As a measure of heterogeneity in meta-analysis, the coefficient of variation (CV) has been recently considered, providing researchers with a complement to the very popular I[superscript 2] measure. While I[superscript 2] measures the proportion of total variance that is due to variance of the random effects, the CV is the ratio of the standard…

This study demonstrates how to evaluate a university-wide online course designed to support student transition into university by using Propensity Score Matching (PSM) and Doubly Robust Estimation (DRE). Using data from seven academic years, from 2016/17 to 2022/23, with more than 28,000 students, we examine whether enrolment in this optional…

This article presents methods for using extant data to improve the properties of estimators of the standardized mean difference (SMD) effect size. Because samples recruited into education research studies are often more homogeneous than the populations of policy interest, the variation in educational outcomes can be smaller in these samples than…

We study the external validity of instrumental variable estimation. The key assumption we impose for external validity is conditional external unconfoundedness among compliers, which means that the treatment effect and target selection are independent among compliers conditional on covariates. We study this assumption with a case study about the…

In this article we find the thermodynamics of some large N particles systems and some small N particles classical systems using micro canonical ensemble. Small N particle systems are seldom done in textbooks, since statistical mechanics(SM) systems work for large N systems. We show that small N systems will help the students to get an insight…

We propose new ways of robustifying goodness-of-fit tests for structural equation modeling under non-normality. These test statistics have limit distributions characterized by eigenvalues whose estimates are highly unstable and biased in known directions. To take this into account, we design model-based trend predictions to approximate the…

There is a longstanding debate on whether the analysis of covariance (ANCOVA) or the change score approach is more appropriate when analyzing non-experimental longitudinal data. In this article, we use a structural modeling perspective to clarify that the ANCOVA approach is based on the assumption that all relevant covariates are measured (i.e.,…

Objective: The current math course-taking plan for U.S. high school students is not optimized for all, with advanced math course participation skewed toward White and Asian students and varying across schools due to resources and policies (Dalton et al., 2007; Byun et al., 2015). These disparities widen achievement gaps and reduce STEM diversity.…

How can we measure the resource mobilization (RM) efforts of social movements on Twitter? In this article, we create the first ever measure of social movements' RM efforts on a social media platform. To this aim, we create a four-conditional lexicon that can parse through tweets and identify those concerned with RM. We also create a simple RM…

This article is concerned with a subset of numerically stable and scalable algorithms useful to support computationally complex psychometric models in the era of machine learning and massive data. The subset selected here is a core set of numerical methods that should be familiar to computational psychometricians and considers whitening transforms…

A reference interval, or an interval in which a prespecified proportion of measurements from a healthy population are expected to fall, is used to determine whether a person's measurement is typical of a healthy individual. For a specific biomarker, multiple published studies may provide data collected from healthy participants. A reference…

Over the past decade, statisticians have developed methods to improve generalizations from nonrandom samples using propensity score methods. While these methods contribute to generalization research, their effectiveness is limited by small sample sizes. Small area estimation is a class of model-based methods that address the imprecision due to…

To present time-varying evidence, cumulative meta-analysis (CMA) updates results of previous meta-analyses to incorporate new study results. We investigate the properties of CMA, suggest possible improvements and provide the first in-depth simulation study of the use of CMA and CUSUM methods for detection of temporal trends in random-effects…

Random encouragement designs evaluate treatments that aim to increase participation in a program or activity. These randomized controlled trials (RCTs) can also assess the mediated effects of participation itself on longer term outcomes using a complier average causal effect (CACE) estimation framework. This article considers power analysis…

Multisite cluster randomized trials (MCRTs), in which, the intermediate-level clusters (e.g., classrooms) are randomly assigned to the treatment or control condition within each site (e.g., school), are among the most commonly used experimental designs across a broad range of disciplines. MCRTs often align with the theory that programs are…