Multivariate analysis of variance (MANOVA) is widely used to test the null hypothesis of equal multivariate means across 2 or more groups. MANOVA rests upon an assumption that error terms are independent of one another, which can be violated if individuals are clustered or nested within groups, such as schools. Ignoring such nesting can result in…

In two-level designs, the total sample is a function of both the number of Level 2 clusters and the average number of Level 1 units per cluster. Traditional multilevel power calculations rely on either the arithmetic average or the harmonic mean when estimating the average number of Level 1 units across clusters of unbalanced size. The current…

Hierarchical data is often observed in education data. Analyzing such data with Multilevel Modeling becomes crucial to understanding the relationship at the individual and group levels. However, one of the most significant problems with this kind of data is small sample sizes and very low Intraclass Correlations. The multivariate Latent Covariate…

Multivariate count data is ubiquitous in many areas of research including the physical, biological, and social sciences. These data are traditionally modeled with the Dirichlet Multinomial distribution (DM). A new, more flexible Dirichlet-Tree Multinomial (DTM) model is gaining in popularity. Here, we consider Bayesian DTM regression models. Our…

Coping with evolution and the changes it brings to the workplace remains a major concern for organizational leaders. This study explores the hotspots, trends, and future directions of the field of organizational unlearning to complement the extant research. A bibliometric analysis based on the literature collected by the Web of Science database…

The clustered observational study (COS) design is the observational study counterpart to the clustered randomized trial. In a COS, a treatment is assigned to intact groups, and all units within the group are exposed to the treatment. However, the treatment is non-randomly assigned. COSs are common in both education and health services research. In…

In this article, we discuss our attempt to teach applied statistics techniques typically taught in advanced courses, such as clustering and principal component analysis, to a non-mathematical educated audience. Considering the negative attitude and inclination toward mathematical disciplines of our students we introduce them to our topics using…

Clustering methods are often used in physics education research (PER) to identify subgroups of individuals within a population who share similar response patterns or characteristics. Among these, k-means (or k-modes, for categorical data) is one of the most commonly used clustering methods in PER. This algorithm, however, is distance-based rather…

Purpose: This article provides a tutorial introduction to ordinal pattern analysis, a statistical analysis method designed to quantify the extent to which hypotheses of relative change across experimental conditions match observed data at the level of individuals. This method may be a useful addition to familiar parametric statistical methods…

Previous studies that examined the associations among bullying experiences, psychological disturbances, and executive functions showed mixed results. They focused on certain subcomponents of the three sets of variables and did not reflect the comprehensive relationship. The present study explored these associations through regularized generalized…

Mixed Membership Models (MMMs) are a popular family of latent structure models for complex multivariate data. Instead of forcing each subject to belong to a single cluster, MMMs incorporate a vector of subject-specific weights characterizing partial membership across clusters. With this flexibility come challenges in uniquely identifying,…

Purpose: This study analyzed segment differences of student preference for video use in lecture classes and university use of video lecture classes. The authors then conducted novel gap analyses to identify gaps between student segments' preferences for videos versus their level of exposure to in-class videos. Multivariate analysis of variance…

This is a study of 12,372 professors in 116 colleges that are the four top US News-ranked colleges in each of 30 states that collect political registration data. We devised the sample to highlight variation in registration arising from individual, college-level, and state-level characteristics. We find an overall Democratic-to-Republican…

Cluster memberships associated with the mediation effect are often changed due to the temporal distance between the cause-and-effect variables in longitudinal data. Nevertheless, current practices in multilevel mediation analysis mostly assume a purely hierarchical data structure. A Monte Carlo simulation study is conducted to examine the…

The process model of vocational identity was well applied in various Western countries to study the vocational identity process and statuses of college students. However, such research is limited in Hong Kong. Moreover, the relation between vocational identity development and academic performance was inconclusive in the literature, and it was also…