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Chance News 2.18
(21 October to 7 November 1993)
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Prepared by J. Laurie Snell 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
Current and previous issues of chance
news can be found on our chance gopher.
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How Marilyn vos Savant managed, in such a short time to
write such a delightful, informative, and accurate book
about the probable proof of Fermat's last theorem beats
me!
Martin Gardner
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ARTICLES ABSTRACTED
>>>>>==========>> This was election week and the pollsters had some explaining to do in the governor's race in New Jersey.
The 1993 elections: Polls; New Jersey voting experts try to figure out where they went wrong. The New York Times, 4 Nov. 1993, B9 Elizabeth Kolbert The polls typically were giving Florio a ten point advantage going into the election. Whitman was the winner by a small margin. This article considers what could have gone wrong. Factors mentioned were Whitman's final campaign blitz in which she presented herself in a "warmer light", the general volatility of the New Jersey electorate and a higher than expected turnout in traditionally Republican counties. One expert suggested the polls themselves might have done the damage. Those, who did not like Florio but thought he was not quite as bad as Whitman, may have stayed home thinking they could get Florio without having to personally vote for him. Only one publicly released poll, by the Asbury Park Press, had the race an even race. This poll was the least professional of the lot, conducted by an editor who confessed to being "very nervous" when he saw how much his poll was at variance with the others. <<<========<<
>>>>>==========>> Backtalk: Basketball's Lessons for Science. The New York Times, 7 Nov 1993, Section 8 page 9 Carl Sagan Carl Sagan discusses ways in which basketball can be used to liven up a science course. Of course, he spends a lot of time on the problem of recognizing streaks and getting basketball players and fans to recognize that their "hot hands" are not as recognizable as they think are. There is nothing very new here for those that have followed this drama but the fact that it is a long article in the Sport section of the New York Times might give the subject an aura of respectability. <<<========<<
>>>>>==========>> Court weighs jury-selection by sex. The New York Times, 3 Nov, 1993, A22 Linda Greenhouse Having essentially eliminated race as a factor in jury selection, the Supreme Court is now asking if lawyers have a right to remove jurors just on the basis of their sex. John Porter, a lawyer for a man who lost a paternity case before an Alabama jury of 12 women, argued that the same constitutional principle of equal protection applies to considerations of sex as well as of race in jury selection. In the trial the State of Alabama used its jury challenges to remove men from the jury pool, as allowed in most state and Federal courts. When Porter said that the probability that most women might have one point of view did not justify excluding all the women, Justice Scalia interrupted to exclaim "But that's what peremptory challenges are all about -- playing the odds!" Justice O'Conner, among others, was concerned that, if they exclude peremptory challenges based on sex, they will have to extend this to ethnic origin, religion etc. "Then what's left of peremptories? -- besides the postman" she asked. This article suggested to Bob Norman the following interesting problem: Assume that prospective jurors for a 12-person jury are equally likely to be men or women. The lawyer for the defense is allowed three peremptive challenges and will use them all to try to keep women off the jury. Neither the judge nor the other lawyer makes any other challenges. What is the probability that the jury will end up all men? Pascal and Fermat would have had no difficulty with this problem! <<<========<<
>>>>>==========>> The next five articles were provided by our Boston reporter, Bill Peterson. "Doonesbury" cartoon strip. The Boston Globe, 8 October 1993. Garry Trudeau An amusing use of statistical vocabulary. Mike Doonesbury's imaginary Mr. Butts character is in China trying to spread the tobacco habit. When a youth points out that "with the current trend, over 50 million of my generation will die from tobacco", Mr. Butts responds: "Anecdotally, you'll probably live to 100." Pressed for an explanation of the term 'anecdotally', he adds "...the Marlboro man is an individual. He lives outside the statistics." <<<========<<
