Journal of Statistics Education v.6, n.2 (1998)
Robert C. delMas
University of Minnesota
333 Appleby Hall
Minneapolis, MN 55455
William P. Peterson
Department of Mathematics and Computer Science
Middlebury, VT 05753-6145
This column features "bits" of information sampled from a variety of sources that may be of interest to teachers of statistics. Bob abstracts information from the literature on teaching and learning statistics, while Bill 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. We realize that due to limitations in the literature we have access to and time to review, we may overlook some potential articles for this column, and therefore encourage you to send us your reviews and suggestions for abstracts.
ed. Ene-Margit Tiit (1997). Proceedings of the Tartu Conference, Tartu, Estonia, June 3-8, 1996.
The preface to the Proceedings states that "The collection of reports reproduced in the `Proceedings' reflects a `statistically representative sample' of the problems discussed at the conference. The first part of the book, `Statistical Software as an Environment for Teaching Statistics,'... contains the papers of these authors who have approached the problems from the viewpoint of computational statistics. The second part of the book, `Statistical Education -- Where Are We Going?' carries the spirit expressed in the papers of the invited speaker Anne Hawkins and other specialists of statistical education."
ed. Maria Gabriella Ottaviani (1996). A seminar organised under the auspices of Dipartimento di Statistica, Probabilita e Statistiche Applicate, Rome University "La Sapienza."
This book presents articles by seven Italian authors on the use of multimedia, hypertext, and computer simulations in the teaching of statistics. Each article is printed in both Italian and English. The contents of the book are as follows:
by Paula Grafton Young (1998). The Mathematics Teacher, 91(5), 402-406, 412-415.
The article describes an interesting problem that can be addressed by probability modeling. The author states the problem as follows: "Suppose that three trees are located around a small lake or pond. One of the trees becomes infested with an insect population that destroys the leaves or fruit of the tree." The article describes activities which use basic probability, simple random walks, matrices, and Markov chains to model the path of a single insect and to determine the spread of the insect population to the remaining trees. Example activity sheets are provided in appendices.
by Richard L. Schaeffer (1998). STATS: The Magazine for Students of Statistics, No. 22, 8-12.
The author provides a perspective on the Advanced Placement Statistics Exam by describing its history, the content and structure of the exam, grading schemes, results of a comparability study, and implications for student preparation.
by Jane Booker (1998). STATS: The Magazine for Students of Statistics, No. 22, 17-19.
Jane Booker is a group leader of the Statistics Group at Los Alamos National Laboratory. This article can provide students with a good idea of the work and challenges that statisticians encounter in their careers.
by Karen D. Rappaport, Nouna Kettaneh, and Svante Wold (1998). The American Statistician, 52(2), 152-159.
In the competitive environment of today's chemical industry, an efficient approach of experimentation is necessary in all facets of research and development. This article discusses the tools of statistical modeling and design in this perspective, and reports the development of a program for the increased use of these tools at Hoechst Celanese Corporation, on international chemistry and polymers company based in New Jersey, USA.
by Andrew Gelman and Deborah Nolan with Anna Men, Steve Warmerdam, and Michelle Bautista (1998). The American Statistician, 52(2), 160-166.
An important theme in an introductory statistics course is the connection between statistics and the outside world. This article describes some assignments that have been useful in getting students to learn how to gather and process information presented in the newspaper articles and scientific reports they read. We discuss two related assignments. For the first kind of assignment, students work through prepared instructional packets. Each packet contains a newspaper article that reports on a scientific study or statistical analysis, the original report on which the article was based, a worksheet with guidelines for summarizing the reported study, and a series of questions. In the second kind of assignment, each student is required to find a newspaper article themselves, track down the original report, summarize the study using our guidelines, and write a critique of the article. Here, we describe the guidelines we developed to help the student in reading the newspaper article and original source, and the procedures we used for each type of assignment. Examples of handouts and assignments appear as appendixes.
by Andrew Gelman (1998). The American Statistician, 52(2), 167-174.
