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CHANCE News 2.19
(8 November to 24 November 1993)
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Prepared by J. Laurie Snell as part of
the CHANCE Course Project supported by
the National Science Foundation and the
New England Consortium for Undergraduate
Science Education.
Please send suggestions to
dart.chance@dartmouth.edu
Current and previous issues of chance
news can be found on our chance gopher.
Just point your gopher to
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Statistical thinking will one day be as necessary for
efficient citizenship as the ability to read and write.
H.G.Wells
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ARTICLES ABSTRACTED
>>>>>==========>> The last Chance News mentioned an article in the Boston Globe that discussed recent studies on family history as a risk factor for breast cancer. The article was motivated by an error in a recent study. This study reported an estimate that 6% of the breast cancer cases occur in women with a family history of the disease but should have reported 2.5%. The Globe article also reported that a recent Utah study estimated this percentage to be 17%. My abstract mentioned only these percentages and Jerry Grossman commented: I don't know if this is your fault or the fault of the original articles, but the statistics cited here are useless to the average reader! Unless I know what fraction of all women are deemed to have a family history of breast cancer, then knowing the percentage of women with breast cancer who have a family history is meaningless. For example, if the criteria for being judged to have the history are such that only 1% of the population meets it, then knowing that 2% or 6% or 17% (or whatever the figure actually is) of all women with breast cancer meet this definition tells me that family history is a risk factor; but if 20% meet the history criterion, then breast cancer is less prevalent among those with the history than among those without. More to the point, the real percentages we want to know are the chances of getting the disease if you do have the history, and the chances of getting the disease if you don't. One could then see if there was a significant difference (statistically or practically) between these two numbers. In fact, why not give the entire 2 X 2 contingency table for the number of women in the study (or extrapolated to the population) who fall into each of the categories (do or do not get breast cancer) versus (do or do not have a family history of breast cancer)? The Globe article did mention the actual relative risks at the very end but it could certainly have been improved by the above suggestions. These are the kinds of things we are trying to teach our Chance students and I hope that others will contribute such critiques of either my abstracts or the full text articles. <<<========<<
>>>>>==========>> Ask Marilyn. Boston Globe Parade Magazine, 14 Nov 1993, p 29 Marilyn vos Savant Marilyn answers another probability question: There are five cars on display as prizes, and their five ignition keys are in a box. You get to pick one key out of the box and try it in the ignition of one car. If it fits, you win the car. What are your chances of winning a car? Marilyn observes that one is tempted to say 1/25, but of course the answer is 1/5. She comments that the probability you win the red car secretly preferred by a member of the audience is 1/25, while if it is you that prefers the red car, the probability switches back to 1/5.
Alas, Marilyn made a serious error last week arguing that Fermat's theorem was not proven because Wiles used results from hyperbolic geometry. Perhaps she thinks that irate letters from mathematicians can only help her image now, even if this time they are correct. <<<========<<
>>>>>==========>> A statistical analysis of hitting streaks in baseball. JASA, Vol 88, No 424 pp 1175-1194 S. Christian Albright with comments by Jim Albert, and Hal Stern and Carl N. Morris Ever since Tversky and Gilovch (Chance, Winter 1989) challenged the evidence for streaks in basketball, sports fans have wanted to show that streaks exist. This article is the most ambitious effort to date. Albright obtained data on the hitting performance of all major league players who had at least 500 at bats in a given year. This gave him 501 season records with forty players represented in all four years. Besides the outcome of each at bat, the data provides information on situation variables thought to be correlated with hitting performance such as: home or away game, earned run average etc. Albright found only a couple of players with significant streaky performance as would be expected in 501 Bernoulli trials of length about 500. With the logistic regression model with situation variables included, more of the nonindependent records indicated the opposite of streakiness rather than indicated streakiness. He concludes that "actual performance is being generated in a manner reasonably consistent with a model of randomness (biased coin-tossing)." The commentators made interesting additional analyses of the data and all agree the final word is not in. Professor Albright(abright@indiana.edu) has offered to provide the data to those who want to further investigate this fascinating question. We will also put the data on our chance gopher. Our Chance students this term had a fine time exploring this data. <<<========<<
