CHANCE News 5.06
(24 April 1996 to 23 May 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
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:
Bonnie Cochran Doyle gave us a wonderful book "Ripley's Believe it or Not! Book of
Chance" that is full of great quotes like the following:
Julius Caesar the Roman general and statesman
assassinated by a group
of nobles received 23 stab wounds -- but only one was fatal
Ripley's Believe it nor Not! Book of Chance
answers commonly asked questioins about weather prediction.
In particular you will find the following definition for the
probability of percipitation (POP):
PROBABILITY of PRECIPITATION (POP) is the likelihood of
occurrence (expressed as a percent) of a precipitation event at
any given point in the forecast area.
You will also find the equivalences between probabilities
and descriptive words: for example 10% chance of rain
= slight chance for rain.
Does this definiton of POP mean that
the forecaster is supposed to assume that the probability is
the same at each point in the region?
Robin Pemantle suggested the following article:
Juries do not apply mathematical formulae.
The Times, 9 May 1996, Features section
The Court of Appeal, Criminal Division, allowed an appeal against conviction and ordered
a retrial of Denis John Adams who had been sentenced to several years' imprisonment
for rape. The judges stated that the prosecution case rested entirely on the expert evidence
in relation to the DNA profile obtained from semen on vaginal swab taken
from the victim.
This expert evidence involved the use of Bayes' theorem in evaluation of the DNA profile.
The use of this theorem required that items of evidence be assessed separately according
to their bearing on the guilt of the accused before being combined in the overall formula.
While not passing judgment on the reliability of this presentation,
the judges expressed grave doubts as to whether this evidence was admissible because
it trespassed on an area exclusively within the jury's province, namely the way in
which the jurors evaluate the relationship between one piece of evidence and another.
The court stated that jurors evaluate evidence and reach conclusions not by means
of a formula, mathematical or otherwise, but by the joint application of their individual
common sense and knowledge of the world to the evidence before them.
In a previous Chance News (3.05) we reported a challenge in the U.K. courts of a conviction
on the basis that the prosecutor had committed the "prosecutor's paradox". That
is, the prosecutor presented the probability that an individual will match the DNA
found on the victim, given that he is innocent, instead of the probability that he
is innocent given a match. Since the latter probability requires the use of Bayes'
formula, would the prosecutor in this case been better off committing the prosecutor's
The power of statistics to affect lives -- even when they're wrong.
Christian Science Monitor, 2 May 1996, p. 12
In her 1985 book "The Divorce Revolution" Lenore Weitzman gave the statistical estimate
that a year after divorce, women's standard of living declines by 73%; while men's
improves by 42%. These statistics were widely quoted by policy makers, reporters,
and in journal articles. They have been cited in at least 24 state appellate and supreme
court decisions and once by the United States Supreme Court.
The results seemed too striking to Richard Peterson who re-analyzed the same data
using the same methodology and found less striking results. His analysis found that
women's standard of living one year after divorce went down 27% and men's went up
10%. His findings will be published in the June issue of the American Sociological Review
and are in line with other national studies on the issue.
Gardner pointed out that even if there had not been a mistake, there should have been
some concern about the influence Weitzman's statistics had since her sample was only
228 individuals, all of whom received a divorce in Los Angeles.
How do you think they estimate the standard of living of a women before divorce?
Are U.S. men less fertile? Latest research says no.
The New York Times, 29 April, 1996, A14
In a previous Chance News (5.04) we discussed articles suggesting that the sperm count
of men is decreasing dangerously. Now two studies in the United States have found
that the average sperm count for men in certain cities may be greater than it was
20 years ago. The studies have also shown that the average sperm count varies significantly
in U.S. cities. New York consistently has the highest sperm count which is more
than 50 percent higher than the sperm counts for men in Los Angeles. These differences
in cities are considered very surprising by the experts who have no explanation why
this should be.
The U.S. studies are reported in the May issue of "Fertility and Sterility". One of
the studies was carried out by Dr. Harry Fisch and colleagues at Columbia College.
