M. Leigh Lunsford, Ginger Rowell Holmes, and Tracy Goodson-Espy
Classroom Research: Assessment of Student Understanding of Sampling Distributions of Means and the Central Limit Theorem in Post-Calculus Probability and Statistics Classes

We applied a classroom research model to investigate student understanding of sampling distributions of sample means and the Central Limit Theorem in post-calculus introductory probability and statistics courses. Using a quantitative assessment tool developed by previous researchers and a qualitative assessment tool developed by the authors, we embarked on data exploration of our students’ responses on these assessments. We observed various trends regarding their understanding of the concepts including results that were consistent with research completed previously (by other authors) for algebra-based introductory level statistics students. We also used the information obtained from our data exploration and our experiences in the classroom to examine and conjecture about possible reasons for our results.

Key Words:Action Research.

Stijn Vanhoof, Ana Elisa Castro Sotos, Patrick Onghena, Lieven Verschaffel, Wim Van Dooren, and Wim Van den Noortgate
Attitudes Toward Statistics and Their Relationship with Short- and Long-Term Exam Results

This study uses the Attitudes Toward Statistics (ATS) scale (Wise 1985) to investigate the attitudes toward statistics and the relationship of those attitudes with short- and long-term statistics exam results for university students taking statistics courses in a five year Educational Sciences curriculum. Compared to the findings from previous studies, the results indicate that the sample of undergraduate students have relatively negative attitudes toward the use of statistics in their field of study but relatively positive attitudes toward the course of statistics in which they are enrolled. Similar to other studies, we find a relationship between the attitudes toward the course and the results on the first year statistics exam. Additionally, we investigate the relationship between the attitudes and the long-term exam results. A positive relationship is found between students’ attitudes toward the use of statistics in their field of study and the dissertation grade. This relationship does not differ systematically from the one between the first year statistics exam results and the dissertation grade in the fifth year. Thus, the affective and cognitive measures at the beginning of the curriculum are equally predictive for long-term exam results. Finally, this study reveals that the relationship between attitudes toward statistics and exam results is content-specific: We do not find a relationship between attitudes and general exam results, only between attitudes and results on statistics exams.

Key Words: Assessment; Attitudes Toward Statistics scale.

Eric Langford
Quartiles in Elementary Statistics

The calculation of the upper and lower quartile values of a data set in an elementary statistics course is done in at least a dozen different ways, depending on the text or computer/calculator package being used (such as SAS, JMP, MINITAB, Excel, and the TI-83 Plus). In this paper, we examine the various methods and offer a suggestion for a new method which is both statistically sound and easy to apply.

Key Words: Percentiles; Quantiles.

Mary S. Fowler and Joseph B. Kadane
Oil and Gas on Indian Reservations: Statistical Methods Help to Establish Value for Royalty Purposes

Part of the history of oil and gas development on Indian reservations concerns potential underpayment of royalties due to under-valuation of production by oil companies. This paper discusses a model used by the Shoshone and Arapaho tribes in a lawsuit against the Federal government, claiming the Government failed to collect adequate royalties. Portions of the case have been settled out of court with compensation paid to the Tribes. Other portions remain pending. This material can be used as a real example in a calculus-based probability and statistics course.

Key Words: Expectation; Law; Location-scale family.

Gail E. Tudor
Teaching Introductory Statistics Online – Satisfying the Students

This paper describes the components of a successful, online, introductory statistics course and shares students’ comments and evaluations of each component. Past studies have shown that quality interaction with the professor is lacking in many online courses. While students want a course that is well organized and easy to follow, they also want to interact with the professor and other students. Interactions in this course took place through small group discussions, emails, weekly announcements and graded exams. The course also contained lecture slides with audio prepared by the professor. As the variety and quantity of interaction increased, student satisfaction with the amount of interaction with the professor increased from 75% the first year of the course to 99% the fifth year. Overall satisfaction with the online course increased from 93% the first year to 100% the fifth year.

Key Words: Course design; Online versus traditional learning; Statistics education.

Larry Winner
NASCAR Winston Cup Race Results for 1975-2003

Stock car racing has seen tremendous growth in popularity in recent years. We introduce two datasets containing results from all Winston Cup races between 1975 and 2003, inclusive. Students can use any number of statistical methods and applications of basic probability on the data to answer a wide range of practical questions. Instructors and students can define many types of events and obtain their corresponding empirical probabilities, as well as gain a hands-on computer-based understanding of conditional probabilities and probability distributions. They can model the rapid growth of the sport based on total payouts by year in real and adjusted dollars, applying linear and exponential growth models that are being taught at earlier stages in introductory statistics courses. Methods of making head-to-head comparisons among pairs of drivers are demonstrated based on their start and finish order, applying a simple to apply categorical method based on matched pairs that students can easily understand, but may not be exposed to in traditional introductory methods courses. Spearman’s and Kendall’s rank correlation measures are applied to each race to describe the association between starting and finishing positions among drivers, which students can clearly understand are ordinal, as opposed to interval scale outcomes. A wide variety of other potential analyses may also be conducted and are briefly described. The dataset nascard.dat.txt is at the driver/race level and contains variables including: driver name, start and finish positions, car make, laps completed, and prize winnings. The dataset nascarr.dat.txt is at the race level and contains variables including: number of drivers, total prize money, monthly consumer price index, track length, laps completed, numbers of caution flags and lead changes, completion time, and spatial coordinates of the track. These datasets offer students and instructors many opportunities to explore diverse statistical applications.

Key Words:Kendall’s ; Matched pairs; Ordinal data; Spearman’s ; Sports statistics.

John C. Kern II
Pig Data and Bayesian Inference on Multinomial Probabilities

Bayesian inference on multinomial probabilities is conducted based on data collected from the game Pass the Pigs®. Prior information on these probabilities is readily available from the instruction manual, and is easily incorporated in a Dirichlet prior. Posterior analysis of the scoring probabilities quantifies the discrepancy between empirical and prior estimates, and yields posterior predictive simulations used to compare competing extreme strategies.

Key Words: