Prepared by J. Laurie Snell, with help from Jeanne
Albert, William Peterson and Fuxing Hou, 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 in the Multimedia Online
Document Library at the Geometry Center
(http://geom.umn.edu/) or from the Geometry
Center Gopher (geom.umn.edu) in Geometry Center
Resources.
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"I just don't think humankind needs to
hear how much smarter this one is than
that one. I just don't have that much
faith in statistics"
Kaye Postman
=====================================
IN THIS NEWS LETTER
* FROM OUR READERS
* Robert Griffin
* ARTICLES ABSTRACTED
* 1. Single-parent home: what will result?
* 2. The Bell Curve.
* 3. Now we know what Americans do in bed.
* 4. Malpractice award reversed.
* 5. College tries to make the grade mean something.
* 6. Link of cancer to birth drugs.
* 7. Fertility drugs tied to ovarian tumors.
* 8. Avalanche survival chances.
* 9. Is there logic in the placebo?
* 10.Study on Europe's wage rigidity.
* 11.Exercise can reduce risk of breast cancer.
* 12.Cardiac methods questioned.
* 13.Ask Marilyn.
* 14.Sampling errors in polls.
* 15.The 1994 campaign: The New York Governor
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FROM OUR READERS
Robert Griffin sent us some comments on the following
article:
Single-parent home: what will result?
The Milwaukee Journal, 18 Sept. 1994, p. 1.
Associated Press
The Census Bureau reports that 27% of all children are living
with a single parent, up from 20% in 1980 and 12% in 1970.
"Single parent" means no spouse in house. This article
provides interesting but conflicting expert opinion on the
consequences of this increase to the children and to society.
Robert Griffin wrote a letter to the editor pointing out some
confusing graphs and statistics in the article. For example,
a graph labeled "marital trends" had two curves: one labeled
"never-married parents" that increased from 4.2% in 1960 to
35% in 1993 and the other labeled "divorced parents" that
increased from 23% in 1960 to 37.1% in 1993. There was
no further explanation what these were percentages of.
Griffin pointed out that the obvious interpretations of this
graph did not make much sense. His letter led the editor to
publish the clarification that the two curves represented the
proportions of children living with single parents in the two
categories. Thus, what the graph really tell us is that, in
1960, 73% of the children living with a single parent were
living with a parent who had been married but not divorced
and in 1993 this proportion was down to about 28%. This makes
the graph rather irrevelent to the statistics about the total
number of children living with single parents discussed in
the text, but does provide dramatic chance and an interesting
result in its own right.
In a letter to Griffin the editor commented:
As the person in charge of the national/world
stories for that Sunday's paper, I approached
this material - as we do all statistics-based
stories and graphics, within the available time-
as a potential minefield. Despite my caution,
it appears we stepped on a few mines this time.
DISCUSSION QUESTIONS:
(1) Can you give an explanation for the dramatic change
exhibited in the graph.
(2) A graphical display was headed "Single parent families in
largest cities" and gave a percentage of 37% for Milwaukee.
This figure was mentioned later in the article.
Griffin remarked that this display, which made the local
situation seem higher than the national average of 27% quoted
earlier, was misleading. Why was it misleading?
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The Bell Curve;
Intelligence and Class Structure in American Life.
By Richard J. Herrnstein and Charles Murray.
Illustrated. 845 pp. New York
The Free Press. $30.
There have been many reviews of this book and I have read a
lot of them. I am sure that most of you have also read at
least one and know that this book attempts to show that I.Q.
is a much better predictor of success and failure in life
than most people are willing to admit and that public policy
should take this into account.
This book cannot be assessed by reviews, and we need to read
it to judge the strength of the statistical arguments
presented. I will do so. I invite others who read the book
to send me their comments. I will then combine our efforts to
try to say something more intelligent about the book in the
next Chance News.
DISCUSSION QUESTIONS:
(1) What do you think is meant by a person's I.Q.?
(2) What kind of evidence would be needed to show that low
I.Q. was a better predictor of criminal behavior than, say,
poverty?
(3) What kind of evidence would be needed to show that I.Q.
is at least partly genetically determined?
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So, now we know what Americans do in bed. So?
The New York Times, 9 Oct 1994, Section 4 Page 3
Tamar Lewin
The sex survey whose results were announced this week started
as a government supported survey with the title "Social and
Behavioral Aspects of Fertility-Related Behavior." It was
carefully chosen to avoid scrutiny by Senator Helms and
others. This failed and the government withdrew support for
the survey. However, it was carried out by the National
Opinion Research Center at the University of Chicago
supported by private funds.
