Simulation studies are the basic tools of quantitative methodologists used to obtain empirical solutions to statistical problems that may be impossible to derive through direct mathematical computations. The successful execution of many simulation studies relies on the accurate generation of correlated multivariate data that adhere to a particular…

Algebra has been identified as a gatekeeper to careers in STEM, but little research exists on how algebra appears for practitioners in the workplace. Surveys and interviews were conducted with 77 STEM practitioners from a variety of fields, examining how they reported using algebraic functions in their work. Survey and interview reports suggest…

When reporting the results of clinical studies, some researchers may choose the five-number summary (including the sample median, the first and third quartiles, and the minimum and maximum values) rather than the sample mean and standard deviation (SD), particularly for skewed data. For these studies, when included in a meta-analysis, it is often…

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.

This article offers some less-than-rigorous explanations for the notion of degrees of freedom, and for the particular formulae to be used when computing those values.

This article advocates that introductory statistics be taught by basing all calculations on a single simple margin-of-error formula and deriving all of the standard introductory statistical concepts (confidence intervals, significance tests, comparisons of means and proportions, etc) from that one formula. It is argued that this approach will…

Probability and independence are difficult concepts, as they require the coordination of multiple ideas. This qualitative research study used clinical interviews to understand how three undergraduate students conceptualize probability and probabilistic independence within the theoretical framework of APOS theory. One student's reasoning was…

Learning by invention is an alternative approach to teaching statistics where students are tasked with attempting to solve a problem before being taught the canonical formula for solving it, often resulting in increased understanding of material compared with traditional instruction. The first study, conducted in a college statistics classroom…