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CHANCE News 3.05
(21 March to 12 April 1994)
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Prepared by J. Laurie Snell, with help from Jeanne
Albert and William Peterson, as part of the CHANCE
Course Project supported by the National Science
Foundation and the New England Consortium for
Undergraduate Science Education.
Please send suggestions to: dart.chance@dartmouth.edu
Previous issues of CHANCE News can be found on our
chance gopher. Just point your gopher to:
chance.dartmouth.edu
==========================================
An appropriate answer to the right problem is worth a
good deal more than an exact answer to an approximate
problem.
John Tukey
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COMING ATTRACTIONS: Should you quite taking your
vitamin pills?
Jim Hilton sent the following answer to my query about the probability of rain. (For a related story, see CHANCE News 3.04: 6 to 20 March, 1994, "Ask Marylin" .)
Here in San Diego we have a local weekly paper (magazine)
called The Reader. There is a section called "Straight From
The Hip" by Matthew Alice. This section attempts to answer
questions submitted by readers. The Thursday March 24,
1994 edition had the following question and reply:
Question: If a weather forecaster says there is a 10%
chance of rain today, 20% tonight, and 30% tomorrow,
what happens if it rains early today? Does it stay 20%
chance for tonight or is that gone? If it doesn't rain earlier
today, do you add the 10% to the 20%, making it 30%
chance of rain tonight? Or what?
--Jeffrey Michael Austin
Foxmore, La Jolla
Answer: Put away the calculator and clear your mind of
all extraneous thoughts. Weather predicting is not simple.
Though you may be sorry you asked, cause you'll know
less about the likelihood of rain in your particular
neighborhood after I explain this than you did before. But
if you're a faithful reader, maybe you're used to that situation.
Anyway, if the National Weather Service says there's a 30%
chance of rain in the San Diego area tomorrow, what they're
saying is the odds are three in ten that someplace (or places)
in the area will get wet. In some large geographical areas,
the probability is expressed slightly differently.
If the meteorologist sees a 60% chance of rain over half the
area, he'll express the pre-iction as a 30% chance of rain.
Doubly misleading, it seems to me. But weather predictors
know the general public doesn't understand the system anyway
so maybe it doesn't matter The National Weather Service's
system of calculation is called the Precipitation Probability
Program. It's based on computer models of weather patterns,
and they've been refining the models since early 1970s. They
now can predict weather for the next 72 hours with about 85%
accuracy, though weather prediction is still a bit of an art as
well as a science.
-- Mathew Alice
DISCUSSION QUESTION: What is the answer to the
question that the reader asked?
<<<========<<
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<<<========<<
>>>>>==========>> Predictions That Use Percentages Can Cloud The Issue. Los Angeles Times, 16 Feb 1986, Part 2 Page 4 Steve Harvey This article pretty much agrees with the remarks of Mathew Alice and adds the information that rain is defined by the Weather Service as "the occurrence of a measured amount that is greater than or equal to 1/100th of an inch of liquid precipitation during a specific period of time (normally 12 hours)." <<<========<< >>>>>==========>> "Predicting Climate: Harder Than We Thought"
The Boston Globe, 21 March 1994, p25. Scott Allen
This article discusses the extent to which the mechanisms of the greenhouse effect are still poorly understood, leading to a great deal of uncertainty associated with climate predictions.
Many climatologists still predict a 3 to 7 degree F increase in global temperatures over the next 100 years if nothing is done about current trends in greenhouse gas emissions, although these estimates are down a degree or so from those after the hot summer of 1988.
The article states, however, that "they [climatologists] concede that the forecast is so uncertain that it comes down to a value judgment." In other words, people must decide how much to do to avoid the risk. One surprising quote, from federal researcher Thomas Karl: "It's like if the forecast says there's a 60 percent chance of rain, do you take an umbrella?"
DISCUSSION QUESTION: What do you think of the umbrella analogy? <<<========<<
>>>>>==========>> "Probability Experts May Decide Pennsylvania Vote. "
New York Times, 11 April 1994, A15 Peter Passell
In a special election to fill a Senate vacancy in Pennsylvania's Second State Senatorial District in Philadelphia, Bruce Marks (Republican) received 19,691 votes on the voting machine and William Stinson (Democrat) received 19,127 votes. In absentee ballots Stinson received 1,391 votes and Marks 366, making Stinson the winner.
Charges of fraud in the collection of absentee ballots led Judge Clarence Newcomber of the Federal District Court in Philadelphia to decide whether to give the election to Marks or to call for a new election in this district. To help him decide, he has hired as consultant Professor Orley Ashenfelter, an econometrician from Princeton, and the Republicans and the Democrats have hired their own statisticians.
