Please send comments and suggestions for articles to
jlsnell@dartmouth.edu
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A career is nothing to leave to chance.
American Statistical Association
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FROM OUR READERS
We have no suggestions from our readers this time but
we owe thanks to Goran Djuknic for submitting a previous
article "How Numbers Can Trick You". This should remind
you that some of the best items have come from our
readers!
FROM THE INTERNET
Since we are still talking about the "Bell Curve" you
might want to read the article "The Case for
Conservative Multiculturalism" by Herrnstein and Murray
in the October 31 issue of Newsweek. It can be read on
www from the Electronic Newstand
(gopher://gopher.internet.com:2100/11/).
You can also find a lot of discussions of the "Bell
Curve" on news groups such as sci.stat.consult and
sci.pychology. There were also some interesting
letters to the editor in The New York Times Book
Review on November 13 about their review of "The
Bell Curve" . I will mention some of these next time.
* ARTICLES ABSTRACTED
* 1. How did the polls do?
* 2. Ask Marilyn
* 3. DNA fingerprinting debate settled.
* 4. Science's role in courtrooms reassessed.
* 5. Abortion tie to breast cancer risk
* 6. Extracting the truth from statistics
* 7. Mandatory testing for pregnant women?.
* 8. Forget about high cholesterol if over 70.
* 9. High doses of heart drug may be dangerous.
* 10. Reviews of books from sex survey.
* 11.The Bell Curve (Part 1)
<<<========<<
>>>>>==========>>
How did the polls do?
On Nov 8 the Hotline gave the results of the latest
polls for the senate races together with margins of
errors. We added the final vote and some idea of the
errors in the polls.
STATE ACTUAL LAST MARGIN POLL
VOTE POLL OF ERROR ERROR
ARIZONA
Sam Coppersmith, D 40 30 3.5 .9
Jon Kyl, R 54 42
CALIFORNIA
Dianne Feinstein, D 47 52 3.5 8
Michael Hunington, R 45 36
CONNECTICUT
Joseph Lieberman, D 67 61 3.5 3.4
Jerry Labriola, R 31 24
DELAWARE
Charles Oberly, D 42 37 3.1 1.8
William Roth Jr., R 56 53
FLORIDA
Hugh E. Rodham D 30 28 3.5 0
Connie Mack, R 70 64
HAWAII
Danel K. Akaka, D 72 No data
Maria M. Hustace. R 24
INDIANA
James Jontz, D 31 26 3.5 2.7
Richard M. Lugar, R 67 64
MAINE
Thomas Andrews, D 37 29 4.4 2.7
Olympia Snowe, R 60 53
MARYLAND
Paul S.Sarbanes, D 59 56 3.5 1.9
William Brock. R 41 36
MASSACHUSETTS
Edward M. Kennedy, D 58 53 5 -.4
Mitt Romney, R 41 38
MICHIGAN
Bob Carr, D 43 36 4.5 -4
Spencer Abraham, R 52 37
MINNESOTA
Ann Wynia, D 44 38 4.2 -.2
Rod Grams, R 49 42
MISSISSIPPI
Ken Harper, D 31 28 4 -.8
Trent Lott, R 69 60
MISSOURI
Alan Wheat, D 36 29 3.5 4.2
John Ashcroft, R 60 58
MONTANA
Jack Mudd, D 38 37 3.5 -4
Conrad Burns, R 62 51
NEBRASKA
Bob Kerrey, D 55 58 3.4 6.7
Jan Stoney, R 45 36
NEVADA
Richard H. Bryan, D 51 55 3.5 8.6
Hal Furman, R 41 31
NEW JERSEY
Frank R. Lautenberg, D 50 47 3.5 4.5
Chuck Haytaian, R 47 37
NEW MEXICO
Jeff Bingaman, D 54 47 4 1.3
Colin R. McMillan, R 46 38
NEW YORK
Daniel P. Moynihan, D 55 60 3.5 2.3
Bernadette Castro, R 42 27
NORTH DAKOTA
Kent Conrad, D 58 60 4.5 10.2
Ben Clayburgh, R 42 28
OHIO
Joel Hyatt, D 39 34 4.2 .4
Mike DeWine, R 53 47
OKLAHOMA
Dave McCurr y, D 40 40 3.5 -3.4
James Inhie, R 55 48
PENNSYLVANIA
Harris Woflord, D 47 44 5.2 1.6
Rick Santnrum, R 49 43
RHODE ISLAND
Linda J. Kushner, D 36 27 5 4.2
John Chafee, R 64 58
TENNESSEE
Jim Sasser, D 42 42 3.5 -5.9
Bill Frist, 56 44
Jim Cooper, D 39 40 3.5 -7
Fred Thompson, R 61 47
TEXAS