They examined data from semen analyses of 1,283 men who donated semen to sperm banks
before having vasectomies. The sperm banks were in New York, Los Angeles and Roseville,
Minn. The average sperm count for New York City was 131.5 million sperm per milliliter
of semen, in Minnesota it was 110.8, and in Los Angeles 72.7.
In a second paper Dr. C. Alvin Paulsen from the University of Washington collected
semen samples, from 1972 to 1993, from 510 healthy Seattle men. This study found
no decline in sperm counts or semen quality during the period of the study. The sperm
counts went from 46.5 million sperm per milliliter of semen in 1972 to 52 million in 1993.
In a third paper in the same issue of the journal, Fisch and his colleagues consider
global variations to show how previous researchers might have been led to believe
that counts were declining. Recall that a major meta-study had concluded that sperm
counts were declining and the authors of this meta-study suggested was the result of environmental
pollution. Fisch and his colleagues observed that most of the early studies involved
New York men where the sperm counts are now known to be unusually high while most of the recent studies involve men from the developing countries where sperm counts
tend to be lower, again for unknown reasons. Dr. Fisch has said: "I can explain
all the decline in sperm count by geographical variability".
(1) Can you conclude from the two studies that the sperm counts in Seattle are lower
even than Los Angeles? If not, why not?
(2) Do you think these studies settle the issue of declining sperm counts?
Academics challenge stock-owning theory.
USA Today, 25 April 1996, 3B
Academics debate worth of stocks.
Pensions % Investments, 25 Dec. 1995, p. 31
Marlene Gilvant Star
The long-term case for equities.
Journal of Portfolio Management (1995) Vol. 21, No. 1, p. 15
Paul A. Samuelson
Kadlec reminds us that conventional wisdom about investments says that the risk of
holding stocks is less in the long run than in the short run. Presumably that is
why we are advised when young to put a lot of our retirement funds into stocks but,
as we near retirement, advised to put a greater proportion in bonds.
He then says: "Now, a small but noteworthy group of academics is airing a sobering
concept: History be damned, the risk of owning stocks goes up -- not down -- with
time." He gives no reference for where this airing is taking place but I think the
article is based on a forum that took place November 30, 1995 in Cambridge, Mass. This
forum was described in the article by Star.
The forum consisted of a debate between Jeremey Siegel of Wharton, who believes that
stocks are the best investment for long term growth, and Zvi Bodie of Harvard, who
believes that this theory is fundamentally flawed. The moderator was Paul Samuelson
who apparently gave up attempts to remain neutral and came down on the side of Bodie.
Siegel's arguments are based upon looking at stock performance over long periods.
He presented data from three periods: 1926 to the present, 1871 to 1925, and 1803
to 1871. The real return was around 6.5% in all cases, and this is considerably
better than bonds do.
Bodie asks, if stocks really do become less risky the longer the holding, why isn't
the cost of portfolio insurance for equities less over longer periods, for every
Bodie and Samuelson are both worried about making statistical estimates based upon
past histories when we really have only one long sample in a stochastic process in
which different samples over the same period of time can look very different. They
observe that we cannot even look at long samples from other stock markets, since most of
them do not have the same long uninterrupted history that ours does.
In his article in the "Journal of Portfolio Management", Samuelson writes:
The Law of Large Numbers does not reduce riskiness toward zero as the investing period
extends toward infinity. If you are maximizing the expected logarithms or expected
square root of your wealth at retirement, you will hold exactly the same portfolio
proportions at every age. Thus, there cannot be any sure-thing syllogism putting long-term
investors into more equity tolerance than short-term investors. (Yes, when you are
young, stocks may have more time to recover from crashes, but they also have more
time to encounter crashes!)
How might Siegel try to convince you that the proportion of stocks in your retirement
portfolio should depend on your age? How might Samuelson try to convince you that,
if you have a logarithmic utility function, you should have the same portfolio proportions at any age?
Study details CUNY successes from open-admissions policy.
The New York Times, 7 May 1996, A1
Karen W. Arenson
A new study has found that the open-admissions policy, that 25 years ago transformed
the City University of New York by guaranteeing entry to almost all New York City
high school graduates, was far more successful in educating needy students than earlier
research suggested. Of the 100,000 who entered CUNY's two-and four-year colleges from
1970-1972, about 48,000 would not have qualified if the policy had stayed the same.