Ashenfelter's approach was to do a standard regression analysis on the difference between the voting outcomes by voting machine and absentee ballots using the results, of the 22 state senatorial contests in Philadelphia since 1982. He estimated that there was about a 6% chance of obtaining an outcome as extreme as the one being contested by normal chance fluctuations.
Paul Shannon, the statistician from the Wharton school hired by the Democrats, and Elizabeth Hotzman, who has had a lot of experience in analyzing voting behavior, challenge the appropriateness of projecting voter sentiment from historical relationships.
Statistician Brian Sullivan, working for the Republicans, analyzed the findings of a post-election poll of registered voters and estimated that 84 percent of the absentee ballots had been illegally solicited or cast and that if every legitimate voter had voted Democratic the Republican would still win. Shannon challenges the survey and the argument goes on and on.
DISCUSSION QUESTION
The article concludes with the remark that Lowell Finley, who specializes in election law, thinks the burden of choice should rest on those who would declare a winner in the absence of certainty. "In a democracy voters ought to have the last word not judges." Is Finley expressing an opinion about the current situation? If so, what is this opinion? <<<========<<
>>>>>==========>>
How Convincing is DNA Evidence?
Nature, 24 March 1995
D. J. Balding and P. Donnelly
This is a report from the two fellows who pointed
out, in a UK challenge to a conviction based on DNA
evidence, the "prosecutor's fallacy".
This occurs when the prosecutor presents the match
probability which is the probability that an individual
will match, given that they are innocent, and suggests
instead that it is the probability that an individual
is innocent given a match. The latter probability is
what the jury is interested in and can be much larger
than the match probability. See Chance News 3.02.
<<<========<<
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"Study Says Power Line Emissions Too Weak to Endanger
Health "
Chicago Tribune, 12 April, 1994, News p. 4
Reuters
A study by a Yale physicist Robert Adair, published
April 12 in the Proceedings of the National Academy of
Science, concludes that electromagnetic fields emitted
by power lines are far too weak to affect human cells
and pose no health risk.
A discovery in 1992 that the human brain cells are rich
in magnetite, a magnetic iron compound, led to the
speculation that magnetite could react to the magnetic
pull from power lines to explain a slightly higher
occurrence of cancer and leukemia among those who live
near power lines.
Adair remarks that the pull is negligible compared to
the Earth's magnetic pull. To those who say the danger
is due to the constant change in the magnetic field of
alternating household currents, he replies that it
would be impossible for human magetosomes, in which
magnetite is encased, to move fast enough to respond to
such weak alternating fields.
<<<=== MORE =====<<
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Leukemia Linked To Power Fields In Hydro Study; But
Results Are Inconclusive.
The Gazette (Montreal), 31 March 1994, A1
Graeme Hamilton
A study funded by two major power companies, one in
Canada and one in France, has found a link between the
magnetic fields generated by electric currents and an
increased incidence of leukemia among utility
workers. The study will be reported in the next issue of
the American Journal of Epidemiology.
The researchers studied more than 223,000 people in
Quebec, Ontario and France. They found that workers
with above-average exposure to magnetic fields were
three times more likely to develop acute myeloid
leukemia than less-exposed workers. However, because of
the small number of cases, the difference was not
statistically significant. No link was found between
the other 29 cancers studied.
They did not find that the frequency of leukemia
multiplied as exposure increased above the average,
leading them to write "Caution must be exercised in
interpreting the present results as evidence of a
causal association."
The study is considered an improvement over previous
studies because readings were taken to measure the
actual exposure of workers to the magnetic fields
instead of being based on an employee's job
description.
Experts remark that these results do not say much about
the general population who are exposed to much weaker
fields, but show that we should continue to worry about
this problem
DISCUSSION QUESTION: How could the number of cases of
leukemia affect statistical significance?
<<<========<<
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Long Run Predictions.
Math Horizons, Spring 1994
Mark F. Schilling
"Math Horizons" is a new journal published by the
Mathematical Association of American to be read by
undergraduate mathematics students - so we have some
hope of understanding the articles.
This article shows how to test the hypothesis that a
sequence of outcomes H (heads) or T (tails) is
consistent with tossing a biased coin with probability
p for H and 1-p for T on each toss, using the statistic
of length of longest run of H's.
To start a H's run, other than on the first toss, we
first need a T. In n tosses of a p-coin we expect
about n(1-p) T's. A fraction p^r of these are expected
to be followed by r or more H's. Thus we expect about
n(1-p)p^r runs of length r or greater. One's intuition
suggests that the most likely value for the longest run
is when this is equal to 1. (We really can trust our
intuition most of the time in probability.) This leads
to the estimate for the most likely value for the
longest run as the nearest integer to the logarithm of
n(1-p) to the base 1/p.
