In educational and psychological research, we are often interested in discrete latent states of individuals responding to an assessment (e.g., proficiency or non-proficiency on educational standards, the presence or absence of a psychological disorder). Diagnostic classification models (DCMs; also called cognitive diagnostic models [CDMs]) are a…

The Poisson distribution describes the probability of a certain number of events occurring in an interval of time when the occurrence of the individual events is independent of one another and the events occur with a fixed mean rate. Probably the best-known example of the Poisson distribution in the physics curriculum is the temporal distribution…

The thriving developer community has a significant impact on the widespread use of R software. To better understand this community, we conducted a study analyzing all R packages available on CRAN. We identified the most popular topics of R packages by text mining the package descriptions. Additionally, using network centrality measures, we…

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…

Educators who teach programming subjects are often wondering "which programming language should I teach first?" The debate behind this question has a long history and coming up with a definite answer to this question would be farfetched. Nonetheless, several efforts can be identified in the literature wherein pros and cons of mainstream…

A Machine Learning framework for predicting enrollment is proposed. The framework consists of Amazon Web Services SageMaker together with standard Python tools for data analytics, including Pandas, NumPy, MatPlotLib, and ScikitLearn. The tools are deployed with Jupyter Notebooks running on AWS SageMaker. Based on three years of enrollment history,…

The Schwarz or Bayesian information criterion (BIC) is one of the most widely used tools for model comparison in social science research. The BIC, however, is not suitable for evaluating models with order constraints on the parameters of interest. This article explores two extensions of the BIC for evaluating order-constrained models, one where a…

Survival analysis is an important analytic method in the social and medical sciences. Also known under the name time-to-event analysis, this method provides parameter estimation and model fitting commonly conducted via maximum-likelihood. Bayesian survival analysis offers multiple advantages over the frequentist approach for measurement…

In this article, we outline several activities revolving around soccer players who participated in the 2018 FIFA World Cup and 2019 FIFA Women's World Cup. Classroom activities are described from different perspectives, useful for a range of different statistics courses. In a first semester probability theory course, students investigate the…

This paper describes an investigation looking at the underlying mathematics of poker machines. The aim of the investigation is for students to get an appreciation of how poker machines are designed to ensure that in the long-term players will inevitably lose when playing. The first part of this paper describes how students can model a simple poker…

Simulation modeling is an effective tool for solving problems that cannot be explained analytically or when data cannot be collected. This is done by simulating the observed behavior of a problem under study using a computer program. In math education, this can develop knowledge and fundamental competencies of simulation modeling at a higher level…

R and Python are commonly used software languages for data analytics. Using these languages as the course software for the introductory course gives students practical skills for applying statistical concepts to data analysis. However, the reliance upon the command line is perceived by the typical nontechnical introductory student as sufficiently…

Stan is a probabilistic programming language for specifying statistical models. A Stan program imperatively defines a log probability function over parameters conditioned on specified data and constants. As of version 2.14.0, Stan provides full Bayesian inference for continuous-variable models through Markov chain Monte Carlo methods such as the…

Stan is a free and open-source C++ program that performs Bayesian inference or optimization for arbitrary user-specified models and can be called from the command line, R, Python, Matlab, or Julia and has great promise for fitting large and complex statistical models in many areas of application. We discuss Stan from users' and developers'…

In this paper, we describe a tool coined as artificial intelligence-based student learning evaluation tool (AISLE). The main purpose of this tool is to improve the use of artificial intelligence techniques in evaluating a student's understanding of a particular topic of study using concept maps. Here, we calculate the probability distribution of…