>>>>>==========>> $100,000? Think again. The Boston Globe, 20 October 1993 A1. Don Aucoin State to pay the whole $100,000. The Boston Globe, 21 October 1993, A1. Don Aucoin An unprecedented 33 players hit the winning combination on the Massachusetts Lottery's "Mass Cash" drawing on Monday night (10/18). Mass Cash is a megabucks-style game (pick 5 out of 35 numbers), except that here the grand prize is fixed--no pun intended--at $100,000. The back side of each ticket, however, states in the fine print that "If the total of prizes won for any event exceeds 150% of the net sales for that drawing the prize amounts will be based on a formula detailed in the rules and regulations or administrative bulletins issued hereunder." What the formula means in the present case is that the 33 grand prizes were each reduced to $42,000. The previous record number of Mass Cash winners was 15, too low for the formula to be invoked. The apparent problem this time was that the winning numbers were 1-2-4-5-7, all from the single digit numbers most frequently played. The first article details the players' outrage over being cheated out of what they understood to be a "guaranteed" $100,000 grand prize. The second article reports that, in an apparent public relations maneuver, the Lottery officials would yield to the pressure and grant the full payoffs--this time! An advertising campaign is expected to clarify the situation for the future. "We can't afford to do this again," noted the treasurer. <<<========<<
>>>>>==========>> Lottery's Keno kickoff is met with protest by clergy on values. Boston Globe 1 Oct 1993 Mitchell Zuckoff and Doug Bailey, Globe Staff This is an account of the clergy versus the state of Massachusetts in the starting of Keno in the taverns of Boston. We used this in our Chance course and it was a nice example. It is rather striking how much more interesting it is to play when you choose 10 numbers than when you choose just 1 number. The article ends with the following description of Keno in Massachusetts: Q. What is Keno? A. Keno is a "lotto" style game that originated in ancient China. In the version introduced yesterday by the Massachusetts Lottery,the game is played by choosing 1 to 12 numbers from a card of 80 numbers. To win, players must match their numbers from 20 numbers chosen in random drawings. Q. How many times can you play? A. Drawings are held every 5 minutes from noon to 11 p.m. every day. Players can choose to bet their numbers in one, two, three, four, five, 10 or 20 consecutive games. Q. How much does it cost to play? A. Players can wager from $1 to $10 per drawing, or up to $200 on one ticket if $10 is bet for 20 consecutive drawings. Q. How much can I win? A. That depends on how much you wager and how many numbers you choose in any game. Winning a one spot game - in which just one number is chosen - wins $2.50 on a $1 bet. Matching all five numbers in a five spot game wins $450 if $1 is wagered. In a 12 spot game, players can win $4 if they have no matches. Picking all 12 numbers in a 12 spot game returns $1 million on a $1 bet. <<<========<<
>>>>>==========>> US: Cab drivers at top risk to be slain on the job. The Boston Globe, 26 October, 1993, A4. Associated Press The National Institute for Occupational Safety and Health reported that 7603 people were murdered on the job in the US from 1980-1989, for an average of 15 a week. As noted in previous CHANCE news, homicide is the leading cause of death for women on the job, and the third leading cause for men. Taxi-cabs and taxi- dispatch offices are the most dangerous places in which to work, with 26.9 of every 100,000 workers murdered during the decade. This is forty times the national on-the-job rate of 0.7 per 100,000. After cab drivers and chauffeurs, the next riskiest occupation is police officer, with a 9.3 per 100,000 rate. (This sounds like a candidate for a Kahneman/Tversky availability- bias-in-risk-assessment questionnaire!) It might also be interesting to see how well readers do at interpreting an N-deaths-per-100,000-per-decade risk figure. What are my chances to be killed on the job if I drive a cab for a year? <<<========<<
>>>>>==========>> Breast cancer: success is imminent in search for key gene. Boston Globe, 11 October 1993, A35 Richard Saltus Scientists appear to be close to identifying a gene that makes women highly prone to breast cancer. The story reports that only 1 woman in 200 carries the gene, but 82% of those who do develop breast cancer by age 70, compared to 8% of those who don't. Much of the article deals with anticipated public demand for a test for the gene's presence and what advice to give women who turn out to have it. A Chance course might try to reconcile the various figures presented in a graphic in the article. <<<========<<
>>>>>==========>> Rivalry holds up discovery of breast cancer gene: Scientists bicker over research. The Independent, 31 October, 1993, Page 11 Home News. Steve Conner and Rhonda Siddall The collaboration between the teams in Britain, the United States, France and Canada, working on finding the gene that causes breast cancer, has been abandoned. The reason for this is the expected rewards in terms of future research support, for the team that gets there first. Collaboration started three years ago when Mary-Clair King at the University of California placed the breast-cancer gene somewhere on chromosome 17. Scientific teams around the world exchanged information regularly to identify regions of the chromosome that could be eliminated. Now there are even hints of researchers giving their rivals a false trail. There is also serious competition between the Science journals to publish the results. On the positive side one researcher pointed out that the competition is causing researchers to work night and day. "Roger Bannister would never have run the mile in four minutes if he had been holding hands with someone else." <<<========<<
