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## CHANCE News 5.06

### (24 April 1996 to 23 May 1996)

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Prepared by J. Laurie Snell, with help from William Peterson, Fuxing Hou, Ma.Katrina Munoz Dy, and Joan Snell, as part of the CHANCE Course Project supported by the National Science Foundation.

Back issues of Chance News and other materials for teaching a CHANCE course are available from the Chance web site:

http://www.geom.umn.edu/locate/chance

Bonnie Cochran Doyle gave us a wonderful book "Ripley's Believe it or Not! Book of Chance" that is full of great quotes like the following:

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Julius Caesar the Roman general and statesman assassinated by a group
of nobles received 23 stab wounds -- but only one was fatal
Ripley's Believe it nor Not! Book of Chance
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Contents
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The FAQ answers commonly asked questioins about weather prediction. In particular you will find the following definition for the probability of percipitation (POP):

PROBABILITY of PRECIPITATION (POP) is the likelihood of occurrence (expressed as a percent) of a precipitation event at any given point in the forecast area.

You will also find the equivalences between probabilities and descriptive words: for example 10% chance of rain = slight chance for rain. DISCUSSION QUESTION: Does this definiton of POP mean that the forecaster is supposed to assume that the probability is the same at each point in the region?
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Robin Pemantle suggested the following article:

Juries do not apply mathematical formulae.
The Times, 9 May 1996, Features section

The Court of Appeal, Criminal Division, allowed an appeal against conviction and ordered a retrial of Denis John Adams who had been sentenced to several years' imprisonment for rape. The judges stated that the prosecution case rested entirely on the expert evidence in relation to the DNA profile obtained from semen on vaginal swab taken from the victim.

This expert evidence involved the use of Bayes' theorem in evaluation of the DNA profile. The use of this theorem required that items of evidence be assessed separately according to their bearing on the guilt of the accused before being combined in the overall formula. While not passing judgment on the reliability of this presentation, the judges expressed grave doubts as to whether this evidence was admissible because it trespassed on an area exclusively within the jury's province, namely the way in which the jurors evaluate the relationship between one piece of evidence and another.

The court stated that jurors evaluate evidence and reach conclusions not by means of a formula, mathematical or otherwise, but by the joint application of their individual common sense and knowledge of the world to the evidence before them.

DISCUSSION QUESTION:

In a previous Chance News (3.05) we reported a challenge in the U.K. courts of a conviction on the basis that the prosecutor had committed the "prosecutor's paradox". That is, the prosecutor presented the probability that an individual will match the DNA found on the victim, given that he is innocent, instead of the probability that he is innocent given a match. Since the latter probability requires the use of Bayes' formula, would the prosecutor in this case been better off committing the prosecutor's paradox?
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The power of statistics to affect lives -- even when they're wrong.
Christian Science Monitor, 2 May 1996, p. 12
Marilyn Gardner

In her 1985 book "The Divorce Revolution" Lenore Weitzman gave the statistical estimate that a year after divorce, women's standard of living declines by 73%; while men's improves by 42%. These statistics were widely quoted by policy makers, reporters, and in journal articles. They have been cited in at least 24 state appellate and supreme court decisions and once by the United States Supreme Court.

The results seemed too striking to Richard Peterson who re-analyzed the same data using the same methodology and found less striking results. His analysis found that women's standard of living one year after divorce went down 27% and men's went up 10%. His findings will be published in the June issue of the American Sociological Review and are in line with other national studies on the issue.

Gardner pointed out that even if there had not been a mistake, there should have been some concern about the influence Weitzman's statistics had since her sample was only 228 individuals, all of whom received a divorce in Los Angeles.

DISCUSSION QUESTION:

How do you think they estimate the standard of living of a women before divorce?
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Are U.S. men less fertile? Latest research says no.
The New York Times, 29 April, 1996, A14
Gina Kolata

In a previous Chance News (5.04) we discussed articles suggesting that the sperm count of men is decreasing dangerously. Now two studies in the United States have found that the average sperm count for men in certain cities may be greater than it was 20 years ago. The studies have also shown that the average sperm count varies significantly in U.S. cities. New York consistently has the highest sperm count which is more than 50 percent higher than the sperm counts for men in Los Angeles. These differences in cities are considered very surprising by the experts who have no explanation why this should be.