David E. Lavin, a professor at the university's Graduate School and at Lehman College,
and David Hyllegard, director of institutional research at Manhattan Community College,
originally had a sample of 35,000 students which they had studied in depth. They
followed up on about 5,000 students, 12 to 14 years after they first entered the university
as members of the first 3 open-admissions classes.
Earlier studies showed high dropout rates among open-admissions students, but Lavin
and Hyllegard found that, given time, many of them did eventually graduate. Many
minority students were usually poorer than other students and often worked full time
while they went to college and so took much longer than 4 years to graduate.
Detractors argue that lax standards of admissions are detrimental to under-prepared
students because their lack of preparation holds them back in remedial classes.
Others insist that the students' high school preparation was so poor that the college
was forced to lower standards and stoop to their level. Lavin and Hyllegard admit that
some students are held back by poor preparation and that a large part of the university
is dedicated to remedial classes. They counter, however, that the education being
offered is still sound and that many students do succeed, not drop out, as earlier studies
The study estimates that 5,000 eventually went on to receive master's degrees or doctorates.
In addition, Lavin and Hyllegard's data indicate that the educational opportunity
resulted in direct benefits in the job market and improved the economic base of New York City and New York State. The study estimated that, during one year in the
1980s, graduates admitted under open-admissions earned a total of almost $67 million
more than they would have if the university's program had not been installed. Their
additional lifetime earnings were estimated at about $2 billion.
The benefits of open-admissions flowed to both minority and white communities. The
number of minority freshmen jumped to more than 8,000 in 1970 from fewer than 1,700
in 1969, and the number of whites went from 16,000 in 1969 to almost 26,000 from
1970 to 1972.
There was no discussion in this article about how and when the original sample of
35,000 was obtained and how the 5000 to follow up were chosen and which 5,000 went
on to receive graduate degrees. What additional information would you need to have
to make sense out of all this?
Unconventional wisdom: New facts and hot stats from the social sciences.
The Washington Post, 5 May 1996, C5
Crystal ball gazing and other political games.
With the presidential race shaping up and the elections a few months away, political
analysts have been crunching numbers trying to predict who the winner will be in
November. Some polls say Bill Clinton leads Bob Dole by 20 percentage points, but
predict a much closer race. How do these prognosticators come by their numbers? Here, a
1) Michael Lewis-Beck of the University of Iowa uses a mathematical model which includes
presidential job approval rating, changes in the GNP, and Gallup survey questions
about which party would most likely bring peace and prosperity. He has 50.9 percent
for Clinton and 49.1 percent for Dole at this time.
2) Robert Erikson and Christopher Wlezien of the University of Houston use presidential
approval and cumulative income growth over a president's term in their election model.
Their current forecast is 53 percent for Clinton and 47 percent for Dole.
3) Alan Abramowitz of Emory University uses a model that includes the president's
approval rating, GDP growth during the first 6 months of the year, and a "time for
change" variable which factors in how long the incumbent party has been in the White
House. Current data in this model produced 55 percent for Clinton and 45 percent for Dole.
4) Allan J. Lichtman of The American University in Washington
D.C., uses a yes/no test of 13 questions which would determine the winner of every
election since 1860. When the answer to 8 or more of his questions is yes, the incumbent
president has won. 6 or more no answers indicate that the incumbent president will
lose. The answer to his questions for the current election gives 6 yes, 3 possible
yes and 4 no answers, so, Lictiman says it is not "in the bag" for Clinton yet.
(1) Why do you think there is such a disparity between the polls and the mathematical
models? Which do you think is more likely to be correct?
(2) Morin also mentions some of the "coincidence models" such as: there have been
only 5 left-handed presidents including Clinton and none have won re-election; in
9 of the 11 elections when hemlines rose going into the election, the Democrat won;
a National League victory in the World series meant a Democrat victory. How do Clinton's
chances look for each of these criteria?
(3) The latest price for a Clinton share on the Iowa Electronic Market was .592 for
the Democrat nominee and .378 for the Republican nominee. This is a winner take-all-market.
