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CHANCE News 3.06
(13 April to 28 April 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 suggestions to: dart.chance@dartmouth.edu
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Every third person in Israel saw 1.8 public theater shows last year.
Newspaper headline posted on Maya Bar Hillel's board.
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>>>>>==========>> Maya also recommended several books of interest to a Chance course. One I found particularly interesting was: Paradoxes of gambling behaviour. L Erlbaum Associations, 1984 Wagenaar, Willem
Wagenaar did experiments observing gamblers and tried to figure out why they do what they do. For example, why do black jack players play so poorly when at least the basic strategy is so easy to learn? He also carried out experiments to determine when a person will attribute something to luck as compared to chance. The answer seems to be something like this: if you are observing roulette and you see 7 red numbers in a row you might attribute this to chance, but if you are actually betting on red you are apt to say that it is luck. Wagenaar discusses a lot of ideas on why people gamble, but admits, in the end, that he regards this a major unsolved problem. Another interesting book Maya suggested is: The Winner's Curse Free Press, 1991 Richard Thaler Thaler suggests that the models of economic theorists often do not describe how we behave because they assume we act rationally in situations where we do not. He presents a series of examples, that he calls anomalies, where human behavior does not follow economic theory. The title of the book comes from the observation that the winning bidder in an auction is likely to have overbid when the number of bidders is large. As in many of his examples, Thaler explains the behavior and supports his claims with experimental evidence (bidders for oil leases). Another example is over-betting on long shots at the horse races so that a bet on the favorite has positive expectation. Similarly, people choose numbers in a lottery that are apt to be chosen by lots of other people. They may then have to divide the pot if they win. <<<========<< >>>>>==========>> I am continuing to try to find out what is the meaning of "there is a 20% chance of rain". A survey on what people think this means was reported in: Misinterpretations of Precipitation. Bulletin American Meteorological Society, Vol. 61, No 7, July 1980, p.695-701. Murphy, Licthenstein, Fischoff and Winkler
The authors wanted to see if there was a misunderstanding about the event being predicted, the meaning of probability or both. To test the understanding of the event, subjects were asked if the event being predicted was "rain somewhere in the region", "rain at a particular point in the region" "rain 20% of the time etc. Their answers led the authors to the conclusion that there is considerable misinterpretation on the meaning of the event. On the other hand, the subjects' answers to questions on the possible meaning of "20% chance" led them to conclude that the subjects did understand what the probability itself meant. I also talked to a couple of meteorologists who stated that it is unlikely that the public could understand what a 20% chance of rain means. Harold Brooks provided the following reference. According to the National Weather Service Operations Manual, The Probability of Precipitation (PoP) is: The likelihood of occurrence (expressed as a percent) of a precipitation event at any given point in the forecast area. The time period to which the PoP applies must be clearly stated (or unambiguously inferred from the forecast wording) since, without this, a numerical PoP value is meaningless. That is, it is the average point probability within the forecast area and the same PoP is assigned to each point. It can be shown that the PoP is equal to the expected area coverage of the precipitation (Schaefer, J. T. and R. L. Livingston, 1990: Operational implications of the "Probability of Precipitation". Weather. Forecasting, 5, 354-356.). <<<========<< >>>>>==========>> Ask Marilyn. Marilyn vos Savant Parade Magazine, 24 April 1994, p18.
Marilyn is asked to settle a dispute on the probability that a man having four children will have two boys and two girls, given that he has at least one boy. The proposed answers, are .375 and .50. (The reader favors the former, and has a friend who insists on the latter). Marilyn gives the answer (under the Bernoulli trials model) of .40 by enumerating the 15 possible four child families other than GGGG and counting up the 6 that have two B's and two G's. Curiously, in a previous column Marilyn discussed the more familiar version of this problem: Given that a family has two children and at least one is a boy, what is the probability that the family has two boys? In this earlier discussion Marilyn seemed to understand that the probability may depend upon the story about how you learned that there was at least one boy. She gave a story that would suggest the answer 1/3. It is easy to give stories for which the answer would be 1/2. While 1/3 is the answer we expect in the text book version of this problem, I have never been able to find a simple realistic story that leads to this answer. If you know one please send it to me! An excellent discussion of this dependence of the story in this, and other "paradoxes" can be found in Bar-Hillel, M., Falk, R. (1982) Some teasers concerning conditional probability. Cognition, 11, 109-122 <<<========<< >>>>>==========>> Vitamin Supplements are Seen as No Guard Against. Diseases.