We present several classroom demonstrations that have sparked student involvement in our undergraduate course in decision theory and Bayesian statistics. Some of the demonstrations involve student participation, while others are essentially lectures with extra class discussion.
A regular component of the Teaching Bits Department is a list of articles from Teaching Statistics, an international journal based in England. Brief summaries of the articles are included. In addition to these articles, Teaching Statistics features several regular departments that may be of interest, including Computing Corner, Curriculum Matters, Data Bank, Historical Perspective, Practical Activities, Problem Page, Project Parade, Research Report, Book Reviews, and News and Notes.
The Circulation Manager of Teaching Statistics is Peter Holmes, firstname.lastname@example.org, RSS Centre for Statistical Education, University of Nottingham, Nottingham NG7 2RD, England. Teaching Statistics has a website at http://www.maths.nott.ac.uk/rsscse/TS/.
"The American Statistics Poster Competition" by Jerry Moreno and John Schollenberger
The article covers the history and organisation of the American Statistics Poster Competition, describes the authors' view on what constitutes a statistical poster, and presents a future outlook for the competition.
"Using Spreadsheets to Calculate Prob(X + Y = w)" by John C. Turner
The author describes how spreadsheets can be set up to calculate the sum of two or more discrete random variables with arbitrary distributions. From the summary, the author states that use of the spreadsheet "allows the student to confirm properties of the sum of binomial and Poisson random variables... In addition, it also allows the student to compute the probabilities associated with the difference of random variables, and thus find the probability that one random variable exceeds another (or exceeds a given amount)."
"A Probability Game" by Jean Merles
The author describes a simplified form of snakes and ladders that can be used to initiate an open ended investigation of probability. The game provides an opportunity for students to experience chance and probability in a situation where the theoretical probabilities are not obvious. The game can be extended using different type of dice and modifying the game board to have different numbers of squares. This allows the instructor to engineer games where analysis of the probabilities is relatively simple and then help the students generalise to more complex game situations.
"Knock 'm Down" by Gordon Hunt
The author describes a game that engages students in collecting data and interpreting results. "Knock 'm Down" is played with two dice and twelve counters. A shelf is marked off into 11 sections that are numbered from 2 to 12. Twelve cans are placed on the shelf with no restriction on how many cans are placed into each section. The game is played by rolling two dice, summing the values, and removing all cans from the section of the shelf that has the same label as the sum. The goal of the game is to strategically place the cans on your shelf so that you knock off all the cans in the least number of rolls. The author describes three different approaches that students typically take to identifying the optimal arrangement of the cans and questions that can be used to guide students in their investigations. Data collection is motivated by encouraging students to compare the results from different arrangements. The author discusses extensions of the activity with probability modeling and computer simulations.
by Ridgely Ochs. Newsday, 24 February 1998, C11.
Ochs reports on a British study in the February issue of the Journal of Epidemiology and Community Health with the imposing title "Is Forced Dextrality an Explanation for the Fall in the Prevalence of Sinistrality With Age?"
Ochs recalls the famous 1981 study by Stanley Coren, popularized in Coren's 1992 book The Left-Hander Syndrome (Free Press). Coren's data showed that, among 5147 people ranging in age from 8 to 100, 15% at age 10 were left-handed, compared to only 5% at age 50, and less than 1% at age 80. The apparent conclusion is that left-handers have lower survival rates. Coren estimated that the lefty effect represented a two- to five-year decrease in life expectancy.
Simon Ellis, the author of the new British study, points out that if Coren is right then the effect is about as large as the difference in life expectancy between men and women. He worries that insurance companies might logically be led to quote different rates to left-handers. Ellis' own study looked at 6097 people aged 15 to 70. He found that the prevalence of left-handers decreased from 11.2% at age 15 to 4.4% at age 70. Unlike Coren, Ellis doesn't see a decreased ability of left-handers to survive. Rather, he explains that social prejudices against left-handers have forced them, over the course of their lives, to switch hands. In order to adjust for this, Ellis removed questions about writing and drawing, since these skills are particularly susceptible to being changed. Still, this didn't completely remove the lefty effect among older people, and Ellis reports that the case is still not closed.