Unlike previous sex studies, whose subjects were self
selected, this study was carried out by in-person interviews
with a random sample of 3,432 men and women aged 18 to 59.
The results will be published in a book "Sex in American"
(Little, Brown and Co. with Gina Kolata as a co-author with
the investigators.)
The survey showed a marked contrast between the sex that most
people have compared to T.V. and movie images of sexual
behavior. American women typically have two sexual partners
during their life and men about six. 78% of the men and 86%
of women say they have been faithful to their spouses while
married.
The study provides more evidence that the 10% estimate for
homosexuality is not correct. Only 2.8% of men and 1.4% of
women identified themselves as "gay,". However, in the 12
largest cities this was 9% for men and 3% for women.
There was a large gap between the percentage (22.8) of the
women who said they had been forced to do something sexually
they did not want to and the percentage (2.8) of the men who
said they ever forced women into a sexual act.
One of the purposes of the study was to help in the
strategies for combatting AIDS. In this connection the study
suggested that people had sex pretty much with those they
resemble in race, religion, age, and socioeconomic level,
suggesting that AIDS would be slow in moving from groups
where it is prevalent to groups where it is not.
DISCUSSION QUESTIONS:
(1) As is usual in such surveys, men seem to have a lot more
sexual partners than women. How is this possible?
(2) How truthful do you think people are in describing their
sex life?
(3) Do you think the fact that 78% of the men and 85% of the
women claim that they had always been faithful is believable
if one-third to one-half of recent marriages are expected to
end in divorce?
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Here are two articles from our local newspaper.
Malpractice award against Hitchcock Clinic reversed.
Valley News, 22 Sept 1994
Norma Love
Here is the article's description of the history of the case:
Judy Bronson visited her local doctor in
November 1985 complaining of shortness of
breath and an irregular heartbeat. After an
X-ray, the doctor discovered a large, irregular
mass in her chest and referred her to the
clinic for diagnosis and a treatment biopsy
was performed on the mass on Dec. 3, 1985, but
while performing the biopsy, the surgeon
accidentally cut an artery. The cut artery
required emergency surgery to prevent her from
bleeding to death.
On Feb. 11, 1986, a team of cancer specialists
reviewed the case and believed she may be
suffering from a form of Lymphoma, but wanted
another tissue sample to make a firm diagnosis.
The surgeon who did the biopsy recommended
waiting and monitoring her condition. During the
next three months, her personal doctor monitored
her health. In May, she returned to the clinic
because her condition had worsened. On May 14, a
second biopsy was done and treatment begun
immediately for Hodgkins disease, a cancer of
the lymph nodes.
Judy Bronson died of Hodgkins disease in
January 1988.
During the civil trial following this, an expert witness
testified that Judy Bronson had a 75% chance of survival in
November 1985 when she first sought help, but only a 50%
chance in May 1986 when a second biopsy was done.
The New Hampshire Supreme Court has now decided to overturn
the award made in the previous trial commenting:
Such evidence may form the underlying
basis for an opinion on causation,
but bare percentages alone are not
sufficient to establish causation.
The plaintiff must produce expert
medical testimony that the defendant's
negligence caused the patient's injury
or loss.
DISCUSSION QUESTIONS:
1. The clinic argued that Roland Bronson's expert witness
showed Judy Bronson was equally likely to have died from the
pre-existing cancer as from a negligent delay in diagnosis.
Where does the "equally likely" come from?
2. The court ruled that statistical evidence "may form the
underlying basis for an opinion on causation, but bare
percentages alone are not sufficient to establish causation."
Do you agree?
3. You are about to play a game of Russian Roulette. Two of
the chambers of your 8-shooter are loaded. Unbeknownst to
you, your roommate slips bullets into two more of the
chambers. You die, and your family sues your roommate for
wrongful death. The court rules in favor of your roommate,
arguing that bare percentages alone are not sufficient to
establish causation. How do you feel about this?
4. The spokesperson for the clinic said that "the Supreme
Court decision reaffirms what we have always understood the
medical malpractice statute to be." If this were your
hospital how would you feel about
this?
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College tries to make the grade mean something.
Valley News, 15 October, 1994
Ellen Swain
As we have reported, Dartmouth (starting with this years'
class) will put on a student's transcript, next to the
student's grade for a course, the median grade for the
course. This article provides student and faculty reaction at
Dartmouth to this change as well as the opinion of people at
other graduate schools, about how useful they will find this
change.