The New York Times, 14 April 1994, A1 Gina Kolata
A study involving 29,000 Finnish men to determine if taking vitamin E and beta-carotene supplements helps protect against cancer and heart disease has found no proof of such claims. In fact, the study, sponsored by the National Cancer Institute in Bethesda, MD, and published in "The New England Journal of Medicine", has, instead, suggested that vitamins may have harmful effects. The participants in the study, all of whom were long- term smokers over 50 years old, were divided into 4 groups: those taking only vitamin E, those taking only beta-carotene, those taking both vitamins, and those taking a placebo. After five to eight years, no positive results were found. Further, Ms. Kolata reports that the study found that those in the beta- carotene group were "somewhat more likely" to die from lung cancer and heart disease. The group taking vitamin E had slightly more strokes from bleeding in the brain, and slightly fewer cases of prostate cancer, but researchers claimed that both of these effects "could be due to chance." Previous studies have shown a benefit from eating large amounts of fruits and vegetables high in beta-carotene and vitamin E, and also from taking supplements. However, as Ms. Kolata remarks, "the question remained: Did the protective effect lie in the vitamins or in some other aspect of the people's behavior?" Dr. Gilbert S. Omenn, Dean of the School of Public Health at the University of Washington in Seattle, said that smokers were good subjects for the study because they were more likely to develop diseases and hence a positive effect from vitamins would be easier to verify. He also remarked, "if you want to do a study with 29,000 people rather than 100,000 people, you have to look at high-risk people." DISCUSSION QUESTIONS: ¥ What do you think it means that some of the harmful effects "could be due to chance"? ¥ Do you think it was smart to conduct the study on smokers? Should the results of the study be applied to non-smokers (or to women or to people under 50)? ¥ What do you think Dr. Omenn meant when he said, "if you want to do a study with 29,000 people rather than 100,000 people, you have to look at high-risk people."? <<<========<< >>>>>==========>> Beta-Carotene: Helpful or Harmful. Science, 22 April 1994, p 500 Rachel Nowak
This article discusses the portion of the study reported in the last article as it effects the results relating to beta-carotene. It reports there were 18% more lung cancer cases at the trials end for those who took beta- carotene as compared with those that did not. This was significant at the 1% level by a log-rank test. Representatives of the monitoring committee remark that they did see a hint of this difference a couple of years ago, but allowed the study to continue since the difference was not seen to be significant at that time. The article points out that this very surprising result has implications for ongoing and future studies involving beta-carotene. The head of the National Cancer Institute's division of cancer prevention and control has asked principle investigators and safety monitoring boards of NCI sponsored trials of beta- carotene to consider notifying the over 800,000 participants in such studies of the new findings. The article remarks that the worst scenario would be if beta-carotene itself is a carcinogenic. However,, researchers are inclined to believe that the 1 in 100 result is do to chance. DISCUSSION QUESTION: ¥Why do you think that the New York Times article placed so little emphasis on the significance of harmful effect of beta carotene? ¥If you were taking beta-carotene pills would you stop taking them? <<<========<< >>>>>==========>> Mind over Matter: Psychology Can Help to Explain the Eccentric Behavior of Financial Markets. The Economist, April 23rd-29th 1994
One often hears rational explanations for changes in the stock market such as: if interest rates go up, we will have inflation and then the market will go down. Increasingly, experts are identifying aspects of human psychology that can also effect the market. This has led to a new branch of economics called "behavioral finance" that relies heavily on experiments and theories of Tversky and Kahneman to explain some of the market's apparent irrationalities. (Amos Tversky tells me that he is often asked how he invests his money) An example of human behavior that might effect the market is: people place too much emphasis on recent data rather than long-run averages. A second example is that investors like to be fashionable (they won't mind a loss so much if it is what everyone else is doing -- for example buying General Motors stock). Notice that this last