CHANCE News 5.05

(29 March 1996 to 23 April 1996)


Prepared by J. Laurie Snell, with help from William Peterson, Fuxing Hou, Ma.Katrina Munoz Dy, and Joan Snell, as part of the CHANCE Course Project supported by the National Science Foundation.

Please send comments and suggestions for articles to jlsnell@dartmouth.edu.

Back issues of Chance News and other materials for teaching a
CHANCE course are available from the Chance web site:



From a photograph of California graffiti by Paul Gardner.


From our readers:

Brendan Lilley and Jim Hilton noted that the quote in the last Chance News we attributed to a current movie should be attributed to Louis Pasteur. The complete quote is: "Where observation is concerned, chance favors only the prepared mind!" Brendan remarks: "He said this after discovering that mirror image isomers of tartaric acid crystallized separately, thus beginning the field of stereochemistry."

We said in the last chance news that, in the game of Monopoly, you should like greens because it has been shown that the highest expected return for hotels occurs for the green properties. Albyn Jones writes:

The expected income, given that there are hotels, is not the same as the expected income, which will be affected by the difficulty of building hotels. The cost of building hotels also affects the players' cash reserves, another crucial factor in the game. The fanatical monopoly players I know turn up their noses at the greens, and fight to the death for the oranges. I'll leave the proper analysis as an exercise for the reader....


Math professor shares $15 million lotto jackpot.
Denver Post, 9 April 1996, B3
Peter G. Chronis

Math professor Celestino Mendez was discussing expected value in his class at Metropolitan State College and remarked that, in a lottery, the expected winning increases when the jackpot gets higher. He told his students that they ought to buy a ticket in the current Colorado Lottery because the expected value was positive (14 cents when you buy a $1 ticket). Professor Mendez thought he should put his money where his mouth is, and so, on the way home, he stopped and bought ten tickets. One of these had the lucky numbers, and he shared the $15 million prize with one other winner.

Discussion question:

In the Colorado lottery you choose 6 distinct numbers from the numbers from 1 to 42 and order does not count. The article states that the odds of winning are 1 in 5.25 million. Is this correct? If so, why was the expected winning only 14 cents?

Chance Magazine, Winter 1996

This current issue of "Chance Magazine" has the following articles:
The time management article is particularly appropriate for Chance News. It starts with several quotes from New York Times sports writers' extolling the virtues of controlling the ball. For example:

12/11/93--During a Vikings versus Cowboys game, former coach and analyst Mike Ditka said "...not going to score if they can't put their hands on the ball. Keep their offense off the field...."
The authors go on to assess the value of ball control using mathematical modeling and the techniques of Markov dynamic programming. They conclude: "Our results clearly indicated that the intent to use a ball-control offense to keep the other team from scoring is misguided. In fact, a team is better off simply using its usual unconstrained strategy (which requires no knowledge of optimization) than using a ball-control offense."


What do you think football and basketball coaches' reaction would be to the conclusions of this article?

The power of logical thinking.
Marilyn vos Savant
Saint Martin's Press, 1996, New York

Marilyn vos Savant's latest book organizes material from her recent columns according to three themes: Part 1, how our own minds can work against us; Part 2, how numbers and statistics can mislead; and Part 3, how politicians exploit our innocence.

Part 1 features a discussion of the now famous Monte Hall problem and the other related paradoxes that came her way inspired by the interest in the Monte Hall problem.

Part 2 is Marilyn's version of "How to lie with statistics".

Part 3 is the most original. Here she uses the 1992 election to show how politicians use numbers to their own advantage. Clips are chosen from the major news sources and analyzed to show how they do this. Two examples are the statements from the Clinton campaign: "most people are working harder for less money than they were earning ten years ago" and "there is something wrong with our tax code, if your income went up 65 percent in the 1980's and your taxes went down 15 percent".

One of the most interesting contributions in the book is an appendix which gives a popular account written by Donald Granberg of an article he wrote with T. Brown, "The Monte Hall Dilemma," Personality and Social Psychology Bulletin, 1995, vol. 31, pp. 711-723. Ms. vos Savant gave Professor Granberg the mountains of correspondence she received after her analysis of the Monte Hall problem. Granberg and Brown analyze this correspondence to assess the concerns of the writers. They also report on experiments designed to estimate the proportion of people who start with a misconception of this problem and how hard it is to get these people to change their minds in repeated experiments. They do similar experiments with a different but equivalent version of the problem they call Russian Roulette. In this version there are two cars and one goat and Monte opens a door with a car, making this car no longer available to the contestant. Now the contestant should not switch and, unlike the Monte Hall version, most people get this right.


