Data are everywhere. Data collected from samples are often reported in the form of polls, medical studies, and advertisement information and an understanding of sampling distributions and statistical inference is important for evaluating data-based claims (Bargagliotti et al., 2020). Despite the importance of understanding statistical inference…

In today's era of large-scale data, academic institutions, businesses, and government agencies are increasingly faced with heterogeneous datasets. Consequently, there is a growing need to develop effective methods for extracting meaningful insights from this type of data. Quantile, expectile, and expected shortfall regression methods offer useful…

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…

We consider Bayesian estimation of a hierarchical linear model (HLM) from small sample sizes. The continuous response Y and covariates C are partially observed and assumed missing at random. With C having linear effects, the HLM may be efficiently estimated by available methods. When C includes cluster-level covariates having interactive or other…

This dissertation's idea began with my class notes and questions in the statistics courses I attended in my doctoral program. These notes and questions originally were about the concepts of the bell shape, statistical distribution, and hypothesis testing. They then became my inquiries of p-values because what I learned in the courses about how the…

Online networks, as digital images reflecting every aspects of real world especially under the current context of information technology, have become the most massive and opulent data source these days, where vast amount of information keeps being produced and transmitted. Their rapid expansion in scale and data volume draws wide attention and…

This dissertation is composed of a study of estimation methods in classical and test theories and the elaboration and application of a cluster-robust variance estimator. Variance estimators derived from generalized estimating equations are known to be robust to most covariance structures and are therefore well suited for psychometric analysis of…

This dissertation will look at large scale collaboration through the lens of online communities to answer questions about what makes a collaboration persist. Results address how collaborations attract contributions, behaviors that could give rise to patterns seen in the data, and the properties of collaborations that drive those behaviors. It is…

Student misconceptions have been studied for decades from a curricular/instructional perspective and from the assessment/test level perspective. Numerous misconception assessment tools have been developed in order to measure students' misconceptions relative to the correct content. Often, these tools are used to make a variety of educational…

This thesis examined middle school students' current understanding of variability using a constructed response item assessment question. Variability is an essential concept in the teaching and learning of statistics. However, many students have difficulty with the concept of variability especially when constructing boxplots. Using a framework…

The purpose of this study was to determine if there was a statistically significant difference in the percentage of suspensions and expulsions between African American males and the combination of males of other ethnicities based upon school district settings of city and county in K-12 public school divisions in Region II of Virginia. The…

The ability to classify the political leaning of a large number of articles and items is valuable to both academic research and practical applications. The challenge, though, is not only about developing innovative classification algorithms, which constitutes a "classifier" theme in this thesis, but also about how to define the…

This study aims to evaluate a multidimensional latent trait model to determine how well the model works in various empirical contexts. Contrary to the assumption of these latent trait models that the traits are normally distributed, situations in which the latent trait is not shaped with a normal distribution may occur (Sass et al, 2008; Woods…

There are essential connections between the isoperimetric theory and information theoretic inequalities. In general, the Brunn-Minkowski inequality and the entropy power inequality, as well as the classical isoperimetric inequality and the classical entropy-moment inequality, turn out to be equivalent in some certain sense, respectively. Based on…

Numerous organizations collect and distribute non-aggregate personal data for a variety of different purposes, including demographic and public health research. In these situations, the data distributor is responsible with the protection of the anonymity and personal information of individuals. Microaggregation is one of the most commonly used…