For example, in 128 tosses of a fair coin we expect 64
T's, followed by 32 H's, followed by 16 H's, 8H's 4H's,
2H's, 1H leading to 6 as the most likely value for the
maximum run length.
To get a 95% confidence interval for the maximum run
length, you use the distribution for the difference
between the expected value of the longest run and the
observed longest run. Rather remarkably, this
distribution does not depend on the number n of
tosses, but only on the probabiliy p of getting an H.
The author uses these ideas to check if standard run
records, such as Dimaggio's 56 consecutive games with a
hit and the roulette wheel at Monte Carlo that stopped
26 times on a red number, are outside the 95% confidence
limits for the maximum run in the appropriate long coin
tossing sequence -- none are.
<<<========<<
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Fraudulent Breast Research Places Burden on Cancer
Field.
The Boston Globe, 31 March 1994, p1.
Richard A. Knox
Here we find more on the findings of falsified data in
the research study that led to the recommendation of
lumpectomy and radiation as an equally effective but
less disfiguring alternative to mastectomy in treating
breast cancer.
On 29 March, Dr. Bernard Fisher was removed as head of
the National Surgical Adjuvant Breast and Bowel
Project (NSABP). Although Fisher himself has not been
accused of any fraud, he has been criticized for not
acting quickly enough to correct the public record when
the falsified data was first discovered.
DISCUSSION QUESTIONS:
(1) Was it essential for Dr. Fisher to make an immediate
announcement of the fraud, even though the original
incident concerned only one of 5000 physicians in his
project, and the tainted data did not affect the
overall conclusions of the study?
(2) The issue seems to be the harm done in shaking the
public's confidence in the study's recommendations. Do
you think media coverage has exacerbated or helped to
alleviate this problem?
(3) In the original study there were three treatment
groups: total mastectomy (n = 590), lumpectomy (n =
636), and lumpectomy and irradiation (n =629). At the
end of the observational period (average 81 months),
the numbers alive with no evidence of disease were:
total mastectomy 373 (63.2%), lumpectomy 371 (58.3%)
and lumpectomy and irradiation 412 (65.5%).
(a) What would be a reasonable margin of error for
thepercentages alive with no evidence of disease?
(b) What would be the effect on this margin or error if
16% of the data were removed?
<<<========<<
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"Campus Racial Lines May Be Blurring: Study Counters"
Notion That Minorities Segregate Selves
The Boston Globe, 5 April 1994, p1.
Alice Dembner
This article describes the results of the first
national study of student interactions across racial
lines. While people often perceive strong tendencies
towards segregation, particularly among minorities, the
study offers evidence to the contrary. For example,
the following are percentages of students, broken down
into racial/ethnic group, who reported that they
frequently studied with members of another group: 15%
of whites, 49% of blacks, 60% of Asians and 72% of
Chicanos.
A survey was conducted of a "nationally
representative" sample of 6107 students. One of the
investigators is quoted as saying that the goal of the
study was to inject some real data into an otherwise
highly politicized debate. The article raises several
possible criticisms of the study's methodology. First,
the results are based on student's own accounts of
their behavior, not on outside observation. Also, the
study did not assess whether the interaction was
greater than would be expected, given the small numbers
of minorities on most campuses. It was noted, however,
that the interaction with other races did not increase
significantly as the minority population grew. The
wording of the questions does not allow one to
determine whether minority students' interactions
outside their own group was, in fact, with whites or
with other minorities.
DISCUSSION QUESTION: What strategy -- other than simply
asking students about their behavior -- could be used
to get a representative view of group study habits?
[I (Bill Peterson) went to a talk by Uri Treisman who
reported having investigators move into dorms at
Berkeley to find out whether students were studying
math alone or in groups]
<<<========<<
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Drug For Alzheimer's Disease Gets Mixed Reviews.
The Boston Globe, 6 April 1994
Richard Saltus
Richard Saltus reports that a study on tactrine, the
only Federally approved drug for treating Alzheimer's
disease, shows statistically significant benefits for
some patients. The study, appearing in the Journal of
the American Medical Association, was led by
Dr. Margaret J. Knapp, a clinical scientist with the
Parke-Davis division of the Warner-Lambert Company, the
maker of tactrine.
