This article presents brief summaries (introductions) for the two reports that came from the Guidelines for Instruction and Assessment in Statistical Education (GAISE) initiative of American Statistical Association (ASA). The reports focus on Pre-K-12 and college statistics education respectively.
We present examples in which the addition of variances is key to gaining insight when dealing with binomial probabilities, inference and the central limit theorem.
This article shows K-12 teachers how the bootstrap and permutations tests can be used to make abstract concepts such as sampling distributions and standard error concrete. Some background information on the bootstrap is provided before a demonstration on the mechanics of the bootstrap, including the calculation of confidence intervals and standard errors is provided. Finally a comparison of bootstrap confidence intervals with classical intervals is presented.
On the basis of the literature on children's probabilistic conceptions and on the results of a survey of introductory statistics college students, this article argues that subjective probability should play a larger role in the probability curriculum in the schools. Also, a simple method for teaching conditional probability and illustrate Bayesian thinking is described. Other activities that are useful for applying subjective and alternative probability interpretations are suggested.
This article examines some techniques that teachers and other individuals interested in school-related data may find helpful and informative in examining tabular displays of data that are frequently found in local newspapers and school publications. Such techniques include looking for tabular patterns, median polish, and examining trifold percents in a table of cross-categorized values.
This article is based on the mark-recapture activity (capture-recapture). We will (1) document how considering solutions approaches led students (and instructors) to discover a problem inherent in this approach, (2) examine approaches to pooling results from multiple cases, (3) highlight the differences between the framed mathematical problem and the actual practice of ecologists, and (4) propose two sampling activity formats that teachers can choose on the basis of their goals for students. These two formats allow students to mathematically contrast two approaches to handling data or to provide a real-world simulation.
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.
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.
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.
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 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 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.