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CHANCE News 4.06
(22 March 1995 to 8 April 1995)

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

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/locate/chance

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Data, data everywhere, but not a thought to think.
Jesse Shera's paraphrase of Coleridge
========================================

We found this quote in John Paulos' new book
"A Mathematician Reads the Newspaper".

FROM OUR READERS

Jerry Johnson sent us the following excerpts from a
discussion on a journalism listserve group.

I teach statistics at the University of
Texas at Arlington. Two weeks ago I read in
the science section of a local paper an
article defining the difference between the
median, the mean, and the average. Everything
was fine until he defined the mean as the
average of the largest and smallest numbers
in a set of data. I have always used and
taught that the (arithmetic) mean is the same
as the average of the numbers. When I talked
to him about this, he indicated that this was
the definition given in an Associated Press
list of definitions. Is this the definition
used by journalists?

Thanks for everyone who answered my question
concerning the mean. I have contacted the
Associated Press and hope to change their
definition. One of the problems seems to come
from dictionaries that define the mean as
midway between extremes. I contacted Merriam-
Webster and got one editor there to agree that
midway between extremes is in a philosophical
sense and not a mathematical sense. Webster's New
World Dictionary has a more specific definition
as "a middle or intermediate position as to place,
time, quantity, kind, value,..."

After discussion with Norm Goldstein, Director
of APN Special Projects, the Associated Press
Style Book will be modified to indicate that the
calculation of the mean is identical to that
of the average.
<<<========<<

>>>>>==========>>
Note:  Apparently not only the Associated Press but
also most major newspapers have style books.  Perhaps
we should have a "Chance Style Book".
<<<========<<

>>>>>==========>>
Harold Brooks sent the following two contributions.

From the story "A 'Dream' Deferred" by Jonathan Alter
in the March 24-26, 1995 edition of USA Weekend, on p.
5 discussing the movie "Hoop Dreams".

Still, the unmistakable message is that
'hoop dreams' often are cruel dreams. With
just 54 players drafted by the NBA each year,
the odds of making it to the pros are one in
a million at best.  And with hundreds of
thousands of young players, even the more
immediate dream -- winning a scholarship to
one of the 302 U.S. colleges with major
basketball programs -- is a 100-foot one-
handed shot.

DISCUSSION QUESTIONS

(1) When Arthur had his "Hoop Dreams"  as
a first year high school student, what
would reasonable odds be for his making
the NBA?

(2) What odds are being specified by the remark
"a 100 foot one-handed shot?"  What odds
would you give for Arthur winning a
scholarship?
<<<========<<

>>>>>==========>>
From Walter Scott's "Personality Parade" in the March
26, 1995 edition of Parade Magazine,

Q. Despite satellites and the rest of
their high-tech paraphernalia, weather
forecasters still seem to get it wrong
as often as they get it right. How
accurate are their predictions?
Arun Raj, New York, N.Y.

A. Todd Glickman, a CBS weatherman and
assistant executive director of the
American Meteorological Society, tells
PARADE there have been notable advances
in weather-prediction accuracy over the
last few decades, thanks to sophisticated
computer models.  And he predicts that
accurate seven-day forecasts will be
possible within the next decade--a big
improvement over the current four- or
five-day forecasts.  According to statis-
tics kept by the National Weather Service,
forecasters are accurate 91% of the time
when predicting precipitation for a
particular 12-to 24-hour period.  Their
temperature predictions for a 12-to 24-hour
period are accurate within 2.8 F.  Of
course, the most accurate forecast is
still yesterday's weather report.

DISCUSSION QUESTIONS

(1) What do you think it means to say that forecasters
are accurate 91% of the time when predicting
precipitation for a particular 12-to 24-hour period?
Could this be correct for all parts of the country?

(2) Do you really believe that temperature predictions
for a 12-to 24-hour period are accurate within 2.8 F?

(3) Would you prefer going by yesterday's weather
report rather than today's?

