The variance-stabilizing Freeman-Tukey double arcsine transform was originally proposed for inference on single proportions. Subsequently, its use has been suggested in the context of meta-analysis of proportions. While some erratic behavior has been observed previously, here we point out and illustrate general issues of monotonicity and…

Test takers wishing to gain an unfair advantage often share answers with other test takers, either sharing all answers (a full key) or some (a partial key). Detecting key sharing during a tight testing window requires an efficient, easily interpretable, and rich form of analysis that is descriptive and inferential. We introduce a detection method…

The import or force of the result of a statistical test has long been portrayed as consistent with deductive reasoning. The simplest form of deductive argument has a first premise with conditional form, such as p[right arrow]q, which means that "if p is true, then q must be true." Given the first premise, one can either affirm or deny…

Mediation analysis in Single Case Experimental Designs (SCEDs) evaluates intervention mechanisms for individuals. Despite recent methodological developments, no clear guidelines exist for maximizing power to detect the indirect effect in SCEDs. This study compares frequentist and Bayesian methods, determining (1) minimum required sample size to…

The number of meta-analyses of aggregate data has dramatically increased due to the facility of obtaining data from publications and the development of free, easy-to-use, and specialised statistical software. Even when meta-analyses include the same studies, their results may vary owing to different methodological choices. Assessment of the…

In recent years, the growing incidence of blended and online learning has highlighted instructional design concerns, especially STEM instructional design. Existing studies have often adopted observations, questionnaires, or interviews to evaluate STEM instructional design plans. However, there is still a lack of quantitative, measurable, and…

Qualitative thematic analysis is a commonly used and widely applicable form of qualitative analysis, though it can be challenging to implement. Due to its use across research questions, qualitative traditions, and fields, thematic analysis is also prevalent in mixed methods studies. Despite its widespread use, the term "thematic…

Recently, deep learning has become a pervasive tool in prediction problems for structured and/or unstructured big data in various areas including science and engineering. In particular, deep neural network models (i.e. a basic core model of deep learning) can be viewed as an extension of statistical models by going through the incorporation of…

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 consider a class of multiple-group individually-randomized group trials (IRGTs) that introduces a (partially) cross-classified structure in the treatment condition (only). The novel feature of this design is that the nature of the treatment induces a clustering structure that involves two or more non-nested groups among individuals in the…

A simulation study was conducted to examine the efficacy of nine frequently-used HOV tests, including Levene's tests with squared residuals and with absolute residuals, Brown and Forsythe (BF) test, Bootstrap BF test, O'Brien test, Z-variance test, Box-Scheffé (BS) test, Bartlett test, and Pseudo jackknife test under comprehensive simulation…

Latent profile analysis (LPA) identifies heterogeneous subgroups based on continuous indicators that represent different dimensions. It is a common practice to measure each dimension using items, create composite or factor scores for each dimension, and use these scores as indicators of profiles in LPA. In this case, measurement models for…

The use of unidimensional scales that contain both positively and negatively worded items is common in both the educational and psychological fields. However, dimensionality investigations of these instruments often lead to a rejection of the theorized unidimensional model in favor of multidimensional structures, leaving researchers at odds for…

A research question that is of interest across many disciplines is whether and how relationships in a network are related to the attributes of the nodes of the network. In this dissertation, we propose two joint frameworks for modeling the relationship between the network and attributes. In the joint latent space model in Chapter 2, shared latent…

There is increasing interest in using factor scores in structural equation models and there have been numerous methodological papers on the topic. Nevertheless, sum scores, which are computed from adding up item responses, continue to be ubiquitous in practice. It is therefore important to compare simulation results involving factor scores to…