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
Please send comments and suggestions for articles to firstname.lastname@example.org.
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
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.
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:
- "Designing cost-effective environmental sampling using
concomitant information" by Glen D. Johnson, Harry D.
Nussbaum, Ganapati P. Patil, and N. Phillip Ross.
- "The politics of statistical reform: a cautionary tale,
1978-1980" by James T. Bonnen.
- "The geometry of random images" by Keith J. Worsley.
- "Time management in sports: ball control and other
myths" by Harold Sackrowitz and Daniel Sackrowitz.
- "Can the World Wide Web make statistics textbooks
more fun?" by Graeme D. Ruxton.
- "A Nobel graph" by John W. Durso and Howard Wainer.
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
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
(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
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
(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.
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
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
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,
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
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
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.
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
(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
(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
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?
- 1) In Canadian studies, two researchers recorded the
spontaneous utterances of parents at 111 births and
surveyed relatives of newborn infants. They found
that paternal resemblance was noted significantly
more than maternal resemblance.
- 2) In Mexico, Jeanne Regalski of the University of
Pittsburgh interviewed 198 parents and relatives of
49 newborns and found by more than a 2 to 1 margin
they said that the child looked more like the
father than the mother.
- 3) In the U.S., a Washington Post study found that 53%
of those interviewed said they were told as
children that they looked like their fathers, while
only 38% said they looked like their mothers.
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
(2) How do you think the public impression of recent
presidents would compare with that of those of the
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
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
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
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
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
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
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.
- THE AIR OF ASTRAVA
by Jeff Wheelwright
Three years ago, when the Czech Republic was born, it
inherited from its former rulers a state of staggering
pollution and environmental insult. With the help of the
EPA, the Czechs are beginning to assess their legacy of risk
--and reduce it.
- BEYOND THE LAB RAT
by Mark Caldwell
Cancer researchers are scrutinizing the complex interactions
between human carcinogens and human cells, hoping to find
hints of tumors before they start.
- TRUST ME, I'M YOUR SOFTWARE
by Evan I. Schwartz
On the outside, computers have become ever more simple and
user-friendly. But inside, the software that now runs them
is often so complex that we can never know precisely what it
- A FISTFUL OF RISKS
Don't make another move until you've checked it against our
compendium of life's potential mishaps. Here are a couple of
If you live in Lafayette, Indiana, here's how the risk
of death from traveling to two popular vacation spots
Driving 100 miles to Chicago and back: 1 in 588,000
Flying 5,000 miles from Chicago and back: 1 in 500,000.
The risk of being hit, directly, by a former celestial
body: 1 in 150 trillion.
- GUNSLINGING IN AMERICA
by Fred Guter
A handgun is the most dangerous consumer product around,
but do the risks of owning one outweigh the risks of not
- THE MATHEMATICS OF MAKING UP YOUR MIND
by Will Hively
What's the most rational way to wring some sense from a
tangle of conflicting data and opinions? Go ask a
twentieth-century statistician--or an eighteenth-century
- AFTER THE CRASH
In their quest to make cars ever safer, researchers
are looking past crash dummies and highway statistics
to the physics of the crashes themselves. By reconstructing
what went wrong, they are learning how to get it right.
Adam M. Finkel
One of the country's leading risk assessors reflects on
the current rage for risk assessments in Washington.
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
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
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:
RATE YOUR RISK 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
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
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?
4. Which of the following is most likely to kill you in the
next 12 months?
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
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?
9. What are the chances, in the next 12 months, that you will
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 email@example.com
CHANCE News 5.05
(29 March 1996 to 23 April 1996)