CHANCE News 5.07

(24 May 1996 to 17 June 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

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



It's what I do for a living: debugging human intuition. If you 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 testing hypotheses.
Amos Tversky

Note: We appreciate your suggestions for articles. If it is from a national newspaper just e-mail your suggestion. If it is a local newspaper you can fax a copy to 603-646-1312. Include the name of the newspaper, the date and the page number. Of course if you want to include an abstract and or discussion questions that is even better.



Amos Tversky, expert on decision making, is dead at 59.
The New York Times, 6 June 1996
Karen Freeman

Outsider who challenged dismal science.
Wall Street Journal, 6 June 1996, C1
Roger Lowenstein

Sure, markets are rational, just like life.
Wall Street Journal, 13 June 1996, C1
Roger Lowenstein

Chance lost a friend and a great scholar with the untimely death of Amos Tversky. The "New York Times" article provides a good account of the highlights of Tversky's life and research. Our own favorite account of Tversky's pioneering work with Kahneman is in "Discover Magazine", June 1985, pp. 22-31.

The June 6 "Wall Street Journal" article by Lowenstein emphasizes Tversky's role in convincing economists to pay attention to what people actually do instead of what they would do if they behaved rationally. Lowenstein quotes Tversky as saying that much of his work would have been familiar to advertisers and used-car salesmen but not to economists. Here is an example of what he was talking about. If there is a 10% chance that you will buy the blue Chevy when the salesman shows only that one car, then you will have a greater than 10% chance of buying it when the salesman shows you both the blue Chevy and a green Ford at same price but less desirable to you then the Chevy. A good car salesman would never show you just one car.

In the June 13 Wall Street Journal article Lowenstein continues to discuss the effect of Tversky's work in terms of behavioral economics applied to financial markets. This includes challenges to the efficient market hypothesis. The work of economists Robert Schelling and Richard Thaler is discussed. Thaler observes that in 1926, when a ticket to the movies cost 25 cents, the average share on the Big Board was $35. It is still, roughly, $35. Investors apparently like it that way. But there is no logic to it.

All three of these articles remind us of Tversky's ability to formulate significant behavioral principles by looking at simple and sometimes even folksy examples.

Tor Tosteson suggested the next article. Tor is a bio-statistician who works on clinical trials projects and was probably horrified by the fact that people think that he
and his colleagues are poisoning their subjects.

Public faith in science stays high.
Nature, 30 May 1996, Washington News, p 355

The National Science Foundation recently published their biennial report "Science and Engineering Indicators 1996: on the statistical status of US science".

Jon Miller, the main author of the report's section on public understanding of science, stated that there is no evidence of the much touted anti-science movement. The percentage of people who believe that: "The benefits of scientific research have outweighed the harmful results" has been very close to 70% since the survey was started in 1979 with the exception of 1988 when it was a bit over 80%.

However, Miller reported that the public's support of science is not matched by an understanding of how it works. For example, although half the sample agreed that a clinical trial should put 500 subjects on a drug and keep 500 off it--rather than putting 1,000 people on the drug right away--almost half of them thought the reason for keeping the 500 on placebo was to save them from the risk of being poisoned.


Do you think the 10% difference in public support of science in 1988 was a statistical aberration, or do you have some other explanation for this?

Tom Moore sent us the next two items.

Public employees paid handsomely, study says.
Des Moines Register, 27 May 1996, p 1
David Yepsen

A conservative think tank, the Public Interest Institute at Iowa Wesleyan College, charged that public workers were a "privileged class" because of high salaries. To back up their claim they presented statistics from the U.S. Department of Labor comparing average salaries of private wages compared to government wages by states. In 1994 the national average for government workers ($29,528) was 11% higher than private workers ($26,494) while, in Iowa, the average salary for government workers ($31,910) was 47% higher than the average salary for private workers ($21,689).

Officials commenting on this difference stated that it is difficult to compare private and public workers. The president of the State Educational Association remarked that private school teachers do not need and, often do not have, as high qualifications as public school teachers. They also include those doing religious or mission work. Another official observed that the public average has increased by the requirement that women be paid equal amounts for equal work, while this is not required in the private sector. Another said that, when there is a hiring freeze, public employees are paid more for doing the extra work, while this is less true for private workers. In a letter to the editor it is stated that wage and salary information collected by the U.S. Department of Labor does not include private-sector workers who are self-employed. These include professional workers with high salaries.

Letters to the editor from Union leaders say that the difference is due to the fact that unions for public workers have grown stronger in Iowa while those for private workers have grown weaker. They suggest that government wages are not too high, but rather that private wages are too low.


(1) In Wisconsin the average salary for the private worker is $23,769 and for Government worker $30,931. Does Iowa seem significantly different from Wisconsin?

(2) Can you think of other reasons why it might be difficult to compare salaries of public and government workers?

Exactly how many spaces?
Des Moines Register, 27 May 1996, Main news p 6
Russ Lenth

A previous article reported that the American Trucking Association claimed there was a shortage of 969 parking spaces in Iowa, 1,982 in Pennsylvania, 1,352 in North Carolina and 28,412 nationwide. Reader Russ Lenth writes: "In my experience, 85.7143% of the people who report data to exaggerated precision have an ax to grind. They figure that such exact numbers look more scientific."

