From the Literature on Teaching and Learning Statistics

Deborah J. Rumsey
The Ohio State University

Journal of Statistics Education Volume 9, Number 3 (2001)

This text may be freely shared among individuals, but it may not be republished in any medium without express written consent.

Research and Resources on Teaching and Learning Statistics

STAR Library: Statistics Teaching and Resource Library on the WWW

Deborah Rumsey, Editor, and Christopher Bilder, Chief Associate Editor and Webmaster.
www.starlibrary.net

STAR Library is a new peer-reviewed collection of teaching activities for statistics. It is designed to provide activities that are easy to access, free of charge, easy to customize, and of high quality. Each activity includes a clear objective, a list of the materials required, and estimate of the time needed to implement the activity, a description of the activity, ideas for assessment, and teacher notes. A ready-to-print student version of each activity is also available. Additional resources for activities may include digital photos and video demonstrations, data sets, and applets. The first collection of activities is now available.

“The World of Chance”

Alice Richardson (2001), Teaching Statistics, 23(2), 61-64.

"The World of Chance" is an unconventional statistics course taught at the University of Canberra since 1998, modeled on the Chance courses devised at Dartmouth College. Statistical concepts are introduced via a mixture of lectures, class discussions of news stories, and activities. There is flexibility in content, and no required syllabus. A high level of math skill is not required of the students; virtually no formulae are introduced. The aim is to teach statistical thinking, rather than statistical techniques. The course consists of 26 fifty-minute lectures and 12 two-hour tutorials. Guest lecturers are occasionally employed, with the aim of allowing experts in a variety of fields to present statistical aspects of their work. The article provides information regarding resources and references.

Teaching Ideas and Applications

"Green Statistics"

Vic Barnett (2001), Teaching Statistics, 23(2), 35-37.

Excerpt: “We are all familiar with the examples (used to) back up the teaching of probability and statistics such as balls in urns, drawing pins falling the wrong way up and deaths of Prussian army officers from horse kicks. Some very different statistics color the contemporary scene and suggest that it may be becoming too late to protect the environment we all depend on.”

Current issues relating to the environment are presented in this article to motivate students to learn about organizing data, and thinking about nontrivial sampling issues related to environmental work (for example, how to take samples to monitor pollution levels in terms of e-coli measurements).

"A Role for Statistics in International Cricket"

Frank Duckworth (2001), Teaching Statistics, 23(2), 39-44.

Abstract: As a rule, statistics only enters into sports for describing player and team performances. But one-day cricket has provided a use for both mathematical modeling and the statistical analysis of data, in the form of the Duckworth/Lewis method for setting revised targets in rain-interrupted matches. Teachers might find the story related here a good advertisement for the value of their subject and some light relief from the usual textbook examples.

"Eliciting Honesty: How to Tell the Truth with Statistics"

Joseph Eisenhauer (2001), Teaching Statistics, 23(2), 45-48.

Excerpt: “The practice of statistics is often portrayed as a vehicle of deception, as in Darrel Huff's 1954 treatise, How to Lie with Statistics. But statisticians can also be the victims of deceit. For a variety of reasons, including modesty, shame and fear of punishment, survey respondents are often reluctant to answer personal questions concerning income, political preferences, illegal activity, and the like ... Such dissembling [responses] introduces what has been called 'evasive answer bias' into survey data. One obvious approach to the problem is to guarantee the confidentiality (or anonymity) of responses. (But this also has limitations.)”

This paper illustrates the use of randomized response sampling (RRS) to deal with these issues. As an example, the author looks at the problem of estimating the proportion of students who have cheated on an examination.

"Once Upon a Time – Including an Unlikely Tale of Shocking Increase in Deaths as Electricity Sales Rise"

Sidney Tyrrell (2001), Teaching Statistics, 23(2), 55-57.

The data bank used for this article gives six data sets which exhibit very regular seasonal patterns, are suitable for time series analysis, and provide more variety than some of the other seasonal data sets that currently exist. Some of the variables include gas and electricity sales, deaths, and temperature. Some “shocking” results can be found by analyzing this data, leading to interesting class discussions regarding correlation and causation.

"Correlation: From Picture to Formula"

Peter Holmes (2001), Teaching Statistics, 23(3), 67-71.

