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CHANCE News 4.03
(2 February to 15 February 1995)

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

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

Back issues of Chance News and other materials for
teaching a CHANCE course are available from the
Chance Web Data Base
http://www.geom.umn.edu/docs/snell/chance/welcome.html

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Chance is lumpy.
Robert P. Abeleson
===========================================

Professor Abelson sent us a copy of his new book
"Statistics as Principled Argument" just published by
Lawrence Erlbaum Associates, Hillsdale NJ. I will
review this book next time -- a welcome relief after
"The Bell Curve". As a preview, the main argument of
the book appears to be that data analysis should go
beyond a formal analysis. "It should make an
interesting claim; it should tell a story that an
informed audience will care about, and it should do so
by intelligent interpretation of appropriate evidence
from empirical measurements or observations."
<<<========<<

>>>>>==========>>
Pete Hayslett sent us the following article:

Sex education programs that work.
Parade Magazine, 12 Feb. 1995, pp 18-20
Earl Ubell

Games also teach interaction.  In the old
sex-ed courses, a teacher might say:'If you
have intercourse once a month, your chances
are one in six of becoming pregnant.'  Such
a dry approach soon loses teenagers' attention
Instead, today, the teacher starts a game:

TEACHER:  Class, write down any number from
1 to 6.  Now I'll draw a number from this box.
(Draws and reads) No. 6.  All those who picked
No. 6, please stand up.  You or your partner
just got pregnant.  Remain standing. OK.  Now
I've drawn No 3.  All those with a 3, please
stand.  You just got pregnant.  Soon, all the
students are standing.  The lesson: Frequent,
unprotected sex raises your chances of pregnancy."

DISCUSSION QUESTION:

(1) What do you think the teacher means by "If you have
intercourse once a month, your chances are one in six
of becoming pregnant"?

(2)  What is wrong with this game (activity) as a way
to illustrate a probability?
<<<========<<

>>>>>==========>>
Goran Djuknic pointed out that an ad for "The Club"
(anti-theft device for cars,) claims there is a 1 in 43
chance of your car being stolen, but with The Club the
chance goes to 1 in 10,000.

DISCUSSION QUESTION
How do you think The Club promoters came up with the 1
in 10,000 figure?
<<<========<<

>>>>>==========>>

ARTICLES ABSTRACTED

1.   Teachers' diligence finds fame.
2.   Mid-life weight gain and heart disease.
3.   Hard times for Britain's lost boys.
4.   Many don't practice safe sex.
5.   Men, women, sex, go figure.
6.   Weird dice.
7.   Statistics misused.
8.   Genes, race, IQ and "The Bell Curve".
9.   Cancer study to be reviewed.
10.  Soybeans and leukemia.
11.  HIV transmission risk in sports minimized.

<<<========<<

>>>>>==========>>
Martin Tanner remarked that we missed the following
interesting article last time.

Teachers' diligence finds fame, free lunch.
The Morning Call (Allentown), Jan. 21, 1995, B1
Joseph P. Ferry

This article reports on what should be a very simple
mathematics error, and I, at least, could not figure
out what the problem was from the details of the
article.

The article states that Bob Swain, a Souderton High
School mathematics teacher, found a mistake in an ad of
the restaurant chain Boston Chicken.  With much
effort, he got them to change the ad. He received a free
lunch with thirty of his students.  He also obtained
instant fame, appearing, for example, on the CBS program
Good Morning America.

Here is what you learn from the article about the
mathematics of the problem.

Boston Chicken's ad, featuring quarterback Joe Montana,
claimed that there are 3,360 possible combinations of
three-item meals available to customers. (I think this
should have been three-item side dishes to accompany

confused the formula for figuring permutations and
combinations.  By Swain's calculations, there are only
816 different combinations available. Swaim said the
company would have to increase its list of side dishes
from 16 to 27 to obtain the number of combinations
given in the ad.

Boston Chicken agreed to change their ad to say 816
possible combinations.

DISCUSSION QUESTIONS.

(1)  (a) How did Boston Chicken arrive at the number
3360? (b) How did Swain arrive at the number 816?

(2) If you are stuck on part (a) of problem (1), as I
was, here is a hint: 16*15*14 = 3360.  What is wrong
with counting this as the number of possible three item
side dishes?

(2) If you are stuck on part (b) of problem (1) as I
also was, show that the number of ways to choose 3
items from 16 allowing repetitions but not counting
order is 816. Does this make the revised ad reasonable?

(3) Show that the number of ways to choose 3 objects
from 18 without repetitions is also 816.  Why is this
the same as the number of ways to choose 3 items from
16 with repetition?
<<<========<<

>>>>>==========>>
Ruma Falk suggested the next study.

