An International Journal on the Teaching and Learning of Statistics

## JSE Volume 9, Number 3 Abstracts

#### Amy Biesterfeld The Price (or Probability) Is Right

The Price is Right is a popular U.S. television game show in which contestants play product-pricing games in order to win prizes. Games involve some knowledge of prices, but many involve the element of chance as well. This paper describes a classroom activity I have designed to help teach probability concepts to students in an upper-level course. It is based on the television game show The Price is Right. This exercise is designed to help students better understand basic concepts such as probability rules, common distributions, and expectations. The exercise is intended for an upper-level statistics course, but could easily be adapted for use in an introductory statistics course as well. This paper describes The Price is Right classroom activity in detail. Student evaluations of the activity are also included.

Key Words: Classroom activity; Master Key; Plinko; Probability applications; Range Game.

#### Nick J. Broers Analyzing Propositions Underlying the Theory of Statistics

Conceptual understanding of statistics is usually considered one of several aspects of statistical knowledge. It refers to the ability of students to tie their knowledge of statistical ideas and concepts into a network of interrelated propositions. In this study an attempt was made to analyze the theory of descriptive regression analysis into its constituent propositions. Content analysis of the work of nine students revealed that these propositions were used by the students as cognitive units in their mental representation of the statistical theory. Suggestions for a use of constituent propositions as learning tools are discussed.

Key Words: Cognitive units; Conceptual understanding; Statistics education; Statistical knowledge.

#### Jeffrey M. Stanton Galton, Pearson, and the Peas: A Brief History of Linear Regression for Statistics Instructors

An examination of publications of Sir Francis Galton and Karl Pearson revealed that Galton's work on inherited characteristics of sweet peas led to the initial conceptualization of linear regression. Subsequent efforts by Galton and Pearson brought about the more general techniques of multiple regression and the product-moment correlation coefficient. Modern textbooks typically present and explain correlation prior to introducing prediction problems and the application of linear regression. This paper presents a brief history of how Galton originally derived and applied linear regression to problems of heredity. This history illustrates additional approaches instructors can use to introduce simple linear regression to students.

Key Words: Correlation; Francis Galton; History of statistics; Karl Pearson.

#### W. Robert Stephenson Statistics at a Distance

In 1993 the Statistics Department at Iowa State University entered into a collaborative agreement with General Motors to develop and deliver a new sequence of courses titled "Applied Statistics for Industry." This paper describes the development and content of these courses as well as their method of delivery. In order to accommodate on campus students as well as students at a distance, the course is presented live at Iowa State University and by videotape delay at General Motors Technical Education sites in Michigan, Ohio, Arizona and Mexico, and across the country at sites of other partner industries. Some of the differences between a statistics course taught in the traditional campus setting and a statistics course taught at a distance will be highlighted. Since there are two audiences (on campus and off campus), several compromises are made in how the course is conducted. These compromises, and their possible effects on students in both environments, are discussed. A summary of how on and off campus students did in these courses over the past five years is included.

Key Words: Assessment; Distance education; Industrial statistics; Videotape.

#### Carolyn Keeler and Kirk Steinhorst A New Approach to Learning Probability in the First Statistics Course

The probability unit in a first statistics course is difficult to teach because there is not much time, the concepts and mechanics are difficult, and the students do not see the relevance of learning it. Research by Cosmides and Tooby (1996) supports our findings that instructors should avoid fractions and decimals and capitalize on students' affinity for counting things. In addition, we avoid the use of normal tables at the beginning of our discussion of continuous random variables by using uniform and triangular distributions. These ideas may be used in traditionally structured classes or in group-based and activity-based classes.

Key Words: Cognition; Inquiry-based; Reform.

#### Teaching Bits: A Resource for Teachers of Statistics

This department features information sampled from a variety of sources that may be of interest to teachers of statistics. Deb Rumsey abstracts information from the literature on teaching and learning statistics, while Bill Peterson summarizes articles from the news and other media that may be used with students to provoke discussions or serve as a basis for classroom activities or student projects.

#### Mitchell Watnik and Richard A. Levine NFL Y2K PCA

The dataset associated with this paper is from the 2000 regular season of the National Football League (NFL). We use principal components techniques to evaluate team "strength." In some of our analyses, the first two principal components can be interpreted as measure of "offensive" and "defensive" strengths, respectively. In other circumstances, the first principal component compares a team against its opponents.

Key Words: Multivariate analysis; National Football League (NFL); Summary ranking measures.