Take a family of independent events. If some of these events, or all of them, are replaced by their complements, then independence still holds. This fact, which is agreed upon by the members of the statistical/probability communities, is tremendously well known, is fairly intuitive and has always been frequently used for easing probability…

Refined tracking allows students and teachers to more accurately understand students' learning growth. To provide refined learning tracking with longitudinal diagnostic assessment, this article proposed a new model by incorporating probabilistic logic into longitudinal diagnostic modeling. Specifically, probabilistic attributes were used instead…

Common response-time-based approaches for non-effortful response behavior (NRB) in educational achievement tests filter responses that are associated with response times below some threshold. These approaches are, however, limited in that they require a binary decision on whether a response is classified as stemming from NRB; thus ignoring…

Involuntary musical imagery (INMI; more commonly known as "earworms" or having a song "stuck in your head") is a common musical phenomenon and one of the most salient examples of spontaneous cognition. Despite the ubiquitous nature of INMI in the general population, functional roles of INMI remain to be fully established and…

Background: We examined trends in mental health service utilization before, during, and in the immediate return to in-person learning throughout the COVID-19 pandemic. Methods: Retrospective chart review was assessed for changes in odds of any visit being a mental health encounter from five school-based health centers from the 2018-2019 to the…

Data visualization is an important tool for communicating research results. This manuscript discusses a method that instructors can use to introduce political science students to visualizations and discusses strategies that instructors can share with students about how to create high-quality visualizations. These strategies can help students make…

Bullying is a problem that affects children and teenagers around the world and its repercussions can endure throughout adult life. The main objective of this research is to study the incidence of bullying on the academic performance of students in schools in the Madrid Region. The databases used are those of Competency Tests, a census evaluation…

This dissertation measures and describes the factors that impact doctoral student persistence. Using a mixed methods cases study design, I analyzed institutional student record data, survey data on caregiving responsibilities, and data from semi-structured interviews with PhD students at a STEM-focused, public research university in the American…

A design experiment where students in Grade 5 (11-12 years old) play the Color Run game constitutes the context for investigating how students can be introduced to informal hypothesis testing. The result outlines a three-step hypothetical learning trajectory on informal hypothesis testing. In the first step, students came to favor sample space…

Problem-based learning (PBL) has been widely applied as an alternative to improve learning outcomes, but it is still little studied in the context of the probability theory course. This study described how implementing the PBL model improves students' problem-solving and critical thinking skills in probability theory course and evaluates its…

Mental model (Johnson-Laird, 2001) and probabilistic theories (Oaksford & Chater, 2009) claim to provide distinct explanations of human reasoning. However, the dual strategy model of reasoning suggests that this distinction corresponds to different reasoning strategies, termed "counterexample" and "statistical,"…

The typical collegiate introductory statistics course poses significant challenges for students. Many do not fully comprehend key course skills, and it is common for students to exit the class with a neutral or negative attitude toward statistics. To measure the impact of using relevant contextual examples as an instructional strategy during a…

Objectives: To examine the discrepancy between 'told' and screened blood pressure (BP) category, and the association between body composition and told BP category. Methods: Between 08/2019-03/2020 college students (n = 1057) were asked what category they had previously been told their BP falls into prior to having their BP and body composition…

Newly precise evidence of the trajectory of top incomes in the United States and around the world relies on shares and ratios, prompting new inquiry into their properties as inequality measures. Current evidence suggests a mathematical link between top shares and the Gini coefficient and empirical links extending as well to the Atkinson measure.…

The present study replicated and extended previous research by exploring the extent to which rules altered participants' engagement in risky betting in an electronic blackjack game. A multiple-baseline across-participants design with predetermined phase changes was used to assess 4 recreational gamblers' betting patterns in blackjack across 3…