Study rebuts 'Acceptable' mid-life weight gain.
The New York Times, 8 Feb. 1995, C11
Jane E. Brody

Current guidelines consider an increase in weight of
from 10 to 40 pounds for women during mid-life
acceptable and even desirable.

Researchers at Harvard School of Public Health and
Harvard Medical School report in the "Journal of
American Medical Association" (Feb 8, 1995) on a 14
year study involving 115,818 women. The study found
that women who gain 11 to 18 pounds in adult life
had a 25 percent greater chance of suffering or dying
of a heart attack compared with women who gained less
than 11 pounds after the age of 18.

Coronary risk rose to a 60 percent increase for weight
gains of 18 to 25 pounds and to a 200 to 300 percent
increase for weight gains above 25 pounds.

Authors of the study criticized the guidelines issued
in 1990 by the United States Departments of Agriculture
and Health and Human Services saying "The guidelines
provide false reassurance to the large fraction of the
population who are not defined as overweight, but who
are at substantially increased risk of coronary heart
disease." They say that these guidelines were based
upon studies that did not control for factors such as
smoking as their study did. The 1985 guidelines, based
upon the 1959 Metropolitan Life Desirable Weight Table,
did not suggest that it was desirable to gain more
weight in mid-life.

The news director of the Public Health Service stated
that the next edition of "Dietary Guidelines for
Americans" to be published at the end of this year will
reflect current concerns about gaining weight.

The director of the Framingham Heart Study said that
their studies show that significant weight increase
after age 25 is also a risk factor for heart disease in
men.

DISCUSSION QUESTION:

(1) Why is it necessary to control for smokers in a
study of the effects of weight gain?

(2) Do studies of this kind show that gaining weight
causes heart attacks?
<<<========<<

>>>>>==========>>
Hard times for Britain's lost boys.
New Scientist, 4 February 1995, pp 12-13
Karon Gold

In Britain, girls are overtaking boys on the GCSE exams
subject by subject.(These are exams in a number of
subjects taken by all 16-year-olds in Britain). In the
most recent scores available, 45% of the girls received
five or more GCSE grades between A to C as compared to
37% for the boys.

Researchers at the University of Sheffield developed a
data base of 30,000 students giving such things as
social status and test scores over a wide range of
ages. They found that the best predictor of a 16-year-
old's GCSE result, in any subject, is the reading score
between ages 10 and 12. From their data, they determined
a linear predictor for an overall GCSE grade as a
function of the reading score at age 12.  Individual
schools then made scatter plots based on these two
scores for students in their school.  Students above
the predicted line were considered over-achievers and
those under the line were considered under-achievers.
Girls tended to be over-achievers and boys under-
achievers.

Schools then looked at records of the boys who were
under-achievers to see if they could have predicted
these. Standard explanations such as not being bright
and not being literate were not born out.  Rather, they
seemed to show a pattern of poor attendance,
misbehavior, and summer birthdays--a known factor for
under-achievement.

DISCUSSION QUESTIONS

(1) The article reports that Education Secretary
Gillian Sheperd warned in a speech "Although girls'
academic advances are a cause for pride, there is a
danger of going too far."  What do you think was meant?

(2) Why should students with summer birthdays be a risk
factor for under-achievement?
<<<========<<

>>>>>==========>>
Many don't practice safe sex, survey finds.
The Boston Globe, 14 Feb. 1995, p3.
Associated Press

A survey of the sex lives of 1000 adults, funded by the
pharmaceutical firm Burroughs-Welcome, found that 75%
of Americans don't believe they can catch a sexually
transmitted  disease, even though doctors diagnose 12
million new (non-AIDS) cases a year.

The survey turned up the familiar pattern (discussed in
a previous Chance News) of men reporting more sex
partners:  51% claimed six or more, whereas only 25% of
women claimed that number;  28%  of men claimed eleven
or more, compared to 10% of women.  There were also
indications that people do not really know their
partners' behavior.  Only 18% of women under 30 years
old believe their partners have had at least five
partners, while 42% of the men that age and 57% of
those 30-39 claim they have.

DISCUSSION QUESTIONS:

(1)  Is there an inherent contradiction in the figures
on number of partners, or is it possible to reconcile
them numerically on the basis of behavior patterns?
How might reporting bias contribute to the apparent
discrepancy?