Correlation is introduced intuitively early in the K-12 school curriculum by considering patterns in scatter diagrams. Later on, various formulas are used for calculating correlation coefficients. Students often have a difficult time connecting the formulas to the scatterplots; in particular, they have a hard time using the scatterplots to get an intuitive understanding of the formulas. This article suggests ways in which the formulas can be related to the scatter diagrams. (The Pearson product moment correlation, as well as Spearman's rank correlation coefficient and Kendall's rank correlation coefficient are discussed.)

"Musical Means: Using Songs in Teaching Statistics"

Lawrence Lesser (2001), Teaching Statistics, 23(3), 81-85.

Abstract: Students' ready understanding of (and interest in) the context of songs can be utilized throughout the probability and statistics curriculum. This article presents several types of examples, including generating descriptive statistics, conducting hypothesis tests, analyzing song lyrics (for specific terms as well as “big picture” themes), exploring music as a data analysis tool, and exploring probability and statistics as compositional tools. Examples include testing whether the proportion of hit songs written by more than one person is significantly greater than .5 and looking at a bar chart of the notes or chords used in songs featured on the 'Hot 100' sales chart in Billboard magazine. The examples span several genres, time periods, countries and cultures, and the reader is encouraged to supplement this collection with his or her own favorites.

"Beer Tasting and the Problem of Coincidences"

Paul Murrell (2001), Teaching Statistics, 23(3), 94-96.

Abstract: This article describes a matching problem. Given k unlabelled items and k labels, how hard is it to correctly match the labels to the items? The problem is an example of a very old one known as the problem of coincidences, which was originally motivated by a game played in the 18th century. The context for the example involves trying to match the correct brand to each of 15 unmarked beers.

"A Computer-Based Lab Supplement to Courses in Introductory Statistics"

P. Cabilio and P. J. Farrell (2001), The American Statistician, 55(3), 228-232.

Abstract: The computer continues to assume a role of increased importance in university education, and professors must determine appropriate means for its integration into the curriculum. This article describes the incorporation of a studio lab component into undergraduate courses in introductory statistics. We detail the objectives of these courses and describe the motivations, general structure, and main features of our approach. The labs typically involve a two-step frequentist approach where a simple hands-on experiment is performed that is subsequently replicated using the computer. We describe in detail two labs that typify the main features of our approach, and discuss the flexibility of the labs with regard to the target audience. A discussion of our perception of their impact on student learning is given, along with some comments on alternative modes of delivery.

"Using Permutation Tests to Study Infant Handling by Female Baboons"

Thomas Moore and Vicki Bentley-Condit (2001), STATS, 31, 7-14.

Permutation tests are exemplified in this article to be a viable alternative for contingency table analysis where a conventional chi-square analysis would be invalid because basic assumptions are violated. The data was collected by observing baboons in twenty-minute focal samples over an 11-month period in 1991-1992 for a troop including 23 females, 11 of which were mothers with infants. Interactions between females and infants were observed. One of the research hypotheses is the following: “Females will tend to handle the infants of females who are ranked the same as or lower than themselves.”

"Breaking the Code –- A Graphical Exploration Using Bar Charts"

John Gabrosek and Michael Shuckers (2001), STAR Library.
www.starlibrary.net/activities/gabrosek_schuckers2001.htm

This activity engages students in constructing and interpreting bar charts, and testing a hypothesis to encode a message that was created using a location shift of the alphabet. After decoding the message, students are asked a series of questions that assess their ability to see patterns. The questions are geared for higher levels of cognitive reasoning.

"What Makes the Standard Deviation Larger or Smaller?"

Robert delMas (2001), STAR Library.
www.starlibrary.net/activities/delmas2001.htm

Abstract: As they learn about the standard deviation, many students focus on the variability of bar heights in a histogram when asked to compare the variability of two distributions. For these students, variability refers to the “variation” in bar heights. Other students may focus only on the range of values, or the number of bars in a histogram, and conclude that two distributions are identical in variability even when it is clearly not the case. This activity can help students discover that the standard deviation is a measure of the density of values about the mean of a distribution and to become more aware of how clusters, gaps, and extreme values affect the standard deviation.

"The Role of Probability in Discrimination Cases"

James Higgins (2001), STAR Library.
www.starlibrary.net/activities/higgins2001.htm

Abstract: An important objective in hiring is to ensure diversity in the workforce. The race or gender of individuals hired by an organization should reflect the race or gender of the applicant pool. If certain groups are under-represented or over-represented among the employees, then there may be a case for discrimination in hiring. On the other hand, there may be a number of random factors unrelated to discrimination, such as the timing of the interview or competition from other employers, that might cause one group to be over-represented or under-represented. In this exercise, we ask students to investigate the role of randomness in hiring, and to consider how this might be used to help substantiate or refute charges of discrimination.