The U.S. studies are reported in the May issue of "Fertility and Sterility". One of the studies was carried out by Dr. Harry Fisch and colleagues at Columbia College. They examined data from semen analyses of 1,283 men who donated semen to sperm banks before having vasectomies. The sperm banks were in New York, Los Angeles and Roseville, Minn. The average sperm count for New York City was 131.5 million sperm per milliliter of semen, in Minnesota it was 110.8, and in Los Angeles 72.7.

In a second paper Dr. C. Alvin Paulsen from the University of Washington collected semen samples, from 1972 to 1993, from 510 healthy Seattle men. This study found no decline in sperm counts or semen quality during the period of the study. The sperm counts went from 46.5 million sperm per milliliter of semen in 1972 to 52 million in 1993.

In a third paper in the same issue of the journal, Fisch and his colleagues consider global variations to show how previous researchers might have been led to believe that counts were declining. Recall that a major meta-study had concluded that sperm counts were declining and the authors of this meta-study suggested was the result of environmental pollution. Fisch and his colleagues observed that most of the early studies involved New York men where the sperm counts are now known to be unusually high while most of the recent studies involve men from the developing countries where sperm counts tend to be lower, again for unknown reasons. Dr. Fisch has said: "I can explain all the decline in sperm count by geographical variability".

DISCUSSION QUESTIONS:

(1) Can you conclude from the two studies that the sperm counts in Seattle are lower even than Los Angeles? If not, why not?

(2) Do you think these studies settle the issue of declining sperm counts?
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USA Today, 25 April 1996, 3B

Pensions % Investments, 25 Dec. 1995, p. 31
Marlene Gilvant Star

The long-term case for equities.
Journal of Portfolio Management (1995) Vol. 21, No. 1, p. 15
Paul A. Samuelson

Kadlec reminds us that conventional wisdom about investments says that the risk of holding stocks is less in the long run than in the short run. Presumably that is why we are advised when young to put a lot of our retirement funds into stocks but, as we near retirement, advised to put a greater proportion in bonds.

He then says: "Now, a small but noteworthy group of academics is airing a sobering concept: History be damned, the risk of owning stocks goes up -- not down -- with time." He gives no reference for where this airing is taking place but I think the article is based on a forum that took place November 30, 1995 in Cambridge, Mass. This forum was described in the article by Star.

The forum consisted of a debate between Jeremey Siegel of Wharton, who believes that stocks are the best investment for long term growth, and Zvi Bodie of Harvard, who believes that this theory is fundamentally flawed. The moderator was Paul Samuelson who apparently gave up attempts to remain neutral and came down on the side of Bodie.

Siegel's arguments are based upon looking at stock performance over long periods. He presented data from three periods: 1926 to the present, 1871 to 1925, and 1803 to 1871. The real return was around 6.5% in all cases, and this is considerably better than bonds do.

Bodie asks, if stocks really do become less risky the longer the holding, why isn't the cost of portfolio insurance for equities less over longer periods, for every dollar invested?

Bodie and Samuelson are both worried about making statistical estimates based upon past histories when we really have only one long sample in a stochastic process in which different samples over the same period of time can look very different. They observe that we cannot even look at long samples from other stock markets, since most of them do not have the same long uninterrupted history that ours does.

In his article in the "Journal of Portfolio Management", Samuelson writes:

The Law of Large Numbers does not reduce riskiness toward zero as the investing period extends toward infinity. If you are maximizing the expected logarithms or expected square root of your wealth at retirement, you will hold exactly the same portfolio proportions at every age. Thus, there cannot be any sure-thing syllogism putting long-term investors into more equity tolerance than short-term investors. (Yes, when you are young, stocks may have more time to recover from crashes, but they also have more time to encounter crashes!)

DISCUSSION QUESTION:

How might Siegel try to convince you that the proportion of stocks in your retirement portfolio should depend on your age? How might Samuelson try to convince you that, if you have a logarithmic utility function, you should have the same portfolio proportions at any age?
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Study details CUNY successes from open-admissions policy.
The New York Times, 7 May 1996, A1
Karen W. Arenson

A new study has found that the open-admissions policy, that 25 years ago transformed the City University of New York by guaranteeing entry to almost all New York City high school graduates, was far more successful in educating needy students than earlier research suggested. Of the 100,000 who entered CUNY's two-and four-year colleges from 1970-1972, about 48,000 would not have qualified if the policy had stayed the same.