Note:  Harold Brooks, who does research on weather
forecasting, says that he has no idea what the 91%
means.  He believes the 2.8 F. is the mean absolute
error for the low and the high predictions that are
made 12 hours in advance for 12 hour periods. You hear
the high temperature prediction for the afternoon
period on the morning news and the low temperature
prediction for the next morning period on the evening
news.
<<<========<<

>>>>>==========>>
ARTICLES ABSTRACTED

1.  Bass Bell curve a real fish story.
2.  Statistics on crimes against women.
3.  A mathematician reads the newspaper.
4.  S.A.T. with new (higher) scoring.
5.  Colleges inflate SAT's.
6.  References for probability paradoxes.
7   ESP: Is the skeptical position tenable?
8.  Ask Marilyn: flying with a friend.
9.  Treatments for breast cancer.
10.  New HIV virus thought to be in U.S.
11.  Fewer found to read or watch news.
12.  Aspirin may cut cancer risks.
13.  Genetic tests for cancer.

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

>>>>>==========>>
Paul Gunty suggested the following article:

Bass Bell curve a real fish story.
The Chicago Tribune, 31 March, 1995, News, p 2.
From Tribune Wires

Researchers in the Texas Wildlife Department have been
hard at work trying to determine whether intelligence
among bass is passed on genetically.

110 bass that had never before encountered fishermen
were isolated in a pond.  Biologists fished in the pond
and the fish caught wer marked and put back.  Some of
the fish were caught several times and others not at
all. They all had plenty of chances for being caught.
Then the bass had a month's vacation, allowed to swim
free in the pond.

After draining the pond, the researchers made a tally
of marked and unmarked bass. They classified the 8
percent that had been caught at least three times as
"dumb" and the 22 percent never caught as "smart". The
two groups were separated for spawning, their offspring
were put into separate ponds,  then both groups of
offspring were preyed upon by biologist-fishermen. 17
percent of the "dumb" offspring were never caught; 48
percent of the "smart" offspring were never caught.

The official determination: "Smartness is passed on
genetically.

DISCUSSION QUESTION.

(1) The researchers believed that the results of their
study would permit them to improve the fishing for
those who buy fishing licensees.  How would they use
the results of this study to accomplish this?

(2) Do you think these results support the theory that
intelligence is inherited?
<<<========<<

>>>>>==========>>
Note:  You will find  a discussion in "Statistics" by
Freedman, Pisani, Purves, and Adhikari, 2rd edition, p
46, of a similar experiment with rats. As part of  his
Phd thesis, Robert Tryon tested Spearman's theory of
general intelligence on rats.

Rats ran through mazes and those who made few errors
were called "maze-bright" and those who made many
errors, "maze-dull".  The two groups were bred
separately and after several generations the maze-
bright rats still made significantly less errors in
going through the maze than the maze-dull rats. However
they did not do better than the maze-dull rats on other
animal intelligence tests, such as discriminating
between geometric shapes or intensities of light. Tryon
concluded that general intelligence does not exist at
least for rats.

There were psychological differences between the two
groups. The "brights" appeared to be unsociable
introverts, well adjusted to their life in the maze
but neurotic in their relations to others rats; while
the "dulls" were the opposite.
<<<========<<

>>>>>==========>>
Milt Eisner suggested the following article:

In debate over crimes against women, statistics gets
roughed up.
The Washington Post, 27 March, 1995, A4
John Schwartz

President Clinton recently announced a new Justice
Department program to combat the problem of crimes
against women.  He cited statistics that have long been
used by women's advocates to support the claim that
stronger government action is needed.

Clinton was immediately attacked by David Murray,
research director for the Statistical Assessment
Service.  This service offers itself to journalists to
"try to get the junk science out of the bloodstream".
According to Murray,  the seed money for his
organization came from "largely conservative-leaning
organizations."

The article states that "statisticians familiar with
the violence debate say that all sides selectively use
numbers to make their cases, sometimes twisting the
numbers as much as those they critique -- and that
Murray is no exception."

The origin of Clinton's claim that violence is the
number one health risk for women between ages of 15 and
44 is a study mentioned in a CDC report using too small
a sample to have statistical significance.  The CDC has
repeatedly disavowed the statistics.

