Simulation studies involving mixture models inevitably aggregate parameter estimates and other output across numerous replications. A primary issue that arises in these methodological investigations is label switching. The current study compares several label switching corrections that are commonly used when dealing with mixture models. A growth…

Count responses with grouping and right censoring have long been used in surveys to study a variety of behaviors, status, and attitudes. Yet grouping or right-censoring decisions of count responses still rely on arbitrary choices made by researchers. We develop a new method for evaluating grouping and right-censoring decisions of count responses…

The purpose of this study was to write programs to define sampling sizes and observation units by probability sampling methods and to provide an idea for software developers. The algorithms of the programs were written in Python 3. The programs may be run by double-clicking on the Windows operating system or by the command prompt of the DOS…

This direct replication study compared the use of dichotomized likelihood ratios and interval likelihood ratios, derived using a prior sample of students, for predicting math risk in middle school. Data from the prior year state test and the Measures of Academic Progress were analyzed to evaluate differences in the efficiency and diagnostic…

Intelligent tutoring systems adapt the curriculum to the needs of the individual student. Therefore, an accurate representation and prediction of student knowledge is essential. Bayesian Knowledge Tracing (BKT) is a popular approach for student modeling. The structure of BKT models, however, makes it impossible to represent the hierarchy and…

Stan is a new Bayesian statistical software program that implements the powerful and efficient Hamiltonian Monte Carlo (HMC) algorithm. To date there is not a source that systematically provides Stan code for various item response theory (IRT) models. This article provides Stan code for three representative IRT models, including the…

The omega (?) statistic is reputed to be one of the best indices for detecting answer copying on multiple choice tests, but its performance relies on the accurate estimation of copier ability, which is challenging because responses from the copiers may have been contaminated. We propose an algorithm that aims to identify and delete the suspected…

Students of all ages face severe conceptual difficulties regarding key aspects of evolution-- the central, unifying, and overarching theme in biology. Aspects strongly related to abstract "threshold" concepts like randomness and probability appear to pose particular difficulties. A further problem is the lack of an appropriate instrument…

Instead of reserving the study of probability and statistics for special fourth-year high school courses, the Common Core State Standards for Mathematics (CCSSM) takes a "statistics for all" approach. The standards recommend that students in grades 6-8 learn to summarize and describe data distributions, understand probability, draw…

As adaptive tutoring systems grow increasingly popular for the completion of classwork and homework, it is crucial to assess the manner in which students are scored within these platforms. The majority of systems, including ASSISTments, return the binary correctness of a student's first attempt at solving each problem. Yet for many teachers,…

This study is motivated by the desire to address some of the enormous challenges faced by the students as well as the lecturer in fulfilling their respective expectations and duties demanded by the process of learning--teaching of mathematics and statistics within the framework of the constraining schedules laid down by the academic institutions…

A general program for item-response analysis is described that uses the stabilized Newton-Raphson algorithm. This program is written to be compliant with Fortran 2003 standards and is sufficiently general to handle independent variables, multidimensional ability parameters, and matrix sampling. The ability variables may be either polytomous or…

This dissertation is a compilation of several studies that are united by their relevance to probabilistic judgment aggregation. In the face of complex and uncertain events, panels of judges are frequently consulted to provide probabilistic forecasts, and aggregation of such estimates in groups often yield better results than could have been made…

The area of statistics is one in which teachers may be encouraged to make important links to other curriculum areas and social issues. Statistical literacy is a key component of being numerate and living as an informed citizen. The teaching of statistics provides an opportunity to inform and educate students about social issues and moral…

Survey sampling is fundamentally an applied field. The goal in this book is to put an array of tools at the fingertips of practitioners by explaining approaches long used by survey statisticians, illustrating how existing software can be used to solve survey problems, and developing some specialized software where needed. This book serves at least…