(1) What is wrong with the Clinton clipps?

(2) Granberg poses the following formulation of the Monte Hall problem that he attributes to Joseph Moder: In the Monte Hall problem suppose that everything is the same except that Monte forgot to ask which door had the car and, in the spirit of "the show must go on", he makes a guess at which of the two doors to open and lucks out, getting a door without a goat. Now should the contestant switch?

(3) Granberg also discusses the following variation of the Monte Hall problem. You have observed the show for a long time and found that the car is put behind door 1 45 percent of the time, behind door 2 40 percent of the time and behind door 3 15 percent of the time. Assume that everything else about the show is the same. Again you start to go to door 1. Monte opens a door with a goat and offers to let you switch. Should you? Knowing that Monte was going to give you a chance to switch, should you have initially chosen door 1?

Bob Carver suggested the following article and provided the discussion questions.

Those scary college costs.
Newsweek, 29 April, 1996, pp 52-56
Tom Morganthau and Seema Nayar

This article discusses the rising cost of a college education with a number of interesting statistics. For example, colleges today offer 23 percent fewer days for 1110 percent more money than in 1910. Having analyzed the current costs the authors ask "does it all pay off?" They cite a study by three University of Pennsylvania economists on the lifetime earnings of women who earned degrees from elite universities, versus those who did not. The Newsweek authors caution that "the conclusions were based on a sample of identical twins that included exactly 156 people, a very small database."

In concluding their article, the Newsweek authors point to "a common flaw of the dismal science, which is their reliance on the AVERAGE earnings of an AVERAGE graduate. "There are no 'average' students at Harvard or Smith or Stanford or Duke -- for, at $1000 a week, how could there be?"


(1) What do you suppose the economists did compare in their study of twins?

(2) Does it seem likely that, in a study of twins, the comparison was between the "average" earnings of graduates?

(3) Does a sample of data from 78 pairs of twins constitute a small database?

(4) When the authors refer to "average" earnings, "average" graduates, and "average" students, does the word 'average' mean the same thing in each context?

Fright by the numbers: Alarming disease data are frequently flawed.
The Wall Street Journal, 11 April 1996, p.B1
Cynthia Crossen

Projections of the incidence of disease are rampant these days, as a growing number of health-advocacy groups compete for people's limited attention and money. Most of these projections are largely extrapolations or estimates. Often, they are reported by the media uncritically and out of context.

It is impossible to tally exactly how many people suffer from most diseases or health conditions. As a result, many health statistics consist of a sample that is projected to the entire population. Such projections are flawed because in such surveys some people will refuse to participate, making the sample nonrandom and less projectible to the population as a whole. In addition, future projections are problematic because they are often too linear--just because an incidence of a disease has risen 10% for the past few years does not mean it is going to keep on rising at the same rate.

Most health statistics make use of two numbers: the population of the country (about 260 million) and the annual number of deaths (about 2 million). Half of these deaths are the result of heart or other circulatory problems; a quarter are from all kinds of cancer; and another quarter are from everything else.

Crossen gives a number of examples of recent health statistics reported this year and the problems associated with interpreting them. Here are three of her examples.

1) Time Magazine cover story on prostate cancer states that one in five men will get this cancer. But this risk is a lifetime risk, accumulated over 80 years of life. On the other hand, if someone is 40 years old and does not have prostate cancer, the chance of getting it within the next ten years is 1/1000 and over the next 20 years is 1/100 which is less than the chance of getting lung cancer.

2) One in three Americans are obese. Jeff Lancashire of the National Center for Health Statistics says this is supposed to be 1/3 are overweight, not obese. Obesity is defined as weighing 20% more than your ideal body weight. Overweight is a skewed ratio between height and weight.

3) Two million Americans are schizophrenic, and two million are manic-depressive. Both projections apply to people 18 years or older and were based on a sample of five areas of the country conducted by the National Institutes of Health. The data was old, having been collected between 1980 and 1984, and the latest figures (1990) were derived by using the percentage of various mental disorders from the 1980s' surveys and projecting them onto the 1990 adult population. Treatments for these diseases change in time and vary between doctors and regions in the country.


The article ends with an example of an informative way to give risks of a disease.

