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CHANCE News 3.07
(29 April to 20 May 1994)
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Prepared by J. Laurie Snell, with help from Jeanne
Albert and William Peterson, as part of the CHANCE
Course Project supported by the National Science
Foundation and the New England Consortium for
Undergraduate Science Education.
Please send comments and suggestions for articles to:
jlsnell@dartmouth.edu
Previous issues of Chance News can be found on the
the Dartmouth gopher: Dartmouth.edu in the classroom
folder.
The Chance welcome page on Mosaic is:
http://www.geom.umn.edu/docs/snell/chance/welcome.html
Contents
==================================== Lest men suspect your tale untrue, Keep probability in view. John Gay (Fables) ==================================== We plan to mention from time to time other internet sources that sometimes discuss chance issues. One such source is provided by James R. Garven at the University of Texas, who provides information on risk management and insurance . Garvin maintains a RISKNet Mailing List that you can subscribe to at jgarven@mcl.cc.utexas.edu, a Gopher: riskweb.bus.utexas.edu and a World Wide Web Home Page: http://riskweb.bus.utexas.edu The most recent Risk Digest (No 70) suggests the possibility of using fuzzy probability to assess insurance rates. For example if you are 6'2" you might be classified tall, if 5'2" not tall, but if you are 5'8" you might be classified as 60% tall and 40% percent not tall. ============================================= The last Chance News mentioned that Marilyn Vos Savant was asked to settle a dispute over the probability that a man, having four children, will have two boys and two girls, given that he has at least one boy. The dispute was between .375 and .50. Marilyn gave the answer .40 Stephen JW Evans writes: I am often wrong on matters of conditional probability but I wonder if there is an ambiguity in the problem about families of 2 boys & 2 girls. It seems to me to depend on the way the problem is posed. If the person concerned has only 1 child now and that is a boy, then the probability of having 1 boy and 2 girls in the next three children is indeed 0.375 On the other hand if the person already has 4 children, and you just know that one of them is a boy (which could have been the first-, second-, third-, or fourth- born), then Ms. Savant's answer is clearly correct. I could have read the way the problem was set as referring to either of these scenarios and I think they lead to different solutions. ================================================= Again we see that answers to problems like this depend on how the story is told. Maybe someone can come up with a story for which .5 is the correct answer. ================================================= Meredith Warshaw suggested that we include the following article by Jane Brody in the NY Time intended to put the Finnish vitamin study discussed in the last Chance News in a better perspective. ================================================== Personal Health The New York Times, 20 April, 1994, C11 Jane E. Brody
Ms. Brody discuss how one should react to the rather surprising results of the Finnish study that showed no apparent protection against lung cancer or cardiovascular disease from daily supplements of the antioxidant nutrients vitamin E or beta carotene and that in fact suggested possible harmful affects of beta carotene.
She observes that the study should be examined in the context of other studies. She asks: does the finding make biological sense? how does it mesh with observational studies among large groups? and was the study designed in a way that would give a meaningful answer to the research question? The answers to these questions suggests to her that we should not be immediately alarmed by this study.
DISCUSSION QUESTIONS:
1. The 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% percent chance that each subject would be given beta carotene.
If beta carotene has no effect then it might be reasonable to assume number of deaths among those who took beta carotene can be compared to the number of heads in tossing a coin 876 times. What is the approximate probability of getting 474 or more heads when a fair coin is tossed 876 times? Is this consistent with the claim that the increase in incidence of lung cancer for those taking beta carotene is significant at the 95% level? <<<========<<
>>>>>==========>> A somewhat different view on the Finnish vitamin study is expressed in the following article. Method and madness: believing in vitamins. New York Times Magazine, 22 May 1994 p 20 Nicholas Wade
This article also discusses the Finnish study on vitamins. It begins with a quite careful discussion of the differences between observational and controlled studies. It ends by suggesting that the many reasons put forth to discount the Finnish study would not have been presented if the results had gone the other way. <<<========<<
>>>>>==========>> Peter Tannenbaum pointed out the following chance "gem".
