Popular item response theory (IRT) models are considered complex, mainly due to the inclusion of a random factor variable (latent variable). The random factor variable represents the incidental parameter problem since the number of parameters increases when including data of new persons. Therefore, IRT models require a specific estimation method…

Van der Linden's hierarchical model for responses and response times can be used in order to infer the ability and mental speed of test takers from their responses and response times in an educational test. A standard approach for this is maximum likelihood estimation. In real-world applications, the data of some test takers might be partly…

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 is the third in a series of articles describing CODAP and where it might be used to address content in the "Australian Curriculum: Mathematics" v9.0 (ACARA, 2022). We've talked before about model-ling and about statistics; this time, we'll talk about exploring probability using CODAP. As before, we have also prepared online pages…

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…

Reference intervals, or reference ranges, aid medical decision-making by containing a pre-specified proportion (e.g., 95%) of the measurements in a representative healthy population. We recently proposed three approaches for estimating a reference interval from a meta-analysis based on a random effects model: a frequentist approach, a Bayesian…

Interactive web-based applets have proven effective in teaching statistics. This article presents new implementations of web-based applets primarily targeting a traditional introductory statistics course in two particular areas: (a) using real-time response data to engage students in simulations and (b) generating randomized datasets for…

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…

Conventionally, regression discontinuity analysis contrasts a univariate regression's limits as its independent variable, "R," approaches a cut point, "c," from either side. Alternative methods target the average treatment effect in a small region around "c," at the cost of an assumption that treatment assignment,…

Data Analytics has grown dramatically in importance and in the level of business deployments in recent years. It is used across most functional areas and applications, some of the latter including market campaigns, detecting fraud, determining credit, identifying assembly line defects, health services and many others. Indeed, the realm of…

In the classroom, we traditionally visualize inferential concepts using static graphics or interactive apps. For example, there is a long history of using apps to visualize sampling distributions. The lineup protocol for visual inference is a recent development in statistical graphics that has created an opportunity to build student understanding.…

The analysis of cross-lagged relationships is a popular approach in prevention research to explore the dynamics between constructs over time. However, a limitation of commonly used cross-lagged models is the requirement of equally spaced measurement occasions that prevents the usage of flexible longitudinal designs and complicates cross-study…

We designed an asynchronous undergraduate introductory statistics course that focuses on simulation-based inference at the University of Nebraska-Lincoln. In this article, we describe the process we used to design the course and the structure of the course. We also discuss feedback and comments we received from students on the course evaluations,…

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…

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.