classroom-level (L2) construct in multilevel analyses; and (b) rely on manifest-variable models rather than on latent-variable models that control measurement error at L1 and L2, and sampling…