Richard Fisher, D 38 29 3 4.7
Kay Bailey Hutchison, R 61 57
UTAH
Patrick A. Shea, D 28 24 4.2 0
Orin G. Hatch, R 69 59
VERMONT
Jan Backus, D 41 37 5 0
James Jeffords,R 50 45
VIRGINIA
Charles S. Robb, D 46 39 3.5 4
Oliver L. North, R 43 31
Other 11
WASHINGTON
Ron Sims, D 45 41 3.5 -3.2
Slade Gorton, R 55 44
WEST VIRGINIA
Robert C. Byrd, D 69 70 5 12.4
Stan Klos. R 31 16
WISCONSIN
Herb Kohl, D 58 61 4.5 7.6
Robert Welch, R 41 32
WYOMING
Mike Sullivan, D 40 38 4.5 -3.8
Craia Thomas. R 59 48
Note that you would have been correct every time
except for Pennsylvania if you had just predicted
the winner to be the person with the highest percentage
in the poll. I don't have the similar figures for the
governors races but I certainly lost my bet that
the outcome for Cuomo would be within the margin
of error!
It is hard to say how you should determine the actual
error in the poll, since these percentages do not add up
to 100% because of undecided voters and other
candidates. To make them comparable we normalized the
percentages to add up to 100% for both the poll results
and the final results. Using these normalized
percentages, we determined the poll error as the
difference between the predicted and the actual vote for
the candidate who led in the poll.
I hope this is not a fair way to judge the pollsters
since about 1/3 of them did not fall in the margin of
error and some are way off.
I asked in a discussion question last time, at what
stage the New York Times pollsters carry out their
adjustments? I am told that the outfit in Connecticut
only provides the pollsters with a random telephone
sample for the state's telephones. The adjustments,
demographic and others, appear to be made after the poll
is taken. I am still not certain how all this is done.
If anyone knows where the procedure is written down in
all gory detail, I would appreciate knowing about it.
DISCUSSION QUESTIONS
(1) Is it fair to expect polls taken a few days before
the election to accurately predict the outcome of the
election?
(2) What would a pollster say about our attempts to see
if the final results fell within the margin of error of
the poll?
(2) Do you think that polls have a serious affect on the
way people vote?
(3) How do you think pollsters explain their being so
far wrong in the governor's race in New York?
(4) The Times says that Giuiani received the poll
results saying that Cuomo had taken the lead before they
were announced and this led him to announce his support
for Cuomo. Do you think this will cause him to change his
opinions about polls?
<<<========<<
>>>>>==========>>
Ask Marilyn.
Parade Magazine, 6 November 1994, p10.
A reader asks Marilyn whether he was being "taken" in a
dice game, where he bet on his throw of a single die
coming out higher than an opponent's. The reader gives
a symmetry argument that led him to think the game was
fair: "If he [opponent] throws a 1, there are five
numbers higher (2,3,4,5,6); but if he throws a 6, there
are five numbers lower (1,2,3,4,5). If he throws a 2,
there are four numbers higher; but if he throws a 5
there are four numbers lower. And if he throws a 3,
there are three numbers higher; but if he throws a 4
there are three numbers lower. It looks the same to me..."
Marilyn correctly points out that the reader's chances
of winning were only five out of twelve. The above
argument overlooks ties, on which the opponent wins.
<<<========<<
>>>>>==========>>
For one-time antagonists, DNA fingerprinting debate
settled.
The Boston Globe, 27 October, 1994, p11.