Probability of developing cancer (given cancer-free at current age) in 10, 20, 30 years and eventually at selected ages:

Current age  20      30    40      50    60

In the next 10 Years
Men 0.4% 1.0% 2.0% 6.0% 15.4%
Women 0.5 1.2 3.2 6.4 10.8

In the nest 20 Years
Men 1.4 2.9 7.7 19.6 34.3
Women 1.7 4.4 9.3 16.2 23.2

In the next 30 Years
Men 3.3 8.5 20.6 36.3 44.6
Women 4.8 10.4 18.8 27.5 31.8

Men 45.6 46.1 46.6 47.1 46.6
Women 39.6 39.5 39.1 37.5 34.2
(1) Note that for women the chance of getting cancer in the next ten years given that you do not have it goes up as you get older. On the other hand the probability of getting it sometime in your life goes down as you get older.

Ruma Falk (see chance news 4.10) suggested this is similar to the following problem. You are looking for an object in one of 5 drawers. There is a 20% chance that it is not in any of the drawers, but, if it is in a drawer, it is equally likely to be in any of the five drawers. Show that, as you look in the drawers, the probability of finding it in the next drawer, if you have not found it so far, goes up but the probability of eventually finding it goes down.

(2) Does the same behavior occur for men? If not do you have any explanation for why it does not?

How a drug firm paid for university study, then undermined it.
Wall Street Journal, 25 April, 1996, A1
Ralph T. King Jr.

This story would fit well into Cynthia Crossen's famous book "Tainted Truth" except that it is so extreme no-one would believe it.

The story involves a drug called Synthroid taken daily by about eight million Americans to control hypothyroidism. It is distributed in the U.S. by the drugstore chain Boots Co. There are cheaper drugs which their producers believe are "bioequivalent". However, these drugs have not been sufficiently tested so doctors tend to stay with the more expensive Synthroid so it continues to capture about 84% of the market.

Feeling threatened by a drug called Levoxyl, which was claiming bioequivalence, Boots decided to support a new study hoping to show that the other drugs were not bioequivalent. They asked Dr. Betty Dong at the University of California San Francisco to head a team to carry out the study, agreeing to provide significant financial support for the study (eventually they provided about $250,000). She accepted and the study was carried out. The conclusion of the study was that other drugs used in the study were bioequivalent to Synthroid. A paper providing the results of the study was submitted to the "Journal of the American Medical Association". It was reviewed by five reviewers and accepted for publication in the Jan 25 1995 issue of JAMA.

This article explains in great detail how the company tried to convince JAMA and administrators at UCSF that the study was seriously flawed and should not be published. All these attempts failed and finally Boots had to resort to brute force. It turns out the lengthy contract for the study included a clause that said that the results of the study were "not o be published or otherwise released without written consent" of the company. This clause actually violated UCSF policy however, and so Dr. Dong should not have signed the contract in the first place as she naively did.

Finally, the company demanded that Dr. Dong withdraw the article, threatening to sue her if she did not. Pressured by Boots, the UCSF legal department said that they would refuse to support Dr. Dong if she would not withdraw the article. With no support to fight the case, Dr. Dong had little choice but to withdraw the article making eight years of research rather useless. As added insurance against it ever being published, Dr. Mayor, a researcher for the company Boots hired to stop the JAMA publication, wrote a sixteen page analysis of Dong's data, aimed at showing it was too flawed to reach a definitive result. Dr. Mayor published this article in a peer-reviewed journal for which he was an editor.


Does this seem too bad to be true?

E.P.A. plans radical change in calculation of cancer risk.
The New York Times, 16 April 1996, A1
John H. Cushman, Jr.

The Environmental Protection Agency (EPA) is proposing major changes in how it determines which chemicals and pollutants cause cancer, relying less on animal tests and more on new microbiological techniques. The changes would affect regulatory decisions under most of the nation's main environment laws.

Under the new guidelines, the agency would consider evidence beyond the single standard that has been its main guide: whether a chemical actually produced tumors in people or in animals, like mice and rats, exposed to large doses in laboratory experiments. All carcinogens are not alike, and some have similar effects in rats and humans while others do not. In the past, cancer rates of lab animals dominated decisions about whether a chemical was carcinogenic in humans, if only because other information was usually too scarce to play anything but a secondary role.

The heavy reliance on animal testing using huge doses has long been a point of debate among scientists, environmentalists, and industry officials. The question has been whether that method, adopted when there was no other prudent basis for making regulatory decisions, overstates the risks of some chemicals because it tends to ignore how the chemicals behave in people, particularly at low exposures.