behavior seems to be the opposite of what Thaler suggests that we do at the races. Kahneman and Tversky's prospect theory suggests people weight their prospective losses about twice as much as their prospective gains. Another of their heuristics suggest that how a problem is "framed" is important. The following example is given: "If an investor owns two stock worth $20, one of which he bought at $10 and the other at $25, he might not sell the latter one (even if its price is falling) because he did not want to suffer a loss. If he thought about the combined value of the two shares, however, he might be happy to sell both, as that would produce a net gain." Not surprisingly, economists differ on the importance they give this psychological theory. DISCUSSION QUESTION: Note that Kahneman and Tversky suggest that, in the market, people bet on the favorites while Thaler suggests that, in betting on horses, people seem to bet on the long shots. Can you give an explanation for this apparently different behavior? <<<========<< >>>>>==========>> Diet and Health: What Should We Eat? Science, 22 April 1994 Walter C. Willett
This is a review of what we know from recent studies about the effect of diet on prevention of diseases including heart disease, cancer, birth defects, and cataracts. The author concludes that "there is strong evidence that vegetables and fruits protect against these diseases; however, the active constituents are incompletely identified. Whether fat per se is a major cause of disease is a question still under debate, although saturated and partially hydrogenated fats probably increase the risk of coronary heart disease." This a good article to show how inconsistent studies can be. <<<========<< >>>>>==========>> Black Heart Care is Unequal, but Survival Called Similar.
The Boston Globe, 20 April 1994, National p. 8 Richard A. Knox
A study involving 34,000 patients from 158 VA hospitals has found that, although black men routinely undergo far fewer high-technology cardiac procedures after a heart- attack than do white men, the survival rates one and two years later for the two groups are equal. The study found that, compared to whites, blacks had 54 percent less chance of having a coronary artery bypass graft within 90 days of their heart attack, and had 42 percent lower rates of coronary angioplasty. Nevertheless, blacks had 18 percent higher survival rates 30 days after their heart attack, 7 percent higher survival after one year, and virtually the same survival rates after two years. The researchers gave the following possible explanations for their results: -Since other studies have shown that black patients are less likely to be resuscitated outside the hospital, those patients who reached the VA hospital may represent a healthier population than the white VA patients; -There may be biological factors, such as higher levels of "good" cholesterol, that help protect black patients; -It may require more than two years to detect a survival advantage for white patients. DISCUSSION QUESTION: ¥Do you feel that racial discrimination plays a role in the differences found in this study? <<<========<< >>>>>==========>> Mental decline in aging need not be inevitable
New York Times, 26 April 1994, C1 Daniel Goleman
This month's issue of the American Psychologist contains the most recent findings of a major study to try to understand the decline of mental abilities with age. The study is under the direction of K. Warner Schaie, a psychologist at Pennsylvania State University. For more than 35 years his study has followed more than 5000 men and women who have been tested regularly on: spatial orientation, inductive reasoning, verbal meaning, word fluency, and number skill. Those who developed severe disabling disease or became senile were dropped from the study. Decline in these facilities begins in the early sixties and accelerates in the late seventies. The largest decline for both men and women was in the number skill. From the graphs provided, it seems that, in general, the decrease in mental abilities is slower for women than men. The article also discusses other studies that suggest that it is possible to slow down the decline by continued mental activity, exercise, etc., and also one can be successfully coached to maintain certain mental skills. DISCUSSION QUESTIONS: ¥ Why do you think that authors put such a positive "spin" on reports on decline in mental abilities with aging (for example, note the headline)? ¥ Read the article and look at the graph provided. Do you agree with the author's conclusions from the graphs? <<<========<< >>>>>==========>> Research Fraud Breaks Chain of Trust; Investigation Interrupts Ongoing Studies.