>>>>>==========>> Mathematical challenge to DNA testing in rape cases. The Sunday Telegraph, 21 November 1993, p 13 Robert Matthews This article reviews the now familiar argument that the extremely small probabilities for a match in DNA fingerprinting may be suspect because of errors in measurement and an unjustified assumption of independence between different bands. The article remarks that now statisticians also point out the odds usually quoted represent the probability of getting so good a DNA match from a person not connected with the crime, while the jury needs the probability of a person not being connected with the crime, given so good a DNA match. The latter probability depends upon the prior estimate of guilt and can be significantly higher when the other evidence is weak. A discussion of the use of Bayes probabilities in DNA fingerprinting can be found in articles by Berry and Cohen in Chance magazine Vol.3. No.3. <<<========<<
>>>>>==========>> Sex and selective memories. New Scientist, 30 Oct, p 10 William Brown Britain's large survey on sexual attitudes has been questioned because of its finding that, on average, men reported having 2.5 heterosexual partners in the past five years while women said they had only 1.5 partners. A member of the research study said that she believed the respondents tried very hard to tell the truth. While men and women reported compatible numbers in the short run, it is suggested that, over longer times, the men have, or choose to have, a better memory of their encounters than women do. Other explanations given were possible encounters between men and female prostitutes or other women not covered by the survey, such as those under 16 years of age. <<<========<<
>>>>>==========>> Odds differ on a Southern California Quake. The New York Times, 27 Nov 1993, Sec. 1 Page 7 Los Angeles (AP) A panel of scientists from the U.S. Geological Survey will delay its planned announcement on Dec.2 of quake probabilities to March or later because of disagreements, within the panel, as to the appropriate probabilities. Some members say a 60 percent chance is too high for the likelihood that a 'great' earthquake (8 or more on the Richter scale) will strike the San Andreas fault in Southern California in the next 30 years. Similarly, some think that a 90 percent chance for a 'major quake' (7 or more on the Richter scale) striking any of 300 other important faults in the region during this time is too high. Reasons given for scaling back the probabilities are: the fault has historically been too irregular to justify the probability, and scientists may have double- counted some big quakes that have affected more than one segment of the fault. The panel may also reconsider the probabilities it issued in November 1992 for a 5 to 12 percent chance of a major Southern California quake each year and a 47 percent chance of such a quake within five years given that a year has passed without a significant quake. <<<========<<
>>>>>==========>> To help girls keep up: math class without boys. New York Times, 24 Nov 1993, A1 Jane Gross Research has shown that girls generally score lower on standardized mathematics tests and tend to avoid advanced math and science classes. It has been suggested this is because of differences in attitudes and learning styles between boys and girls. In response to this, three California schools, two public and one private, are segregating girls in some math and science classes. This is having a very positive effect on the interest and performance of the girls in their study of mathematics and science. There is obvious concern about legal challenges, and apparently even some of those who did the research that led to this decision would prefer trying to change the aspects of the classroom teaching and behavior that discourages girls. <<<========<<
>>>>>==========>> Minneapolis' goal: raising test scores of minority pupils. Minneapolis Star Tribune, 21 Nov 1993, A1 Mary Jane Smetanka In the mid-1980's, Minneapolis schools were moving toward their goal of raising the test scores of minority students. By giving extra help to students having difficulties, they narrowed the gap between the test performance of white and minority students. Budget cuts halted the extra effort and this, together with an increase in the number of needy students, caused minority students' scores to drop, making the gap on some tests greater then ever. Plans are now being made to attack this problem again. A spokesman for the SAT said that the issue is not a white-minority issue but rather a have and have-not issue. "When white and minority students take similar high school courses and have parents with similar education and income, test score differences 'virtually disappear'". Others suggest that issues of race cannot be overlooked. <<<========<<
