In "Maths for Business," a large first-year mathematics module, the continuous assessment component comprises 10 weekly quizzes which combine to contribute 40% of the final module mark. If students did not receive the full five marks on their weekly quiz, they were provided with the opportunity to resubmit their corrected weekly quiz…

Using the capabilities of expert knowledge structures, the researcher prepared test questions on the university calculus topic of "finding the area by integration." The quiz is divided into two types of multiple choice items (one out of four and one out of many). After the calculus course was taught and tested, the results revealed that…

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…

For many scientists, researchers and students Markov chain Monte Carlo (MCMC) simulation is an important and necessary tool to perform Bayesian analyses. The simulation is often presented as a mathematical algorithm and then translated into an appropriate computer program. However, this can result in overlooking the fundamental and deeper…

This article offers a transcript of author Allan Rossman's interview with Jessica Utts, Professor and Chair of Statistics at the University of California-Irvine. Utts is also a Fellow of the American Statistical Association and a recipient of a Founders Award from ASA. Additionally, she has been elected as President of ASA for the year 2016. The…

To compute the probability of having a disease, given a positive test result, is a standard probability problem. The sensitivity and specificity of the test must be given and the prevalence of the disease. We ask how a test-maker might determine the tradeoff between sensitivity and specificity. Adding hypothetical costs for detecting or failing to…

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…

The goal of this work is to provide instructors with detailed information about their classes at each assignment during the term. The information is both on an individual level and at the aggregate level. We used the large number of grades, which are available online these days, along with data-mining techniques to build our models. This enabled…

Although Bayesian methodology has become a powerful approach for describing uncertainty, it has largely been avoided in undergraduate statistics education. Here we demonstrate that one can present Bayes' Rule in the classroom through a hypothetical, yet realistic, legal scenario designed to spur the interests of students in introductory- and…

Completing a PhD on time is a complex process, influenced by many interacting factors. In this paper we take a Bayesian Network approach to analyzing the factors perceived to be important in achieving this aim. Focusing on a single research group in Mathematical Sciences, we develop a conceptual model to describe the factors considered to be…

The Dirac delta function has been used successfully in mathematical physics for many years. The purpose of this article is to bring attention to several useful applications of this function in mathematical statistics. Some of these applications include a unified representation of the distribution of a function (or functions) of one or several…

Explains a new way of viewing Bayes' formula. Discusses the revision factor and its interpretation. (YP)

What people mean by randomness should be taken into account when teaching statistical inference. This experiment explored subjective beliefs about randomness and probability through two successive tasks. Subjects were asked to categorize 16 familiar items: 8 real items from everyday life experiences, and 8 stochastic items involving a repeatable…