David E. Lavin, a professor at the university's Graduate School and at Lehman College, and David Hyllegard, director of institutional research at Manhattan Community College, originally had a sample of 35,000 students which they had studied in depth. They followed up on about 5,000 students, 12 to 14 years after they first entered the university as members of the first 3 open-admissions classes.

Earlier studies showed high dropout rates among open-admissions students, but Lavin and Hyllegard found that, given time, many of them did eventually graduate. Many minority students were usually poorer than other students and often worked full time while they went to college and so took much longer than 4 years to graduate.

Detractors argue that lax standards of admissions are detrimental to under-prepared students because their lack of preparation holds them back in remedial classes. Others insist that the students' high school preparation was so poor that the college was forced to lower standards and stoop to their level. Lavin and Hyllegard admit that some students are held back by poor preparation and that a large part of the university is dedicated to remedial classes. They counter, however, that the education being offered is still sound and that many students do succeed, not drop out, as earlier studies have asserted.

The study estimates that 5,000 eventually went on to receive master's degrees or doctorates. In addition, Lavin and Hyllegard's data indicate that the educational opportunity resulted in direct benefits in the job market and improved the economic base of New York City and New York State. The study estimated that, during one year in the 1980s, graduates admitted under open-admissions earned a total of almost \$67 million more than they would have if the university's program had not been installed. Their additional lifetime earnings were estimated at about \$2 billion.

The benefits of open-admissions flowed to both minority and white communities. The number of minority freshmen jumped to more than 8,000 in 1970 from fewer than 1,700 in 1969, and the number of whites went from 16,000 in 1969 to almost 26,000 from 1970 to 1972.

DISCUSSION QUESTION:

There was no discussion in this article about how and when the original sample of 35,000 was obtained and how the 5000 to follow up were chosen and which 5,000 went on to receive graduate degrees. What additional information would you need to have to make sense out of all this?
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Unconventional wisdom: New facts and hot stats from the social sciences.
The Washington Post, 5 May 1996, C5
Richard Morin

Crystal ball gazing and other political games.

With the presidential race shaping up and the elections a few months away, political analysts have been crunching numbers trying to predict who the winner will be in November. Some polls say Bill Clinton leads Bob Dole by 20 percentage points, but predict a much closer race. How do these prognosticators come by their numbers? Here, a brief overview:

1) Michael Lewis-Beck of the University of Iowa uses a mathematical model which includes presidential job approval rating, changes in the GNP, and Gallup survey questions about which party would most likely bring peace and prosperity. He has 50.9 percent for Clinton and 49.1 percent for Dole at this time.

2) Robert Erikson and Christopher Wlezien of the University of Houston use presidential approval and cumulative income growth over a president's term in their election model. Their current forecast is 53 percent for Clinton and 47 percent for Dole.

3) Alan Abramowitz of Emory University uses a model that includes the president's approval rating, GDP growth during the first 6 months of the year, and a "time for change" variable which factors in how long the incumbent party has been in the White House. Current data in this model produced 55 percent for Clinton and 45 percent for Dole.

4) Allan J. Lichtman of The American University in Washington
D.C., uses a yes/no test of 13 questions which would determine the winner of every election since 1860. When the answer to 8 or more of his questions is yes, the incumbent president has won. 6 or more no answers indicate that the incumbent president will lose. The answer to his questions for the current election gives 6 yes, 3 possible yes and 4 no answers, so, Lictiman says it is not "in the bag" for Clinton yet.

DISCUSSION QUESTIONS:

(1) Why do you think there is such a disparity between the polls and the mathematical models? Which do you think is more likely to be correct?

(2) Morin also mentions some of the "coincidence models" such as: there have been only 5 left-handed presidents including Clinton and none have won re-election; in 9 of the 11 elections when hemlines rose going into the election, the Democrat won; a National League victory in the World series meant a Democrat victory. How do Clinton's chances look for each of these criteria?