Jingle man retreads pieces of pop hits in car-dealer ditties.
The Wall Street Journal, 11 June 1996, p 1
Oscar Suris

John Giaier is a former studio musician who now makes a career writing jingles for ads for car dealers. To cut his costs in this competitive business, he has turned to an interesting application of sampling. Using a database of snippets from songs featured in weekly issues of "Billboard" magazine, his computer links selections into potential jingles--and even prints out the sheet music! This approach allows Giaier's firm to turn out about 5 successful "new" jingles a week. The resulting tunes apparently contain enough familiar notes and chords to have listeners readily humming them but are not so close to published songs that Giaier has to pay royalties.

John Lofrumento, CEO of the American Society of Composers, Authors and Publishers (ASCAP), believes the approach may violate copyright laws. Defending his firm's practices, Giaier says he learned from his experience in the music industry that "anything you write musically has been written before."


1. One of Giaier's staffers says that: "We're in good shape because we're using statistically proven material." What does the phrase "statistically proven" mean here?

2. Phil Dusenberry, a New York advertising executive, rejects Giaier's defense: "It's like saying to a painter, 'You can't paint a great painting because every color has already been used.'" What do you think of this analogy?

3. In "Statistics: Concepts and Controversies", David Moore explains how ASCAP uses sampling to charge royalties to radio stations that play its members' songs. (ASCAP tapes about 50,000 hours of the 53 million total hours of local radio programming, and uses the sample data to estimate how often given songs are played.) Do you think that statistical analysis of Giaier's jingles could be used as evidence of copyright infringement?

The tipping point.
New Yorker, 3 June 1996, pp. 32-38
Malcolm Gladwell

The crime rate in New York City has dropped dramatically in the last few years. There have been a number of attempts to explain this decrease. William J. Bratton, who was New York Police Commissioner during most of the decline, argues that new policing strategies made the difference. Criminologists put forward more general demographic and social explanations -- the aging of the population, the stabilization of the crack trade, the longer prison terms etc. However, the scale of these changes seem too small to fit the scale of the changes that have occurred in the crime rates in New York. This has suggested looking for a new explanation. This article reports that researchers are turning to the theory of epidemics to explain changes in crime rates.

The mathematical theory of epidemics was developed to study the spread of a disease through a population -- such as the spread of AIDS. A simple model for epidemics can be described as follows: Let N be the population size, assumed to be constant. Let S(t) be the number of people at time t who are susceptible to getting the disease, I(t) be the number infected at time t and R(t) the number removed by time t either by already having had the disease, having died, or becoming immune. It is assumed that the rate of change of number infected, I(t), is proportional to the number of contacts between the infected and the susceptible people and that the rate of change of the number removed, R(t), is proportional to the number infected. Thus

         S'(t) = -bSI, b > 0

R'(t) = rI, r > 0

where b is the infection rate and r the recovery rate. Since

S(t) + I(t) + R(t) = N we have S'(t)+I'(t) + R'(t) = 0 and

         I'(t) = bSI - rI = (bS-r)I.

From this last equation we see that, if S < r/b, the number of infected decreases and, in fact, the model predicts it will decrease to 0. If S > r/b, the number infected increases resulting in an epidemic. Solving the equations shows that the number infected increases to a maximum value and then decreases to 0. The number of susceptible decreases to a limiting value > 0, so there will always be some people not affected by the disease.

This model suggests intervening to try to make S < r/b by decreasing S, increasing r, or decreasing b. The number of susceptiples S could be decreased, for example, by vaccination.

In applying this epidemic model to the problem of crime rates, one might interpret the susceptible people as those who might become criminals, the infected as those who become criminals and the removed as those who end up in jail or die. The model predicts a threshold effect (called tipping in this article). If the number susceptible to becoming criminals is small enough, the crime rate will decrease, but, if it is greater than the critical value (r/b), the crime rate will increase significantly. You could try to prevent a crime epidemic by intervening. The number of susceptiples S could be decreased by providing more jobs, the removal rate r could be increased by giving longer jail terms, and the threat of longer jail sentences might also decrease the infection rate b.

Of course the New Yorker article does not have all this math stuff and does not really explain what a mathematical model is or how it might be used. However, the author mentions specific researchers who have used non-linear models to explain social phenomena. One of the most interesting is described in an early paper by Thomas Schelling ("Journal of Mathematical Sociology", Vol. 1, No. 1, 1971, pp 143-186) whom we have already mentioned in connection with Tversky's work.

Schelling wanted to try to understand how people of different races segregate themselves when they have a choice of where to live. He discusses his model in terms of the movement in and out of a neighborhood with blacks and whites, but his ideas apply just as well to segregation of men and women, students and faculty, young and old and other dichotomies.