>>>>>==========>> Breast cancer-abortion link under attack; authors outraged by religious right's interpretation of studies. The Washington Post, 1 Nov 1993, A1 Laurie Goodstein Activists on the religious right have seized on studies that suggest that abortions may be a risk factor for breast cancer, as a new tool in their fight against allowing abortions. According to this article, cancer researchers say that, while some studies have suggested abortion is a risk factor, the most reliable studies show no increased risk. They say that the overall evidence suggests that abortions are not a risk for breast cancer. The claim that it is a risk factor has been widely publicized by Joel Brind who holds a doctorate in medical science, and Scott Somerville, a lawyer. They speak on Christian radio, write and distribute articles for church and anti-abortion publications. Somerville reports that Brind was able to show, by averaging the results of all the studies, that one abortion increases the risk of breast cancer by 50 percent. While they cite articles that support their claims, the authors of these articles themselves seem horrified that their results are being reported to have established abortion as a known risk factor for breast cancer. Louise Brinton, chief of the environmental studies section at the National Cancer Institute, says that previous studies have involved too few women and have failed to control for important variables. She is evaluating now the data on a new study involving 6,000 women younger than 45 with breast cancer, many of whom have had abortions. She hopes to have published the results in the next six months. <<<========<<
>>>>>==========>> Panel tells cancer institute to stop giving advice on mammograms. The New York times 22 October, 1993 Gina Kolata An advisory panel to the National Cancer Institute has recommended that, instead of giving advice about breast cancer screening, the Institute should simply give the public the facts and let them decide for themselves. The Institute's current guidelines, adopted in 1988, recommend that women 40 to 49 years old should have a mammogram every year, or every other year, and that women over 50 should have one every year. Data from large studies have shown repeatedly that mammograms can cut the death rate from breast cancer by as much as 30 percent in older women. However, recent studies failed to show that mammograms for women 40 to 49 years old saved lives. It is suggested that recommendations go far beyond just giving the facts since they have to take into account economic, legal and other considerations that may be outside the field of expertise of the Institute. The panel is only advisory and the Institute need not follow its advice but usually does. <<<========<<
>>>>>==========>> Gene tie to male violence is studied. The New York Times, 22 October, A21 Natalie Angier Researchers from the Netherlands and the United States studied a large Dutch family that had a history of hostile behavior among some but not all male members of the family. Those who exhibited this behavior often reacted to very mildly stressful situations with aggressive outbursts and assaults on the person they deemed a threat. They have committed arson and attempted rape. In addition they have a low IQ of 85 to 90. The researchers linked the abnormal behavior to mutations in the gene responsible for the body's production of an enzyme critical for breaking down chemicals that allow brain cells to communicate. Among 17 males the five who had the mutation showed a predisposition to aggressive, impulsive behavior and the 12 who did not have it did not show such behavior. The gene lies on the X chromosome so only men can suffer from this enzyme deficiency. Women can carry the defective gene but are protected from its effects by the other copy that will most likely not be defective. The researchers estimate that not more than 1 person in 100,000 will have this defective gene. The article observes that research into the genetic causes of violence has been highly controversial in recent years. <<<========<<
>>>>>==========>> Dangers seen in death row appeals rules. Houston Chronicle, 22 October, 1993, A18 William E. Clayton Jr. Representative Don Edwards, chairman of the House Civil Rights subcommittee, is concerned that the "Omnibus crime bill pending in Congress would water down the right of a person to challenge his imprisonment". The staff of the committee studied 48 cases in the past 20 years, in which inmates had been released from prison after being sentenced to death, and concluded that there is a "real danger of innocent people being executed in the United States". The question of the number of innocent people there are on death row came up in our discussion on the meaning of "beyond a reasonable doubt" <<<========<<
>>>>>==========>> Speaking of "beyond a reasonable doubt" ---- Perspective on the Denny verdicts; better to let 100 guilty go free, the founding fathers decided, than to punish one innocent. Los Angeles Times, 5 Nov 1993, B7 William W. Bedsworth A letter from a judge suggests that, in judging the outcome of the Denny case, people should remember how the law works. Speaking as a judge he says "We tell every jury that, unless they are convinced to a moral certainty of the guilt of the defendant, they must return a verdict of not guilty. We don't define that term; we leave it to the jury to decide if their feeling about the case rises to a level they'd describe as 'moral certainty' -- still a very stiff test for conviction." "What's more, we tell the jury they must acquit even if they think the defendant is probably guilty, if there is a reasonable doubt about that guilt. And we tell them they must be unanimous in that decision. That is not a system designed to arrive at truth, folks. It is a system designed not to punish innocent people." <<<========<<