The Washington Post, 19 April 1994, Health Z6 Robin Herman
The debate over the use of the drug tamoxifen in preventing breast cancer in healthy women continues. Last month it was revealed that, in a landmark breast cancer study sponsored by the National Cancer Institute (NCI), a participating doctor had falsified some of his records. The study found that women with breast cancer that had not spread to the lymph nodes who received lumpectomy and radiation therapy fared as well as women who underwent the more radical mastectomy surgery. Because of the falsified data, there has been much concern over the validity of the study's findings, but NCI has reassured women and their doctors that the results of the study are confirmed by separate studies. In related trials, the drug tamoxifen has been tested on healthy women who are at high risk for developing breast cancer, and has come under scrutiny because of possible links to uterine cancer. Bernard Fisher, the leader of the research group that had been coordinating the lumpectomy and tamoxifen studies, has been forced to step down amid the controversy. Since tamoxifen is being used in a prevention trial -- one in which the patients are healthy, as opposed to a treatment trial in which patients already have a disease -- there is much debate over the risks posed to participants. Adrian Fugh-Berman, of the National Women's Health Network cites eye problems, liver toxicity and blood clots as additional side effects of tamoxifen and asks, "at what point do the risks become high enough to stop this trial?" Others think that it is more important to examine the ratio of benefits to risks, not the risks alone. Medical researchers have estimated that women over 60 have a one-in-ten chance of developing breast cancer, compared to a one-in-47 chance of uterine cancer. NCI officials also claim that uterine cancer is easier to detect and treat. Fisher generated more controversy last week when he published an article on the latest uterine cancer rates in breast cancer patients treated with tamoxifen. Fisher cites two different rates: when compared to a placebo group, the women receiving tamoxifen had 7.5 times the risk of developing uterine cancer, as opposed to 2.2 times the risk when compared to the general population. In the tamoxifen group, 23 out of 2,639 women contracted uterine cancer. DISCUSSION QUESTIONS: ¥ In prevention trials, is it better to examine risks of side-effects, or ratios of benefits to risks? ¥ Should the rates of uterine cancer in the tamoxifen group be compared to the placebo group, or to the general population? Does the overall rate (23 out of 2639) make any difference in your decision? <<<========<< >>>>>==========>> September's Children Born With Football Boots On.
The Guardian, 13 April 1994, Home p. 24 Tim Radford
A Dutch psychologist has discovered that twice as many English football players are born from September to November as are born from June to August. Ad Dudink of the University of Amsterdam, writing in the journal "Nature", (14 April 1994) has assembled the birthdays of 2,777 players in the English football league during the 1991-1992 season, and found that 1,020 of them were born between September and November. He then noted that in England, the season starts in August. He remarked: "Children who participate in sports are placed in age groups, and my results imply many athletes in organized sports may never get a fair chance because of this method of classification." Discussion Question: ¥ Do you agree with the remark attributed to Mr. Dudink? ¥ What would be a alternative explanation for the results found in this study? How would you explain the results of this study? ¥ In a previous article in Nature (Season of Birth and Cognitive Development, Williams et al, Vol 228, pp. 1033- 1036) evidence is provided that certain groups of educationally and psychologically handicapped children in the British educational system contain a high incidence of those born in the summer. What explanation might you give for this? How would you test your explanation? <<<========<< >>>>>==========>> High Blood Pressure Tied to Memory Decline.
The New York Times, 26 April 1994, C10 Daniel Goleman
Dr. Merrill Elias, a psychologist at the University of Maine, has found that high blood pressure can lead to mental decline in later years and that "the longer you have high blood pressure, the worse the decline, especially on tests of short-term memory and attention." The findings corroborate earlier studies on hypertension and mental decline. Each rise of 20 millimeters of mercury in diastolic blood pressure (the lower of the two readings), continued for 8 to 10 years was associated with a drop of about a quarter of a standard deviation on some memory tests -- equivalent to 2 or 3 points on a scale where 100 is average. Older people with diastolic pressure above 90 had the greatest memory decline. <<<========<< >>>>>==========>> Blood Tests Favored Over Amniocentesis.