Other claims made by Clinton were (a) 700,000 rapes or
attempted rapes are committed each year, (b) 3 million
to 4 million women annually are victims of domestic
violence and (c) The FBI estimates that a violent crime
is committed against a women every 12 seconds.

The two most respected sources for this kind of
information appear to be the National Crime
Victimization Survey from the Bureau of Justice
Statistics (BJS) and a 10-year study conducted by
Richard Gelles of the University of Rhode Island and
Murray Strauss at the University of New Hampshire.

The 700,000 estimate for the number of rapes or
attempted rapes comes from a 1992 survey published by
the National Victims Center in Arlington.  Gelles was a
consultant on the study and said that its findings of
683,000 rapes each year is the most accurate available.
Murray claimed that the BJS estimated this number to be
150,000.  However, while the BJS had estimated numbers
in the range of 100,000 to 150,000 for twenty years,
last fall they estimated the number to be in excess of
300,000.

The source of the 3 to 4 million women victims of
domestic violence appears to be the survey of Gelles
and Strauss.  Their survey found 1.8 million women
annually to be victims of serious violence by their
husbands and indicated that this number could be
doubled because of under reporting.

Gelles also remarked that the 12-second figure has long
been inaccurately attributed to the FBI and in fact
also came from their work, although the 12 should be a
15.
<<<========<<

>>>>>==========>>
A pragmatic view of newspapers and life.
Los Angeles Times, 28 March 1995
Lee Dembart

Finding the social aspects of math.
The New York Times, 12 April, 1995, C22
Richard Berstein

These are two reviews of John Paulos' new book:
A mathematician Reads the Newspaper.
Basic Books, \$18, 212 pages
ISBN 0-465-04362-3

Paulos wants to show that mathematics and related
areas  such as psychology and philosophy are lurking
in all  aspects of the news. The book is written in the
style of a newspaper itself with the early sections
on national and local news, medical news, living styles
etc.

The mathematics is woven into the news story so as to
make the reader almost unaware that it is going on. For
example, there is a nice discussion of Kolmogorov
complexity woven into an remarks about why presidents
who oversimplify do better than those who overanalyze
and why some issues (for example the savings and loan
scandal or more currently derivatives) are too complex
to be compressed into your daily newspaper.

A tribute to Paulos' success with this integration is
the comment: in Dember's L. A. Times review: "The
book is not about mathematics and it's not really about
newspapers.  It should be called "A Clear Thinker
Explains the World."

Dembert enjoyed the discussion of the stock
market as a random walk.  One of my favorites was
Paulos' discussion of how to liven up the society page
by using incidence diagrams.

Our readers will surely want to read  this book so
I will not try to give a detailed review.   Like all of
Paulos's books, it is a lot of fun to read.  You will
find some old favorites and some new ones.
<<<========<<

>>>>>==========>>
S.A.T. with familiar anxiety but new (higher) scoring.
The New York Times, 2 April, 1995, 1-22
David M. Herszenhorn

The College Board has adjusted its scoring system for
the first time since 1941.  At that time, the average
was set at 500 for both math and verbal and the
standard deviation 100.  Since then the averages have
steadily declined to 424 for the verbal and 479 for
math. To permit comparisons between years, SAT scores
were not re-normalized in successive years.

This year the scores are being renormalized to have
mean 500 and standard deviation 100 again.

To allow colleges to compare this years and last years
students, the College Board has sent around a
conversion slide rule.  The director of admissions at
Haverford said: "Its almost as incomprehensible as
adjusting from Fahrenheit to Celsius." The National
Collegiate Athletic Association has announced it is
raising the minimum score for sports eligibility from a
combined score of 700 to a combined score of 820.

In most cases the scores will increase: a verbal score
of 730 becomes a perfect 800.  For a few math whizzes,
scores will decrease.  A 670 on the new test means a
680 on the old test.

In 1941, 10,000 students with quite similar backgrounds
took the exam and this year 1.8 million students from a
wide range of backgrounds will take the test.