>>>>>==========>> Long Island Q&A: Judith Tanur; How public-opinion surveys can be used and misused. The New York Times 31 October, 1993, Section 13LI;Page 2; Long Island Weekly Desk Thomas Clavin This is an interview with the well-known expert on surveys, Judith Tanur. The interviewer mentions the book "Questions about questions: inquiries into the cognitive bases of surveys" which Tanur edited and which was published last year by the Russell Sage Foundation. The questions are interesting and the obvious ones to ask a survey expert and with answers, as you would expect from Judith Tanur, quite expert. She stresses the importance of surveys being done by people who know what they are doing. <<<========<<
>>>>>==========>> Luck or logic? Debate rages on over 'efficient-market' theory. Wall Street Journal, 4 Nov, 1993, C1 John R. Dorfman The well-known 'efficient market' theory says that the market reacts so quickly to any new information that an uniformed person, or for that matter a chimp, can do as well as an expert. This leads to the random walk model for the market, championed by economists Malkiel, Burton in his best selling book "A random walk down Wall Street" For the past five years, the Wall Street Journal has been testing this theory through a contest, in a series of overlapping six month-contests, pitting experts against dart throwers. The pros have won 24 times and the dart throwers 17 times. The average six-month gain for the pros, 8.4%, is quite a bit larger than the 3.3% gain achieved by the dart throwers. It would seem that the professionals are signficantly ahead. But Malkiel and Metcalf recently wrote a paper, analysing the Dartboard contests from 1990 through 1992, which suggests that this difference can be explained by two factors. First the experts are picking riskier, more volatile, stocks than the dart throwers. Even the random walk theory allows for riskier stocks to gain more on the average over a long time. They found that the pros' stocks were 40% more volatile than the overall market, compared to 6% for the dart stocks. Once you adjust for risk, the pros' margin is just .4% and this is not significant. They claim as well that the pros also get an advantage from an "announcement effect" that causes their stocks to surge the day they appear in the Wall Street Journal. <<<========<<
>>>>>==========>> The 5 November, USA Snapshots on page 1A shows graphically how median full-time wages for men and women compare, by education: for a high school degree, men $26,766, women $18,648. For a bachelor's degree , men $40,381, women $29,284 and for a master's degree, men $47,260, women $35,081. The source is the Census Bureau (1992 median incomes of people 25 and older) <<<========<<
>>>>>==========>> Studies detail possible precursors to Loma Prieta earthquake. Los Angeles Times, 25 Oct 1993, A3 Kenneth Reich Geological survey reports on the 1989 Loma Prieta earthquake of magnitude 7.1 showed increased ultra-low- frequency magnetic noise and dramatic increases in stream flow as possible significant precursors of the quake. The scientist hope that these observations might help in the search for ways to predict earthquakes. They stressed that further observations on other quakes were necessary to verify that these two observations represent genuine precursor events for a quake. <<<========<<
>>>>>==========>> Did Shoeless Joe Jackson throw the 1919 World Series? American Scientitian Vol 47 No 4, Nov 1993 pp241-250. Jay Bennett Introduces a new statistic called the player-game percentage (PGP) for studying a player's performance. The PGP is the sum of changes in the probability of winning the game for each play in which the player participates. Discusses its advantages vis-a-vis standard baseball statistics, which have the disadvantages of (1) not accounting for the game situation and (2) not providing a way to compare hitters' and pitchers' performance (3) ignoring the significance of both relief pitching and players' fielding performance. The statistical details may be a bit much for a CHANCE course, but the discussion of appropriate performance measures is interesting (if we can hadle another sports example). The conclusion, by the way, is that Shoeless Joe played to his full potential, which supports his own claims of innocence. <<<========<<
>>>>>==========>> Through a funnel slowly with ball bearing and insight to teach experimental design. Anerican Statistian Vol 47 No 4, Nov 1993 pp 265-269 Bert Gunter, Explicit instructions for building (inexpensively) a device inspired by the famous Deming funnel experiment, which can be used for interactive classroom learning and discussion of experimental design issues. !!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!! CHANCE News 2.01 (20 Dec 1992 to 5 Jan 1993) !!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!! Please send suggestions to: jlsnell@dartmouth.edu >>>==========>>|<<==========<<<
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