This manuscript discusses the common confusion between the terms probability and odds. To emphasize the importance and responsibility of being meticulous in the dissemination of information and knowledge, this manuscript reveals five cases of sources of inaccurate statistical language imbedded in the dissemination of information to the general…

Bayesian methodology continues to be widely used in statistical applications. As a result, it is increasingly important to introduce students to Bayesian thinking at early stages in their mathematics and statistics education. While many students in upper level probability courses can recite the differences in the Frequentist and Bayesian…

In this article, I introduce a novel applet ("module") for exploring probability distributions, their samples, and various related statistical concepts. The module is primarily designed to be used by the instructor in the introductory course, but it can be used far beyond it as well. It is a free, cross-platform, stand-alone interactive…

We describe a web-based interactive graphic that can be used as a resource in introductory classes in mathematical statistics. This interactive graphic presents 76 common univariate distributions and gives details on (a) various features of the distribution such as the functional form of the probability density function and cumulative distribution…

For many students meeting, say, the gamma distribution for the first time, it may well turn out to be a rather fruitless encounter unless they are immediately able to see an application of this probability model to some real-life situation. With this in mind, we pose here an appealing problem that can be used as the basis for a workshop activity…

Understanding counting rules is challenging for students; in particular, they struggle with determining when and how to implement combinations, permutations, and the multiplication rule as tools for counting large sets and computing probability. We present an activity--using ideas from the games of poker and pinochle--designed to help students…

This article describes a probability project used in an upper division, one-semester probability course with third-semester calculus and linear algebra prerequisites. The student learning outcome focused on developing the skills necessary for approaching project-sized math/stat application problems. These skills include appropriately defining…

Mike Shaughnessy is Professor Emeritus of Mathematics and Statistics at Portland State University in Oregon. He served as co-chair for the Board for the Special Interest Group for Research in Mathematics Education of the American Educational Research Association from 2005-2007. A member of the Board of Directors of the National Council of Teachers…

The "Price Is Right" ("TPIR") provides a wealth of material for studying statistics at various levels of mathematical sophistication. The authors have used elements of this show to motivate students from undergraduate probability and statistics courses to graduate level executive management courses. The material consistently generates a high…

This paper describes three spreadsheet exercises demonstrating the nature and frequency of type I errors using random number generation. The exercises are designed specifically to address issues related to testing multiple relations using correlation (Demonstration I), t tests varying in sample size (Demonstration II) and multiple comparisons…

The classroom activity described here allows mathematically mature students to explore the role of mean, median and mode in a decision-making environment. While students discover the importance of choosing a measure of central tendency, their understanding of probability distributions, maximization, and prediction is reinforced through active…

Inspired by the research of Reading and Shaughnessy (2004), we modified an existing lesson from the National Council of Teachers of Mathematics. This lesson, a variation on the "Gumball Task", gives students the opportunity to explore and discuss the variation which occurs in sampling. This paper describes our experience using this lesson as an…

Introductory statistics textbooks rarely discuss the concept of variability for a categorical variable and thus, in this case, do not provide a measure of variability. The impression is thus given that there is no measurement of variability for a categorical variable. A measure of variability depends on the concept of variability. Research has…

A well-designed experiment is the best method for establishing efficacy of any intervention, be it medical, behavioral, or educational in nature. This paper reviews the steps necessary in conducting a comparative experiment in an educational setting, and illustrates how these steps might be fulfilled within the context of a large-scale randomized…

In the branch of probability called "large deviations," rates of convergence (e.g. of the sample mean) are considered. The theory makes use of the moment generating function. So, particularly for sums of independent and identically distributed random variables, the theory can be made accessible to senior undergraduates after a first course in…