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Volume 13 (2005)

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An International Journal on the Teaching and Learning of Statistics

JSE Volume 13, Number 1 Abstracts

G. Rex Bryce
Developing Tomorrow's Statisticians

Many leaders of our profession have called for improvements in the way we educate statisticians. Sound recommendations have been made by many, based on real-world experience in the practice of statistical science. These calls for reform have gone largely unheeded, at least in part because of our current paradigm of statistical education. Statistics is seen, by many, as strictly a graduate discipline, yet constraints on the time to complete a graduate degree makes adopting many of the reforms that have been suggested very difficult. It is argued in this paper that a new paradigm of statistical education is needed that provides for strong undergraduate programs in statistics. Such programs would give the profession wider recognition and provide additional entries into the discipline.

Key Words: Accreditation; Curriculum guidelines; Reforms in statistical education, Undergraduate degrees.

Chris Andrews
The Ultimate Flow

The sport of Ultimate has grown from parking lot fun to international competition in its 35 year existence. As in many sports, the team that scores is subsequently on defense. Thus the probability that a team will score next is dependent on which team has scored most recently. Unlike in many other sports, teams switch ends after each score. Thus field conditions can affect the scoring patterns. The data and analyses described here can be integrated into a variety of courses ranging from introductory statistics to stochastic models.

Key Words: Frisbee; Hot Hand; Hypothesis Testing; Likelihood Ratio Test; Longest Run Test; Sports Modeling.

Ulf Olsson
Confidence Intervals for the Mean of a Log-Normal Distribution

Methods for calculating confidence intervals for the mean are reviewed for the case where the data come from a log-normal distribution. In a simulation study it is found that a variation of the method suggested by Cox works well in practice. An approach based on Generalized confidence intervals also works well. A comparison of our results with those of Zhou and Gao (1997) reveals that it may be preferable to base the interval on t values, rather than on z values.

Key Words: Generalized confidence interval.

Stephen B. Vardeman and Joanne R. Wendelberger
The Expected Sample Variance of Uncorrelated Random Variables with a Common Mean and Some Applications in Unbalanced Random Effects Models

There is a little-known but very simple generalization of the standard result that for uncorrelated random variables with common mean and variance , the expected value of the sample variance is . The generalization justifies the use of the usual standard error of the sample mean in possibly heteroscedastic situations, and motivates elementary estimators in even unbalanced linear random effects models. The latter both provides nontrivial examples and exercises concerning method-of-moments estimation, and also helps “demystify” the whole matter of variance component estimation. This is illustrated in general for the simple one-way context and for a specific unbalanced two-factor hierarchical data structure.

Key Words: Heteroscedastic; Method of moments; One-way model; Two-factor hierarchical model; Standard error of the mean; Variance component.

Timothy S. Vaughan and Kelly E. Berry
Using Monte Carlo Techniques to Demonstrate the Meaning and Implications of Multicollinearity

This article presents an in-class Monte Carlo demonstration, designed to demonstrate to students the implications of multicollinearity in a multiple regression study. In the demonstration, students already familiar with multiple regression concepts are presented with a scenario in which the “true” relationship between the response and predictor variables is known. Two alternative data generation mechanisms are applied to this scenario, one in which the predictor variables are mutually independent, and another where two predictor variables are correlated. A number of independent realizations of data samples are generated under each scenario, and the regression coefficients for an appropriately specified model are estimated with respect to each sample. Scatter-plots of the estimated regression coefficients under the two scenarios provide a clear visual demonstration of the effects of multicollinearity. The two scenarios are also used to examine the effects of model specification error.

Key Words: Multiple regression; Simulation.

Rachel Sturm-Beiss
A Visualization Tool for One- and Two-Way Analysis of Variance

Analysis of variance (ANOVA), a technique included in many introductory statistics courses, analyzes the relationship between a quantitative dependent variable and one or more independent qualitative variables. The nature of the relationship is expressed in a model with unknown parameters. Many textbooks emphasize the mechanics of the technique while the model and its parameters remain abstractions or theoretical entities. We introduce a Java Applet that allows a student to profitably explore the features and factors of one and two-way ANOVA tables together with representational models and model parameters.

Key Words: ANOVA; Java applet.

Datasets and Stories

Robert W. Hayden
A Dataset that is 44% Outliers

The data illustrate outliers that are not mistakes and not observations that are unusually high or low. The reasons for them are all interesting historically. They illustrate that "outliers" need not be errors but may instead be particularly interesting cases. The data also illustrate that different data displays may differ in their ability to reveal interesting data structure.

Key Words: Data displays; Inliers; Interpretation in context; Presidents.

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