(3) The latest price for a Clinton share on the Iowa Electronic Market was .592 for the Democrat nominee and .378 for the Republican nominee. This is a winner take-all-market. You get \$1 back if your candidate wins and nothing otherwise. If you believe the polls, which candidate should you pick? What would you pick if you believe the computer models? Finally, which would you pick?
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Unconventional Wisdom: New facts and hot stats from the social sciences.
The Washington Post, 19 May 1996, C7
Richard Morin

In a recent segment of ABC's "20/20", Lynn Sherr reported that women long for bigger breasts and that this preoccupation has drained them of self-esteem. In addition, men supposedly value the bosom over all body parts.

Sherr's report relied heavily on statistics collected from a mail-in "survey" in "Self" magazine that found that 50% of an unrepresentative group of women said they felt they were inadequate because of their breast size. This report aired on "20/20" despite a contrary national survey conducted by ABC's own polling unit at the request of "20/20", which found that an overwhelming majority of women are satisfied with the breasts they have. More than 9 in 10 said the size of their breasts had no impact on their personalities. 23% said they had wished for a different size, and of that number a little more than 50% said they wished for smaller, not larger, breasts.

On the question of whether men like bigger breasts, Sherr reported that men consider the "face first, breasts come a close second." Again a deviation from the ABC poll. 57% of men interviewed said they considered the face as the most important part when assessing physical appearance, while only 8% valued breasts.

Lock 'em Up.

Harvard economist Richard Freeman reports in the latest issue of Harvard Magazine that the U.S. has proportionally more people in jail than any other nation on earth. More than 1.3 million men were behind bars in 1993. That means more than 5 in every 1,000 residents were doing time. In the U.K., Germany, and France, fewer than 1 in a 1,000 residents are incarcerated. Freeman attributes this large number to the "reduced demand for less-skilled male workers" who are thrown in jail when they commit a crime to survive.

DISCUSSION QUESTION:

What other reasons might explain the differences between the U.S and European countries in the proportion of people in jail?
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Statistics training called a plus for all students.
Chicago Sun-Times, 7 May 1996, p. 3
Thomas Frisbie

Warren Hawley, chairman of the mathematics department at the Latin School in Chicago, believes that 100% of all students going to college can benefit from a general course in statistics. Concepts such as percentiles, percentages, ranking, and fundamental probabilities are all applicable to daily life.

Some current applications for everyday statistics skills are election analyses, standardized tests, gambling (such as the lottery and whether to play or not to play), and consumer issues (such as advertisements that cite statistics but not within the proper context).

Hawley emphasizes that not only is statistics relevant, it has also become much easier to study since a lot of the number-crunching can be done electronically. Thus, more time can be spent on the theories behind the numbers and the ramifications of such figures. Today no more than 10% of college students take a statistics course.

DISCUSSION QUESTION:

Do you agree that theories are easier than number-crunching? What did Hawley really mean here?
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Heart patients need not fear sex, study finds.
The New York Times, 8 May 1996, C10
Jane E. Brody

There has been anecdotal evidence that the risk of a heart attack is increased when you are having sex. Dr. James E. Muller of Harvard Medical School and Boston-based colleagues report in the current "Journal of the American Medical Association" on a study they say will put these fears to rest. The study involved 858 men who survived a heart attack and had been sexually active during the previous year. The researchers found that the risk of a heart attack was increased only during the two-hour period after sexual activity. They estimated the risk of a heart attack during this two-hour period was about two in a million as compared to one in a million for an arbitrary two-hour period.

They also found that heart patients who regularly did moderately strenuous or "conditioning" exercise had little or no added risk from sexual activity.

DISCUSSION QUESTION:

Of the 858 only 27 reported sexual activity within two hours of experiencing the first symptoms of a heart attack. How do think the estimate of 2 in a million was obtained?
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Support for use of DNA profiles as forensic evidence.
Lancet (1996) Vol. 347, No. 11, p. 1321
Paul M. Rowe

The National Research Council convened a second committee to assess the role of DNA fingerprinting in the courts. The first committee had agreed that there were some unsolved statistical problems with the estimation of the probability of a match in DNA fingerprints and recommended a "ceiling principle" that was meant to give conservative estimates. This principle was often misinterpreted in the courts and led to considerable confusion and, at times, to DNA evidence being thrown out.