Ochs did a phone interview with Coren, who said that President Clinton is a lefty, and he suffers bad allergies. Former President Bush is a lefty and suffers from a thyroid condition known as Graves disease. Ochs observed that Barbara Bush also has Graves disease, but Coren reportedly didn't know if Mrs. Bush was left-handed!
While SAT scores have gone up and down over the years -- including one long period of decline from the mid-1960s to the early 1980s -- it seems that IQ scores just keep going up. This went unnoticed for a long time because, unlike SAT scores, IQ tests are re-normed each year to keep the median at 100. Political scientist James Flynn discovered this increase in the 1980s when he looked at scores on tests done for the military that had not been normed. This increase has been called the "Flynn effect." It is estimated that someone who would have scored in the 90th percentile on the Raven's Progressive Matrices test in the late 19th century would score in only the 5th percentile today.
Flynn's observations have been verified by other researchers. The American Psychological Association plans to publish an edited volume this spring titled The Rising Curve: Long-Term Gains in I.Q. and Related Measures. Debate continues over the exact cause of the increase. The largest gains have been observed for the Raven's test, which is based on shapes rather than words to minimize the influence of culture and education. But some observers have pointed out that children today have much more experience working puzzles and mazes, some of which are very close to the problems used on I.Q. tests.
This story gives a less encouraging view than the last one. On February 24, the results of the Third International Mathematics and Science Study (TIMSS) were announced, and American 12th-graders scored well below the world average. In advanced mathematics and physics, the US ranked last.
This report continues a trend which has seen the US ranking worse at higher grade levels. In a previous test for 4th-graders, US students were above average in math and ranked second in science. But later, on the TIMSS test of 8th-grade students, US students had already dropped below international averages. Now we find the 12th-graders lagging even further behind.
In the past, poor performances have been blamed on the fact that US high schools accept all students, while in other countries enrollment is selective. This explanation no longer applies. All 21 countries participating in the TIMSS study enroll more than 90 percent of the secondary-school-age youths. Another explanation held that US students suffer from spending far more time watching television than their peers in other countries. But the TIMSS report showed that US students are now just about average in number of hours watched per week.
The practice of therapeutic touch is used in hospitals all over the world and is taught in some medical and nursing schools. In this therapy, trained practitioners manipulate something that they call the "human energy field." The manipulation is carried out without actually touching the patient's body. Practitioners claim that anyone can be trained to feel this energy field.
Some researchers say that no reliable evidence exists showing that this technique actually heals patients. Dr. Donald O'Mathuna, a professor of bioethics and chemistry at the Mount Carmel School of Nursing in Columbus, Ohio, has reviewed more than 100 papers and doctoral dissertations on this technique without finding any convincing data.
James Randi, a professional magician who is also known as a skeptic of some types of alternative medicine, has tried for years to test the practice of therapeutic touch. So far, only one practitioner has agreed to submit to his test, and she did no better than chance in detecting the energy field.
The present story is about an 11-year-old Colorado girl named Emily Rosa, who was able to recruit 21 practitioners for an experiment she conducted two years ago. Emily's mother, a nurse who is herself skeptical about the therapy, thinks Emily was successful because practitioners did not feel threatened by a 9-year-old girl working on a science fair project!
For her experiment, Emily placed a screen between a practitioner's eyes and hands, and then held her own hand over one of the practitioner's hands. If the human energy field can be felt, then practitioners should be able to identify which of their hands Emily held hers over. Emily conducted 280 tests with the 21 subjects, and they identified the correct location of her hand in 44% of the tests.
The results of her study were reported in the Journal of the American Medical Association ("A Close Look at Therapeutic Touch, 1 April 1998, pp. 1005-1010). Proponents of the therapeutic touch technique were quick to dispute the findings. Meanwhile, Emily received a letter from the Guiness Book of World Records saying she may be the youngest person ever to publish a paper in a major scientific journal.