Richard A. Knox
"The public needs to understand that the DNA finger-
printing controversy has been resolved. There is no
scientific reason to doubt the accuracy of forensic DNA
typing results." The article cites these remarks by
Eric Lander and Bruce Budowle made in their article in
the current issue of "Nature". The remarks are
particularly noteworthy because Lander had been a critic
of the lack of scientific standards for DNA
fingerprinting in earlier use. And Budowle, chief
scientist for the FBI, has been a staunch defender of
its use. The latest standards, however, use deliberately
conservative assumptions about the possibility of a
"four-point match" (match at four genetic loci), which
can still provide odds of more than six million to one
against accidental misidentification. These are based on
the "ceiling principle" recommended by the 1992 report
of the National Research Council which may be described
as follows.
If a population is made up of sub-populations with
different gene frequencies, then the independence
assumption cannot be assumed. The NRC proposed that gene
frequencies be determined for the various possible sub-
populations. Then, to estimate the probability for
agreement at several sites, choose, for each gene, the
highest frequency among all subpopulations and multiply
these "worse case" probabilities. This is called the
ceiling principle.
The authors suggest that the independence computation
could also be given in the trial, but with the
understanding that the truth might well be somewhere in
between this and the estimate given by the ceiling
principle.
James E. Stars, professor of law and forensic sciences
at George Washington University, still criticizes the
standards, maintaining that "it's not scientists who are
supposed to give the benefit of the doubt. It's the
jury and the law that are supposed to give the benefit
of the doubt."
DISCUSSION QUESTIONS
1. What do you think Stars meant by his remark?
2. Another report on this article asserts that a
spokesman for the FBI once said that it had done six
proficiency tests without an error and so its error rate
was zero. How high an error rate could they have, in
fact, and still have a reasonable chance for six tests
in a row to be without an error?
3. Do you think this article was timed to affect the
Judge's decision in ruling on the admissibility of DNA
evidence in the Simpson trial? If so, is that bad?
<<<========<<
>>>>>==========>>
Science's role in courtrooms reassessed.
The Boston Globe, 20 October 1994, p1.
Anthony Flint
This article cites a number of recent cases in which
scientific evidence plays a role in court decisions: if
there is a 1 in 40,000 chance that the recovered DNA is
not O. J. Simpson's, does this constitute reasonable
doubt? [see preceding article]; which of the
conflicting studies on cancer risk and cellular phones
is to be believed?; does Gulf War Syndrome exist?
The article reviews the Frye admissibility standard for
scientific evidence and the 1993 Daubert v. Merrill Dow
Pharmaceuticals case, after which the Supreme Court
ruled that judges needed to be more active gatekeepers
rather than leaving juries to sort out scientific
claims.
The article concludes with the following interesting
quote, relevant to the previous article. With regard to
DNA evidence, Albert A. Scherr of the Franklin Pierce
Law Center notes: "When juries make their decisions,
it's always been more like the decision of whether to
marry someone. Relying on a number makes it a lot
easier, and more like buying a house. If you put a
number on reasonable doubt,--if you make the decision so
quantifiable--you'll totally change the legal system."
DISCUSSION QUESTION
Do you think a number can be put on reasonable doubt?
If so what number would be reasonable?
<<<========<<
>>>>>==========>>
Abortion tie to breast cancer risk is suggested.
The Boston Globe, 27 October 1994, p9.
Associated Press
A study in the Journal of the National Cancer Institute
reports that the annual risk of breast cancer for a 40-
year-old women is 0.6 per 1000 among women who have had
an abortion, as compared to 0.4 per 1000 for women who
have not.
Higher risk was associated with abortions performed when
women are younger than 18 or older than 30. The risk
was not found to be associated with number of abortions
or number of live births or miscarriages. These
findings were base on interviews with 845 breast cancer
patients and 961 healthy women of the same age group.
This is another example of a kind of study that
epidemeologists call "case control studies". In the
last Chance News, we asked how the relative risk is
determined in such a study. I confess that I did not
know the answer but it appears to be as follows:
The "relative risk" of an abortion for breast cancer is:
P(breast cancer|abortion)/P(breast cancer|no abortion)
This can be written as the product of the two terms:
P(abortion|breast cancer)/P(no abortion|breast cancer)
and
P(no abortion)/P(abortion).
We can estimate P(abortion|breast cancer) by the
proportion of the breast cancer cases who say they had
an abortion. We estimate the P(abortion) by the
proportion of the control cases who said they had an
abortion. From these we can estimate the two terms whose
product estimates the relative risk.