The new committee reported that this principle can now be abandoned because data base of allele frequencies in populations and sub-populations have grown to the point where reliable estimates will usually yield unique patterns (except for the case of identical twins).

The report finds no meaningful way to estimate the probability of a laboratory error and says that such procedural error calculations should never be combined with the theoretical probability of a true match. The report recommends that whenever possible forensic samples should be divided into two parts, and at the earliest practical stage, to give the possibility of independent analyses.

The report also recommends that behavioral research be carried out to determine the best way to present data on population genetics to juries, lawyers, and judges. Rowe remarks: "Judging from the baffled faces of people at the press conference held for the release of the report, public understanding of 'probability speak' will take time."
DISCUSSION QUESTIONS: (1) Do you think the committee really have it right this time? Will this report end the controversy over the use of DNA fingerprinting in the courts? (2) The report says that in the not too distant future DNA fingerprinting will be able to make unique identification (except for identical twins). Does this sound reasonable? <<<========<<

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Semtex error could free 12 IRA men; Ministers order review of evidence.
Independent, 15 May 1996, p.1
Heather Mills

The British government revealed that at least 12 IRA prisoners -- one third of all those jailed in the past 6 years -- may have been wrongly convicted because of contamination in a forensic science laboratory.

Two months ago it was accidentally discovered that, in a centrifuge machine used in almost all forensic tests on terrorist bombings since 1989, neither the machine, which spins the dirt out of samples for testing, nor its parts had been tested or changed between experiments -- despite what are supposed to be routine weekly contaminations checks at the laboratory.

DISCUSSION QUESTION:

The article states that: "The forensic tests always included a control sample known not to contain any explosives. But Dr. Marhall (the head of the lab) admits that, if a control sample tested positive, that test would be abandoned." What was the control for?
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In smoking, study sees risk of cancer of the breast.
The New York Times, 5 May 1996, Section 1, p. 31
Jane E. Brody

This article describes recent research in Switzerland that purports to show that both active and passive tobacco smoke can significantly increase a women's risk of developing breast cancer. Previous studies (21 in number) showed no relation, or at most a weak positive relation, to breast cancer. Previous studies on passive smoking, while fewer in number, had more consistently shown a positive relation.

This study, carried out in Switzerland, was a case control study with 244 women recently diagnosed to have breast cancer as cases and 1032 women free of breast cancer as controls. The study found that, for women who smoked less than half a pack a day, the breast cancer risk was doubled, for those who smoked 10 to 19 cigarettes a day, the risk was 2.7 times greater, and, for those who smoked a pack or more a day, the risk was 4.6 times greater. The study also found a three-fold increased risk of breast cancer among non-smoking women who were exposed to tobacco smoke either at home or at work, but this risk did not depend upon the amount of exposure.

The authors of the study attribute the failure of other studies to detect a relationship between smoking and breast cancer to the fact that these studies compared smokers and non-smokers where the non-smokers group included passive smokers.

Other experts found it hard to believe the results of this study. One observed that the study found the risk of passive smoking for breast cancer higher than that for lung cancer and found that hard to believe.

The original article is in the "American Journal of Epidemiology", Vol. 143. No 9, pp. 918-927. The authors have an interesting discussion of how they controlled for other risk factors and for possible biases inherent in case-control studies. They also explain how some of their more surprising results could be correct. Two such surprising results were: the risk factor for passive smokers was of the same order of magnitude as for smokers and the odds ratio increased with increased smoking but not with increased passive smoke exposure.

DISCUSSION QUESTIONS:

(1) Does the author's explanation for why previous results do not agree with their results seem convincing to you?

(2) How are odds ratios computed for a case control study?
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In trying to keep the length down we have had to omit a lot of interesting medical studies reported during this period. Two particularly interesting examples we have omitted are:

Boston Gobe, 22 May, 1996, p. 1
Peter J. Howe

and

How treadmill gets you there faster; Its calorie-burning efficiency is lauded.
Boston Globe, 8 May, 1996, p. 12
Richard A. Knox

You can find the full text of these articles on the web version of Chance News.
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