You get $1 back if your candidate wins and nothing otherwise. If you believe the polls, which candidate should you pick? What would you pick if you believe the
computer models? Finally, which would you pick?
Unconventional Wisdom: New facts and hot stats from the social sciences.
The Washington Post, 19 May 1996, C7
Big breasts and bogust broadcast.
In a recent segment of ABC's "20/20", Lynn Sherr reported that women long for bigger
breasts and that this preoccupation has drained them of self-esteem. In addition,
men supposedly value the bosom over all body parts.
Sherr's report relied heavily on statistics collected from a mail-in "survey" in "Self"
magazine that found that 50% of an unrepresentative group of women said they felt
they were inadequate because of their breast size. This report aired on "20/20"
despite a contrary national survey conducted by ABC's own polling unit at the request of
"20/20", which found that an overwhelming majority of women are satisfied with the
breasts they have. More than 9 in 10 said the size of their breasts had no impact
on their personalities. 23% said they had wished for a different size, and of that number
a little more than 50% said they wished for smaller, not larger, breasts.
On the question of whether men like bigger breasts, Sherr reported that men consider
the "face first, breasts come a close second." Again a deviation from the ABC poll.
57% of men interviewed said they considered the face as the most important part
when assessing physical appearance, while only 8% valued breasts.
Lock 'em Up.
Harvard economist Richard Freeman reports in the latest issue of Harvard Magazine
that the U.S. has proportionally more people in jail than any other nation on earth.
More than 1.3 million men were behind bars in 1993. That means more than 5 in every
1,000 residents were doing time. In the U.K., Germany, and France, fewer than 1 in a 1,000
residents are incarcerated. Freeman attributes this large number to the "reduced
demand for less-skilled male workers" who are thrown in jail when they commit a crime
What other reasons might explain the differences between the U.S and European
countries in the proportion of people in jail?
Statistics training called a plus for all students.
Chicago Sun-Times, 7 May 1996, p. 3
Warren Hawley, chairman of the mathematics department at the Latin School in Chicago,
believes that 100% of all students going to college can benefit from a general course
in statistics. Concepts such as percentiles, percentages, ranking, and fundamental
probabilities are all applicable to daily life.
Some current applications for everyday statistics skills are election analyses, standardized
tests, gambling (such as the lottery and whether to play or not to play), and consumer
issues (such as advertisements that cite statistics but not within the proper context).
Hawley emphasizes that not only is statistics relevant, it has also become much easier
to study since a lot of the number-crunching can be done electronically. Thus, more
time can be spent on the theories behind the numbers and the ramifications of such
figures. Today no more than 10% of college students take a statistics course.
Do you agree that theories are easier than number-crunching? What did Hawley really
Heart patients need not fear sex, study finds.
The New York Times, 8 May 1996, C10
Jane E. Brody
There has been anecdotal evidence that the risk of a heart attack is increased when
you are having sex. Dr. James E. Muller of Harvard Medical School and Boston-based
colleagues report in the current "Journal of the American Medical Association" on
a study they say will put these fears to rest. The study involved 858 men who survived a
heart attack and had been sexually active during the previous year. The researchers
found that the risk of a heart attack was increased only during the two-hour period
after sexual activity. They estimated the risk of a heart attack during this two-hour period
was about two in a million as compared to one in a million for an arbitrary two-hour
They also found that heart patients who regularly did moderately strenuous or "conditioning"
exercise had little or no added risk from sexual activity.
Of the 858 only 27 reported sexual activity within two hours of experiencing the first
symptoms of a heart attack. How do think the estimate of 2 in a million was obtained?
Support for use of DNA profiles as forensic evidence.
Lancet (1996) Vol. 347, No. 11, p. 1321
Paul M. Rowe
The National Research Council convened a second committee to assess the role of DNA
fingerprinting in the courts. The first committee had agreed that there were some
unsolved statistical problems with the estimation of the probability of a match in
DNA fingerprints and recommended a "ceiling principle" that was meant to give conservative
estimates. This principle was often misinterpreted in the courts and led to considerable
confusion and, at times, to DNA evidence being thrown out.