She hopes for a lotto legal luck. National Law Journal, 9 May 1994 Jackie Cohen
Frances Bobnar claims that the Pennsylvania Lottery Commission owes her $1.5 million to compensate for 10 years of losing tickets. Another article says that she estimates that her family and friends buy about $150,000 worth of tickets every year, so apparently she thinks the lottery is a fair game. A veteran lottery player assured her that she should have seen some return on her money which led her to file a complaint that is the first step of a potential lawsuit. Such a lawsuit would be the first of its kind in Pennsylvania and should lead to some interesting probability discussions. <<<========<<
>>>>>==========>> Separate is better. The New York Times Magazine, 22 May, 1994 Susan Estrich
Do all-girl schools produce better students? Are women who graduate from single-sex colleges better educated---indeed, better prepared for life? In this article, Ms. Estrich looks at these and other questions about the American education system.
She reports: ¥ in all-girls schools, 80 percent of the girls take science and math for four years, while the national average for girls in coed schools is two years. ¥ Women who graduate from single-sex colleges do better than their counterparts at coed institutions with regard to test scores, graduate admissions, number of earned doctorates, and "personal satisfaction", according to Elizabeth Tidball, a George Washington University researcher. ¥ Forty-three percent of the math doctorates earned by female students at liberal arts colleges go to graduates of all-women colleges. ¥ Although women's colleges contribute only 4 percent of all graduates, they account for one-third of the female board members of Fortune 1000 companies.
Ms. Estrich also discusses some of the ways that women and girls get shortchanged in coeducational schools and colleges in America, especially in math and science, and suggests that single-sex public schools, or single-sex classes in public schools might be part of a solution.
DISCUSSION QUESTIONS:
1. What can you conclude about single-sex education from the given data?
2. Ms. Estrich states in her article that she is a graduate from Wellesley--an all-women's college. Do you think this influences her conclusions?
3. Is attending a all women's college itself a confounding variable in relation to some of the author's conclusions?
For more information on the topic of gender bias in education, see for example:
¥ Mathematics and Gender, edited by Fennema and Leder, Teacher's College Press, Columbia University,1990.
and the very recent book reporting extensive research on sexism in the classroom:
¥ Failing at Fairness: How America's Schools Cheat Girls, by Myra and David Sadker, Scribner's, 1994. <<<========<<
>>>>>==========>> 99.44 percent pure what? New York Times Magazine, 22 May 1994, page 15 No author provided
This brief article discusses the origin of the famous Ivory Soap claim to be 99.44 percent pure.
A Proctor and Gamble archivist, Edward Rider, claims that the best source for the number is the analysis done Dec. 14, 1882 by a chemist who found the soap to be 72.53% "fatty anhydrides,", 9.28 percent "soda combined and 17.63% "water by difference." giving a total of 99.44.
Another old ad had original Ivory 82.48 percent "true soap" and the article says that this comes from adding up only the combination of fatty acids and soda -- I guess these were measured by another chemist. <<<========<<
>>>>>==========>> May 1-7; lies, damn lies and baseball statistics. The New York Times, 8 May 1994, 4, p.2 Gina Kolata
In April of this year's baseball season there were 708 home runs, compared to 498 last April. Continued at this rate, 1994 would see 5,035 home runs, beating the record year, 1987, by 577 games. What's going on? Even when you compare the home run rates--2.22 per April game this year, 1.58 per April game last year-- there seems to be something strange happening. Or is there? This article tries to find out.
Ms. Kolata notes that last April stood out because there were many fewer home runs than in the rest of the season, and the season as a whole turned out to be a banner year. She also remarks that "Statisticians speak of what they call 'regression toward the mean': If one winter is hit with record snow falls, the next is likely to be closer to normal." Could this April be "wild in the other direction"?
Dr. Carl Morris, a statistician at Harvard University, examined data since the turn of the century and found, using a Poisson distribution test, that the number of home runs in both 1993 and, so far, 1994, are unexpectedly large. He also found strange peaks in home runs during seasons which followed expansion years--years when the number of teams increased. 1993 was an expansion year. On the other hand, 1987, the year with a the record number of home runs, was not an expansion year. So what can we conclude? Dr. Morris suggests, "maybe we'll see a big rise in the number of people studying statistics. Think of it like an expansion year." <<<========<<
>>>>>==========>> The quark and the jaguar: adventures in the simple and the complex, Murray Gell-Mann, W.H. Freeman, 1994
Gell-Mann was awarded the Nobel Prize in 1969 for his work leading up to the discovery of the quark. He is also the directory of the Santa Fe Institute where, among other things, they are trying to crack the stock market problem.