The new procedures would give more weight to a broad range of microbiological evidence, including details on how toxic agents harm human cells and alter the genetic material that controls the cells' reproduction. In addition, the new guidelines will also incorporate new statistical analyses about the effects that chemicals might have at the very small doses that people are typically exposed to, rather than at the very large doses given to animals in the laboratory.

Could It Be? Weather has nothing to do with your arthritis pain?
The New York Times, 3 April 1996, C13
Gina Kolata

This article discusses a new study by psychologist Amos Tversky that indicates that arthritis pain has nothing to do with the weather. The study concludes that patients' belief that arthritis pain is connected to the weather is caused by our innate ability to find patterns whether they are there or not.

The article quotes Tversky as saying: "It's what I do for a living: debugging human intuition. If you take the broader view and look at people as intuitive scientists, you find that we are very good at pattern generation, we are very good at generating hypotheses. It's just that we are not very good at all at actually testing hypotheses. It is easy for humans to guess that an association exists. But testing and, if necessary, rejecting such associations tends to go against all our intuitions."

The belief that joint pain is related to the weather dates to Hippocrates in 400 B.C. However, studies attempting to show a correlation between subjective weather or barometric pressure and pain have led to inconsistent results.

Along with Dr. Donald Redelmeier, an internist at the University of Toronto, Tversky recruited 18 patients with arthritis and followed them for 15 months, assessing pain as reported by the patients; joint tenderness as determined by a doctor; and the patients' functional status (the ability to get along in daily life) as measured by a standard test. They also obtained local weather reports on temperature, barometric pressure, and humidity.

The researchers found no correlation between the patients' symptoms and the weather, no matter what aspect of weather they looked at. Even when the researchers considered 9 different time lags, from two days before to two days after a patient reported pain, they came up with the same conclusion: the weather did not influence the pain.

Tversky and Redelmeier generated sequences of random numbers and labeled one sequence "arthritis pain" and another "barometric pressure." They asked 97 college students if they saw evidence in the data that pain was correlated with barometric pressure. The students found patterns when there were none to be found.

The article quotes some experts in the field who are not convinced by Tversky's findings. Tversky said that he knew from experience that people often don't want to hear arguments that go against long-standing beliefs. He said that his research on the lack of evidence for "hot hands" did not change many people's minds about their existence and, in fact, lost him some good friends.


How many of your uncles' favorite theories about when it is good fishing do you think would be verified by a careful study by Tversky?

In a recount, cyber census still confounds.
The New York Times, 17 April 1996, D1
Peter H. Lewis

Last August, Nielsen Media Research and Professors Donna L. Hoffman and Thomas P. Novak of Vanderbilt University's Graduate School of Management designed an ambitious telephone survey to estimate the number of adult Internet users. The initial Nielsen estimate was 22 million users which was twice previous estimates and had a large effect on companies who hoped to make a fortune on the Internet.

In December, Professor Hoffman disavowed the Nielsen report, saying the conclusions were invalid. She said that her own analysis of the data suggested that there were less than 10 million adult users in the United States and Canada combined. Nielsen was selling the report for $5,000 and, not surprisingly, Hoffman's public announcement had a serious affect on the sales of the report. Last Friday, after a more detailed analysis of Nielsen's raw numbers, Hoffman, joined by Thomas Novak and William Kalsbeek, a biostatistician at the University of North Carolina, posted their analysis on the web. You can find it at: http://www2000.ogsm.vanderbilt.edu/

Their conclusion was that a reasonable estimate was 16.4 million, 5.6 million fewer than the original estimate but significantly higher than the 10 million initially estimated by Hoffman. They concluded that Nielsen's 16.9 million estimate for American users should have been 11.5 million and the estimate of 1.97 million for the number who had purchased something on the Internet should be 1.51 million.

Nielsen in turn revised their estimates to be 19.4 million on the Internet, 14.6 million web users, and 1.9 million who bought something on line.

Another researcher, Sunial Gupta, who had access to the data remarked that the survey was well done but Nielsen made a sloppy analysis of the data at the end. He said that both sides seemed to have made mistakes initially and, no matter which one you believe now, it is probably the best survey among all that have been done.

From their Internet paper you find that the first concern of Hoffman, Kovak and Kaspeek with the Nielsen analysis was with the weightings used for the various groups. Restricting themselves to U.S. users, they use the 1995 census to determine what they regard as more up-to-date estimates of the numbers in the various groups used in the study. They find the Nielson weights consistently overestimate certain groups that are likely to use the Internet and consistently underestimate other groups that are unlikely to use the Internet. Correcting for this leads to a lower estimate in the number of Internet users.