DISCUSSION QUESTION
(1) The findings are preliminary, and a co-author of the
report said it would be "premature" for women to make
any abortion decision based on the study. Do you think
the difference found in the study is large enough to be
taken seriously?
(2) Other reports on this study described the outcome of
the trial by saying that the risk of breast cancer for
women under 40-years old who had an abortion was 50%
higher than for a women who had not had an abortion. Is
that consistent with the information given in this
report? Which method of reporting the results do you
think is most informative?
(3) A commentator on this study remarked that the small
difference could be due to errors from the interview
process. She suggested that a person who had had cancer
would be more apt to admit having an abortion than one
who did not. Why might this might be true?
(4) In an observational study the relative risk is
directly estimated from the outcome of the study. How
might you think of this case control study as an
observational study?
<<<========<<
>>>>>==========>>
Extracting the truth from statistics.
The Boston Globe, 17 October 1994, p11.
Gordon McKibben
This article describes a report by Arnold Barnett of MIT
Sloan School of Management, called "How Numbers are
Tricking You" which appeared in Oct issue of MIT
Technology Review. Barnett says the ideal way for
readers to be better served by numbers is to use the
newspaper as a prod for future research--assuming the
newspaper gives the source. Even when this is not
possible, common sense is called for. [This almost
sounds like a plug for a CHANCE course!]
Barnett cites an example of ambiguity from an Associated
Press story which appeared in the Globe last spring [and
in Chance News], reporting that outbursts of anger can
double your risk of heart attack. Since the conclusion
was based only on interviews with recent heart attack
victims, Barnett wonders about healthy people who get
angry. Might not they benefit from letting off steam in
a way that reduced their heart risk?
The author gives the readers lots of good advice about
how to handle articles that include statistical
analysis, concluding with: "Don't be frightened by
statistics, just apply common sense."
DISCUSSION QUESTION
The article gives a number of cases where people have
challenged the Globe's use of statistics. One example
is the following: An editorial plugging handgun
controls, mentioned that deaths by firearms exceeded
38,000 a year. A reader suggested it would have been
helpful to mention that the number is more than twice
the one usually given because it includes 18,526
suicides. Do you agree?
<<<========<<
>>>>>==========>>
Discovery that AIDS can be prevented in babies raises
debate on mandatory testing.
New York Times, 3 Nov 1994, B14
Gina Kolata
The current New England Journal of Medicine reports the
result of the study that was stopped early, showing
that, when a pregnant women who has the HIV virus takes
AZT, it helps prevent the virus being passed on to the
child.
The study involved 477 pregnant women infected with the
HIV virus. Half were given the AIDS drug AZT and the
other half a placebo. Only 8.3% of the children of
women who took the drug were infected with the virus as
compared to 25.5 percent of the children of women who
had the placebo.
Editorials in the NEJM recommend that HIV testing of
pregnant women be encouraged but should be voluntary.
Experts are quoted on both sides of the issue of
mandatory testing of pregnant women. On the one hand it
seems likely that this would save the lives of many of
the children; but on the other hand, to be effective,
this would require also mandatory treatment for the
mother which to some, is a significant violation of
civil rights.
DISCUSSION QUESTION
(1) In New York State, a group has been set up to make
recommendations to the Governor relating to this issue.
What would your recommendation be?
(2) Studies of the effectiveness of AZT in extending the
life of those who have the HIV virus have not been very
encouraging. Should this make a difference in
considering mandatory treatment of the mother in an
attempt to save the child?
<<<========<<
>>>>>==========>>
Heart ills and high cholesterol may not be linked in old
age.
New York Times, 2 November 1994, C12
Gina Kolata
A study being published in the "Journal of the American
Medical Association" reports that high cholesterol for
men and women over 70 seems not to affect the chance of
a heart attack or dying of heart disease or, for that
matter, of anything else. They followed 997 men and
women from 1988 to the end of 1992. A third of the
women and a sixth of the men had high cholesterol
levels.
This result is found to be a bit surprising, given other
studies that show that high cholesterol is a risk factor
for heart disease in middle-aged men and women. One
explanation is high cholesterol does not affect the
arteries for some and those for which it does have been,
to some extent, selected out before reaching their 70's.