He illustrates his models in terms of very simple experiments that the reader is invited to carry out. Start with a rectangle divided into small squares like a checkerboard. Randomly choose about 25% of the squares to remain blank and randomly distribute black and white counters on the rest of the squares. The counters represent people living on the square. Consider the eight adjacent squares to be the person's neighbors. Assume that, if a person sees that less than half of his neighbors are of the same color, he desires to move. If he moves he will move to the nearest empty square where he is satisfied: i.e. where at least 50% of the neighbors are his color. Now choose a method for deciding on the order in which people are allowed to move and let them move until everyone is satisfied. See what kinds of patterns arise.

Schelling shows what happens in such a model as you change some of the rules. For example, one color might want to move if even 20% of the neighbors are of a different color.

Schelling applies his model to try to explain the observed phenomena of "white flight" from neighborhoods in the '50's. The percentage of the minority that would cause this flight was called "the tipping point" and about 20% was considered the tipping point for most whites.


(1) To be useful it is necessary to assume that the parameters in the epidemic model, the rate of infections and rate of removal, are constant over a reasonable period of time. Would this be a problem in modeling crime rates?

(2) For the version of the Schelling's model we discussed, do you think the movement will typically lead to a situation where everyone is satisfied? Try it!

Milt Eisner suggested the following article pointing out it is another example where we are given ratio comparisons rather than actual sample proportions.

Well-done steak raises cancer risk.
Chicago Tribune, 23 April 1996, news p. 6
Associated Press

Red meat has long been in the doghouse because of its high-fat link to heart disease and as a risk factor for some kinds of malignancy, especially colon cancer.

Now a study has been carried out to see if it matters how the steak is cooked. The study used Nebraska farmers -- 176 stomach cancer victims and 503 healthy people

The findings of the study were presented recently at a meeting of the American Association for Cancer Research. Mary Ward, who presented the results, reported that they found increasing risk with increasing doneness. People who prefer their meat medium, medium-well or well-done are about three times more likely to get stomach cancer than are those who eat their beef rare or medium rare.

The researchers found that those who ate mostly roasted meat, which cooks at a much lower temperature than frying or grilling, have no increased risk of stomach cancer, even if they prefer their meat well-done.

Ignoring how the meat was cooked, the researchers found that those who ate beef at least once a day had about double the risk of those who ate it only once a week.

However, cooking duration seemed to be more important than the amount eaten.

Discussion questions:

(1) What else would you want to know to decide if you should really worry about doubling your risk of stomach cancer by eating your steak well-done?

(2) What sort of confounding factors might come into a study like this?

Bob Norman suggested the next topic.

Clean air regulations are paying off, EPA says.
Washington Post, 10 June 1996, A17
Gary Lee

The Environmental Protection Agency (EPA) has been under attack by GOP lawmakers for spending too much of the taxpayers' money without much to show for it. The EPA carried out an analysis to weigh the costs against the benefits by the enforcement of the 1970 Clean Air Act. A draft of the study has been made available to lawmakers and the press. The report found that: "In 1990, Americans received roughly 20 dollars in value in reduced costs, risks of death, illness, and other adverse effects for every one dollar spent to control air pollution."

The Clean Air Act required industry to reduce and control emissions of sulfur dioxide, nitrogen oxide, ozone, particulate matter, carbon monoxide and lead.

The authors of the report estimated that, over the 20-year period reviewed, industry and private individuals paid over $436 billion in anti-pollution technology and increased costs for goods. The study expressed amounts in 1990 dollars.

The authors calculated the effect of the reductions of pollutants on public health. Over this period they estimated that the decreased pollution reduced the number of heart attacks by 18,000, the number of strokes by 13,000, the cases of respiratory illnesses by 15,000 and of hypertension by 16,000.

They estimated the each death due to air quality problems cost $4.8 million, each heart attack $587,000 and each hospital admissions for respiratory problems $7,500. Each workday lost due to air quality problems cost $83 and each IQ point lost due to lead poisoning or other air pollutants cost $5,550. Taking all this into account led to an estimate of $6.8 trillion in benefits over the 20-year period.


(1) Do the estimates for the costs of deaths, heart attacks, etc. seem reasonable to you? How do you think they estimated the cost of losing 1 IQ point?

(2) An article in the "Wall Street Journal" stated that the report yielded benefits of $2.7 trillion to $14.6 trillion in 1990 dollars during the 20 year period studied, with a "central estimate" of 6.8 trillion. They reported the same estimate of cost $436 million as the "Washington Post". Why do you think they gave a range for the estimate of benefits but not for costs? Where did the 20 to 1 ratio come from?

Shunhui Zhu bought an air-conditioner recently and read the yellow "Energyguide" that is required by the Federal Trade Commission to permit comparison with other manufacturers' products. At the bottom of the guide he read: "This model's estimated yearly operating cost is $40". He asked if we could find how this number was obtained. Other than to say that it must be some kind of national average, we were not much help.

Modest research found that, in 1994, changes were to be made in the Energyguide that would include replacing this national average estimate by an average for the area where the product is sold. Apparently that never done.


(1) How do you think the FTC arrived at the $40 estimate.

(2) Does the estimate seem reasonable as a national average?

(3) Should Shunhui expect to do better or worse than 40$ in Hanover New Hampshire?