The questionnaire used in the study had several questions designed to learn if and how a respondent used the Internet. The authors say that the Nielson analysis did not correct for inconsistent responses in these questions and, eliminating those with inconsistent answers, again led to a lower estimate for the number of Internet users.


(1) Some argue that all that matters is that the number of users of the Internet is increasing exponentially and who cares about the exact number. Hoffman, Kovak and Kalsbeek argue that it is important that the first serious estimate be reliable as a future benchmark. Is this important?

(2) If a respondent's answer to one question suggests that he or she uses the Internet and a later question suggests not, should that person be counted as a user or non-user?

(3) Why is it necessary to use an old-fashioned instrument like a telephone to estimate the number of users of the Internet?

Mathematicians say asteroid may hit earth in a million years.
The New York Times, 25 April 1996, B10
Malcolm W. Browne

A result published in the current issue of "Nature" by European mathematicians claims that an asteroid named 433 Eros could hit Earth within the next 1.14 million years.

433 Eros is the second biggest asteroid known to be in a near-earth orbit. It's size is thought to be 25 miles long, nine miles deep and nine miles wide. At the moment its orbit is more apt to intersect the orbit of Mars rather than that of the Earth. However, it is claimed that the constantly changing gravitational interactions of the major planets with small solar-system objects like 433 Eros make their orbits unstable and easily perturbed.

When gravitational fields act on only two objects there are exact solutions to calculate their trajectories. However, for 3 or more there is no exact solution, so approximations must be used. Such approximations are sufficient to predict the orbits of spacecraft or major planets but break down chaotically and unpredictably for very large distances.

Using improved approximations and taking into account all the planets except Pluto, the researchers found that a "resonance" could develop between Mars and 433 Eros which, under certain circumstances, could push it into an earth-crossing orbit. However, we are assured this will not happen in the next 100,000 years.

Looking at eight mathematically plausible orbits of 433 Eros over the next two million years, three orbits began to intersect with Earth's orbit and one actually produced a collision with earth 1.14 million years from now.

Curiously, this article makes no mention of the fact that, on February 17th of this year, NASA launched a spacecraft on a four-year mission to study the asteroid 433 Eros. It will spend a year circling the asteroid 200 million miles from earth, sometimes as close as 10 miles, hoping to learn more about the asteroid and the risk that asteroid collisions pose to the earth.

Study doesn't find portable phone risk.
The Boston Globe, 11 April 1996, p 3.
Dolores Kong

A preliminary study, to be published in the May issue of the journal "Epidemiology," finds no increase in death rate for portable phone users as compared with users of mobile phones. Portable phones have antennas in the handset, while mobile phones have a separate antenna. To the extent that there is a risk from radio waves, that risk would presumably increase with portable phones. (In fact, a Florida man has sued a cellular phone maker, claiming that his wife's brain cancer was caused by radio waves from the phone.)

The study compared 1994 death rates from all causes for more than 250,000 portable and mobile phone customers in the Boston, Chicago, Dallas and Washington areas. Among those who had accounts for at least three years, portable phone users actually had a 14 percent lower death rate.


(1) Why is a study with 250,000 participants still considered only "preliminary?"

(2) A 14% difference in death rate sounds important--especially with 250,000 participants. Why aren't the experts suggesting that portables are in fact safer than mobile phones?

(3) Mobile phones are primarily used in cars, where they can distract drivers and might lead to more accidents. Portable phone use does not automatically include this risk. So maybe the greater radio wave risk for portables is being offset by the greater highway risk of mobile phones. What do you think of this argument? How could the study have controlled for such effects?

(4) Do you think death rates for the general population should be included for comparison?

Unconventional Wisdom: New facts and hot stats from the Social Sciences.
The Washington Post, 21 April 1996, C5
Richard Morin

Fat, Bald, and Drooling -- Just Like Dad

Evidence from several studies conducted around the world suggests that a newborn more often resembles the father than the mother.
According to genetics, however, just as many children should look like mom as those that look like dad. So where does the discrepancy come from?

Steven Gaulin, an anthropology professor at the University of Pittsburgh, explains that such assurances are there to counter "paternal uncertainty." Mothers are certain that their babies are their own, while fathers are never positively sure. Studies that compared the blood types of children, their mothers, and their presumed fathers have found that about 5 to 10% of the world's children are being raised by fathers who think they are the father, but are not.

