Journal Article

  • Many widely-adopted college textbooks that are designed for a student's first (and possibly last) statistics course have incorporated new trends in statistical education, but are organized in a manner that is still driven by a traditional computational, rather than a conceptual, framework. An alternative approach allows for the treatment of many seemingly-unrelated conventional procedures such as one- and two-sample t-tests and analyses of variance and covariance under a unifying prediction model approach. Furthermore, this approach, combined with the power of modern statistical software packages, prepares the student to solve problems beyond the scope of traditional procedures. Students will appreciate the acquisition of practical research capabilities and might even be stimulated to continue their study of statistics.

  • Basic probability concepts are difficult for some students to understand initially. Through the use of a Venn diagram disguised as a pizza, we will discuss how to explain introductory probability concepts. Students are able to answer probability questions, including conditional probability, by simply looking at a picture. This tool not only enhances learning but retention as well.

  • Well-defined measures of performance are readily available for baseball players, making the modeling of their salaries a popular statistical exercise. In this article, the salaries for non-pitchers for the 1992 Major League Baseball season are provided, along with numerous measures of the players' previous year's performances. Also included are indicators of each player's ability to switch teams. This dataset is useful in upper-division regression analysis courses because it exhibits many "real world" difficulties that can be remedied using techniques outlined in the course.

  • 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.

  • Five case studies based on real situations and real data are presented for use in courses on research methodology and data analysis. Departing from the typical case study approach, students are asked to act as consultants to resolve the issues placed before them, prior to being given a solution. In generic terms, students are given a description of a real problem and a real dataset relevant to solving that problem and are asked for their advice on how the problem may be solved. This approach motivates students to take ownership of the problem at hand and provides them with the opportunities and experiences to use the tools of their education actively, rather than to merely acquire them.

  • The simplest forms of regression and correlation involve formulas that are incomprehensible to many beginning students. The application of these techniques is also often misunderstood. The simplest and most useful description of the techniques involves the use of standardized variables, the root mean square operation, and certain distance measures between points and lines. On the standardized scale, the simple linear regression coefficient equals the correlation coefficient, and the distinction between fitting a line to points and choosing a line for prediction is made transparent. The typical size of prediction errors is estimated in a natural way by summarizing the actual prediction errors incurred in the dataset by use of the regression line for prediction. The connection between correlation and distance is simplified. Despite their intuitive appeal, few textbooks make use of these simplifications in introducing correlation and regression.

  • We explore the varied uses of the uniform distribution on [theta - 1/2, theta + 1/2] as an example in the undergraduate probability and statistics sequence or the mathematical statistics course. Like its cousin, the uniform distribution on [0, theta], this density provides tractable examples from the topic of order statistics to hypothesis tests. Unlike its cousin, which appears in many probability and statistics books, this uniform is less well known or used. We discuss maximum likelihood estimators, likelihood ratio tests, confidence intervals, joint distributions of order statistics, use of Mathematica®, sufficiency, and other advanced topics. Finally, we suggest a few exercises deriving likelihood ratio tests when the range is unknown as well, or for the uniform on [theta - rho, theta + rho].

  • A Research Project in Statistics is proposed as a major requirement of undergraduate statistics curricula to provide hands-on experience to students and equip them with the tools they will need after graduation. Such a requirement will train students to solve real-life problems by choosing a statistical model suitable to a problem, learning the details of that model, collecting and analyzing appropriate data, and interpreting the results obtained. After completing the project, students will have the ability to learn new techniques on their own, to do a literature review, and to carry out sample and survey design, and they will have enhanced their oral and written reporting skills. The case study reported in this paper suggests that students tend to learn more by doing such a project than in any regular coursework. The project is motivating and gives students a feeling of working in an almost real-life environment on a real problem. Such a project incorporates many aspects of the nonmathematical courses suggested by Higgins (1999a) and is expected to better prepare students to meet the needs of potential employers.

  • There are many common misconceptions regarding factor analysis. For example, students do not know that vectors representing latent factors rotate in subject space, rather than in variable space. Consequently, eigenvectors are misunderstood as regression lines, and data points representing variables are misperceived as data points depicting observations. The topic of subject space is omitted by many statistics textbooks, and indeed it is a very difficult concept to illustrate. An animated tutorial was developed in an attempt to alleviate this problem. Since the target audience is intermediate statistics students who are familiar with regression, regression in variable space is used as an analogy to lead learners into factor analysis in the subject space. At the end we apply the Gabriel biplot to combine the two spaces. Findings from a textbook review, a survey, and a "think aloud" protocol were taken into account during the program development and are discussed here.

  • By putting emphasis on applications in two basic statistics courses for chemistry students and chemical engineering students we have enhanced student motivation and increased student activity. In addition to a traditional in-class exam, the students complete a take-home project where statistical problems relevant to chemists are discussed. We give several examples of the course and project material. The main difference between the two courses is that the first is optional, attracting approximately 15 students, while the second is compulsory with approximately 100 students. We discuss how the different requirements affect the learning situation and how separate strategies of teaching have to be developed for the small class and large class situations, respectively.

Pages

register