(2)  How about the figures on women's perceptions of
their partners' behavior?  Answer the same questions as
in 1.
<<<========<<

>>>>>==========>>
Men, women, sex. Go figure.
The Washington Post, 12 Feb. 1995, F1
Henry T. Dunbar

The author remarks that National Public Radio recently
reported a survey that American men average 11 sex
partners per lifetime and American women average 3.  He
states that the explanation usually given is that most
women are virtuous but a few are very promiscuous
providing all the extra sex partners for the men.  He
points out that no such explanation can account for the
difference since every time a man adds a new partner, a
women adds a new partner and the averages have to be
the same under any reasonable assumptions about the
population for the survey.

He comments that if they meant median instead of mean
it could conceivably be correct but he does not think
that is the answer either. He concludes that both men
and women are lying and the answer is somewhere in the
middle.
<<<========<<

>>>>>==========>>
Note: Joe Berger sent a letter that a colleague Bill
Banks sent by e-mail to National Public Radio
(chastising them for quoting the statistics in the
above article as if they were meaningful just because
they came from scholarly survey.)  He received a return
message saying they did not read their e-mail.

We remind you of the following two articles.

M.Morris, "Telling tales explains the
discrepancy in sexual partner reports",
Nature 365:437-440.

Einon, D. (1994) Are Men More Promiscuous
than Women? Ethnology and  Sociobiology
15: 131-143.

Morris points out that the usual explanations center on
two types of errors: sampling bias (men report
encounters with women below the eligible age,
prostitutes are left out, etc.) and reporting errors.

He shows that sampling bias cannot reasonably account
for the differences found.  On the other hand, he shows
that in major surveys, if the data is restricted to the
approximately 90 percent of subjects who report fewer
than 20 lifetime partners, the reporting ratio is
reasonably close to 1. He remarks "the anomaly appears
to be driven by the upper tail of the contact
distribution, an example of the general principal of
outlier influence in data analysis." He suggests ways
to improve this part of the data to get more accurate
results from these surveys.
<<<========<<

>>>>>==========>>
Weird dice.
Math Horizons, Feb. 1995, p30
Joseph Gallian

You are in the middle of a Monopoly game and someone
substitutes a pair of dice labeled 1, 2, 2, 3, 3, 4 and
1, 3, 4, 5, 6, 8 for the standard dice.

DISCUSSION QUESTIONS

(1) Show that the probability that you move k steps when
you roll the dice has not changed. (The article shows
that this is the only possible pair of weird dice that
would achieve this.)

(2)  Show that the switch does improve the value of St.
James Avenue. Hint: St. James is six spaces beyond
jail.  And recall what happens when a player is in jail
(not just visiting).
<<<========<<

>>>>>==========>>
Statistics Misused.
Technological Review, Feb. 1995, Letters page 70
Daniel Whitney

Apparently, you cannot even write an article on the
misuse of statistics without someone claiming that you
misused statistics.  In these letters and in the
letters in the January issue,  Daniel Whitney, Sydney
Freidin, and Ted Tsomides criticize some of the
examples used by Arnold Barnett in his article "How
numbers can trick you." that appeared in the October
1994 issue.

Tsomides feels that Barnett "omits or downplays some
important points about the misuse of statistics".  He
mentions three such points: (1) public policy is often
determined by statistical problems which are very
little understood, for example, the heritability of
I.Q.,  (2) scientific fraud is often cloaked in the
impression of statistical significance, and (3) even
honest researchers make inexcusable errors that render
their statistics useless such as the Love Canal fiasco.
In other words why just blame the media?

One of Barnett's examples considered the Supreme Court
case where odds and probability were mixed up when
comparing the chance that a black defendant would
receive a death sentence according to whether the
victim was white or black.  Tsomides suggests that
Arnold himself gave a biased view of the effect of the
error by choosing for his example an extreme case of a
defendant who has a 99 percent chance of getting the
death sentence where the victim was white.

Finally, Freiden thought that "passenger hours" should
replace "passenger miles" when comparing the safety of
various methods of travel.

Barnett does a pretty good job of defending himself
against these criticisms.
<<<========<<

>>>>>==========>>
Note:  There is an interesting discussion of comparing
the safety of methods of travel by Francis Lopez-Real
in the book "Teaching Statistics at its best"  (pages
142-143).  This  is the best of Vol 6-16 of the journal
"Teaching Statistics".  Both  are published by the
Teaching Statistics Trust at the University of
Sheffield, England and are wonderful resources for an
elementary probability or statistics course.

Lopez-Real observes that when comparing air and train
travel,  air appears safer when miles are used and
train when hours are used.  He argues that this does
not show that statisticians can prove anything but
rather that the choice of statistics used is important
and should be considered carefully.  For example, if
you are convinced that miles is best, he invites you to
consider the hypothetical case of three trips to
Jupiter each with a crew of 4.  The first two trips are
successful but in the third the crew of 4 is lost.  In
terms of miles this would lead to the conclusion that
space travel to Jupiter is safer than air or train but
he wonders how many would take the next trip.
<<<========<<

>>>>>==========>>
Genes, Race, IQ and "The Bell Curve".
OR/MS Today, Feb. 1995
Arnold Barnett

Barnett begins with the remark that there has been no
review from an informed perspective and he is going to
give it a try.