"Simulating Size and Power Using a 10-Sided Die"

Erin Blankenship and Lynda Young (2001), STAR Library.
www.starlibrary.net/activities/blankenship_young2001.htm

Abstract: This group activity illustrates the concepts of size and power of a test through simulation. Students simulate binomial data by repeatedly rolling a ten-sided die, and they use their simulated data to estimate the size of a binomial test. They carry out further simulations to estimate the power of the test. After pooling their data with that of other groups, they construct a power curve. A theoretical power curve is also constructed, and the students discuss why there are differences between the expected and estimated curves.

"Regression on the Rebound"

Trent Buskirk and Lynda Young (2001), STAR Library.
www.starlibrary.net/activities/buskirk2001.htm

Abbreviated Abstract: This activity is an advanced version of the “Keep your eyes on the ball” activity by Bereska, et al. (1999). Students should gain experience with differentiating between independent and dependent variables, using linear regression to describe the relationship between these variables, and drawing inference about the parameters of the population regression line. Each group of students collects data on the rebound heights of a ball dropped multiple times from each of several different heights. By plotting the data, students quickly recognize the linear relationship. After obtaining the least squares estimate of the population regression line, students can set confidence intervals or test hypotheses on the parameters.

"Regression -- Residuals -- Why?"

Jacqueline Miller (2001), STAR Library.
www.starlibrary.net/activities/miller2001.htm

Abstract: As teachers of statistics, we know that residual plots and other diagnostics are important to deciding whether or not linear regression is appropriate for a set of data. Despite talking with our students about this, many students might believe that if the correlation coefficient is strong enough, these diagnostic checks are not important. The data set included in this activity was created to lure students into a situation that looks on the surface to be appropriate for the use of linear regression but is instead based (loosely) on a quadratic function.

Suzanne Levin Weinberg (2001), Mathematics Teaching in the Middle School, 6(8).

Excerpt: “Concepts relating to fractions and measurement are difficult for students in the upper elementary and middle school grades to grasp. As a first-year teacher, I learned the value of relating difficult concepts, especially abstract concepts, to students' real-world experiences. The 'How Big Is Your Foot?' project grew out of a question that I asked my eighth-grade students during my first year of teaching. We had just finished studying conversions in the metric system and had begun working with conversions in the customary system. As a warm-up question, I asked my students to describe the distance from my desk to the door of the classroom. I wrote their responses on the chalkboard as they called out estimates: 1 meter, 60 meters, 25 feet, 300 inches, 300 centimeters. The students did not seem to have any grasp of the length of a meter or an inch. I postponed my planned lesson and launched this activity involving comparisons of standard and nonstandard measurements.”

The author does a nice job of explaining the idea of taking measurements in different units (using a student's foot as a unit to measure arm length, for example), and making conversions between this nonstandard unit, and a standard unit (such as feet or inches). This approach could provide some help to introductory statistics teachers as we contemplate teaching students about the Z-transformation formula (standard units), for example.

"Generating Functions and the Electoral College"

Christopher Stuart (2001), The College Mathematics Journal, November, 2001.

In this article, the author shows that the chance of having a tie in the electoral vote for president is small enough that we don't have to worry about it.

Reviews

Book Review: Statistics Handbook for the TI-83 by Larry Morgan (1997), Texas Instruments.

Barrie Galpin (2001), Teaching Statistics, 23(3), 80.

According to this reviewer, this book provides a helpful introduction to the use of the calculator, and contains some interesting and powerful examples for using this calculator for statistical purposes (59 topics in all). The book is illustrated with many screen captures, which are useful in providing a quick overview of the approach taken in each topic. But the level of the audience is important to note:“The book certainly illustrates the potential power of the calculator in the hands of an experienced statistician and, for teachers wishing to exploit this power in the course of their teaching, this book's approach provides some helpful ideas. However, it is not a book for the student working alone.” Some of the problems cited include notation issues and some difficulty in clarifying the more advanced concepts.

Deborah J. Rumsey
Director, Mathematics and Statistics Learning Center
Department of Mathematics
The Ohio State University
231 West 18th Avenue
Columbus, OH 43210
USA
rumsey@math.ohio-state.edu