One student says: "I think it's a bad idea, because,
unfortunately, it may increase competitiveness among students
to the point where if you know that the average grade is an A
minus or a B plus, you're going to try that much harder to
get above the median in that class."
Those involved in graduate admission seemed to think the
additional information would be helpful to them. The
director of career services at Dartmouth expects corporate
recruiters to welcome the idea, remarking "Recruiters are
always trying to quantify things."
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Study uncovers link of cancer to birth drugs.
The New York Times, 22 September 1994, Pg. 22
Lawrence K. Altman
This article is a report of a study published in the Sept. 22
issue of "The New England Journal of Medicine". According to
the article, women who are treated with infertility drugs
have a risk of developing ovarian cancer that is 2.5 times
that of women in the general population. The study examined
a group of 3,837 women who had sought treatment for
infertility between 1974 and 1986.
Mr. Altman reports that "11 developed ovarian cancer, while
the number expected from statistical calculations was 4.4."
Curiously, Mr. Altman does not mention that some of the 3,837
women in the study did not take fertility drugs and that, in
fact, two of the women with ovarian cancer were in this
category. (See the article "Fertility drugs tied to ovarian
tumors; Medical Notebook", Boston Globe, below, for
additional discussion.)
To put the 2.5 increased risk in perspective, the article
points out that heavy smokers have a risk of lung cancer that
is 10 times that of the general population. In addition,
ovarian cancer is a rare disease, with a lifetime risk of 1.8
percent. By contrast, breast cancer has a lifetime risk of 12
percent.
DISCUSSION QUESTIONS:
1. What do you think a "lifetime risk of 1.8 percent" means?
How could you use this figure to determine the risk of
developing ovarian cancer in the next 10 years for a woman
who is 20 years old? How about 30 years old? 60 years old?
2. The article states that the study was "limited, primarily,
by the small number of women with ovarian cancer." Explain.
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Fertility drugs tied to ovarian tumors; Medical Notebook
The Boston Globe, 22 September 1994, Pg. 3
Judy Foreman
This brief article contains information that complements the
Times article. For example, 9 of the 11 women who had
ovarian tumors took the fertility drug clomiphene, which
corresponds to a risk that is 2.3 times that of infertile
women who did not take the drug. Moreover, those women who
had taken the drug for at least 12 menstrual cycles were at
the highest risk, and "women who have been exposed to
fertility medications but have no family history of ovarian
cancer are not at high risk."
DISCUSSION QUESTIONS:
1. Which article provides more useful information for the
public?
2. The study in the New England Journal states that there was
"no increase in the risk associated with the use of
clomiphene for less than 12 menstrual cycles" and that
"similar proportions of short-term users (1 to 11 cycles,
50.0 percent) and long-term users (at least 12 cycles, 55.4
percent) became pregnant." Neither article noted these
findings. Would you have included these figures?
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Avalanche survival chances.
Nature, 6 October 1994, p.482
Letter from Martin Burtscher
The author analyzed mountain sports accidents in Austria
since 1986. A previous article in Nature concluded that in
an avalanche the depth of burial had no direct influence on
survival chances. This author's data contradicts this
assertion.
Burtscher recorded the rescue outcome, burial time, and depth
of burial for the 774 people caught in avalanches between
1986 and 1992. He did a stepwise logistic regression with
rescue outcome as the dependent variable and burial time and
depth of burial as independent variables. Burial time
entered the model as step 1 and depth of burial as step 2,
and its presence made significant improvement.
DISCUSSION QUESTION:
The author concludes his letter with the remark:
Hence, when an avalanche begins, all
measures helping to keep the skier on
the surface increase the chance of
survival.
What measures do you think he has in mind? Would you have
needed a study to suggest this advice?
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Is there logic in the placebo?
The Lancet, 1 Oct 1994, p. 925
Peter Gotzche
This is the first of a series of articles on placebo. The
author begins by trying to find a satisfactory definition of
a placebo and a placebo effect. He concludes that this is not
possible. He remarks that this should not discourage us from
using them, any more than we should not use a chair just
because we could not define a chair.
Gotzche concludes that the present focus of interest in
placebos should "switch from whether or not an intervention
is a placebo, towards the magnitude of the effect and the
choice of effect variable". He argues that untreated control
groups as well as placebo-treated groups are needed in
clinical trials. "Without them we cannot conclude, as is
current practice, that an intervention is ineffective if no
better than placebo."