DISCUSSION QUESTION:

(1)  How does ETS get SAT scores ranging from 200 to
800 with average 500 and standard deviation 100 from
the raw scroes on the exams?

(2) How do you think the College Board determined the
conversion table?

(3)  If the average scores of math SAT scores are
increased,  how could a 670 on the new test correspond
to a 680 on the old test?

(4) How will SAT convert raw scores to SAT scores in
the future if they again in the future want to allow
comparison between years?

Note:  Here is an e-mail remark relating to the
last question from Paul Holland who was for
many years at ETS but now is at the
University  Berkeley Graduate School of Ed
relating to this last question.

It is funny that you asked about preserving SAT
etc scores over time. I edited a book on the subject
(with Don Rubin) "Test Equating" 1982 Academic
Press, and it was one of my specialities at ETS.
<<<========<<

>>>>>==========>>
Cheat sheets: Colleges inflate SAT's and graduation
rates in popular guidebooks.
The Wall Street Journal, 5 April 1995, A1
Steve Stecklow

This article documents how colleges cheat on reporting
SAT scores and graduation rates.  For college guides,
they want the averages high.  In Money magazine's 1994
college guide, New College of the University of South
Florida was ranked number 1.  New College had been
cutting off the bottom-scoring 6% for years, increasing
the average score about 40% for "marketing purposes".
The most common cheat is to exclude certain groups of
low scoring groups when reporting SAT scores.

Boston University excludes the verbal SAT scores, but
not the math scores, of international students. Of
course the colleges can give arguments for these
practices, but such adjustments are specifically
prohibited by the guide books.

As a way to gauge the extent of this kind of cheating,
the newspaper compared the numbers reported to debt-
rating agencies and investors with those given to
guides such as U.S. News guide, finding more than two
dozen discrepancies in the enrollment data.

Similar games are played with acceptance rates and
graduation rates.  Acceptance rates can appear higher
by not counting the waiting list.  Schools want the
graduation rates high for the College Guides and low
for the NCAA so their student athletes will look good.
This survey found that a number of schools were able to
accomplish this.

DISCUSSION QUESTION:

Should this example appear in the next edition of
Cynthia Crossen's book "Tainted Truth"?
<<<========<<

>>>>>==========>>
An update on probability problem's references.
The College Mathematics Journal, March 1995, p 132
Fallacies, Flaws, and Flimflam by Ed Barbeau

The Marilyn Vos Savant discussion of the Monte Hall
problem led Ed Barbeau in a previous column (The
College Mathematics Journal, 24, (1993), 149-154) to
give a large bibliography of articles related to this
problem and its many relatives.  He has now updated
this with many new references brought to his attention
by the readers of his column.

One of the variations that I found interesting was the
bridge example called "restricted choice".  A good
description is found in Alan Truscott's column in the
August 4, 1991 New York Times on page 65 of section 1.

You are south and the declarer.  You have the ace of
spades and 4 small spades and north has the king, ten
and 2 small spades.  Thus east and west together have
the jack,  queen  and 2 small spades.
You plan to play the ace, and if east plays the jack or
queen then  play a small space and finesse. Is the
finesse correct?

When the ace is played, east will play a jack or queen
if he holds a singleton jack or queen, or both jack and
queen. These  three outcomes are approximately equally
likely. Think of the finesse as switching in the Monte
Hall problem and you see that you should finesse.  The
interesting thing is that the is that the case where
east has the jack and queen corresponds to the case
where Monte Hall has a choice of which door to open.
While, in the Monte Hall problem, it was reasonable to
assume equal probabilities for this choice thus is not
the case for the bridge version of the problem.
<<<========<<

>>>>>==========>>
The skeptical position: is it tenable?
Skeptical Inquirer, May/June 1995, p. 19-29
John Beloff
Replies by Susan Blackmore, Ray Hyman, Paul Kurtz
and Martin Gardner