Census plan for 2000 is challenged on two fronts.
The New York Times, 6 June 1996, A21
Steven A. Holmes

Both minority groups and Republicans are challenging the Census Bureau's plans to count the population in the year 2000. Minority groups argue that the new plan would worsen the problem of undercounting blacks and hispanics, while Republicans counter that the new technique would result in improperly drawn legislative districts.

The Census Bureau plans to count at least 90% of the households in each county and then use statistical sampling methods to estimate the number missed. Representative Carrie P. Meek, Democrat of Florida, who is black, introduced a bill with an alternative method for sampling. It would require the Census Bureau to count 90% of the households in each census tract, a geographical unit that is much smaller and more homogeneous ethnically than a county, and then use statistical sampling methods to estimate the missed population within the tract. She argues that a census taker, counting in a county with a minority-dominated city and predominantly white suburbs, might reach 90% by counting all the white suburbanites but a lower percentage of the minority inner-city dwellers. A greater chance of error in estimating the missed minority population would occur.

On the other hand, representative Tom Petri, Republican of Wisconsin, introduced a plan that would prohibit the Census Bureau from applying sampling techniques of any kind to determine population count. Mr. Petri says the Census Bureau should try to obtain an accurate count without sampling.

The Census Bureau acknowledges that its 1990 count left many Americans uncounted, especially members of minority groups who lived in central cities. The number of blacks undercounted was 6 times greater than the number of uncounted whites, the largest undercount differential since 1940.

Keeping Up.
Fortune Magazine, 10 June 1996, p 161
Daniel Seligman

Mr. Statistics responds to a reader about a bet he made with Warren Buffet (who I gather is in the contest for the countries richest man). He bet that Rodger Maris' 61 home run record would be broken this year. The reader wanted to know if the tax implications should effect the odds. Mr. Statistics says that, if you have to report your winnings, then it does effect the odds and explains how this would work if, for example, you play roulette.

The bet with Mr. Buffet was made on April 30 and Buffet gave Mr. Statistics 4 to 1 odds betting that no player would hit 62 home runs this season. In a previous column ("Fortune", May 13, 1996) Mr. Statistics calculated that there was an 18.4% chance that one of seven players--Albert Belle, Barry Bonds, Matt Williams, Frank Thomas, Ken Griffey Jr., Dante Bichette or Mark McGwire would get 62 home runs this year.

He did this as follows. For each player based on the past two seasons performance he calculated the expected number of times at bat and the probability of getting a homer when at bat. He then uses the binomial distribution to find the probability of 62 or more successes with n = the expected number of times at bat and p = the player's probability of getting a home run when at bat.

Mr. Statistics found that Cleveland player Belle had the best chance to break the record. He estimated that Bell had, at the beginning of the season, an 8.98% chance of hitting a home run when he comes to bat and an expected number of times at bat 604. Using the binomial distribution with n = 604 and p = .0898 he found the probability of Belle breaking the record to be 15%. By the same method he found that the next best bet is Frank Thomas of the White Sox who has a 3% chance of breaking the record. Adding these probabilities for the seven players gave him the estimate of 18.4% that one of the seven will break the record. This would correspond to odds of 4.4 to 1. However, the bet was that someone would break the record so maybe 4 to 1 is about right.


(1) What do you think of Mr. Statistics' method for calculating the probability that a particular player will break the record? If you could estimate the distribution for the number of times Belle will come to bat in the season, how would you calculate the probability that he gets more than 61 home runs? Do you think this would change the estimate obtained by Mr. Statistics using the expected number of times at bat?

(2) What odds would you give now that Belle will break Maris' record this year? that someone will break this record this year?

(3) When you play roulette at Las Vegas, should you take into account the tax laws in calculating your expected winning? If so, how much would this change the expected value for you when you bet $100 that the ball will stop on 17?

Ask Marilyn
Parade Magazine, 28 April 1996, p 6
Marilyn vos Savant

A reader poses the following question:

A company decided to expand, so it opened a factory generating 455 jobs. For the 70 white collar positions, 200 males and 200 females applied. Of the females who applied, 20% were hired, while only 15% of the males were hired. Of the 400 males applying for the blue collar positions, 75% were hired, while 85% of the females were hired.

A federal Equal Employment enforcement official noted that many more males were hired than females, and decided to investigate. Responding to charges of irregularities in hiring, the company president denied any discrimination, pointing out that in both the white collar and blue collar fields, the percentage of female applicants hired was greater than it was fro males.

But the government official produced his own statistics, which showed that a female applying for a job had a 58% chance of being denied employment while male applicants had only a 45% denial rate. As the current law is written, this constituted a violation....Can you explain how two opposing statistical outcomes are reached from the same raw data?"

What we have, of course, is an example of Simpson's paradox: The direction of association between gender and hiring rate appears to reverse when the data are aggregated across job classes. Marilyn correctly notes that, even though all the figures presented are correct, the two outcomes are not opposing.

She also presents her own analogy.

Say a company tests two treatments for an illness. In trial No. 1, treatment A cures 20% of its cases (40 out of 200) and treatment B cures 15% of its cases (30 out of 200). In trial No. 2, treatment A cures 85% of its cases (85 out of 100) and treatment B cures 75% of its cases (300 out of 400)....