Dr. Knapp and her colleagues said that 48% of patients
who took the drug for 30 weeks benefited, compared to
23% who took a placebo for that period. Paul Solomon,
an author of the study and a Williams College
psychologist, said that "seven out of ten patients who
completed the study either held their own or improved"
on tests of memory and mental functioning. However, the
drug only postpones the advance of the disease by about
six months, after which decline continues.
During the study, 29% of the 663 patients involved
developed liver abnormalities and had to discontinue
taking tactrine for several weeks, but 87% of these
patients were later able to resume treatment without
the same liver difficulties.
In all, more than one-third of the patients dropped out
of the study because of side effects which included, in
addition to the liver abnormalities, nausea, vomiting,
diarrhea, and abdominal pains. Solomon said the large
dropout rate does not reflect actual practice, because
researchers involved in the study were not allowed to
relieve the side effects with other drugs.
A separate study found a correlation between
Alzheimer's and economic status that suggests that more
highly educated people with better jobs are at a lower
risk of developing the disease.
DISCUSSION QUESTION:Should the dropout rate affect the
findings of this study?
<<<========<<
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High Blood Pressure and Kidney Disease; How Two Medical
Problems Can Make Each Other Worse.
The Washington Post, 5 April 1994
Sandy Rovner
While high blood pressure can damage or even destroy
the blood vessels that are essential to the kidney's
proper functioning as a blood filter and cleanser, at
the same time certain types of kidney disease,
affecting about 25% of all kidney patients (the
percentage is higher among African Americans) can raise
blood pressure not only within the kidney, but
throughout the body. Thus hypertension and kidney
disease can each reinforce the other with potentially
devastating results.
Although diabetes is the major cause of kidney disease
in the population as a whole, among African Americans
high blood pressure is the leading contributor, and
both African and Native Americans have higher rates of
kidney disease than the general population.
In a study of 840 patients published in the New England
Journal of Medicine, researchers found that rigidly
controlling the blood pressure of certain kidney
patients slowed the progression of the disease. In
patients whose blood pressure was kept at the lowest
levels, the progression of the special form of disease
was half as fast as that of the patients whose blood
pressure was maintained at "normal" levels. The same
treatment, however, was not significantly helpful for
kidney patients as a whole.
At the same time, African Americans in the study
appeared to progress to end-stage kidney disease
(requiring either hemodialysis or a kidney transplant)
much faster than Caucasians with the same blood
pressure. A related study published in the March issue
of the American Journal of Hypertension suggests that
this higher rate among African Americans may be
attributable to the tendency of blood pressure to
remainhigh for this group while sleeping.
In the study, which involved black and white children
and adolescents with normal and roughly equal daytime
blood pressure, the pressure dropped during sleeping
hours for whites, but remained constant for blacks.
<<<========<<
>>>>>==========>>
How now Dow Jones?
Dubious Reporting on Why the Market Moves.
Columbia Journalism Review, March/April 1994
Trevor Nelson
Treveor Nelson writes that "the actual reporting for a
daily market piece generally consists of a series of
phone calls to analysts, who offer their opinion" on
the reasons for daily fluctuations. However, John
Dorfman, a staff writer at the Wall Street Journal,
admits that "the truth is the market is such a vast
place no one knows for sure why it rises and falls".
In particular, the explanations given for day-to-day
fluctuations may be nothing more than after-the-fact
rationalizations.
Richard Sylla, a professor of economics at New York
University, says that "most of us think the short- term
fluctuations of the market--from hour-to-hour, minute-
to- minute--are basically random."
But no one wants to report on market activity without
offering a reason for its behavior. Rick Gladstone,
deputy business editor at the AP in New York, concedes
"we are obliged to say what might have been at
work,"even if there is no obvious connection to other
news. Thus reporting inevitably contains some "informed
speculation" and other simplifications.
DISCUSSION QUESTIONS:
(1) What does it mean to say that the short-term
fluctuations of the market are basically random?
(2) Can reporting on the market affect market behavior?
<<<========<<
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A Disabilities Program That "Got Out Of Hand"
New York Times, 8 April 1994, A1
Michael Winerip
Emily Fisher Landau was 56 years old before she was
diagnosed as dyslexic. This led her to give over $2
million to the Dalton School in Manhattan to create a
learning disability program. Over the years this paid
for 14 full-and part-time learning specialists in
Dalton's kindergarten-to-third grade students. It
financed research to develop a screening test that
would identify learning disabilities at an early age
and provided money for Columbia University Teachers
College to evaluate the program and publish the
results.
The article describes how this program got out of hand.
By 1992 the specialists had almost taken over some of
the classes. Half of the students entering fourth grade
had already received remedial help.
This all ended in the fall of 1992 when the five
kindergarten teachers revolted and refused to use the
screening test.
