Foundations of statistics research aims to establish fundamental principles guiding inference about populations under uncertainty. It is concerned with the process of learning from observations, notions of uncertainty and induction, and satisfying inferential objectives. The growing interest in predictive methods in high-stakes fields like…

The purpose of this dissertation is to develop principles and strategies for and identify limitations of multisite cluster randomized trials in the context of partially and fully nested designs. In the first study, I develop principles of estimation, sampling variability, and inference for studies that leverage multisite designs within the context…

This dissertation project explores the potential for using an inferential statistics test (t-tests) within an existing writing program assessment design. The purpose of using inferential statistics is to provide several perspectives on a data set collected using the existing assessment design thereby improving what a writing program administrator…

Recent advancements in testing differential item functioning (DIF) have greatly relaxed restrictions made by the conventional multiple group item response theory (IRT) model with respect to the number of grouping variables and the assumption of predefined DIF-free anchor items. The application of the L[subscript 1] penalty in DIF detection has…

Many methods are used to measure interrater reliability for studies where each target receives ratings by a different set of judges. The purpose of this study is to explore the use of hierarchical modeling for estimating interrater reliability using the intraclass correlation coefficient. This study provides a description of how the ICC can be…

One of the most serious forms of cheating occurs when examinees have item preknowledge and prior access to secure test material before taking an exam for the purpose of obtaining an inflated test score. Examinees that cheat and have prior knowledge of test content before testing may have an unfair advantage over examinees that do not cheat. Item…

Categorical data become increasingly ubiquitous in the modern big data era. In this dissertation, we propose novel statistical learning and inference methods for large-scale categorical data, focusing on latent variable models and their applications to psychometrics. In psychometric assessments, the subjects' underlying aptitude often cannot be…

Statistical association is a key facet of statistical literacy: claims based on relationships between variables or ideas rooted in data are found everywhere in media and discourse. A key development in introductory statistics curricula is the use of simulation-based inference, which has shown positive outcomes for students, especially in regards…

Research has indicated that undergraduate students struggle with conceptual understanding of confidence intervals, negatively impacting statistical literacy skills, and advocates have suggested the flipped classroom pedagogy as a potential solution. The purpose of this nonequivalent control group quasi-experimental study was to determine if a…

In this dissertation I argue that truth-conditional semantics for vague predicates, combined with a Bayesian account of statistical inference incorporating knowledge of truth-conditions of utterances, generates false predictions regarding negations and metalinguistic inference. I thus propose a fundamentally probabilistic semantics for vagueness…

Much research in autism spectrum disorders (ASD) has focused on the development of efficacious interventions to address the core deficits of ASD. However, the heterogeneous nature of ASD complicates the development of such interventions. With great heterogeneity in the expression of ASD's core deficits, it is unlikely that there is a one size fits…

Scope ambiguity arises when a sentence contains scope-bearing logical operators like quantifiers and negation (Fox, 2003). For instance, in English, the sentence 'Every horse didn't jump over the fence' can be interpreted as either 'None of the horses jumped over the fence' (surface scope) or 'Not all of the horses jumped over the fence' (inverse…

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…

Are fraternities still relevant to the college student experience? By examining the moral, student, and leadership development of IFC fraternity men, while controlling for institutional and student characteristics, the current study analyzed the roots of the purported value-added nature of fraternities using data from the Multi-Institutional Study…

The development in information science has enabled an explosive growth of data, which attracts more and more researchers to engage in the field of big data analytics. Noticeably, in many real-world applications, large amounts of data are imbalanced data since the events of interests occur infrequently. Classification of imbalanced data is an…