Crossen feels that the public must learn to critically analyze statistics as it is reported by the media. She remarks that "it is time for us to reclaim our numbers". and suggests that high schools and colleges can help us do this.
How might we help? We can start by being sure that our library has "Chance Magazine", a magazine of the Statistical Association of American about statistics and its use in society. Chance is written in a lively and readable style to play the role for statistics that Scientific American does for science.
We can, and many do, include critical discussions of current chance news in existing statistics and probability courses. Finally, the adventuresome can take a chance on the CHANCE course inspired by Chance magazine and under development at six colleges: Grinnell, Middlebury, Dartmouth, Spelman, UCSD, and Minnesota under a grant from the National Science Foundation's Undergraduate Development Program.
CHANCE is an introductory course whose aim is to make students more informed and critical readers of chance news. While the schools developing this course have constructed different versions of the course all have this common goal.
I'll illustrate one approach to the CHANCE course by an example from an a CHANCE course Peter Doyle, Joan Garfield and I gave for teachers at the Geometry Center in Minneapolis this summer. We will use the same approach in the Dartmouth CHANCE course this Fall.
We wanted to see if we could clarify some of the issues involved in the newspaper reports of the recent Finnish study which suggested that vitamin E and beta carotene supplements had no effect in preventing lung cancer, at least for smokers. In fact, beta carotene supplements might even have some harmful effects. This was the first controlled experiment reported after a series of epidemiological studies suggested that these supplements were affective in preventing heart disease. Investigators had cautioned that final recommendations would have to wait for the results of controlled studies.
We started by asking the students to divide up into groups of three and read and discuss two articles from the "New York Times" relating to the Finnish study. These two articles arrived at somewhat different conclusions.
We asked them to discuss the following questions:
1. The Jane Brody article states that ``Smokers who took 20 milligrams of beta carotene each day developed 18 percent more lung cancers than those who were given vitamin E or a dummy pill.'' What does this mean? What additional information would you need to decide if this difference is significant?
2. In the original article (New England Journal of Medicine, 14 April 1994) you will find that during the study there were 876 newly diagnosed cases of lung cancer with 474 among those who were given beta carotene and 402 among those who were not. The study was designed in such a way that there was essentially a 50% chance that a subject would be given beta carotene.
If beta carotene has no effect and each person had a fifty-fifty chance of being given beta carotene then the chance of having 474 or more of the 876 deaths among those given beta carotene is the probability of getting 474 or more heads when a fair coin is tossed 876 times. Estimate this probability. Does this coin tossing argument support the claim that the increase in incidence of lung cancer for those taking beta carotene is significant at the 95% level?
3. On the basis of this study, Laurie has quit taking beta carotene. Was this a wise decision?
We also asked the students, as part of their homework, to read an earlier article reviewing the results of the positive epidemiological studies and record their final conclusions about the effectiveness of these vitamin supplements in the journal that they keep for the course.
While we do not limit ourselves to current news, students do seem to enjoy and profit from discussing news as it happens. Discussing the controversy of second hand smoke while congressional hearings are going on and Philip Morris is carrying full page advertisement in all major newspapers made this issue seem more real. We took advantage of the obsessive interest in O.J. Simpson trial to discuss the statistical issues in the use of DNA fingerprinting in such a trial.
We realize that those interested in including current news in their courses will not have the time to search for chance issues in the newspapers and find the related articles in journals such as "Science", "Nature", and the "New England Journal of Medicine". Therefore, as part of our chance project we put out a bi-weekly newsletter that abstracts current chance issues in the news. Whenever possible we suggest questions that might form the basis of a class discussion. If you would like to receive this Chance News just send a request to email@example.com
These newsletters and other information useful for teaching a CHANCE course are available from our Chance data base via Mosaic. You can find this database at the Geometry Center Mosaic (http://www.geom.umn.edu/) in their Online Document Library.
The various versions of the CHANCE course given so far have differed in format but have found surprising agreement on the probability and statistical concepts that are most valuable in helping students interpret the news: simple ideas from the design of experiments, descriptive statistics, exploratory data analysis, elementary probability concepts, sampling and correlation.
We make no attempt to develop the concepts of statistics and probability systematically but do have the students read and do homework from books like "Statistics" by Freedman, Pisani, Purvis, and Adhikari and "Statistics: Concepts and Controversies" by David S. Moore.
We use a number of additional resources to help explain basic probability and statistical concepts. These include computer simulation and the use of a statistical package such as Data Desk or Minitab to analyze data. Another important resource has been the Annenberg video series "Against all Odds." For example, their account of the tobacco and lung cancer studies and the first study of the AIDS drug AZT provide vivid accounts of issues that apply equally to current studies.
A common theme in the current reform of elementary statistics has been the use of hands-on activities to help students develop important statistical ideas. Taking a cue from the discussion of correlation in the "Against all Odds" series, we asked the students in our Minneapolis Chance course to design a test to see if there is an association between taste and cost of chocolate chip cookies. We provided twelve different brands of chocolate chip cookies. The students design resulted in rating the cookies on a scale of 1 to 5 (appearance and taste) and relating the average class ratings for taste and appearance for each cookie with its cost per ounce. The overall results for best tasting cookies were compared to a recent taste test carried out by Consumers Report and found to be in surprising agreement.
The CHANCE course utilizes materials developed by other projects such as activities developed by the activity-based statistics (ABS) NSF project headed by Richard Shaeffer. For example, we used one of their activities, a randomized response survey for sensitive data, to determine the percentage of students in the course who had cheated as well as the percentage who had smoked marijuana. The ABS project activities will be produced in student and instructor manuals and we plan to use more of these activities in future CHANCE courses.
Another valuable tool we used in the Minneapolis CHANCE course is the ElectronicEncyclopedia of Statistical Examples and Exercises (EEEE) and an electronic data base (Data Archive) being prepared by an NSF project headed by William Notz, Dennis Pearl, Elizabeth Stasny, and Paul Velleman.
The Encyclopedia is a Macintosh Hypercard application that provides information about studies in a wide variety of fields. The study is first described using text and visual aids. The student is provided with the data and a series of questions relating to the study. Answers are also provided. The Data Archive will contain the data sets of this encyclopedia and other well-know data sets. It will have a Mosaic interface and so be available from the internet. We have tried a beta version of the encyclopedia in a chance course and feel that it will be a valuable resource for future courses.
There does not seem to be the same level of dissatisfaction with existing statistical text books that one finds in calculus. Perhaps for this reason, the statistics reform has concentrated on developing tools to enhance the use and analysis of data including data from current studies, activities to increase understanding of basic concepts, and the use of laboratories for hands on experience. A discussion of recent NSF projects dealing with these issues can be found in an article by George Cobb in the first volume of the new electronic journal "Journal of Statistical Education" . Easy access to this article as well as abstracts of the NSF projects can by found in the JSE gopher: jse.stat.ncsu.edu.
Just as we have found tools from other NSF projects useful for our CHANCE course, we hope that some of the materials that we have developed for the CHANCE course such as Chance News will be useful in other new courses coming from the NSF projects as well as existing courses in probability and statistics.