John Beloff is a prominent leader in the field of
parapsychology. He describes the "skeptical position"
as the view that there is no evidence, as yet, that
would justify acknowledging any phenomenon as
"paranormal." He discusses several varieties of
skeptics but considers the most serious to be what he
calls "de facto skeptics" who claim to have open minds
but demand stronger evidence than anything that has so
far been produced.  (He puts our own Persi Diaconis in
this group).  He feels that this group will require
"repeatable on demand" as is generally required for
scientific claims. He feels that this is not in the
cards. He notes that even for the ganzfield studies,
which he considers state-of-the-art parapsychology,
only 12 of the 28 studies considered in a recent meta-
study were significant at the 5 percent level.  In the
studies done at Princeton by Jahn and Dunne with a very
large number of trials, very few subjects attain even a
minimal level of significance.

Apparently, the meta-study of the ganzfield experiments
was highly significant but did not convince the
skeptics,  nor has the work of Jahn and Dunne.

Beloff argues that, for the "skeptical position" to be
tenable, we must also consider historical evidence that
has not been refuted.

The introduction of the historical criteria allows
Beloff to conclude that the skeptical position is o.k.
but is not mandatory so we can all make up our own
mind.

The responders are not at all impressed with the
historical argument.  They don't see why they should
pay any attention to claims from the past where they
have little hope of finding out the facts. I guess they
remain skeptics.

DISCUSSION QUESTIONS:

(1) Do you agree that repeatability on demand is a
requirement for scientific acceptance of extra sensory
perception? If not, what do you think should be
required?

(2) Do you think that repeatability is a requirement
for belief in the effectiveness of medical treatments?
<<<========<<

>>>>>==========>>
Ask Marilyn.
Parade Magazine, 2 April 1995, p16.
Marilyn vos Savant

A reader raises the following question on air traffic
safety:

I fly in airplanes but I'd rather not. My
partner survived a plane crash;  remarkably,
she still flies. When I fly with her, which
of the following has the greatest chance of
occurring?

(1)  She'll never be involved in another
plane crash.
(2)  If she's in another plane crash,
she won't survive it.
(3)  If she's in another plane crash,
she will survive it.
(4)  Other.

Marilyn first cagily answers (4), noting that she can
always think of something more likely than (1), (2),
(3).  Restricting the discussion to (1)-(3), she says
that since very few people are involved in plane
crashes, but those that are will most likely perish,
"choices No. 1 and No. 2 together are nearly certain."
Thus she recommends restating things as:

(1')  She'll never be involved in another
plane crash.
(2')  She'll experience a crash that she
won't survive.
(3')  She'll experience a crash that she
will survive.

In this setup, Marilyn says that (1) is overwhelmingly
most likely. She adds that flying with this friend has
no bearing on the reader's chance of being involved in
a crash.

DISCUSSION QUESTIONS:

1. How are (2) and (3) distinguished from (2') and
(3') in the language of conditional probability?

2. Michael Olinick recently reminded me (Bill Peterson)
of the story of a fellow who always carries
a bomb with him when he flies.  He (the bomb-carrier,
not Mike) reasons that this makes him less likely to be
a victim of a terrorist attack, since the probability
of there being two bombs on the same aircraft is
incredibly small.  Comments?
<<<========<<

>>>>>==========>>
Chemotherapy, mastectomy found to be effective mix:
breast cancer patients live up to 20 more years.
The Boston Globe, 6 April 1995, p9
Richard Saltus

A 20-year evaluation of "adjuvant chemotherapy"
(following up mastectomy with chemotherapy treatments
in breast cancer cases) indicates that women receiving
this treatment experience improved survival rates for
as long as 20 years following treatment.

The research was reported in the "New England Journal
of Medicine". Of the 207 women in the study who
received chemotherapy, 70 (37%) were alive at 20 years,
compared with 44 of 179 (25%) in the surgery only
group.