A new study has concluded that women who have mammograms every year for a decade have a 50-50 chance of receiving a false positive result. The study, conducted over a 10-year period, looked at screening test results for 2400 women aged 40 to 69. These women underwent a total of 9762 screening mammograms and 10905 screening breast examinations, with medians of four mammograms and five clinical breast examinations per woman over the 10-year period. If a women had a mammogram or breast examination that (1) was considered indeterminate, (2) aroused suspicion of cancer, or (3) prompted recommendation for additional workup, but cancer was not diagnosed within the next year, then the test was classified as a false positive.
Among the women in the study, 28.8% had at least one false positive mammogram, 13.4% had at least one false positive breast examination, and 31.7% had at least one false positive result (breast exam or mammogram). The estimated cumulative risk of a false positive result was 49.1% after 10 mammograms and 22.3% after 10 breast examinations.
The study appeared in the New England Journal of Medicine ("Ten-Year Risk of False Positive Screening Mammograms and Clinical Breast Examinations," 16 April 1998, 338(16), pp. 1089-1096). You can read the abstract online at
In an editorial accompanying the article, Harold Sox considers whether the risk of false positives is overestimated. He points out that an abnormal result would become a false positive by default if a diagnosis was not made within a year. But presumably in some of these cases cancer actually exists.
On the other hand, a Los Angeles Times article raised the possibility that the risk may be understated (Thomas H. Maugh II, "Study Warns of Mammogram False Alarms, Los Angeles Times, 16 April 1998, A1). This article observed that only 6.5% of mammograms from the study showed an abnormality, whereas nationally about 10% of mammograms show an abnormality. The risk of false positives is highest for women in their forties, and decreases with age.
The last decade has seen some of the warmest years on record, and the latest data indicate that 1997 is the warmest year yet. However, since large scale records for global temperature only go back about 100 years, it has been hard to establish that we are indeed experiencing a long-term trend.
A new study by climate researchers at the University of Massachusetts at Amherst attempts to reconstruct climate records for the last 600 years. The researchers have supplemented historical temperature measurements by collecting data from ice cores, tree rings, and coral reefs from over 100 sites around the world. The results have been published in the journal Nature (M. Mann, R. Bradley, and M. Hughes, "Global-Scale Temperature Patterns and Climate Forcing over the Past Six Centuries," 23 April 1998, pp. 779-787). You can find more details about how temperature information is derived from such data at the National Oceanic and Atmospheric Administration's web page on Paleoclimatology:
The researchers found warm periods and cold periods over the 600 years, but none of the changes compared in magnitude to the warming that began at the start of the 20th century. While acknowledging that uncertainties remain in their novel approach, the researchers were pleased to find that their data do match historically recorded phenomena such as the "year without a summer" of 1816 (caused by the Tambora volcano in Indonesia), and the strong El Nino year of 1791. This suggests the method is sensitive enough to pick up even single-year climate variations. Furthermore, the researchers point out that the magnitude of the uncertainty in their measurements is small compared with the trends being observed.
Sociologist Stanley Presser of the University of Maryland and his research partner Linda Stinson of the US Bureau of Labor Statistics have found that people exaggerate when pollsters ask them about their church-going habits.
The two researchers analyzed time-use diaries from the mid-1960s, 1970s, and 1990s and compared them to polling results obtained by the Gallup Organization and the National Opinion Research Center (NORC). The diaries revealed that the percentage of Americans who attend church was 42% in 1965 and 26% in 1994. By contrast, the Gallup and NORC polls reveal that the proportion has not changed over the past thirty years. A 1993-1994 NORC survey reported that 38% of its respondents attended mass, a number that has varied little since the 1970s.
Presser and Stinson speculate that the discrepancy arises from the way the data were collected. The Gallup/NORC polls specifically ask respondents if they had attended religious services in the past seven days, whereas the time-use diaries are based on random samples of Americans who were repeatedly interviewed and asked how they had spent the previous day. In addition, the researchers suspect that the Gallup/NORC respondents felt the need to impress their interviewers, whereas the diary participants were only asked to account for how they spent their time and were unlikely to have felt the pressure to exaggerate their church-going habits.
