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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 3 Abstracts

Mary Richardson, Neal Rogness, and Byron Gajewski
4 out of 5 Students Surveyed Would Recommend this Activity (Comparing Chewing Gum Flavor Durations)

This paper describes an interactive activity developed for illustrating hypothesis tests on the mean for paired or matched samples. The activity is extended to illustrate assessing normality, the Wilcoxon signed rank test, Kaplan-Meier survival functions, two-way analysis of variance, and the randomized block design.

Key Words:Active learning; Assessing normality; Blinding; Confounding variable; Kaplan-Meier survival function; Paired difference experiment; Randomization; Randomized block design; Right-censored data; Two-way analysis of variance; Wilcoxon signed rank test.

Michael Wood
The Role of Simulation Approaches in Statistics

This article explores the uses of a simulation model (the two bucket story)—implemented by a stand-alone computer program, or an Excel workbook (both on the web)—that can be used for deriving bootstrap confidence intervals, and simulating various probability distributions. The strengths of the model are its generality, the fact that it provides a powerful approach that can be fully understood with very little technical background, and the fact that it encourages an active approach to statistics—the user can see the method being acted out either physically, or in imagination, or by a computer. The article argues that this model and other similar models provide an alternative to conventional approaches to deriving probabilities and making statistical inferences. These simulation approaches have a number of advantages compared with conventional approaches: their generality and robustness; the amount of technical background knowledge is much reduced; and, because the methods are essentially sequences of physical actions, it is likely to be easier to understand their interpretation and limitations.

Key Words:Active learning; Approaches to statistical thinking; Bootstrapped confidence intervals; Computer simulation; Probability distributions; Resampling.

Pam Boger
Building the Numeracy Skills of Undergraduate and Elementary Students

This paper describes a project with the goal of exposing both elementary school and undergraduate students to the concepts associated with the experimental method, from the formulation of a researchable question to the analysis and interpretation of the results. Under the guidance of their university mentors, fourth and fifth grade students formulated a research question, designed an experiment to answer that inquiry, recorded the appropriate measurements, calculated the necessary statistics, created visual displays of their results, and interpreted their findings at a student-centered Numeracy Conference.

Key Words:Active learning; Elementary statistics education, Numeracy.

John Dutton and Marilyn Dutton
Characteristics and Performance of Students in an Online Section of Business Statistics

We compare students in online and lecture sections of a business statistics class taught simultaneously by the same instructor using the same content, assignments, and exams in the fall of 2001. Student data are based on class grades, registration records, and two surveys. The surveys asked for information on preparedness, reasons for section choice, and evaluations of course experience and satisfaction. Using descriptive statistics, regression analysis and standard hypothesis tests, we test for significant differences between the online and lecture sections with regard to performance and satisfaction with the course as well as motivation and preparedness for taking an online course. We report several differences, including better performance by online students.

Key Words:Distance education; Internet course; Online education.

I. Elaine Allen and Norean Radke Sharpe
Demonstration of Ranking Issues for Students: A Case Study

This article uses a case study of 2001 town and city data that we analyzed for Boston Magazine. We use this case study to demonstrate the challenges of creating a valid ranking structure. The data consist of three composite indices for 147 individual townships in the Boston metropolitan area representing measures of public safety; the environment; and health. We report the data and the basic ranking procedure used in the magazine article, as well as a discussion of alternative ranking procedures. In particular, we demonstrate the impact of additional adjustment for the size of population, even when per capita data are used. This case study presents an opportunity for discussion of fundamental data analysis concepts in all levels of statistics courses.

Key Words:Data Analysis; Demographics; Graphics.

Sheldon Stein
Sums and Products of Jointly Distributed Random Variables: A Simplified Approach

Three basic theorems concerning expected values and variances of sums and products of random variables play an important role in mathematical statistics and its applications in education, business, the social sciences, and the natural sciences. A solid understanding of these theorems requires that students be familiar with the proofs of these theorems. But while students who major in mathematics and other technical fields should have no difficulties coping with these proofs, students who major in education, business, and the social sciences often find it difficult to follow these proofs. In many textbooks and courses in statistics which are geared to the latter group, mathematical proofs are sometimes omitted because students find the mathematics too confusing. In this paper, we present a simpler approach to these proofs. This paper will be useful for those who teach students whose level of mathematical maturity does not include a solid grasp of differential calculus.

Key Words:Covariance; Joint probability distribution; Means; Variances.

Datasets and Stories

John Holcomb and Angela Spalsbury
Teaching Students to Use Summary Statistics and Graphics to Clean and Analyze Data

Textbooks and websites today abound with real data. One neglected issue is that statistical investigations often require a good deal of “cleaning” to ready data for analysis. The purpose of this dataset and exercise is to teach students to use exploratory tools to identify erroneous observations. This article discusses the merits of such an exercise and provides a team project, problem data, cleaned data for instructors, and reflections on past experiences. The main goal is to give instructors a prepared project for their students to perform realistic data preparation and subsequent analysis. The data for this project involve categorical and continuous variables for subjects age 65 and over testing calcium, inorganic phosphorus, and alkaline phosphatase levels in the blood. The project described in this article involves summary analysis, but the cleaned data could also be used for projects on independent samples t-tests, analysis of variance, or regression.

Key Words:Activity-based learning; Data cleaning; Team projects.

Juana Sanchez and Yan He
Predicting Body Fat Using Data on the BMI

Statistics textbooks for undergraduates have not caught up with the enormous amount of analysis of Internet data that is taking place these days. Case studies that use Web server log data or Internet network traffic data are rare in undergraduate Statistics education. And yet these data provide numerous examples of skewed and bimodal distributions, of distributions with thick tails that do not follow the usual models studied in class, and many other interesting statistical curiosities. This paper summarizes the results of research in two areas of Internet data analysis: users' web browsing behavior and network performance. We present some of the main questions analyzed in the literature, some unsolved problems, and some typical data analysis methods used. We illustrate the questions and the methods with large data sets. The data sets were obtained from the publicly available pool of data and had to be processed and transformed to make them available for classroom exercises. Students in Introductory Statistics classes as well as Probability and Mathematical Statistics courses have responded to the stories behind these data sets and their analysis very well. The message in the stories can be conveyed at a descriptive or a more advanced level.

Key Words:Exponential; Internet traffic; Inverse Gaussian; Maximum likelihood; Negative Binomial; Poisson; Web server log data.

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