So, in two trials, treatment A scored 20% and 85%. Also in two trials, treatment B scored only 15% and 75%. No matter how many people were in those trials, treatment A (at 20% and 85%) is surely better than treatment B (at 15% and 75%), right?

Wrong! Treatment B performed better. It cured 330 (300+30) out of the 600 cases (200+400) in which it was tried--a success rate of 55%...By contrast, treatment A cured 125 (40+85) out of the 300 cases (200+100) in which it was tried, a success rate of only about 42%.

She notes that this is exactly what happened to the employer. Because so many more men applied for the blue collar positions, even if the employer hired all the women, it wouldn't satisfy the government.


1. Verify that the calculations leading to the percentages reported in the reader's question correspond to those in Marilyn's example. Do you find that the medical analogy clarifies the situation?

2. Marilyn says "This common situation is a good illustration of the weakness of applying even the most straightforward statistics to draw conclusions in human affairs." Is she saying that statistical reasoning is not useful in human affairs? What is your opinion of this?

3. Do you agree with Marilyn's statement that "Treatment B performed better" in her example?

Influence and power of the media.
Lancet, 1 June 1996 p 1533
Tim Radford

In this lengthy article on the media, Tim Radford explores how the media influences the information people receive and how the population, in turn, discerns tabloid news and relevant news.

For instance, Radford writes that people are fairly open-minded about stories concerning astrology, alien abduction, magic cellulite creams, and lotteries, but are unlikely to believe news reports that there is no link between HIV and AIDS even though such reports have been published in venerable papers such as "The Times" of London.

Most of what people know about HIV and AIDS comes from the media, but it is also this same medium that supplies information about anti-aging creams and alien sightings. Why then do people believe some things but not others? Radford hypothesizes that "people seem quite content to believe in almost anything, but they also seem to be able to sort out the dangerous rubbish from the merely self-indulgent."

Radford suggests that newspapers will die if readers stop reading when they don't want to hear the stories they are being told. When newspapers sense there is a particular story that is "going down well" they all start telling it. Radford cites the stories on haemolytic streptococcus and necrotising fasciitis (the notorious flesh-eating species) and the numerous reports on "mad cow disease."

Despite his criticisms of the press, Radford acknowledges that most of the time the press tries to get things right. It has an important responsibility to the public which relies on the media for information. The press, however, cannot act self-importantly because the public dislikes pomposity. What the press has to say is often concealed, sometimes completely lost, in the stories it chooses to tell. It must try to report the news accurately but at the same time, try to please its own perceived audience.

Radford concludes that, despite the onslaught of information from the media, newspaper readers and news program watchers remain sensible individuals: they are perfectly happy to be entertained by the absurd, they are capable of discerning important patterns in the flood of competing signals, and they are unlikely to be misled about the things that will truly alter their lives.

The Ingelfinger rule, embargoes, and journal peer review--Part 1: Lancet, 18 May 1996, p 1382
Part 2: Lancet, 25 May 1996, p 1459
Part 3: Lancet, 25 May 1996, p 1462
Lawrence K. Altman

In 1967, soon after he became editor of the "New England Journal of Medicine", Franz Ingelfinger learned that two publications, sent free to doctors, had reported details of a paper before its publication in the NEJM. Inglefinger thought that these publications "demolished" the newsworthiness of the forthcoming paper with resulting commercial damage to the profitability of his journal. He announced that henceforth NEJM's policy would be to reject a paper if it had been published elsewhere, in whole or substance. This rule became known as the "Inglefinger rule" and has since been adopted by many other journals including Lancet.

Lawrence Altman is a doctor and one of the principal science writers for "The New York Times". This series of articles reviews the history of the Inglefinger rule and its effect on the dissipation of medical news. Altman feels that the rule does more harm than good and summarizes his position as follows:

The Ingelfinger rule was invented to counter stiff economic competition and later was justified as "enlightened self-interest". When the rule was widely attacked, its supporters shifted justification for its existence to the importance of peer review before disseminating information to the profession and public. But peer review is a subjective and mysterious process that itself is under intense scrutiny. The question that must be asked is what purpose the peer-review system and the Ingelfinger rule serve when the overwhelming majority of papers are published, even after they have been rejected by many journals, and all but 5% of the published material, even in the leading journals, is said to be "rubbish". Peer review should be called what it is--editing, or a tool of editing.


(1) How do you think the editors of the New England Journal of Medicine would answer Altman's criticism of the Inglefinger rule?

(2) Does the Ingelfinger rule seem reasonable to you?

(3) Does Altman seem a little hard on the medical reserch articles that are published and the peer review system?

Of fame and fortune, and medical attention.
The Boston Globe, 23 May 1996, p 3
Peter J. Howe

A survey of physicians in the Cleveland area sought to determine whether the rich and famous get preferential medical treatment. Two versions of the question were sent out. The first asked doctors how they would treat a 45-year old with back pain and a 32-year old who seems to have bronchitis. The second version added the information that the 45 year old was a lawyer, and the 32-year old was the spouse of their hospital's CEO. While doctors who received the second version did not order any more diagnostic tests, they were 50% more likely to schedule a follow-up visit within a week.