>>>>>==========>> Kids' TV ads are high in fatty foods. Parents are warned of unhealthy trend. The Atlanta Constitution, 9 Nov 1993 Charles Seabrook A new study presented at the annual American-Heart Association meeting says that, between 1988 and 1993, Saturday morning TV advertising for high-fat foods - including candy, packaged meals, fast-food hamburgers and pizzas - increased from 16 percent to 41 percent of all food ads. A child who watches five hours of TV on Saturday morning sees an average of 65 food commercials. Earlier research has shown that the more TV children watch the more likely they are to be overweight and have higher cholesterol levels. The researchers recommended that the food industry develop more healthy foods for children and advertise them. <<<========<<
>>>>>==========>> Jury to hear statistics on genetic fingerprints. Star Tribune, 18 Nov 1993, News B1 Conrad deFiebre For the first time in four years, a Minnesota criminal trial jury will hear testimony on the statistical probability of a mistaken identification by DNA fingerprinting. The case under consideration is a St.Paul rape case. The trial is expected to bring a showdown between the Minnesota Legislature and the Minnesota Supreme Court. The Supreme Court has allowed testimony about the statistical incidence of individual markers, but not about the overall probability derived from these. The Legislature has passed legislation calling for the admission of full DNA statistical evidence. Minnesota and Wyoming are the only two states where DNA match probabilities are routinely suppressed, on the grounds that the astronomical figures cited have an exaggerated impact on the juries. In the case being considered, one of the seven individual DNA markers has a 1/15 chance of occurring in the data base being used, and the least common marker has probability 1/48. However, based on the independence assumption, the jurors will be told that there is one chance in 121 million that the semen recovered at the scene of the crime belongs to anyone but the accused. <<<========<<
>>>>>==========>> Beliefs reported to shorten life. The New York Times, 7 November, 1993 Sandra Blakeslee UCSD sociologist David Phillips has produced another study receiving a lot of attention in the press. The last such study showed that men tend to die before their birthday and women after their birthday. This study is a large study giving evidence that psychosomatic beliefs can shorten life. Phillips examined a traditional belief in Chinese astrology that specific diseases are correlated with the year of birth. Each birth year is associated with one of five phases, with each phase linked with an organ of the body and a disease symptom. Phillips and his colleagues examined California death records from 1969 to 1990 for the 15 leading natural causes of death. They compared the death certificates of 28,169 adults of Chinese descent with 412,632 randomly selected white adults. The study found that Chinese-Americans who develop a disease linked to their birth year appear to die one to five years prematurely. For example, earth years are thought to be associated with cancer. The study found that Chinese Americans cancer patients born in earth years, have an average lifetime of 67.61 years, while those born in non-earth years had an average lifetime of 69.21 and a control group of white cancer patients born in an earth year have an average lifetime of 69 years. The study appears in Lancet and compliments other studies that have shown that positive thinking produces positive results, such as a study showing that cancer patients in support groups live longer than patients not getting such help. We discussed this in our Chance class, and the Chinese members of the class said that this generation did not pay much attention to such things and expressed some skepticism. <<<========<<
>>>>>==========>> Castration: still not a good route to longevity. Washington Post, 23 Nov 1993, Z5 Rick Weiss Men are more prone to hardening of the arteries and heart disease than women. One theory is: this is caused by the male hormone testosterone, made in the testes. Women also produce testosterone but in smaller amounts than men. As reported in the current issue of Nature, a research team in Germany, despairing of getting permission to castrate a group of men, documented the life spans of choir singers born between 1581 and 1858. They comp- ared the life spans of 50 men, castrated in boyhood to retain their soprano voices, with data from a control group of bass, baritone and tenor singers. The average lifetime was 65.5 for the castrated group and 64.3 for the control group. They concluded that "prepubertal removal of the testes had no influence on the longevity of men". A cardiologist is quoted as saying that most cardiologists are convinced that testosterone does play some role in men's increased risk of heart disease. <<<========<<
>>>>>==========>> The following book was suggested by Goran Djuknic