Los Angeles Times, 22 April 1994, C1 Robert Cooke
A study of pregnant women over 35 conducted by the Foundation for Blood Research and the California Public Health Foundation has found that blood tests are safer than amniocentesis. When used as a preliminary tool to screen for Down's syndrome, blood tests could save $250 million a year in medical costs. The overall risk of having a baby with Down's syndrome is 1 in 700, but this risk rises to 1 in 270 at age 35 and to 1 in 40 at age 40. Screening based on blood tests, which cost about $75 per test in the US, diagnosed 89% of Down's cases, while amniocentesis, at about $1000 for the entire procedure, detected nearly 100% of all cases. According to an editorial that accompanied the study, screening by blood tests alone would translate into finding an additional 320 Down's syndrome babies each year. If the blood tests are given first, with amniocentesis then given to women found to have at least a 1 in 200 chance of having a Down's syndrome baby--about 25% of women over 35 given blood tests would fall into this group--not only could money be saved, but the study indicates that 14,000 amniocentesis-linked miscarriages could be avoided. The blood tests are believed to carry no risk of miscarriage. Discussion Question: ¥ The article states that amniocentesis carries "a small risk of causing miscarriage." How would knowledge of the actual risk help in weighing the relative merits of the procedures discussed? Do you think cost is a relevant issue? <<<========<< >>>>>==========>> Big Picture of Cancer Process is Being Seen for the First Time.
The New York Times, 19 April 1994, C3 Gina Kolata
Since a cancer cell does not stop growing while a normal cell does, molecular biologists have long thought that defects in the genes that control the cell cycle: from growth to division into two daughter cells and then back to a resting state. Verification of this hypothesis was hard to find until recently. In the last year two important cancer genes were found that effect the cell cycle indirectly. In addition, the cancer gene p53 acts indirectly on the cell cycle by preventing cells from making proteins needed to stop growing. The April 15th issue of "Science" announced that a recently discovered cancer gene plays a major role in the cell cycle by making a protein product called p16 that helps stop growth. This article gives an very clear description of how all this is thought to work and why scientists are so hopeful that they are beginning to understand what is going on allowing them to start thinking about drugs to target specific molecular defects. <<<========<< >>>>>==========>> AIDS Virus Just as Mysterious 10 Years After its Discovery
The San Francisco Chronicle, 14 April 1994 David Perlman
The optimism expressed in the previous article about cancer is certainly not shared in this article about AIDS. While researchers feel that they have learned a lot about the HIV virus in the past ten years, there are no cures, no vaccines and none are likely in the near future. While the principle drug AZT has been disappointing in the control of AIDS, it has been shown to be successful in helping prevent the transmission of AIDS from an infected mother to her unborn child. Like the previous article, this article is very well written and gives a clear summary of what has been discovered about AIDS, the current state of the epidemic, how it is changing, and what researchers are looking at to learn more its causes and how it can be slowed down. <<<========<< >>>>>==========>> Pesticides and Breast Cancer: No Link? Science, 22 April 1994, p 144-145 Gary Taubes
One year ago a study reported in the "Journal of the National Cancer Institute" found that breast cancer was four times more common among women with the highest blood level of DDE, a breakdown component of DDT, than among women with the lowest levels. This week, in the same journal, the results of a larger study finds no connection between the pesticide and cancer. This later study was based on blood samples drawn and frozen during routine physical examination of women at the Kaiser Foundation in Oakland California in the late 60's. From a large archive, researchers chose samples from 150 women (50 black, 50 white, 50 Asian) who had gone on to develop breast cancer an average of 14 years later. 150 matched samples completed the study group. A comparison of the two groups found no significant difference in levels of DDE.
!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!! CHANCE News 3.06 (13 April to 28 April 1994) !!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!! Please send suggestions to: dart.chance@dartmouth.edu
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