These results stand in contrast to past studies on the effect of socioeconomic status on medical attention, which have found that doctors usually order more tests and more aggressive treatment when they perceive that their patients are well off financially.


What information is furnished to doctors in the current survey beyond the fact that their hypothetical patients are well off? How might this affect the responses?

Three coins in the fountain.
The College Mathematics Journal, May 1996, p 204
Fallacies, Flaws and Flimflam, Ed Barbeau (ed.)

When three fair coins are tossed independently, what is the chance that they all come up alike? This article presents a paradoxical solution attributed to Sir Francis Galton, which will be discussed by Ruma Falk in a forthcoming article in "Teaching Statistics". Galton gave the correct answer of 1/4, noting that HHH and TTT are the two favorable outcomes among the eight equally likely possibilities. But he went on to say that he had heard the following proposed solution: "At least two coins must turn up alike, and it is an even chance whether the third coin is heads or tails; therefore the chance of all alike must be 1/2".


Galton is quoted as saying "I doubt that here are many who, without recourse to pencil and paper, could distinctly specify off-hand where the fallacy lies". Where is the fallacy?

John Finn has remarked to us that the press and researchers often, by their choice of words to describe a social phenomena, introduce bias and confusion in accounts of the results of research. One of his favorite examples is the use of the term "binge drinking", in reporting results of surveys of student drinking. Here is an exchange of letters related to this issue.

Campus crime arises from a moral vacuum.
The New York Times 12 May 1996, Section 4 p 12
Henry Wechsler

To the Editor:

At the heart of the fraternity-related violence and crime you report (front page, May 5 and 6) is the long-held tradition of heavy alcohol use. Our national study of 17,000 students at 140 colleges in 40 states disclosed that 86 percent of fraternity house residents were binge drinkers and that 51 percent binged several times a week. The single strongest predictor of binge drinking was residence in a fraternity.

The heavy drinking of these students produces effects that harm others on campus through excessive noise, verbal abuse, vandalism and physical and sexual assaults.

Alcohol abuse has been allowed to exist at fraternities on many campuses under the protection of powerful alumni and a "see no evil, hear no evil" response by university officials. This denial can no longer be maintained in the face of documentation of serious harm to other students. Legal liability actions are sure to accelerate, and the ensuing monetary remedies will bring change.

Director, College Alcohol Study
Harvard School of Public Health
Boston, May 6, 1996

John Finn sent the following letter to the New York Times:

To the Editor:

In his 12 May letter to the editor, Henry Wechsler, Director of the Harvard School of Public Health's College Alcohol Study, tells us that a recent study showed that 51 percent of American college fraternity residents "binged several times a week".

Those of us over 40 may wonder if this is a misprint: isn't a drinking binge something that lasts at least several days? Indeed, Charles Jackson's "The Lost Weekend" (Farrar & Rinehart, 1944), crucial in popularizing the AA view of alcoholism, is precisely an account of a six-day binge, which the protagonist regards as minor: "... in his present weakened condition he knew that six days would be about the limit of his endurance. No three-week bender this time, ending up in Chicago, Philadelphia, the Fall River boat, a filthy room in a 9th Avenue hotel ---God knows where." (page 44).

Mr. Wechsler has neglected to include the fine print that he and his fellow reformers have "defined" binge drinking to mean having 5 or more drinks in a single evening; 4 or more for a woman.

I am very disturbed to find this sort of semantic sleight of hand, against which George Orwell and others have warned us, coming from such august institutions as Mr. Wechsler's.

I am also disturbed by Mr. Wechsler's statistical sleight of hand. In his first paragraph he barrages us with statistics which do indeed support the claim that "binge drinking" ---as he defines it--- is high in college fraternities. Then in his second he asserts that this "heavy drinking" causes physical and sexual assaults ---without any statistical verification whatever.

Finally, I am disturbed by Mr. Wechsler's choice of words in lamenting that alcohol abuse has been "allowed" to exist at fraternities. Assuming that what he calls binge drinking constitutes alcohol abuse, he is here suggesting that colleges not "allow" a 21-year-old man to drink five beers in the privacy of his fraternity room. I hesitate to think of just how Mr. Wechsler would suggest that colleges implement the prohibition he advocates, since they will have to go beyond the law to do so.

I support those who endeavor to effect changes in the drinking habits of college students. But I also feel we may rightly expect these reformers themselves to show some sobriety and restraint in their approach.

Sincerely, John Finn

Alas, the New York Times chose not to publish John's letter but Jonh sent a copy to Henry Wechsler who sent the following one sentence reply:

You can always tell a Dartmouth man but not much.


(1) The press often states that X was arrested for "drunken driving" when the actual charge is "driving while under the influence of alcohol". Do these mean the same thing?

(2) An article in the June 21, 1996 "Atlantic Journal and Constitution" entitled "Olympic Weekly" begins by stating:

In celebration of the human athletic body and in recognition of the fact that the early Greeks were a bunch of drooling perverts, Life magazine has included in its July issue a photographic study of today's Olympians in an ancient state of undress.