The new committee reported that this principle can now be abandoned because data base
of allele frequencies in populations and sub-populations have grown to the point
where reliable estimates will usually yield unique patterns (except for the case
of identical twins).
The report finds no meaningful way to estimate the probability of a laboratory error
and says that such procedural error calculations should never be combined with the
theoretical probability of a true match. The report recommends that whenever possible
forensic samples should be divided into two parts, and at the earliest practical stage,
to give the possibility of independent analyses.
The report also recommends that behavioral research be carried out to determine the
best way to present data on population genetics to juries, lawyers, and judges. Rowe
remarks: "Judging from the baffled faces of people at the press conference held for
the release of the report, public understanding of 'probability speak' will take time."
(1) Do you think the committee really have it right this time?
Will this report end the controversy over the use of DNA
fingerprinting in the courts?
(2) The report says that in the not too distant future DNA
fingerprinting will be able to make unique identification
(except for identical twins). Does this sound reasonable?
Semtex error could free 12 IRA men; Ministers order review of evidence.
Independent, 15 May 1996, p.1
The British government revealed that at least 12 IRA prisoners -- one third of all
those jailed in the past 6 years -- may have been wrongly convicted because of contamination
in a forensic science laboratory.
Two months ago it was accidentally discovered that, in a centrifuge machine used in
almost all forensic tests on terrorist bombings since 1989, neither the machine,
which spins the dirt out of samples for testing, nor its parts had been tested or
changed between experiments -- despite what are supposed to be routine weekly contaminations
checks at the laboratory.
The article states that: "The forensic tests always included a control sample known
not to contain any explosives. But Dr. Marhall (the head of the lab) admits that,
if a control sample tested positive, that test would be abandoned." What was the
In smoking, study sees risk of cancer of the breast.
The New York Times, 5 May 1996, Section 1, p. 31
Jane E. Brody
This article describes recent research in Switzerland that purports to show that both
active and passive tobacco smoke can significantly increase a women's risk of developing
breast cancer. Previous studies (21 in number) showed no relation, or at most a
weak positive relation, to breast cancer. Previous studies on passive smoking, while
fewer in number, had more consistently shown a positive relation.
This study, carried out in Switzerland, was a case control study with 244 women recently
diagnosed to have breast cancer as cases and 1032 women free of breast cancer as
controls. The study found that, for women who smoked less than half a pack a day,
the breast cancer risk was doubled, for those who smoked 10 to 19 cigarettes a day, the
risk was 2.7 times greater, and, for those who smoked a pack or more a day, the risk
was 4.6 times greater. The study also found a three-fold increased risk of breast
cancer among non-smoking women who were exposed to tobacco smoke either at home or at
work, but this risk did not depend upon the amount of exposure.
The authors of the study attribute the failure of other studies to detect a relationship
between smoking and breast cancer to the fact that these studies compared smokers
and non-smokers where the non-smokers group included passive smokers.
Other experts found it hard to believe the results of this study. One observed that
the study found the risk of passive smoking for breast cancer higher than that for
lung cancer and found that hard to believe.
The original article is in the "American Journal of Epidemiology", Vol. 143. No 9,
pp. 918-927. The authors have an interesting discussion of how they controlled for
other risk factors and for possible biases inherent in case-control studies. They
also explain how some of their more surprising results could be correct. Two such surprising
results were: the risk factor for passive smokers was of the same order of magnitude
as for smokers and the odds ratio increased with increased smoking but not with increased passive smoke exposure.
(1) Does the author's explanation for why previous results
do not agree with their results seem convincing to you?
(2) How are odds ratios computed for a case control study?
In trying to keep the length down we have had to omit a lot of interesting medical
studies reported during this period. Two particularly interesting examples we have
Warnings about salt disputed.
Boston Gobe, 22 May, 1996, p. 1
Peter J. Howe
How treadmill gets you there faster; Its calorie-burning efficiency is lauded.
Boston Globe, 8 May, 1996, p. 12
Richard A. Knox
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CHANCE News 5.06
(24 April 1996 to 23 May 1996)