He starts by criticizing the authors' assumption that
the best way to reflect differences among a set of
numerical outcomes is by standard deviation.  He also
feels that the authors are too enamored with the normal
distribution.

There is considerable discussion in the book and much
in the press about the part of I.Q. that is inherited.
Barnett asks what it means for intelligence to be, for
example, 60 percent heritable?  From the author's
discussion he assumes that it means: Suppose that a
large set of genetically identical newborns grew up in
randomly chosen environments and their I.Q.'s were
measured when they became adults.  The variance of
these scores would be 60% less than that for the entire
population. The corresponding drop in standard
deviations would be about 37%, so Barnett concludes
that it would not be reasonable to assume that
differences are primarily due to genetic factors.
While the authors do not assume this, Barnett shows
that their discussion of this issue is confusing to say
the least.

Barnett shows that assuming intelligence can be
measured by a single number also causes real problems
that would not occur if we assumed that there were ways
to measure different aspects of intelligence.  He uses
the authors' own examples to demonstrate this.

While far from a comprehensive review, Barnett
identifies certain areas where he thinks the authors
err and explains why he thinks they do.

Finally, Barnett reflects on why the book was written.
At the beginning of the article he remarks that he is a
good friend of Charles Murray. He concludes by
remarking that he regards Murray to be a decent and
honest man but "he and Herrnstein made errors in
judgment that the nation has reason to regret."
<<<========<<

>>>>>==========>>
Cancer study to be reviewed.
The Toronto Star, 15 Feb. 1995, A4
Reuters

Last year the National Breast Cancer Screening Study
determined that routine mammograms have no benefit in
terms of mortality reduction for women between 40 and
49 years old.  Now Dr. Daniel Kopan, director of breast
imaging at Mass. General Hospital and a leading critic
of the study, says he has evidence that the patient
selection procedure was not random.  He claims that
nurses wanted to ensure that women with symptoms of
breast cancer received mammograms.

As a result, an independent team of researchers will
investigate the random selection process and report
back in two or three months.

DISCUSSION QUESTION:
Dr. Kopan's reasoning is not fully explained in the
article.  How could including symptomatic women bias
the study against screening?  Wouldn't it inflate the
cancer detection rate and make screening look
beneficial?
<<<========<<

>>>>>==========>>
The following article was suggests by Mary Paige.

Experiments offer hope of killing leukemia cells.
Chicago Tribune, 13 February 1995, p7
Wire services.

As reported in an article in the current "Science
Magazine", a large biotherapy project at the University
of Minnesota has shown that a substance obtained from
soybeans has shown promise in killing leukemia cells
resistant to traditional cancer treatments.

The soybean substance was tested on mice and killed
cells of B-cell precursor (BCP) leukemia.  This is the
most common childhood cancer and the second most common

The aim of this project is to find biotherapeutic
treatments that will supplement, but not replace,
chemotherapy or radiation. It is stated that, for the
kind of leukemia studied, about 30 percent of the
patients, chemotherapy and radiation do not succeed in
wiping out the cancer cells.
<<<========<<

>>>>>==========>>
HIV transmission risk in sports minimized.
The Boston Globe, 15 Feb. 1995, p8.
Reuters

In an article in "The Annals of Internal Medicine,"
doctors from the Centers for Disease Control in Atlanta
report that the risk for HIV transmission during sports
events is so low that "athletes need not be excluded
from participation solely because they are infected."
It was recommended that prevention efforts be focused
on off-the-field settings.

A separate report in the same issue of the Annals
studied injuries in 155 NFL (National Football League)
games during 1992 estimated the risk of accidental
transmission during a football game was no more than
once in 58.6 seasons.

DISCUSSION QUESTION:

How does a risk of "once in 58.6 seasons" express the
risk of transmission during a single football game?
What is the one-game risk for an individual player?
<<<========<<

>>>>>==========>>
Correction to the last Chance News. Barry Brunson
pointed out that correct reference for the letters from
Gould and Murray relating to Gould's November 21 review
in the "New Yorker" of the "The Bell Curve" is "The New
Yorker", 26 Dec 94 - 2 Jan 95 combined issue on page
10.

!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!

CHANCE News 4.03
(2 February to 15 February 1995)

!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
Please send suggestions to: jlsnell@dartmouth.edu

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