Investment compensation consultant Graef Crystal carried out this study for the Times. It purports to find a strong correlation between the stock performance of major companies and the golfing prowess of their chief executives. Crystal obtained data on C.E.O.'s golf handicaps from the journal Golf Digest, and used his own data on the stock market performance of 51 Fortune 500 companies. He created a "stock performance ranking" which gave each company a score based on how investors who held their stock did over a three-year period, with 100 being the highest rating and 0 the lowest. Here, reproduced from the article, is Crystal's dataset.
CEO Company Handicap Stock_Score Melvin_R._Goodes Warner-Lambert 11 85 Jerry_D._Choate Allstate 10.1 83 Charles_K._Gifford BankBoston 20 82 Harvey_Golub American_Express 21.1 79 John_F._Welch_Jr. General_Electric 3.8 77 Louis_V._Gerstner_Jr. IBM 13.1 75 Thomas_H._O'Brien PNC_Bank 7.1 74 Walter_V._Shipley Chase_Manhattan 17.2 73 John_S._Reed Citicorp 13 72 Terrence_Murray Fleet_Financial 10.1 67 William_T._Esrey Sprint 10.1 66 Hugh_L._McColl_Jr. Nationsbank 11 64 James_E._Cayne Bear_Stearns 12.6 64 John_R._Stafford Amer._Home_Products 10.9 58 John_B._McCoy Banc_One 7.6 58 Frank_C._Herringer Transamerica 10.6 55 Ralph_S._Larsen Johnson_&_Johnson 16.1 54 Paul_Hazen Wells_Fargo 10.9 54 Lawrence_A._Bossidy Allied_Signal 12.6 51 Charles_R._Shoemate Bestfoods 17.6 49 James_E._Perrella Ingersoll-Rand 12.8 49 William_P._Stiritz Ralston_Purina 13 48 Duane_L._Burnham Abbott_Laboratories 15.6 46 Richard_C._Notebaert Ameritech 19.2 45 Raymond_W._Smith Bell_Atlantic 13.7 44 Warren_E._Buffett Berkshire_Hathaway 22 43 Donald_V._Fites Caterpillar 18.6 41 Vernon_R._Louckes_Jr. Baxter_International 11.9 40 Michael_R._Bonsignore Honeywell 22 38 Edward_E._Whitacre_Jr. SBC_Communications 10 37 Peter_I._Bijur Texaco 27.1 35 Mike_R._Bowlin Atlantic_Richfield 16.6 35 H._Lawrence_Fuller Amoco 8 33 Ray_R._Irani Occidental_Petroleum 15.5 31 Charles_R._Lee GTE 14.8 29 John_W._Snow CSX 12.8 29 Philip_M._Condit Boeing 24.2 25 Joseph_T._Gorman TRW 18.1 24 H._John_Riley_Jr. Cooper_Industries 18 22 Richard_B._Priory Duke_Energy 10 22 Leland_E._Tollett Tyson_Foods 16 20 Bruce_E._Ranck Browning-Ferris 23 15 William_H._Joyce Union_Carbide 19 13 Thomas_E._Capps Dominion_Resources 18 12 Scott_G._McNealy Sun_Microsystems 3.2 97 William_H._Gates Microsoft 23.9 95 Sanford_I._Weill Travelers_Group 18 95 Frank_V._Cahouet Mellon_Bank 22 92 William_C._Steere_Jr. Pfizer 34 89 Donald_B._Marron Paine_Webber 25 89 Christopher_B._Galvin Motorola 11.7 3
Crystal identified the last seven points on the above list as outliers and removed them from the analysis; this procedure is described in the article as scientific sifting. The correlation coefficient between stock rate and handicap for the remaining data points is -0.414. This value is not reported in the article, but Crystal is quoted as saying: "For all the different factors I've tested as possible links to predicting which C.E.O.'s are going to perform well or poorly, this is certain the oddest -- but also the strongest -- I've seen. There's got to be something there."
