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An International Journal on the Teaching and Learning of Statistics

JSE Volume 9, Number 2 Abstracts

Dexter C. Whittinghill and Robert V. Hogg
A Little Uniform Density With Big Instructional Potential

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 $[\theta-\rho, \theta+\rho]$.

Key Words: Confidence intervals; Efficiency; Estimation; Maximum likelihood; Sufficiency; Tests of hypotheses.

Robert F. Bordley
Teaching Decision Theory in Applied Statistics Courses

There has been much concern about making the curriculum for engineering statistics more relevant to the needs of industry. One proposed solution is to include decision risk analysis in the curriculum. However, the current coverage of decision risk analysis in statistics textbooks is either nonexistent or very introductory. In part, this reflects the fact that decision risk analysis, as currently taught, relies on the complex notion of a utility function.

Recent research in decision theory suggests a way of comprehensively and rigorously discussing decision theory without using utility functions. In this new approach, the decision risk analysis course focuses on making decisions so as to maximize the probability of meeting a target. This allows decision theory to be integrated with reliability theory. This course would be more comprehensive than the conventional introductory treatment of decision theory and no more difficult to teach. In addition, integrating decision theory with reliability theory facilitates its incorporation in curricula that currently exclude decision theory.

Key Words: Decision theory; Goal; Introductory statistics; Reliability theory; Utility function.

Linda S. Hirsch and Angela M. O'Donnell
Representativeness in Statistical Reasoning: Identifying and Assessing Misconceptions

The purpose of the study was to develop a valid and reliable test instrument to identify students who hold misconceptions about probability. A total of 263 students completed a multiple-choice test that used a two-part format rather than the typical one-part format. Results of the study showed that even students with formal instruction in statistics continue to demonstrate misconceptions. The test instrument developed in this study provides instructors with (1) a valid and reliable method of identifying students who hold common misconceptions about probability, and (2) diagnostic information concerning students' errors not frequently available through other formats. The test instrument was further evaluated in an instructional intervention study.

Key Words: Cognitive conflict; Group learning; Instructional intervention.

Lorraine Garrett and John C. Nash
Issues in Teaching the Comparison of Variability to Non-Statistics Students

One of the main themes of statistics courses is to teach about variability, as well as location. This is especially important for non-statistics students, who often overlook variability. We consider particularly the problem of comparing variability among k samples (k > 2) that are not necessarily drawn from Gaussian populations. This can also be viewed as testing for homoskedasticity of samples. We examine tools for this problem from the perspective of their suitability for inclusion in elementary statistics courses for students of non-mathematical subjects. The ideas are illustrated by an example that arose in a student project.

Key Words: Homoskedasticity; Teaching statistics; Test; Variability.

Christopher J. Malone and Christopher R. Bilder
Statistics Course Web Sites: Beyond syllabus.html

Student-instructor and student-student interaction outside of the classroom are very important to learning statistics. A successful statistics course Web site increases these interactions by creating a forum for the instructor and students to communicate with statistical language. The development of a successful statistics course Web site involves determining the Web site's purpose, deciding what Web pages are needed, organizing the Web pages, implementing the Web site, and assessing the Web site. The purpose of this article is to discuss the development of a statistics course Web site for a Web-enhanced or Web-centric course and to provide a detailed example of one such course.

Key Words: Chat room; Internet; Message board; Web-centric; Web-enhanced; Web page.

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.

Singfat Chu
Pricing the C's of Diamond Stones

Many statistical problems can be satisfactorily resolved within the framework of linear regression. Business students, for example, employ linear regression to uncover interesting insights in the fields of Finance, Marketing, and Human Resources, among others. The purpose of this paper is to demonstrate how several concepts arising in a typical discussion of multiple linear regression can be motivated through the development of a pricing model for diamond stones. Specifically, we use data pertaining to 308 stones listed in an advertisement to construct a model, which educates us on the relative pricing of caratage and the different grades of clarity and colour.

Key Words: Categorical variables; Data transformation; Multiple linear regression; Standardized residuals.

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