We have expanded Stein's "Sweetness of Aspartame" laboratory project (Stein, P. J. "J. Chem. Educ." 1997, 74, 1112, DOI: 10.1021/ed074p1112) to include extensive use of statistical testing. Students test the statistical significance of a nonzero intercept in a linear regression, bias in comparison to a true value, and…

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…

All of our choices and all that sets us apart are governed by what we can do, what we want to do, and what we know. This dissertation aims to quantify two of these channels to better understand why we differ. The first two chapters focus on what we know and how it shapes societal gaps. The first chapter attacks the question of how much of the gap…

Causal mediation analysis is a popular approach for investigating whether the effect of an exposure on an outcome is through a mediator to better understand the underlying causal mechanism. In recent literature, mediation analysis with multiple mediators has been proposed for continuous and dichotomous outcomes. In contrast, methods for mediation…

The present work focuses on the performance of two types of shrinkage priors--the horseshoe prior and the recently developed regularized horseshoe prior--in the context of inducing sparsity in path analysis and growth curve models. Prior research has shown that these horseshoe priors induce sparsity by at least as much as the "gold…

Teachers need instructionally useful data to make timely and appropriate decisions to meet their students with intensive needs (Filderman et al., 2019). Teachers have still experienced difficulty in instructional decision making in response to students' CBM data (Gesel et al., 2021). This is because data itself that was used for simply determining…

This study explores how blended classroom teaching (the integration of online courses with face-to-face instructions) equalizes educational outcomes across regions. We point out that besides the medium function, ICT can also transmit educational resources across regions, and the resource transmission function facilitates the equalization of…

The main objective of this article is to use the logistic regression model as one of the generalized linear models to determine some factors that influence academic tripping at the University of Tabuk. In this case, student status (tripped, non-tripped) is considered as a binary variable. The data of this article were collected using a survey…

Network meta-analysis has been an essential methodology of systematic reviews for comparative effectiveness research. The restricted maximum likelihood (REML) method is one of the current standard inference methods for multivariate, contrast-based meta-analysis models, but recent studies have revealed the resultant confidence intervals of average…

This article presents generalizations of SIBTEST and crossing-SIBTEST statistics for differential item functioning (DIF) investigations involving more than two groups. After reviewing the original two-group setup for these statistics, a set of multigroup generalizations that support contrast matrices for joint tests of DIF are presented. To…

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…

As data have become more prevalent in academia, industry, and daily life, it is imperative that undergraduate students are equipped with the skills needed to analyze data in the modern environment. In recent years there has been a lot of work innovating introductory statistics courses and developing introductory data science courses; however,…

Many generalization studies in education are typically based on a sample of 30-70 schools while the inference population is at least twenty times larger. This small sample to population size ratio limits the precision of design-based estimators of the population average treatment effect. Prior work has shown the potential of small area estimation…

In education, machine learning (ML), especially deep learning (DL) in recent years, has been extensively used to improve both teaching and learning. Despite the rapid advancement of ML and its application in education, a few challenges remain to be addressed. In this thesis, in particular, we focus on two such challenges: (i) data scarcity and…

This paper presents a tool for creating student models in logistic regression. Creating student models has typically been done by expert selection of the appropriate terms, beginning with models as simple as IRT or AFM but more recently with highly complex models like BestLR. While alternative methods exist to select the appropriate predictors for…