The Broken Dice And Other Mathematical Tales of Chance. Ivar Ekeland, translated by Carol Volk, University of Chicago Press, 1993, 183 pp, $19.95. This book consists of six essays on the faces of chance: randomness, fate, anticipation, chaos, risk, and statistics. In the preface, Ekeland remarks that he "brings together a few pages from an ancient saga and fragments of a modern treatise on chance. While one text speaks of fate, magic or destiny, and the other of chance, chaos, or risk, they are telling the same story". Ekeland vividly demonstrates this in his first chapter on chance and randomness. He starts by telling a story of the kings of Norway and Gautland in the thirteenth century who decided to settle the disputed ownership of an island by rolling dice. Some strange things happened that could be the result of divine intervention of cheating. A manuscript by a Brother Edvin in the file of the king of Norway describes ways to cast lots so that the outcome is only governed by divine will. For example, to the kings he would suggest that each king choose a number and give their numbers to a clerk who would add them and divide by 6, with the remainder determining the roll of the die. Brother Edvin devises more elaborate methods that bear a striking resemblance to the method first proposed by John Von Neumann as a random number generator, and leads Ekeland into a discussion of modern methods for obtaining random numbers. Ekeland takes on some pretty difficult topics, such as Kolmogorov's use of complexity to define a "random sequence". However, he manages to get across the flavor of the topic remarkably well, using only words we all understand. Ekeland's earlier book "The World According to Mathematics", in its original French version, won a major award for scientific writing for laymen. This book surely deserves another such award. <<<========<<
>>>>>==========>> Reese Prosser suggested the next book.
Leave it to chance. The New York Review of Books, 18 Nov 1993, p 48 P. N. Furbank A review of: Enlightenment and the Shadows of Chance: The Novel and the Culture of Gambling in Eighteenth-Century France. by Thomas M. Kavanagh Johns Hopkins University Press, 271 pp. $36.50 I confess that this review and the book itself are over my head. I could only get some vague ideas of what it is all about. The book certainly has a lot of interesting ideas about the relation of probability and gambling to the literature at the time of the enlightenment. Here is one of Kavanaugh's ideas. Before the formalization of probability theory in the eighteenth century, there was not much you could say about the outcome of a chance experiment other than that you did not know what the outcome would be. Chance events were considered rather mystical things. Then along came the "law of large numbers" and statistics and we could describe the "average outcome", "the average man" etc. Just as you cannot say anything about the outcome of a single toss of a coin, so a writer could not say anything about a single event. But the concept of taming chance with the law of large numbers led to the idea that the novel should make some kind of sense out of the many small chance events that effect a person's life leading to the "typical man" or the "typical behavior". <<<========<<
>>>>>==========>> Large-scale test of AIDS vaccine put off. Newsday, 21 Nov 1993, p 6 Michael Unger The prospects for finding a vaccine that would cause the body to make antibodies to fight off infection with HIV has looked promising. In recent years several different vaccines have been given to small numbers of healthy U.S. volunteers. The volunteers' bodies produced neutralizing antibodies that deactivated a strain of HIV virus grown in lab cells for experimental purposes. The National Institute of Allergy and Infectious Diseases had planned a large-scale human test this year, where thousands of non-infected volunteers from high risk-groups would be vaccinated. Their immune responses would be tested. and it would be seen if, over time, they were less likely to get infected than a similar group not vaccinated. However, before doing this, the government sponsored studies to test existing vaccines against the HIV virus that was actually circulating in humans in the United States as compared to the strain developed in the laboratory. The November 12 issue of Science reported the results of three such experiments, all of which failed to be effective against the human HIV virus. These disappointments have led to the decision to postpone the large scale test on humans until more is understood about what went wrong with these experiments. Drug companies expressed serious concerns about delaying the tests for which they have already produced the vaccine. <<<========<<
