An International Journal on the Teaching and Learning of Statistics

## JSE Volume 11, Number 1 Abstracts

#### Daniel W. Schafer and Fred L. Ramsey Teaching the Craft of Data Analysis

We describe our experiences and express our opinions about a non-introductory statistics course covering data analysis. In addition to the methods of statistics, the course emphasizes the process of data analysis, the communication of results, and the role of statistics in the accumulation of scientific evidence. Since it is impossible to provide explicit instructions for all data analytic situations, the course attempts to impart a body of tools, a spirit of approach, and enough thoroughly covered case studies to give students the skills and confidence to apply this craft on their own.

Key Words: Applied statistics; Case studies; Real data; Statistics major; Undergraduate.

#### Mary Richardson and Byron Gajewski Archaeological Sampling Strategies

This paper describes an interactive project developed to use for teaching statistical sampling methods in an introductory undergraduate statistics course, an Advanced Placement (AP) statistics course, or, with adaptation, in a statistical sampling course or a statistical simulation course. The project allows students to compare the performance of simple random sampling, stratified random sampling, systematic random sampling, and cluster random sampling in an archaeological setting.

Key Words: Active learning; Advanced Placement Statistics; Introductory statistics; Simulation.

#### Arthur Bakker The Early History of Average Values and Implications for Education

The early history of average values is used as a source of inspiration for instructional design in middle-school classrooms. This historical study helps to define different layers, aspects, and applications of average values and encourages us to look through the eyes of the students, who do not have the same concepts as teachers and instructional designers have. As a result of this study, possible implications for education are considered, such as estimation as a starting point for a statistics course, allowing the midrange as an initial strategy, a visual way of estimating the mean using bar representations in a simple computer tool, and the reinvention of midrange, median, mode, and mean. There turn out to be striking parallels but also important differences between the historical and students’ individual development of statistical understanding.

Key Words: Design research; Guided reinvention; History of statistics; Measures of central tendency; Middle school.

#### Ian McLeod, Ying Zhang, and Hao Yu Multiple-Choice Randomization

Multiple-choice randomized (MCR) examinations in which the order of the items or questions as well as the order of the possible responses is randomized independently for every student are discussed. This type of design greatly reduces the possibility of cheating and has no serious drawbacks. We briefly describe how these exams can be conveniently produced and marked. We report on an experiment we conducted to examine the possible effect of such MCR randomization on student performance and conclude that no adverse effect was detected even in a rather large sample.

Key Words: Academic integrity; Answer-options arrangement; Cheating; Student evaluation; Teaching large classes.

#### Timothy S. Vaughan Teaching Statistical Concepts With Student-Specific Datasets

The advent of electronic communication between students and teachers facilitates a number of new techniques in the teaching of statistics. This article presents the author’s experiences with providing each student in a large, multi-section class with a unique dataset for homework and in-class exercises throughout the semester. Each student’s sample is pseudo-randomly generated from the same underlying distribution (in the case of hypothesis tests and confidence intervals involving ), or the same underlying linear relationship (in the case of simple linear regression). This approach initially leads students to identify with their individual summary statistics, test results, and fitted models, as “the answer” they would have come up with in an applied setting, while subsequently forcing them to recognize their answers as representing a single observation from some larger sampling distribution.

Key Words: Sampling distribution; Sampling variability; Student simulation.

#### Rose Martinez-Dawson Incorporating Laboratory Experiments in an Introductory Statistics Course

Laboratory experiments using spectrophotometers and pH meters were incorporated into an undergraduate introductory statistics course in order to create an interdisciplinary approach of teaching statistics to non-statistics majors. By conducting laboratory experiments commonly associated with science-based curricula, students were exposed to the relationship between science and statistics through experimental design and data analysis. The laboratory experiments used in the course are related to fields such as chemistry, biology, and environmental sciences and are described in this article.

Key Words: Experiments; Hands-on activities; Interdisciplinary; SAS.

#### James V. Pinto, Pin Ng, and David S. Allen Logical Extremes, Beta, and the Power of the Test

There is a potential misuse of the power function under the logical extreme when the null hypothesis is true. The power function is defined to measure the probability of rejecting the null given any value of the parameter being tested. It can be used to obtain the power and the values only under the alternative hypothesis. When the null is true, the power function can be used to obtain the size of the test. The power and the probability of committing a Type II error are, however, undefined and, hence, the power function should not be used to obtain these values.

Key Words: Power function; Simulations; Type II error.

#### Teaching Bits: A Resource for Teachers of Statistics

This department features information sampled from a variety of sources that may be of interest to teachers of statistics. Deb Rumsey abstracts information from the literature on teaching and learning statistics, while Bill Peterson summarizes articles from the news and other media that may be used with students to provoke discussions or serve as a basis for classroom activities or student projects.

#### Julie M. Hays Forecasting Computer Usage

The dataset bestbuy.dat.txt contains actual monthly data on computer usage (Millions of Instructions Per Second, MIPS) and total number of stores from August 1996 to July 2000. Additionally, information on the planned number of stores through December 2001 is available. This dataset can be used to compare time-series forecasting with trend and seasonality components and causal forecasting based on simple linear regression. The simple linear regression model exhibits unequal error variances, suggesting a transformation of the dependent variable.

Key Words: Causal forecasting; Model-building; Seasonal Variation; Simple linear regression; Time-series forecasting; Transformations.

#### Constance H. McLaren and Bruce J. McLaren Electric Bill Data

The Electric Bill dataset contains monthly household electric billing charges for ten years. In addition, there are values for such potential explanatory variables as temperature, heating and cooling degree days, number in household, and indicator variables for a new electric meter and new heat pumps. The values provide a real dataset to use for applications ranging from simple graphical analysis through a variety of time series and causal forecasting methods. The dataset also is suited to spreadsheet applications for break-even calculations and optimization. With knowledge of the utility’s tiered rate function, the bill amount can be converted to an estimate of the number of kilowatt hours used. A series of assignment questions is included and the accompanying Instructor’s Manual provides solutions.

Key Words: Budgeting; Electrical utilities; Forecasting; Introductory Statistics; Spreadsheet; Time Series.