DISCUSSION QUESTIONS:
(1) Why does the author conclude that, without untreated
groups, we cannot conclude that an intervention is
ineffective if no better than placebo? Do you agree?
(2) What is wrong with the following definitions of placebo
effect and placebo:
The placebo effect is the difference in
outcome between a placebo-treated group and
an untreated control group in an unbiased
experiment.
Placebo is an intervention which is believed
to lack a specific effect--i.e., an effect for
which an empirically supported theory exists
for its mechanism of action--on the condition
in question, but which has been demonstrated
to be better than no intervention.
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Study on Europe's wage rigidity calls standard labor theories
into question.
Wall Street Journal, 3 Oct 1994
Dana Milbank
Europe has had recently a higher unemployment rate than the
United States and Japan. A theory used to explain this says
that European wages are more rigid than those in the United
State and Japan, in the sense that labor costs remain high
even when unemployment rises. This in turn is thought to be
caused by the high degree of unionization in Europe and high
unemployment benefits. It has led to a style of labor
politics (sometimes called the Reagen-Thatcher style) that
recommends union busting and reducing unemployment benefits
to combat unemployment.
This theory has been challenged in a study carried out by two
economists, David Blanchflower of Dartmouth College and
Andrew Oswald of the London School of Economics. Using
government wage and employment data for millions of workers
in 15 countries, they showed that wage flexibility showed
little variation across the globe. In each country, they
found that doubling the local unemployment rate(within a
region or industry) is associated with a drop in pay of
roughly 10%.
The study conflicts with the conclusions of many other groups
including major banking interests that presumably were based
on theories rather than on studies.
The theory contradicted was not clear to me from the article
so I asked Blanchflower. Here is his reply:
The traditional supply-demand equilibrium
that we teach our students says that if wages
go up from equilibrium, unemployment increases.
That is, higher wages go with higher
unemployment with a fixed labor force.
Workers in areas of high unemployment have
to be compensated for the higher risk of
unemployment -- hence wages and unemployment
are positively correlated.
Our stuff shows the reverse -- that they
are negatively correlated with an elasticity
of -0.1. Unemployment doubles and wages fall
by 10%.
It appears to be the same in all time periods
and across all 16 of the countries we have
looked at! It's as close to an economics law
as we have ever seen.
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Exercise can reduce risk of breast cancer, study says.
The Boston Globe, 21 September 1994, p1.
Judy Foreman
A study published in the "Journal of the National Cancer
Institute" gives evidence that exercise represents "an
independent risk factor" for breast cancer. The study
involved 1090 women, ages 40 and above. Of these, 545 were
newly diagnosed with breast cancer, and the other 545
controls were cancer-free and otherwise similar in age, etc.
Women who had exercised 4 or more hours per week throughout
their reproductive years reduced their risk by more than 60%
compared to inactive women. Women who exercised only 1 to 3
hours per week still had a 30% reduction in risk.
Reseachers believe that cancer risk may be related to the
number of menstural cycles a women has during her life in
which ovulation occurs. The link is presumably due to
hormonal fluctuations associated with ovulation. Other
research has shown that adolescents who exercise regularly
often have cycles without ovulation.
DISCUSSION QUESTIONS:
What do you think the term "independent risk factor" means
here?
How do you think the researchers arrived at the 60% reduction
in risk for those who exercised 4 or more hours per week?
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Cardiac methods questioned.
The Boston Globe, 21 September 1994, p3.
Richard A. Kno
A Harvard Medical School study published in the Journal of
the American Medical Association reports that doctors
treating elderly heart attack victims could reduce their use
of the most aggressive treatments by 25% without increasing
patients' chances of dying. The analysis was based on
examining nearly all of the 65-and-older heart attack victims
treated under Medicare in 1987. Care given in the first 24
hours after the attack was found to be the most critical.
Later invasive diagnostic tests and coronary 'replumbing'
operations were often found to provide no benefit in terms of
reduced mortality over the four year period following the
attack.
The actual statistical analysis uses a technique from
economics called "instrumental variables estimation." As
described in the article, the idea is to manipulate the data
to mimic the random assignment of patients to treatment and
control groups.
Dr. Thomas Chalmers of the Dartmouth Medical School rejected
the new method. He is quoted as saying "I don't believe a
word of it. No matter how they manipulate things, they can't
make up for the fact that randomized clinical trials are
essential."
DISCUSSION QUESTION:
1. What is the problem with a randomized control experiment
in this context?
2. What do you think Dr.Chalmers has in mind to overcome
such objections?
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Ask Marilyn.
