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 studentsí 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.
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 studentsí 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.
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.
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.
This paper describes the components of a successful, online, introductory statistics course and shares studentsí 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.
Datasets and Stories
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. Spearmanís and Kendallís 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:Kendallís ; Matched pairs; Ordinal data;
Spearmanís ; Sports statistics.
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.