A companion study on early-stage breast cancer found
that lumpectomy followed up with radiation appears to
be as effective as mastectomy when compared 10 years
later.  This is encouraging in light of last year's
controversy stemming from reports of fraud in research
in this area, which had left many women worrying that
they had made a mistake by choosing lumpectomy over
mastectomy.
<<<========<<

>>>>>==========>>
Highly infectious types of AIDS virus may be in US,
specialist says.
The Boston Globe, 6 April 1995, p8.
Usha Lee McFarling

The chairman of the Harvard AIDS Institute, Dr. Max
Essex, has called for nationwide screening to determine
whether certain highly infectious subtypes of HIV may
be moving through the US.  The viruses are currently
responsible for epidemics among heterosexuals
in Asia and Africa.

The subtype of HIV-1 virus currently most widespread in
the US transmits infection once in 500 to 1000
heterosexual contacts.  The more infectious subtypes
transmit the infection once in every 10 to 40
contacts.
<<<========<<

>>>>>==========>>
Fewer found to read or watch news.
The Boston Globe, 6 April 1995, p11.
(Associated Press)

In a poll conducted by the Times Mirror Center, only
45% of American adults reported having read a newspaper
in the past day, and 61% had watched a TV news program.
Both figures are lower than a year ago, when 58% had
read a paper, and 74% had watched TV news.  It was also
found that political affiliation had little effect
on readership/viewership.

The article suggests the following as possible reasons
for the decline:

More two-income families, so fewer people have
time to read a paper.
Easing of tensions in the post cold war era make
daily news consumption less essential.
More alternatives to network TV, including
videotapes, computer games and [presumably non-
news oriented] cable channels.

The director of the Times Mirror Center also noted that
"the O.J. trial has clearly disrupted news consumption
patterns across the country."

DISCUSSION QUESTIONS:

1.  What do you think of the explanations offered?
(Have world tensions eased dramatically in the last
year?)

2.  Suggest some ways to more scientifically assess the
reasons for declines in news consumption.
<<<========<<

>>>>>==========>>
Studies suggest aspirin may cut some cancer risk.
The Boston Globe, 22 March, 1995, National/Foreign, p 7
Richard Saltus

New studies suggest that a small dose of aspirin, taken
once a day or even less often, may reduce the risk of
colon and rectal cancer. In addition,  experiments with
animals suggest that it might also help prevent lung
cancer.

In at least seven studies in the past few years, people
who took aspirin for other reasons had a 20 to 50
percent lower risk for developing colon and rectal
cancer.

Recent research at the University of Michigan Medical
School found that 80 milligrams a day was enough to
block production of substances in colon and rectal
cells that seem to play a part in the development of
cancer. One baby aspirin contains 80 milligrams. Since
the effect was maintained for as long as 72 hours
taking the aspirin every other day would seem
sufficient. Taking 40 milligrams seemed to have little
or no effect.

Despite this protection and the previous studies
suggesting that aspirin protects against heart disease,
researchers continue to recommend that aspirin not be
regularly taken without the recommendation of a doctor
because of the dangers of allergies, ulcers and other
possible side effects.

DISCUSSION QUESTION:

(1) Why is the medical profession so cautious about
recommending small amounts of aspirin on a regular
basis? Is this consistent with their other
recommendations?
<<<========<<

>>>>>==========>>
Tests to assess risks for cancer raising questions.
The New York Times, 27 March, 1995, A1
Gina Kolata

Genetic tests that can tell if a person is likely to
get cancer are coming on the market at a rapid rate.
This concerns researchers who feel that these tests are
not yet well understood.  The  genes  whose mutations
increase the risk for breast cancer and? other forms of
cancer were only recently discovered.
Also, in some cases, there is nothing that can be done
for a person who is found to have a high probability of
getting the cancer.  On the other hand, it is argued
that in some cases information from the tests will lead
to more regular screening and the benefits from early
treatment. It would also allow health providers to save
money by screening the most likely group to get a
cancer.

While there is considerable argument about whether the
tests should be coming so quickly there seems little
doubt that they are going to be widely available very
soon.

DISCUSSION QUESTION:

Do you think that there should be some control over the
availability of genetic tests?

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

CHANCE News 4.06
(22 March 1995 to 8 April 1995)

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

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