A single discrete random variable is depicted by a stick diagram, a 2D picture. Naturally, to visualize a bivariate discrete distribution, one can use a bivariate stick diagram, a 3D picture. Unfortunately, many students have difficulty understanding and processing 3D pictures. Therefore, we construct an alternative 2D disc plot to depict the…

Item factor analysis (IFA), also known as Multidimensional Item Response Theory (MIRT), is a general framework for specifying the functional relationship between a respondent's multiple latent traits and their response to assessment items. The key element in MIRT is the relationship between the items and the latent traits, so-called item factor…

The treatment of kurtosis in textbooks is both sparse and contradictory with applications rarely discussed. To address this, an easily understood definition of kurtosis is introduced and important applications are demonstrated. Two different approaches to teaching kurtosis are presented based on a financial application.

Statisticians have made great progress in creating methods that reduce our reliance on parametric assumptions. However this explosion in research has resulted in a breadth of inferential strategies that both create opportunities for more reliable inference as well as complicate the choices that an applied researcher has to make and defend.…

The sample mean is sometimes depicted as a fulcrum placed under the Dot plot. We provide an alternative geometric visualization of the sample mean using the empirical cumulative distribution function or the cumulative histogram data.

Background: Despite the increasing need for STEM skills, to date, the connection between STEM subject choices and their impact on students' educational pathways has not been widely studied. Focusing on the mathematics choice (basic/advanced/no mathematics), a large register dataset that covered students admitted to Finnish universities during…

The study explores the development of 11-year-old students' informal inference about random bunny hops through student talk and use of computer simulation tools. Our aim in this paper is to draw on dialogic theory to explain how students make shifts in perspective, from intuition-based reasoning to more powerful, formal ways of using probabilistic…