Volume 9 (2001)

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An International Journal on the Teaching and Learning of Statistics

JSE Volume 9, Number 1 Abstracts

John D. Spurrier
A Capstone Course for Undergraduate Statistics Majors

This article discusses a capstone course for undergraduate statistics majors at the University of South Carolina. The course synthesizes lessons learned throughout the curriculum and develops students' nonstatistical skills to the level expected of professional statisticians. Student teams participate in a series of inexpensive laboratory experiments that emphasize ideas and techniques of applied and mathematical statistics, mathematics, and computing. They also study modules on important nonstatistical skills. Students prepare written and oral reports. If a report is not of professional quality, the student receives feedback and repeats the report. All students leave the course with a better understanding of how the pieces of their education fit together and with a firm understanding of the communication skills required of a professional statistician.

Key Words: Active learning; Oral communication; Written communication.

Erhard Reschenhofer
The Bimodality Principle

In statistics courses, students often find it difficult to understand the concept of a statistical test. An aggravating aspect of this problem is the seeming arbitrariness in the selection of the level of significance. In most hypothesis-testing exercises with a fixed level of significance, the students are just asked to choose the 5% level, and no explanation for this particular choice is given. This article tries to make this arbitrary choice more appealing by providing a nice geometric interpretation of approximate 5% hypothesis tests for means.

Usually, we want to know not only whether an observed deviation from the null hypothesis is statistically significant, but also whether it is of practical relevance. We can use the same geometrical approach that we use to illustrate hypothesis tests to distinguish qualitatively between small and large deviations.

Key Words: Model selection; Selecting the level of significance; Testing.

C. M. Anderson-Cook and Sundar Dorai-Raj
An Active Learning In-Class Demonstration of Good Experimental Design

This article presents an active learning demonstration available on the Internet using Java applets to show a poorly designed experiment and then subsequently a well-designed experiment. The activity involves student participation and data collection. It demonstrates the concepts of randomization and blocking, as well as the need to carefully consider the objective of a study and how well the data collected answer the question of interest. The proposed exercise takes approximately 50 minutes of lecture time and helps to solidify these essential statistical concepts in a visual and memorable way. A variation of the activity could extend the presentation to 75 minutes. Students have reacted positively to the exercise.

Key Words: Blocking; Internet; Java applets; Paired data; Randomization; Teaching; Two-sample t-tests.

Edward H. S. Ip
Visualizing Multiple Regression

Several examples are presented to demonstrate how Venn diagramming can be used to help students visualize multiple regression concepts such as the coefficient of determination, the multiple partial correlation, and the Type I and Type II sums of squares. In addition, it is suggested that Venn diagramming can aid in the interpretation of a measure of variable importance obtained by average stepwise selection. Finally, we report findings of an experiment that compared outcomes of two instructional methods for multiple regression, one using Venn diagrams and one not.

Key Words: Average stepwise regression; Teaching statistics; Type I and Type II sums of squares; Venn diagram.

Eric R. Sowey
Striking Demonstrations in Teaching Statistics

Long-term learning should, surely, be an outcome of higher education. What is less obvious is how to teach so that this goal is achieved. In this paper, one constructive contribution to such a goal is described in the context of statistical education: the introduction of striking demonstrations. A striking demonstration is any proposition, exposition, proof, analogy, illustration, or application that (a) is sufficiently clear and self-contained to be immediately grasped, (b) is immediately enlightening, though it may be surprising, (c) arouses curiosity and/or provokes reflection, and (d) is so presented as to enhance the impact of the foregoing three characteristics. Some 30 striking demonstrations are described and classified by statistical subfield. The intent is to display the variety of devices that can serve effectively for the purpose, as a stimulus to the reader's own enlargement of the list for his or her own pedagogical use.

Key Words: Enrichment materials for teaching; Intellectual excitement; Long-term learning.

Abdulaziz Elfessi and David M. Reineke
A Bayesian Look at Classical Estimation: The Exponential Distribution

Many undergraduate students are introduced to frequentist or classical methods of parameter estimation such as maximum likelihood estimation, uniformly minimum variance unbiased estimation, and minimum mean square error estimation in a reliability, probability, or mathematical statistics course. Rossman, Short, and Parks (1998) present some thought provoking insights on the relationship between Bayesian and classical estimation using the continuous uniform distribution. Our aim is to explore these relationships using the exponential distribution. We show how the classical estimators can be obtained from various choices made within a Bayesian framework.

Key Words: Bayes estimator; Classical estimator; Credibility interval; Improper prior distribution.

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.

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