Algorithmic bias is a pressing concern in educational data mining (EDM), as it risks amplifying inequities in learning outcomes. The Area Between ROC Curves (ABROCA) metric is frequently used to measure discrepancies in model performance across demographic groups to quantify overall model fairness. However, its skewed distribution--especially when…

Solving real-life problems through mathematical modeling is one of the aims of modern mathematics curricula. For this reason, prospective mathematics teachers need to acquire modeling skills and use these skills in learning environments in terms of creating rich learning environments. With this study, it is aimed to examine the reflections of…

Basic knowledge of ideas of causal inference can help students to think beyond data, that is, to think more clearly about the data generating process. Especially for (maybe big) observational data, qualitative assumptions are important for the conclusions drawn and interpretation of the quantitative results. Concepts of causal inference can also…

This paper compares the use of confidence intervals (CIs) and a sensitivity analysis called the number needed to disturb (NNTD), in the analysis of research findings expressed as 'effect' sizes. Using 1,000 simulations of randomised trials with up to 1,000 cases in each, the paper shows that both approaches are very similar in outcomes, and each…

Statistical thinking is essential to understanding the nature of scientific results as a consumer. Statistical thinking also facilitates thinking like a scientist. Instead of emphasizing a "correct" procedure for data analysis and its outcome, statistical thinking focuses on the process of data analysis. This article reviews frequentist…

One of the first simulation-based introductory statistics curricula to be developed was the NSF-funded Change Agents for Teaching and Learning Statistics curriculum. True to its name, this curriculum is constantly undergoing change. This article describes the story of the curriculum as it has evolved at the University of Minnesota and offers…

The "Borel" board game consists of a series of experiments involving dice rolls, coin flips, or drawing colored balls from bags. Before each experiment is conducted, each player bets for or bets against a statement regarding the random outcome. We suggest that the collection of "Borel" experiments be used as a resource to…

In this study, it is aimed to investigate the effects of various factors on the performance of the methods used in the determination of differential item functioning (DIF) in the DINA model included in the Cognitive Diagnosis Models. The current study is limited with Logistic Regression and Wald test methods which were used to determine the…

Methods to generate random correlation matrices have been proposed in the literature, but very few instances exist where these correlation matrices are structured or where the statistical properties of the algorithms are known. By relying on the tetrad relation discovered by Spearman and the properties of the beta distribution, an algorithm is…

A formula is derived for a 'two-dice horse race', in which two ordinary dice are thrown repeatedly and each time the sum of the scores determines which horse (numbered 2 to 12) moves forward one space. This paper answers a question posed in a former "Teaching Statistics" article, and demonstrates the value of simulation.

The theoretical reason for the presence of differential item functioning (DIF) is that data are multidimensional and two groups of examinees differ in their underlying ability distribution for the secondary dimension(s). Therefore, the purpose of this study was to determine how much the secondary ability distributions must differ before DIF is…

The negative hypergeometric distribution is often not formally studied in secondary or collegiate statistics in contexts other than drawing cards without replacement. We present a different context with the potential of engaging students in simulating and exploring data.

Using the famous Birthday problem, we present here a practical activity that allows students to perceive the basic reasoning behind simulation and explore its potential. Through a playful approach with probabilities, students are led along a path that illustrates difficulties with intuition and introduces them to theoretical results for sample…

Using simulation-based inference (SBI), such as randomization tests, as the primary vehicle for introducing students to the logic and scope of statistical inference has been advocated with the potential of improving student understanding of statistical inference and the statistical investigative process. Moving beyond the individual class…

This study analyzes the relationship between the use of learning patterns as a grouping criterion to develop learning activities in the 3D simulation environment at University. Participants included 72 Spanish students from the Education and Marketing disciplines. Descriptive statistics and non-parametric tests were conducted. The process was…