In this popular book that has incorporates a number of statistical ideas in discussion of fundamental concepts -- for example, Zipf's law in the discussion of scaling. In an entertaining chapter on randomness Gell-Mann remarks that a specific sequence of 0's and 1's of length 1000 is random if it cannot be compressed (printed out by a program consisting of less than 1000 0's and 1's). He then remarks that not all sequences produced by a random process such as tossing a coin a 1000 times are random but most of them are.
This is an illusion to the concept of Kolmogorov complexity which is itself a bit more complex than Gell-Mann makes it appear to be. The notion of Kolmogorov complexity and many of its applications is nicely presented in another more technical new book:
"An introduction to Kolmogorov Complexity & Its Applications" by Ming Li; and Paul M. Vitanyi,Springer- Verlag, ISBN:0-387-94053-7 <<<========<<
>>>>>==========>> The world; Asia's having one huge nicotine fit. The New York Times, 15 May 1994, 4, p.1 Philip Shenon
While the anti-smoking movement is beginning to hurt the sales of Philip Morris cigarettes in the United States, this is certainly not the case in the Asian countries. Success in these countries has caused foreign profits to be up nearly 17 percent while the domestic American market fell by nearly half.
This article provides impressive graphics showing the decline in American and the increase in China for the number of cigarettes smoked per adult, the increase in tobacco exports, and the current percentages of men and women who smoke in each of the Asian countries.
In the United States 28% of the men and 24% of the women smoke while in China, 61% of the men and 7% of the women smoke. It is expected that the percentage of women who smoke will increase dramatically in the Asian countries in the coming years. The increase in smoking is caused by increased property and changes in social customs that had discouraged smoking by women.
Epidemiologist Richard Peto at Oxford suggests that the increasing tobacco consumption in Asia will lead to tripling the number of tobacco-related illness over the next two or three decades. He suggests that 50 million Chinese children alive today will eventually die from diseases linked to cigarette smoking.
Tobacco companies are making massive advertising campaigns in Asia but say they are only trying to encourage those who smoke to switch to American made cigarettes and are not trying to increase the number of smokers by their everywhere present neon signs and billboards.
A different look at statistics on smoking can be found in the book "Exploring Data by Landwehr and Watkins", one of five books in the Quantitative Literacy Series published by Dale Seymour Publications.
On Page 119 a table is given containing data on smoking and heart disease for 21 countries.The statistics listed are cigarette consumption per adult per year and deaths per 100,000 people per year from coronary heart disease. (Students are to make a scatterplot relating cigarette consumption to deaths from heart disease, and these data suggest a postive, linear relationship between these two variables).
The countries with highest cigarette consumption (more than 3000 per adult per year) are US, Canada, Australia, New Zealand. No Asian countries are listed. <<<========<<
>>>>>==========>> Study backs breast chemotherapy regimen.
The New York Times, 5 May 1994, A22 Gina Kolata
A study of 1,572 women with breast cancer that has spread to the lymph nodes, has found that the disease- free survival rate associated with the usual dose of chemotherapy is higher than the rate associated with a dose that is lower and has fewer side effects.
The women in the study were divided into three groups: One receiving the standard dose of chemotherapy in four treatment cycles, one receiving the same dose but extended over six cycles, and one receiving half the standard dose in four treatment cycles. The article reports that the women in the third group fared the worst, with a 63 percent chance of living three years free of cancer, while the first group fared best, with a 74 percent chance. The second group did slightly worse than the first, but the difference was not enough "to say it was more than a matter of chance."
However, cancer experts cautioned that the study leaves open the important question which it was originally expected to answer: Does the effectiveness of chemotherapy increase with larger doses, or is there a threshold beyond which higher doses are no better and may even be worse? Dr. Daniel R. Budman, an author of the study points out that in 1985, when the study began, the largest dose was considered high, but that today it is the standard dose used. <<<========<<
>>>>>==========>> Science in the laboratory of the imagination.
The New York Times, 1 May 1994, 4, p. 2 George Johnson
Two recent scientific findings--one on the existence of two planets orbiting a pulsar 1,500 light-years away, the other on the existence of a long-predicted subatomic particle called the top quark--have prompted this article about detecting pattern in possibly random data.