The Columbia researchers said that it was hard to say
if those who had special learning assistance did better
than they would have without the help since all those
who were tested to see if they needed help were given
it. The screening test is still be given for the
purposes of the study, but the results are not being
used by the teachers.
<<<========<<
>>>>>==========>>
Smoking Signals And Uncritical Reporting; Secondhand
Doubts
Washington Times, 5 April, 1994, A14
Matthew Hoffman
A report of the Congressional Research Service
"Cigarette Taxes to Fund Health Care Reform: An
Economic Analysis", claims that the Environmental
Protection Agency's "Passive Smoking" study, which
concludes that 3,000 people die annually from exposure
to other people's tobacco smoke, was seriously flawed.
The report criticizes the agency for relying completely
on other people's studies, changing the significant
level in one of these studies to give the desired
outcome, using subjective judgments as to which studies
had statistical problems, and ignoring two important
studies that did not show a significant effect.
These are pretty much the criticisms made by Alan Gross
and refuted by Howard Rockette in the pair of articles
pro and con that appear in the Winter 1994 issue of
Chance Magazine -- see Chance News 2.20.
DISCUSSION QUESTION: What information would you need
to have to judge if this attack on the EPA decision by
the CRS is justified?
<<<========<<
>>>>>==========>>
Investigating A Medical Maze: Virus Transmission in
Surgery
New York Times, 22 March 1994, C3
Lawrence K. Altman
Transmission of hepatitis from a patient to a health
care worker is fairly common, but since 1987, there
have been only seven clusters reported where the
transmission is from doctor to patient. The most
recent cluster occurred at two hospitals associated
with the University of California at Los Angeles, where
it was found that 18 of the patients of a surgeon, who
had operated on 142 patients, had developed hepatitis,
while none of at least 155 patients operated on by
other surgeons had developed the disease.
The surgeon involved had apparently been infected by a
patient. It appeared that he had followed standard
procedures for his surgery, but reported that when he
operated, on occasion, his fingers would become
irritated; and he speculated that perhaps the pressure
of tying sutures might have something to do with
transmission. In a simulation of his surgical
technique, he tied knots for an hour. Then the inside
of each glove was washed and the washing liquid sent to
a lab for analysis. The virus was found in the liquid,
offering a theory on how it was transmitted.
<<<========<<
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Study Finds Hope in Immune Therapy for Cancer
New York Times, 23 March 1994, A15
Gina Kolata
The current issue of the Journal of the American
Medical Association reports on a study to see if
certain cancers can be attacked indirectly by giving
patients interleukin 2 with the aim of stimulating
white blood cells. Success with interleukin 2 can come
only through improving the immune system, since it has
no effect on the cancer cells themselves.
In this study, 283 patients who had the skin cancer
melanoma or kidney cancer that had spread, and who were
no longer helped by conventional treatments, were
treated with interleukin 2. Their progress was
monitored for several years. Of the 283 patients, 8
were apparently cured and an additional 10 percent of
the melanoma patients and 13 percent of the kidney
cancer patients had their tumors shrink temporarily.
The report noted that side effects can harm the heart,
the kidneys, the liver and the nervous system, and that
three patients died after receiving interleukin 2.
Experts say the importance of the study is that it
appears to indicate this indirect approach has some
positive effect, but the results are not very striking
and the side effects are worrisome. And the fact that
it was not a controlled study makes it hard to be sure
that the successes were the result of the treatment.
<<<========<<
>>>>>==========>>
Gene Experiment to Reverse Inherited Disease is Working
New York Times, 1 April 1994, A1
Natalie Angier
There are a number of studies underway to see if
certain inherited diseases can be prevented by
modifying the genes of a person with gene defects that
cause the disease.
The April 4 issue of Nature reports the first success
for this kind of genetic engineering. Researchers
report that they have partly corrected a cholesterol
disorder, called familial hypercholesterolemia, by
supplying a 30-year old women with copies of a gene she
lacks. Results to be published on Friday in the journal
"Nature Genetics", researchers said that, in the two
years since adding the new genes, the patient's blood
cholesterol has fallen from 525 milligrams per
deciliter to 410 (still twice the normal level), and
the desirable cholesterol level has increased -- though
it is still below 200.
Researchers hope they have brought the unidentified
woman a reprieve from the early death she faced from
premature heart disease. She suffered a heart attack
at age 16, underwent coronary bypass surgery at age 24,
and still her heart disease worsened. Her two brothers
died of the high-cholesterol disorder in their 20s.
!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
CHANCE News 3.05
(21 March to 12 April 1994)
!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
Please send suggestions to: dart.chance@dartmouth.edu
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