Do you think that by pervert the writer means homosexual? If so, does the choice of words make a difference? (Life used neither term)

(3) Does the term "abuse" means the same thing when used in "alcohol abuse" and "drug abuse"? In particular, how much alcohol is needed for "alcohol abuse"? How much drug use is needed for "drug abuse"? Does the term "addict" mean the same when used in the expression "he is a coffee addict" as in is does when used in the expression "he is a heroin addict"?

(4) Can you think of other uses of words the press or others use that convey more of the writer's person feeling than might be appropriate.

Drinkin' and thinkin' can mix.
The Houston Chronicle, 18 June 1996, Business Section, p 1

Penn State College of Medicine professor Siegfried Streufert has studied the effects of a night of drinking on managerial decision- making the following day. A group of 21 managers and professionals, who had had 4 to 6 drinks the night before, were presented with fictitious situations such as running a small country. While the people reportedly did feel terrible and believed that they would perform poorly, Streufert found that their decision-making performance was unaffected.

Genevieve Ames, of the National Institute of Alcohol abuse, notes that previous studies of doctors, pilots and drivers have shown that a hangover does negatively affect performance, and Streufert was careful to note that the study should not be viewed as a sanction to get drunk every night before work.


1. From this description, what do you think of the design of the study? What else would you like to know?

2. Why do you think the exercises involving "running a small country" were used instead of fictitious business situations?

3. Do you think that the tasks faced by doctors, pilots and drivers might differ systematically from those of business executives?

Missing in action: About a million men have left the work force in the past year or so.
The Wall Street Journal, 12 June 1996, p 1.
Bernard Wysocki, Jr.

The US Labor Department recently reported a May unemployment rate of 5.6%, corresponding to a total 7.4 million unemployed people. However, this figure omits a million "missing men" who have effectively dropped out of the work force. It is reported that, in 1995, an average of 838,000 men between the ages of 25 and 54 left jobs and wanted to work, but weren't actively pursuing jobs. Experts estimate that perhaps 200,000 others are not inclined to work again, bringing the total number of drop-outs to 1 million. Reasons for dropping out include depression over being laid off, and refusal to accept potential jobs that would require taking substantial pay cuts.

Some economists put the "missing" figure even higher. Lester Thurow of MIT estimates there are 5.6 million missing from the 25 to 60 age group. Among these are many 55-60-year-old former employees who have taken advantage of early retirement packages. Other groups are the homeless, the disabled, and the urban underclass.

Everitt Ehrlich of the Commerce Department points to a long-term decline in male participation in the labor force, which he calls "one of the barometers of middle class anxiety". If 1971 participation rates were matched today, there would be an additional 734,000 men aged 25-54 in the labor force.


1. In the report that "...in 1995 an average of 838,000 men between the ages of 25 and 54 left jobs and wanted to work...", what do you think has been "averaged"?

2. Do you think it make sense for people who have taken early retirement to be grouped with the unemployed?

3. Why would "middle class anxiety" lead people to drop out of the labor force? Can you suggest any other possible reasons?

William Lott suggested the following article.

Americans lead list in sex survey.
USA today, 24 May 1996, D1
Hillis L. Engley

A survey sponsored by the makers of Sheik, Avanti and Ramses condoms polled 10,000 men and women in 15 countries on questions relating to sexual behaviors. According to this article USA finished "first" in several categories and mentions three of these:

Most sexually active. USA respondents had sexual intercourse an average of 135 times a year, Russia 133, France 128, Britain 124, Poland 119, Australia 116, and South Africa 11, and Thailand 53. The world average was 109.

Earliest sexual intercourse. U.S. 16.2, Britain 16.7, Brazil 16.9, France 17, South Africa 17.1, Australia 17.2, and Hong Kong 18.9

Personal satisfaction. 61% of the USA respondents put "my own personal sexual satisfaction" first on a list of sexual priorities. Only 23% placed satisfying the partner at the top of the list.


(1) Lott pointed out that the data given would make it impossible to establish any significance between USA and Russia on the issue of sexual activity. Is he correct?

(2) Why do you suppose the countries listed are different for the first two questions?

(3) What are some of the problems in a survey of this kind?

Fly me; why no airline brags: "We're the safest"
The New York Times, 9 June 1996, Section 4 p 1
Adam Bryan

Airline officials try to tell the public if it allows a US. airline to fly it is considered safe. However, the public continues to want to know how safe they are. Arnold Barnett at MIT has studied air safety statistics for 20 years. He said that, if you boarded a flight on a randomly chosen airline every day, on average you would fly for about 21,000 years before dying in a crash. However, travelers' suspicions that the Federal Aviation Association (FAA) had a fuller answer were confirmed when an internal ranking of safety records of airlines was obtained by the "Chicago Tribune" and then released to the rest of the press by the FAA. Here is the part of the ranking relating to the major airlines.

The FAA chart below counts an accident as any incident that results in serious personal injury or substantial damage to the plane. It covers the period from 1990 through last month.