Parade Magazine,
25 September 1994, p21.
Marilyn vos Savant
Question: Let's say my friend puts six playing cards face-
down on a table. He tells me that exactly two of them are
aces. Then I get to pick up two of the cards. Which of the
following choices is more likely?
(A) That I'll get one or both of the aces
(B) That I'll get no aces
Marilyn solves the problem by enumerating the C(6,2) = 15
cases for choosing two cards and counting those favorable to
given probability 9/15 for (A) and 6/15 for (B).
<<<========<<
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Sampling errors in political polls.
Teaching Statistics, Autumn 1994, pp. 71-73
Zhigniew Kmietowicz
A typical poll result gives three proportions: the proportion
p(A) of the voters who favor candidate A, p(B) who favor
candidate B and p(U) who are undecided. The newspaper then
gives one margin of error. This might lead the reader to
believe that this margin of error applies to all three
percentages: the leader, say p(A), the candidate who is
behind, P(B), and even how much of a lead A has, p(A)-p(B),
which is often the most interesting quantity. Since all three
of these quantities have different variances it is
interesting to see how hard it is to get more accurate
information about the margin of error. In this note the
author shows that this is quite easy. He also discusses the
use of these formulas in determining confidence intervals and
for testing hypotheses.
DISCUSSION QUESTIONS:
(1) Let n be the number of people sampled, P(A), P(B), and
P(U) the true proportions of voters who favor A, favor B and
undecided respectively. Assume that P(U) = 0. What is the
variance of p(A) and of p(A)-p(B). What is the largest these
variances can be?
(2) Assume now that there are undecided voters in the
population you are sampling. Find the variances for p(A),
p(B) and p(A) - p(B).
<<<========<<
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The 1994 campaign: New York governor; deep discontent
with Cuomo strengthens Pataki, Poll shows.
New York Times, 5 Oct 1994, A1
Kevin Sack
This is a good time of year to discuss polls, and this is an
interesting article to use for this purpose. This poll
showed Pataki holding a lead of 44 percent to 41. the
article remarks: "The distance between Mr. Pataki and Mr.
Cuomo is within the polls' margin of sampling error of plus
or minus three percentage points, meaning that either
candidate could actually be ahead."
The percentages by regions were:
New York City Cuomo 66% Pataki 25%
Suburbs Cuomo 36% Pataki 47%
Upstate Cuomo 34% Pataki 51%
showing the need for adjustments by regions.
Here is the official description of how the poll was carried
out:
How the Poll Was Conducted.
The latest New York Times/WCBS-TV News Poll
of New York State is based on telephone interviews
conducted from Thursday to Sunday with 1,552
adults throughout the state. Of these, 1,148
said they were registered to vote.
The random sample of telephone numbers was
provided by Survey Sampling of Fairfield, Conn.
Within each household, one adult was randomly
designated as the respondent. The results have
been weighted to take into account household
size and number of telephone lines at the
residence, as well as to adjust for variations
relating to region, race, sex, age and education.
In addition, results about respondents' intended
votes in November have been weighted by the
statewide distribution of actual ballots in
recent elections from New York City (31 percent),
its suburbs (24 percent) and the rest of the
state (45 percent).
According to statistical theory, in 19 of 20
cases, the results based on such samples will
differ by no more than 3 percentage points in
either direction from what would have been
obtained by seeking out all registered voters
in New York State.
The potential sampling error for smaller subgroups
is larger. For example, results based on residents
of New York City would be plus or minus 4
percentage points.
In addition to sampling error, the practical
difficulties of conducting any opinion survey
may introduce error into the poll. Differences
in the wording and order of questions, for
instance, can lead to somewhat varying results.
A New York Daily News/WNBC-TV poll conducted Oct 9-12 by Lou
Harris surveyed 805 "probably" voters with a 3.4% margin of
error and found
Pataki 48%
Cuomo 39%
Golisano 4%
giving Pataki a significant lead. This promises to be an
interesting election to follow.
DISCUSSION QUESTIONS:
What article says that "The distance between Mr. Pataki and
Mr. Cuomo is within the polls' margin of sampling error of
plus or minus three percentage points, meaning that either
candidate could actually be ahead." Is the writer saying
anything here?
Why do they care how many telephone lines there are coming
into a house?
How do you think they carry out the adjustments for the
different regions: New York City, the suburbs, and rest of
the state?
!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
CHANCE News 3.14
(22 Sept to 15 Oct 1994)
!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
Please send suggestions to: jlsnell@dartmouth.edu
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