>>>>>==========>> Rise in ultraviolet rays seen in North America. The New York Times, 16 Nov 1993, C11 William K. Stevens While most scientists have assumed that ozone depletion is resulting in long-term increases in ultraviolet radiation around the world, they have not, until now shown that this is the case outside of the Antarctica. The November 12 issue of Science reports the results of a study carried out in Toronto that measured ultraviolet radiation reaching the ground in Toronto at least once every hour from sunrise to sunset of every day during five summers and four winters from 1989 to 1993. During this period, Ozone levels over Toronto decreased about 4 percent a year in winter and about 2 percent a year in summer. The harmful ultraviolet radiation bands reaching Toronto increased by 6.7 percent in the summer and 35 percent a year in the winter. <<<========<<
>>>>>==========>> 3 Drugs for heart attacks are shown to be ineffective. The New York Times, 8 Nov 1993, B10 Lawrence K. Altman Oxford University group led by Richard Peto report results of their most recent study on methods to treat heart attacks. One of their previous studies set a standard for treating heart attacks: aspirin, injection of a drug to dissolve clots in the coronary arteries, and a beta-blocker to dissolve clots in the coronary arteries. Their new study looked at the three drugs that are also in widespread use for treatment of heart attacks: magnesium, nitrates and converting-enzyme inhibitors. The study involved 58,000 patients who were treated for heart attacks in more that 1,000 hospitals in 30 countries from July 1991 to August 1993. The study had only one positive result: The enzyme inhibiting drug Captopril had a small benefit in preventing death, as measured at one month and six months after a heart attack. Speaking of the other results, Richard Peto commented that "These are the most disappointing results I have ever had in my career." Currently more than 70 percent of heart attack patients in the United States receive nitrate drugs, compared to 18 percent in England. Several studies, involving a total of 3,000 patients, have shown that nitrates reduce the death rate by about one-third. However, combining the results of the Oxford study and one carried out in Italy gives a combined study of 80,000 patients that shows no statistically significant improvement caused by nitrate treatment. Peto commented that many of the previous positive results on the use of magnesium and nitrates were not large enough to avoid the problem of statistical quirk, or "the play of chance". <<<========<<
>>>>>==========>> Jobless estimates too low, bureau says. Los Angeles Times, 17 Nov 1993, A17 John M. Berry The Bureau of Labor Statistics says that it has been substantially underestimating joblessness, particularly among women. This has been discovered in the process of testing a new monthly survey technique the department will begin using in January. The most important differences between the old and new survey results come from changing the first question. Currently, the way the first question is asked depends on the age and sex of the person who answers the door. If it is a younger person of either sex the question asked is: "What were you doing most last week, going to school or something else? An adult women is asked, "What were you doing most last week, keeping house or something else?" An adult man is asked "What were you doing most last week, working or something else?" The new questionnaire starts by determining whether anyone in the household has a business or a farm, and then asks, "Last week, did you do any work for pay?" Or if there is a family business or farm,".. pay or profit?" In testing the new survey, more women were found to be working but also many more were unemployed, resulting in a .8% higher unemployment rate for adult women. It showed a .2 percent increase in average unemployment rate for men. A sample of 60,000 households is taken each month. Katherine Abraham, commissioner of labor statistics, said that there are so many statistical uncertainties, with the switch in surveys that her agency will have difficulty interpreting the first official use of the new survey in January. She hopes that the financial markets will not pay any attention to these as well as the February numbers. <<<========<<
>>>>>==========>> Virginity age falls but sex lessons escape blame. The Guardian, 13 Nov 1993, p 10 Chris Mihill The findings of the British National Survey of Sexual Attitudes and Lifestyles are to be published in January, but some of the results are being announced early. Over the past four decades, the average age at which women first have sexual intercourse has fallen from 21 to 17, and for men from 20 to 17. Half of the women in the age group 16 to 24 who had sex before the age of 16, believed that the experience had come too early. Peer pressure and alcohol were involved but apparently not sex education. In fact, there was evidence that those who had good sex education had, on average, the first encounter later than those who did not. Most people have one partner at a time rather than having multiple partners at the same time, although many 24 year old's today have already had more partners than those aged 55 have had. <<<========<<
>>>>>==========>> !!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!! CHANCE News 2.19 (8 November to 24 November 1993) !!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!! Please send suggestions to: jlsnell@dartmouth.edu