Human beings generally want to see pattern--even if it's not there--and will develop elaborate theories to support such a claim. For many years, giant radio telescopes have picked up regular pulses from distant objects--pulsars--which are thought to be the rotating, burned-out remains of dead stars. A slight upset in this regular rhythm has sometimes led astronomers to hypothesize the existence of planets orbiting the pulsar, as in this case. But Mr. Johnson points out that, three years ago, the fluctuations in the blinking of a pulsar which seemed to imply the orbit of a large planet turned out instead, after further analysis, to be fluctuations in the earth's orbit.
Particle physicists, too, search for regularity in what may be random data. After bombarding billions and billions of protons and antiprotons and examining the debris, scientists have a dozen or so of the patterns that might signify the existence of the top quark-- "twice as many patterns as would be expected to occur by chance alone." <<<========<<
>>>>>==========>> Margarine not so great, report says.
San Diego Union-Tribune, 19 May 1994, Food, p. 19 Edward Blonz
A Harvard report says that "trans fatty" acids found in margarine are as bad as--and perhaps worse than--the saturated fats found in butter in terms of contributing to heart disease. Some 30,000 US heart disease deaths per year may be attributable to the presence of these compounds in margarine and processed foods. Studies indicate that trans fats increase "bad cholesterol" (low-density lipoprotein) to the same degree that saturated fats do and may also actually lower "good cholesterol (high density lipoprotein).
This article suggests that the important thing for people to do is to control their fat consumption. They should keep the spreadable fats to a minimum. One way to do this is to use a flavorful olive oil instead of margarine or butter. <<<========<<
>>>>>==========>> What fat to use? A debate spreads.
The Boston Globe, 17 May 1994, p1. Judy Foreman
Further discussion on the study by Drs. Willett and Ascherio of the Harvard School of Public Health and what bewildered readers should do. Also, this cryptic description of the study:
"Theirs was not an experimental study or a meta-analysis of other studies, in which data from various researchers are lumped together and grand conclusions drawn. Rather Willett and Ascherio examined about half a dozen studies of fat in the diet, and offered a new analysis."
DISCUSSION QUESTION: What do you suppose this means? <<<========<<
>>>>>==========>> The trustworthiness of survey research. The Chronicle of Higher Education, 25 May 1994, B1 Judith M. Tanur
The author's main message is "As educators, we have a dual responsibility--to be wise consumers of survey results ourselves and to train our students to be similarly wise."
Tanur points out that our society increasingly relies on survey data for important decisions, and we use the results of surveys routinely in our classes. She feels that it is not enough to leave it to the statistics class to tell students the errors that can be made from not using a probability sample, from non-response bias, from poorly worded questions etc. She feels that if you use surveys you have also to provide the students with the ability to read them critically.
Of special interest to us are Professor Tanur's remarks on the reporting of the results of surveys. She emphasizes that it is often very hard to find verbatim statements of the questions asked. As an example she provides the November 12, 1993, New York Times headline that read "Misconduct in Science is Not Rare, a Survey Finds" and remarks that you have to read the text very carefully to understand that the survey questions related to perceptions of misconduct rather than actual misconduct by the survey respondents. <<<========<<
>>>>>==========>> U. S. poll on holocaust is said to be flawed.
The Gazette( Montreal), 20 May 1994, A7.
According to Burns W. Roper, whose organization conducted a widely publicized poll for the American Jewish Committee, the Holocaust denial question was flawed, and the results should not be cause for alarm. The survey apparently showed that one-third of Americans were open to the possibility that the Holocaust never happened (22% said it was possible that it never happened, and an additional 12% said they did not know).
The flawed question was: "Does it seem possible or does is seem impossible to you that the Nazi extermination of the Jews never happened?" To indicate belief in the Holocaust requires the respondent to answer with a double negative (it was impossible that it never happened), a point which could easily have caused confusion in the telephone survey. <<<========<<
>>>>>==========>> Medicine and Health Wall Street Journal Reports Wall Street Journal, 20 May 1994, R1
This is a series of articles that discusses the relation of biotechnology to health. The articles are titled: How it works: a biotech primer, "Separate but equal: what is cloning anyway?", "The dark side: things that could go wrong", "What's fair?: the pricing debate", "Companies to watch: the hot firms", and "Risky ride: a guide for individual investors".
The article "How it works: a biotech primer" is especially well written and gives a very clear description of DNA, how proteins are made etc.
Other articles discuss the obvious questions related to cloning, genetic engineering of foods, cancer genes etc.
!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!! CHANCE News 3.07 (29 April to 20 May 1994) !!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!! Please send suggestions to: dart.chance@dartmouth.edu
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