Accidents per 100,000 departures for selected airlines

                  Accident rate   Departures

Tower Air 8.680 23,041
Valujet 4.228 118,264
Carnival 2.740 72,988
American Trans Air .562 177,662
United .452 4,651,020
Continental .349 3,150,349
American .338 5,622,932
Delta .308 6,162,160
USAir .242 5,782,745
America West .232 1,281,205
TWA .227 1,763,784
Southwest Airlines .217 3,233,102
Northwest .173 3,477,273
Alaska .126 796,495


(1) The author of this article suggests that it might be unfair to suggest that Tower Air has the worst record when, in fact, it had only two accidents during this period, neither of which resulted in the death of a passenger. He claimed that the casual reader might think that Tower Air has had more than 8 accidents. Do you agree?

(2) The author says that airlines are so safe now that accidents are largely random events. If this is true why does the FAA make such an effort to find out what caused the accident?

We end with a fairy story suggested by Eunice Goldberg. Eunice suggested another fairy story in the same issue of the Chicago Tribune: "The Economics of Michael Jordon: is he priceless?", Commentary p 15, written by Allen Sanderson an economist at the University of Chicago who teaches a course in sports economics. We agree that it is a great article and we did, as Eunice suggested, check the prize of gold to see if his 18 million dollar request would make him "worth his weight in gold", but the article seemed to be leaving little to chance so we will include the full text in Chance News on our web sight and invite you to read it there.
Here is the real fairy story.

Tooth fairy index might just provoke fallout with kids.
Chicago Tribune, 4 June 1996, Metro Chicago p 1
Eric Zorn

Eric Zorn writes a weekly column for the Chicago Tribune and in his May 28th column he wrote:

Notes from a long rainy weekend: When the conversation turned, as it so often does, to the Tooth Fairy, a friend mentioned at a party that a minor controversy had erupted among parents of her son's kindergarten classmates: Some reported that the Tooth Fairy left $5 per tooth under the pillow, while others reported lost-incisor compensation as low as a quarter.

In his June 4 column he writes:

At last week's writing I had no idea "what that quarter I used to find under my pillow would be worth in 1996 dollars. And I also had no real idea what that dollar my son finds under his pillow would have been worth to me when I was his age. So I sat down with the most recent urban consumer price index historical tables from the U.S. Department of Labor and generated the following conversion table, which goes back as far as they keep records.

We are then provided with the following table which tells you what the quarter in year x is equivalent to today and what a dollar today corresponded to in year x. I see that the dollar today corresponded to 11 cents in the days that I got a dime so I guess I was paid enough.

   Year         Quarter    Dollar                                  

1913 $3.94 .06
1914 $3.91 .06
1915 $3.87 .06
1916 $3.58 .07
1917 $3.05 .08
1918 $2.59 .10
1919 $2.26 .11
1920 $1.95 .13
1921 $2.18 .11
1922 $2.33 .11
1923 $2.29 .11
1924 $2.29 .11
1925 $2.23 .11
1926 $2.21 .11
1927 $2.25 .11
1928 $2.29 .11
1929 $2.29 .11
1930 $2.34 .11
1931 $2.57 .09
1932 $2.85 .08
1933 $3.01 .09
1934 $2.91 .09
1935 $2.85 .09
1936 $2.81 .09
1937 $2.70 .09
1938 $2.77 .09
1939 $2.81 .09
1940 $2.79 .09
1941 $2.66 .09
1942 $2.40 .10
1943 $2.26 .11
1944 $2.22 .11
1945 $2.17 .12
1946 $2.00 .12
1947 $1.75 .14
1948 $1.62 .15
1949 $1.64 .15
1950 $1.62 .15
1951 $1.50 .17
1952 $1.47 .17
1953 $1.46 .17
1954 $1.45 .17
1955 $1.46 .17
1956 $1.44 .17
1957 $1.39 .18
1958 $1.35 .18
1959 $1.34 .19
1960 $1.32 .19
1961 $1.31 .19
1962 $1.29 .19
1963 $1.28 .20
1964 $1.26 .20
1965 $1.24 .20
1966 $1.21 .21
1967 $1.17 .21
1968 $1.12 .22
1969 $1.06 .23
1970 $1.01 .25
1971 .96 .26
1972 .93 .27
1973 .88 .28
1974 .79 .32
1975 .73 .34
1976 .69 .36
1977 .64 .38
1978 .60 .41
1979 .54 .46
1980 .47 .53
1981 .43 .58
1982 .40 .61
1983 .39 .64
1984 .38 .66
1985 .36 .69
1986 .36 .70
1987 .34 .73
1988 .33 .76
1989 .32 .79
1990 .30 .84
1991 .29 .87
1992 .28 .90
1993 .27 .92
1994 .26 .95
1995 .26 .97
1996 .25 $1


(1) If you were to plot a graph of the year equivalents of a quarter today what kind of function might best fit the graph?

(2) How do you think the urban consumer price index is determined?

Please send comments or suggestions to jlsnell@dartmouth.edu


CHANCE News 5.07

(24 May 1996 to 17 June 1996)