How do textbooks rate presidents?

In the latest issue of "Social Science Journal", political scientist J.M. Sanchez of Adelphi University reports that U.S. presidents get unfavorable treatment from most introductory college government textbooks. Sanchez reviewed 36 textbooks, and identified each evaluatory reference to a U.S. president as favorable or unfavorable. Of 5,322 evaluative references in the 36 texts, only 2,017 (38%) are positive.

James Madison was the favorite of text writers -- 84% of his references were positive. Richard Nixon, on the other hand, only had 12% of his references as positive. In addition, postwar presidents fared much worse than their 19th century counterparts.


(1) What do you think of Gaulin's explanation for more people being told they are told they look like their father than their mother? Can you offer another explanation?

(2) How do you think the public impression of recent presidents would compare with that of those of the textbook writers>

Daylight saving a dangerous thing.
The Boston Globe, 4 April 1996, p3.
Philip J. Howe

A Canadian study reported in today's "New England Journal of Medicine" finds that switching to daylight savings time briefly increases highway accidents, presumably because drivers have lost an hour of sleep. Researchers looked at data for all highway wrecks in Canada for the period around the time change in 1991 and 1992. The Monday immediately after the time change had 7 to 8 percent more accidents than the Mondays a week before or a week later.


What is the point of focusing attention on Mondays?

Pre-pregnancy obesity linked to greater risk of neural defects.
The Boston Globe, 10 April 1996, p6
Dolores Kong

A study reported in today's "Journal of the American Medical Association" found that babies born to obese women have 2 to 4 times the usual risk of brain and spinal cord defects, such as spina bifida and other neural tube problems. Several years ago, researchers linked such defects to low levels of folic acid in mothers' diets. The new study is seen as identifying a second important risk factor. As many as 10% of women of childbearing age are considered to be obese.

The study considered 2300 infants born or treated at New England hospitals. Women weighing 176 to 196 pounds before pregnancy had about twice the risk of bearing children with neural tube defects compared to women weighing 100 to 130 pounds. Women weighing 240 pounds or more had four times the risk. Even obese women who got the recommeded levels of folic acid had an increased risk.


(1) How high do you think the overall risk of neural tube defects is? About how many cases would there be in a study of 2300 infants?

(2) How precise do you think the estimates of increased risk are?

Method seems to predict some San Andreas fault quakes.
The Boston Globe, 4 April 1996, p 25
David L. Chandler

Areas of the San Andreas fault have been equipped for many years with "creep" meters, which measure the slow, relatively constant movements that occur along the fault. Occasionally, the creep increases to 20-30 times its normal rate. Such increases appear to be associated with imminent risk of earthquakes. Researchers have reported that during three one-year periods of above average earthquake activity in the last 24 years, more than half of the quakes of Richter magnitude 3.3 or were preceded by increased creep activity.

While this phenomenon holds out hope for earthquake prediction, so far it is only apparent during periods of above-average earthquake activity. Also, there is not sufficient data on earthquakes of magnitude above 5, which are of course the more dangerous ones.

Dangerous abstractions.
The New York Times, 7 April 1996
John Allen Paulos

In this Op-Ed piece, Paulos considers whether we can view Ted Kaczynski's background in mathematics as being consistent with the radical anti-technology philosophies espoused by the Unabomber. He gives a number of arguments to suggest that we can. First, because mathematics is axiomatic, many mathematicians view themselves as "radical" in the literal sense of getting to the root of the matter. Second, the Unabomber's manifesto shows a mathematician's attention to detail. Third, although abstract thinking is too often missing from public debate, a capacity for abstraction could in the extreme be consistent with the ability to rationalize violent acts in the name of an idealized "good."


What is the difference between saying a mathematician is likely to have traits X, Y and Z (this is the line of Paulos' argument), and saying that a person with traits X, Y and Z is likely to be a mathematician?

Vitamin C: Is anyone right on dose?
New York Times, 16 April, 1996, C1
Jane Brody

A federally funded study carried out by researchers at the National Institutes of Health (NIH) concluded that the most reasonable daily dose of vitamin C is about 200 milligrams a day and only 10 milligrams a day are needed to prevent vitamin C. At present the Food and Nutrition board recommends 60 milligrams a day by dietary means.

The study was directed by Dr. Mark Levine and published in the current issue of the "Proceedings of the National Academy of Sciences". The study concluded that amounts over 400 milligrams have no apparent value and the amounts as high as 1000 milligrams that many people take daily or occasionally to prevent or treat illness could be hazardous.

