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CHANCE News 4.06
(22 March 1995 to 8 April 1995)
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Prepared by J. Laurie Snell, with help from
William Peterson, Fuxing Hou and Ma.Katrina
Munoz Dy, as part of the CHANCE Course Project
supported by the National Science Foundation.
Please send comments and suggestions for articles to
jlsnell@dartmouth.edu
Back issues of Chance News and other materials for
teaching a CHANCE course are available from the
Chance Web Data Base.
http://www.geom.umn.edu/locate/chance
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Data, data everywhere, but not a thought to think.
Jesse Shera's paraphrase of Coleridge
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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.
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Note: Apparently not only the Associated Press but
also most major newspapers have style books. Perhaps
we should have a "Chance Style Book".
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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?
<<<========<<
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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.
<<<========<<
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ARTICLES ABSTRACTED
>>>>>==========>> 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:
>>>>>==========>> 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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