DISCUSSION QUESTION
Snell has higher than average cholesterol level but will
be 70 in January. Should he go back to eating hot fudge
sundaes after his birthday?
<<<========<<
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High doses of a heart drug are found to be dangerous.
New York Times, 17 October 1994, A14
Lawrence K. Altman
Two studies, designed to test the effectiveness of the
drug heperin routinely used to treat heart attacks, were
stopped (in April) early when it was noticed that high
doses of the drug were causing lethal bleeding in some
of the patients.
Doctors are just now being publicly alerted to this
danger. Authors of the study explain that the delay was
caused by concern about their work being peer-reviewed
and also to allow for a careful presentation that would
not discourage physicians from using the drug in
moderate amounts. On the other hand, the delay was
criticized because it was known that doctors were at
times using doses larger than those that had been found
to produce unacceptable results.
DISCUSSION QUESTION
Do you think the delay in publicizing this result was
justified?
<<<========<<
>>>>>==========>>
A More Perfect Union.
Washington Post, 30 Oct 1994, Book World p x1
Charles C. Mann
This is review of the following two books coming out of
the sex survey we reported in the last chance news.
SEX IN AMERICA A Definitive Survey
By Robert T. Michael, John H. Gagnon,
Edward O. Laumann and Gina Kolata
Little, Brown. 300 pp. $ 22.95
THE SOCIAL ORGANIZATION OF SEXUALITY
Sexual Practices in the United States
By Edward O. Laumann, John H. Gagnon,
Robert T. Michael and Stuart Michaels
University of Chicago. 718 pp. $ 49.95
The first book is a carefully written account of the
survey but with a minimum of technical statistics and
obviously aimed at the best selling list.
The second book is a more technical report of the survey
but also written with the intent of being read by the
non-expert. Indeed, it is, in many ways, a fine primer
on survey sampling. The authors discuss in detail how
they went about making the decision on the nature and the
size of the sample they chose, how they decided between
a telephone survey, interviews, written forms etc. They
also discuss possible biases and how they planned to
check for these. Like the "Bell Curve," they often take
the time along the way to explain in quite simple terms
the statistical techniques they use to determine sample
sizes, look for correlations etc.
This reviewer does a good job of highlighting some of
the inevitable problems in a study of this kind.
Because of the withdrawal of federal support the
researchers had to decrease the size of the sample from
the proposed 20,000 to about 9,004. They had to eliminate
1,141 because they belonged to empty buildings. Again
for financial reasons they had to limit the study to
English speaker adults between 18 and 59. This
eliminated another 3,514. Of the remaining 4,369
households, the researchers interviewed people in 3,432
of them with a response rate of 78.6 percent.
One more for financial reasons, they chose not to cover
people in institutions such as college dormitories,
military barracks or prisons which might cause problems
with the use of their survey for AIDS policies, which was
one of their main objectives.
The reviewer comments on the obvious difficulties of
telling if people are being truthful. The
researchers asked for written responses for some of the
people interviewed and checked them with the interview
but he is not convinced that this is much of a check.
The book itself gives a careful discussion of all these
problems but does put a bit of a positive spin on them.
The reviewer concludes that "The National Health and
Social Survey represents a mountain of hard work, but
its findings should be greeted with more skepticism than
its authors would like."
DISCUSSION QUESTIONS
(1) In discussing possible biases in their survey in the
the more technical book, the authors state that: "Only 6
percent of the interviews took place with the spouse or
other type of sex partner present, and an additional 15
percent had other people present ... These 'others'
were overwhelmingly likely to be children or
stepchildren of the respondent... When interviewed
alone, 17 percent of the residents reported having two
or more sex partners in the past year, while only 5
percent said so when their partners were present during
the interviews."
After discussing how they looked into this potential
problem, the authors remark: "On the basis of these
bivariate analyses, we cannot conclude that the presence
of others caused the reporting differences in the sense
of suppressing the truth."
What else could cause the difference?
(2) The authors list seven possible explanations for the
fact that the median number of sex partners since age 18
was 6 for men and 2 for women and comment on which they
feel is most likely. See if you can come up with some
of their explanations and which is most likely.
!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
CHANCE News 3.15
(16 Oct to 4 Nov 1994)
!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
Please send suggestions to: jlsnell@dartmouth.edu
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