While the government's recommended diet would be expected to satisfy the 200 milligram recommendation, a significant number of people who do not follow the recommended diet would have to use vitamin C supplements to achieve the recommended 200 milligrams.

The study analyzed the biochemical effects of various amounts of vitamin C, administrated to seven healthy young men who lived in the hospital for four to six months. It is stated that nutrient requirement studies are expensive and time consuming and are typically done with a small number of subjects but "their exacting nature can yield meaningful results, unlike clinical studies that require larger numbers for statistical significance."

The restriction to healthy subjects leaves open the question of the benefits and dangers of larger doses for those with health problems. Linus Pauling believed that massive doses of vitamin C could cure diseases including cancer.

The study found that white blood cells were saturated at a dose of 100 milligrams and blood plasma was nearly saturated by a dose of 200 milligrams and completely saturated at 1,000 milligrams. Higher doses leads to the production of breakdown products of vitamin C that could cause problems such as kidney stones.

Dr. Levine said that there was no "absolute proof" that it was best to be saturated with vitamin C, but this seems to agree with what people get from a diet rich in fruits and vegetables thought to prevent certain diseases.

Some experts do not agree with the 200 milligram recommendation, claiming that this amount could be harmful to people with other problems such as iron overload. Also, the idea that the saturation level was the ideal level was also challenged.


Do you think that a study with seven subjects suffices to change existing recommendations on the optimal intake of vitamin C?

Economic scene; the drive to put cost limits on regulatory benefits isn't dead yet.
The New York Times 18 August, 1996, D2
Peter Passell

Last summer the Republicans tried to put through bills to require federal regulators to take into account economic costs as well as benefits in making regulations. They wanted to require that the benefits of regulations exceed the cost. This would require, for example, comparing the benefits with the costs in making post offices accessible to wheelchairs or determining how much Americans would lose if pollutants from distant power plants reduced visibility on the rim of the Grand Canyon to 20 miles from 100 miles. The Democrats managed to kill these efforts by portraying the Republican proposals as attempts to tie up future environmental regulations in legal battles and set back the impressive progress in this area in recent years.

However, there is still bi-partisan support for some form of increased regulation in environmental decisions. One attempt at this is a kinder and gentler version of last summer's Johnson-Dole bill that failed that has been proposed by Democrat Carl Levin of Michigan. His bill would mandate cost-benefit analysis but give the executive branch leeway to use other criteria in judging proposed rules.

Last week a group of leading economists, including Nobel laureate Kenneth Arrow and Bush's advisor on regulation Richard Schmalensee, published a statement in "Science" defending the role of cost-analysis in making federal regulations.


(1) How would you assess the benefit of having wheelchair access to post offices?

(2) Do you think it is reasonable to require that cost-analyses be carried out for environmental decisions?

Life at risk: playing the odds in an uncertain world.
Discover Magazine, May 1996

This is a special issue of "Discover Magazine" devoted to risk.
It has the following articles related to risk.

While all these articles are interesting, those by Finkel and Hively are particularly appropriate for Chance News.

Adam Finkel is the director of health standards of the U.S. Occupational Safety and Health Administration. Finkel claims that it is a myth that risk assessors routinely exaggerate risk, at a huge cost to society. He feels that efforts in the Congress to add new requirement on government regulators are based on this myth and endanger the successful use of risk analysis just when it is coming into its own as a scientific discipline.

He makes fun of the Johnson-Dole bill that was under consideration when the article was written. This bill would , among other things, ask the risk assessors to focus on the risk faced by the "average" person and to pick the "most plausible theory". As an example, Finkel asks how people would like the government to set standards for the safety of wooden ladders appropriate for a 140-pound person.

To show the problems with the "most plausible" theory he gives the following example: a hurricane is brewing off the coast of Florida and two theories are at odds: 40% of recognized experts believe the storm will turn landward and hit Miami, while 60% believe it will turn harmlessly out to sea. Should the weather bureau act on the most plausible theory?

This article shows how difficult it is to write about current events in the time frame of producing a magazine. The Johnson Dole bill has long since disappeared though, as we have seen, some of the issues raised are still alive.

Will Hively writes about the modern use of Bayes Theory in risk assessment. He uses as a basic example the decision that doctors face in deciding whether to use streptokinase or T-PA for a patient who has had a heart attack. T-PA costs about $1,530 and streptokinase $220. Until the large European GUSTO study (see Chance News 2.09) studies had suggested that these two drugs were equally effective.