The article raises a number of questions for discussion relating to data snooping and the treatment of alleged outliers. For the full dataset, the correlation between handicap and stock rating is only -0.042! There are also issues of response bias; it turns out that when Golf Digest asked C.E.O.'s of the 300 largest Fortune 500 corporations for their golf handicaps, only 72 replied. (Of these, Crystal used the 51 for which he had corporate data.) Finally, while the article clearly presents the findings quite seriously, some of Crystal's commentary sounds tongue-in-cheek. He says of C.E.O.'s, "...if they can get their handicap down to 4, why not just pay them an extra 20 million bucks?"
Marilyn gives the following response to a reader who asked for an explanation of the margin of error in an opinion poll.
Good polling is a tricky business, but the guiding principle is simple: The larger the sample, the more accurate it is. After much data collection, pollsters have learned their numerical limits of accuracy and call them collectively the 'margin of error.' The individual numbers are so consistent that they are considered standard. For this reason, the published margin of error on a particular poll merely tells us the size of the sample. It is based on past polls. For example, if a poll has a margin of error of plus or minus 3% this usually tells us that about 1500 people were polled. That is, the margin-of-error percentage is assigned to the poll, not developed from it.
Smaller sample have larger margins, and larger samples have smaller ones, but only slightly. For most purposes, a national sample of 1500 is adequate. In fact, most public-opinion polls use samples ranging is size from only 1000 to 2000 people, but this is amazingly sufficient.
It makes an interesting exercise to sort out what Marilyn is trying to say here.
This article gives one more example of how not to do a poll. It describes a poll conducted by People magazine on the Internet that asked on-line readers to vote for the Most Beautiful Person. The winner of the poll was to be featured in a future print issue of People. In addition to the names of many well-known celebrities, the ballot also included a spot to write in a name.
Radio personality Howard Stern suggested that his fans cast write-in votes for one of his characters on his show -- Hank, the Angry, Drunken Dwarf. His request generated over 230,000 votes, which made Hank the clear winner. This result points out some weaknesses of this form of cyber-polling. Of course, there is no reason to believe that the people who write in form a random sample of the population. Here it also appears there was no way to control how many times an individual voted.
On March 11, front-page newspaper stories reported that Asteroid 1997XF11 was on a course that would bring it within 30,000 miles of Earth in October 2028. That prediction, made by the International Astronomical Union, led to fears that the asteroid might actually hit the Earth. The depiction of deadly collisions by comets and asteroids in the Hollywood movies Armageddon and Deep Impact served to further dramatize the possibilities. However, when the trajectory of 1997XF11 was recalculated by experts at NASA's Jet Propulsion Laboratory (JPL), it was found the most likely path would miss the Earth by 600,000 miles. (Note: this is more than twice the distance to the moon.)
To avoid such sensationalist reporting in the future, scientists are looking for better ways to release their findings on asteroids. New discoveries of asteroids headed in our general direction make headlines, but in most cases more careful calculations subsequently reveal that the threat is minimal. According to Paul Chodas of JPL, fifteen minutes after he received the XF11 data, his calculations revealed that there was "zero threat" to Earth.
In April, NASA proposed guidelines for consultation among experts before public announcements. Chodas says that it might take up to 48 hours for such consultation, and NASA recommended an additional 24 hours before any news release. Earthquake expert Alan Lindh of the US Geologic Survey urged more openness about discoveries, as long as the uncertainty of the initial observations is clearly explained. "You can't control the flow of news," said Lindh, "but you can be as truthful as possible up front."
The article reports that astronomers have identified 123 potentially hazardous asteroids that could pass within five million miles of Earth and have discovered 200 of the estimated 2000 large asteroids that could pass within 30 million miles. You can find more information about asteroid hazards on the NASA Ames web site. The link
has up-to-date information on the 1997XF11 discussion. Related links indexed there include an Asteroid and Comet Impact fact sheet, reviews of recent popular books and films, and a discussion of whether a meteor could have downed TWA Flight 800.