The results of the large GUSTO study, published in 1993, suggested that with T-PA 93.7 of the patients survive but with strepokinase only 92.7% survive. If true, the use of T-PA would lead to the saving of an estimated 5,000 lives a year in the United States. A paper published in the "New England Journal of Medicine" (See Chance News 4.05) carried out a Bayesian analysis which showed that the case for T-PA is not so convincing when you assess prior beliefs based on previous studies or experience. Hively explains how the authors looked at this problem.


(1) Assume that it costs 2 million dollars to board up Miami stores. If you were in charge and had the information that 60% of the experts believe the storm will turn harmlessly out to see and 40% believe it will turn inward and hit Miami. Would you recommend the stores be boarded up? What other information might you want to have to make this decision?

(2) Assume that it is correct that a roughly 7 out of 1000 people treated with T-PA will die and 8 treated with strepokinase will die. A student once suggested that your choice here is like being forced to play Russian Roulette with 8 bullets in 1000 slots. For $1300 you can have one bullet removed. Would you pay to have one bullet removed? What if removing one bullet cost $100,000?

On the Discover web site you are invited to take a risk quiz based on the results of their article "A fist full of risks". We did this in our class. The expected number correct by guessing was 3.3 and the average for the class was 2.5. The best performance was 7 out of 10 correct. With our class of 20 this should happen about 20 percent of the time.

It is also an interesting class activity or assignment to ask the students how you would estimate such things as the number of minutes by which your life will be shortened by smoking one cigarette. Here is the quiz:


How well can you rate life's risks? In this month's DISCOVER, our editors worked some statistics into "A Fistful Of Risks" -- a section that punched out the possibilities of everything
from being clobbered by a comet to having your bicycle stolen. The results raised enough eyebrows that we decided to create an on-line challenge of chances. Take a crack at it and find out your Risk Awareness Quotient (RAQ). (You can assume the questions pertain to the United States unless otherwise noted).

The correct answers, by the way, lie on pages 82 and 83 of our May 1996 edition, but don't let them alarm you: risk calculation is dicey at best, because averages don't reflect individual circumstances -- and because the future needn't always reflect the past.

1. What is your risk of home foreclosure in the next 12 months?

1 in 24
1 in 345
1 in 720

2. Which of the following is most likely to happen to you?

Being struck by lightning
Being infected with flesh-eating bacteria
Being injured in an elevator ride

3. At which establishment are you most likely to be poisoned,
if you eat in Minnesota?

Fast-food restaurant
Mexican restaurant

4. Which of the following is most likely to kill you in the
next 12 months?

Drinking detergent
Dog bite
Snake bite

5. Which of the following is least likely to happen to you?

Winning the Irish Sweepstakes jackpot?
Contracting the Ebola virus, if you're an African
Dying in an earthquake or volcano

6. Which of the following accounts for the most childhood
accidental deaths?


7. Which of the following takes the most off your life expectancy?

Driving once without a seat belt on
Drinking one diet soft drink
Smoking one cigarette

8. What is the safest state for driving?

Rhode Island

9. What are the chances, in the next 12 months, that you will
be murdered?

One in 50,000
One in 32,000
One in 11,000

10. What is the risk of your being wiped out (with nearly
everybody else) next year by a catastrophic comet, meteor,
or asteroid impact?

One in 750,000
One in 20,000
One in 15 million


1. Ans. 2: risk of home foreclosure is 1 in 345.

2. Ans. 2: lightning 1 in 750,000, flesh-eating bacteria 1 in 700,000, elevator 1 in 6 million.

3. Ans. 3: Fast-food 1 in 440,000, Delicatessen 1 in 240,000 Mexican 1 in 136,000.

4. Ans. 2: Detergent 1 in 23 million, dog bite 1 in 20 million, snakebite 1 in 36 million.

5. Ans. 2: Irish Sweepstakes 1 in 5,245,786, Ebola virus 1 in 14 million (for an African), Earthquake or volcano 1 in 11 million.

6. Ans. 1: fire 15%, choking 3%, poison 1%.

7. Ans. 3: Driving without seatbelt 6 seconds, one diet soft drink 9 seconds, one cigarette 12 minutes.

8. Ans. 3: Rhode Island.

9. Ans. 3: 1 in 11,000.

10 Ans. 2: 1 in 20,000.

Send comments and suggestions to jlsnell@dartmouth.edu


CHANCE News 5.05

(29 March 1996 to 23 April 1996)