CHANCE News 3.14          
              (22 Sept to 15 Oct 1994)  

Prepared by J. Laurie Snell, with help from Jeanne  
Albert, William Peterson and Fuxing Hou, as part of the 
CHANCE Course Project supported by the National Science 

Please send comments and suggestions for articles to 

Back issues of Chance News and other materials for 
teaching a CHANCE course are available from the 
Chance Web Data Base in the Multimedia Online 
Document Library at the Geometry Center
(http://geom.umn.edu/) or from the Geometry 
Center Gopher (geom.umn.edu) in Geometry Center

    "I just don't think humankind needs to 
     hear how much smarter this one is than 
     that one. I just don't have that much 
     faith in statistics" 
                             Kaye Postman



>>>>>==========>> FROM OUR READERS Robert Griffin sent us some comments on the following article: Single-parent home: what will result? The Milwaukee Journal, 18 Sept. 1994, p. 1. Associated Press

The Census Bureau reports that 27% of all children are living with a single parent, up from 20% in 1980 and 12% in 1970. "Single parent" means no spouse in house. This article provides interesting but conflicting expert opinion on the consequences of this increase to the children and to society. Robert Griffin wrote a letter to the editor pointing out some confusing graphs and statistics in the article. For example, a graph labeled "marital trends" had two curves: one labeled "never-married parents" that increased from 4.2% in 1960 to 35% in 1993 and the other labeled "divorced parents" that increased from 23% in 1960 to 37.1% in 1993. There was no further explanation what these were percentages of. Griffin pointed out that the obvious interpretations of this graph did not make much sense. His letter led the editor to publish the clarification that the two curves represented the proportions of children living with single parents in the two categories. Thus, what the graph really tell us is that, in 1960, 73% of the children living with a single parent were living with a parent who had been married but not divorced and in 1993 this proportion was down to about 28%. This makes the graph rather irrevelent to the statistics about the total number of children living with single parents discussed in the text, but does provide dramatic chance and an interesting result in its own right. In a letter to Griffin the editor commented: As the person in charge of the national/world stories for that Sunday's paper, I approached this material - as we do all statistics-based stories and graphics, within the available time- as a potential minefield. Despite my caution, it appears we stepped on a few mines this time. DISCUSSION QUESTIONS: (1) Can you give an explanation for the dramatic change exhibited in the graph. (2) A graphical display was headed "Single parent families in largest cities" and gave a percentage of 37% for Milwaukee. This figure was mentioned later in the article. Griffin remarked that this display, which made the local situation seem higher than the national average of 27% quoted earlier, was misleading. Why was it misleading? <<<========<<

>>>>>==========>> The Bell Curve; Intelligence and Class Structure in American Life. By Richard J. Herrnstein and Charles Murray. Illustrated. 845 pp. New York The Free Press. $30.

There have been many reviews of this book and I have read a lot of them. I am sure that most of you have also read at least one and know that this book attempts to show that I.Q. is a much better predictor of success and failure in life than most people are willing to admit and that public policy should take this into account. This book cannot be assessed by reviews, and we need to read it to judge the strength of the statistical arguments presented. I will do so. I invite others who read the book to send me their comments. I will then combine our efforts to try to say something more intelligent about the book in the next Chance News. DISCUSSION QUESTIONS: (1) What do you think is meant by a person's I.Q.? (2) What kind of evidence would be needed to show that low I.Q. was a better predictor of criminal behavior than, say, poverty? (3) What kind of evidence would be needed to show that I.Q. is at least partly genetically determined? <<<========<<

>>>>>==========>> So, now we know what Americans do in bed. So? The New York Times, 9 Oct 1994, Section 4 Page 3 Tamar Lewin

The sex survey whose results were announced this week started as a government supported survey with the title "Social and Behavioral Aspects of Fertility-Related Behavior." It was carefully chosen to avoid scrutiny by Senator Helms and others. This failed and the government withdrew support for the survey. However, it was carried out by the National Opinion Research Center at the University of Chicago supported by private funds. Unlike previous sex studies, whose subjects were self selected, this study was carried out by in-person interviews with a random sample of 3,432 men and women aged 18 to 59. The results will be published in a book "Sex in American" (Little, Brown and Co. with Gina Kolata as a co-author with the investigators.) The survey showed a marked contrast between the sex that most people have compared to T.V. and movie images of sexual behavior. American women typically have two sexual partners during their life and men about six. 78% of the men and 86% of women say they have been faithful to their spouses while married. The study provides more evidence that the 10% estimate for homosexuality is not correct. Only 2.8% of men and 1.4% of women identified themselves as "gay,". However, in the 12 largest cities this was 9% for men and 3% for women. There was a large gap between the percentage (22.8) of the women who said they had been forced to do something sexually they did not want to and the percentage (2.8) of the men who said they ever forced women into a sexual act. One of the purposes of the study was to help in the strategies for combatting AIDS. In this connection the study suggested that people had sex pretty much with those they resemble in race, religion, age, and socioeconomic level, suggesting that AIDS would be slow in moving from groups where it is prevalent to groups where it is not. DISCUSSION QUESTIONS: (1) As is usual in such surveys, men seem to have a lot more sexual partners than women. How is this possible? (2) How truthful do you think people are in describing their sex life? (3) Do you think the fact that 78% of the men and 85% of the women claim that they had always been faithful is believable if one-third to one-half of recent marriages are expected to end in divorce? <<<========<<

>>>>>==========>> Here are two articles from our local newspaper. Malpractice award against Hitchcock Clinic reversed. Valley News, 22 Sept 1994 Norma Love

Here is the article's description of the history of the case: Judy Bronson visited her local doctor in November 1985 complaining of shortness of breath and an irregular heartbeat. After an X-ray, the doctor discovered a large, irregular mass in her chest and referred her to the clinic for diagnosis and a treatment biopsy was performed on the mass on Dec. 3, 1985, but while performing the biopsy, the surgeon accidentally cut an artery. The cut artery required emergency surgery to prevent her from bleeding to death. On Feb. 11, 1986, a team of cancer specialists reviewed the case and believed she may be suffering from a form of Lymphoma, but wanted another tissue sample to make a firm diagnosis. The surgeon who did the biopsy recommended waiting and monitoring her condition. During the next three months, her personal doctor monitored her health. In May, she returned to the clinic because her condition had worsened. On May 14, a second biopsy was done and treatment begun immediately for Hodgkins disease, a cancer of the lymph nodes. Judy Bronson died of Hodgkins disease in January 1988. During the civil trial following this, an expert witness testified that Judy Bronson had a 75% chance of survival in November 1985 when she first sought help, but only a 50% chance in May 1986 when a second biopsy was done. The New Hampshire Supreme Court has now decided to overturn the award made in the previous trial commenting: Such evidence may form the underlying basis for an opinion on causation, but bare percentages alone are not sufficient to establish causation. The plaintiff must produce expert medical testimony that the defendant's negligence caused the patient's injury or loss. DISCUSSION QUESTIONS: 1. The clinic argued that Roland Bronson's expert witness showed Judy Bronson was equally likely to have died from the pre-existing cancer as from a negligent delay in diagnosis. Where does the "equally likely" come from? 2. The court ruled that statistical evidence "may form the underlying basis for an opinion on causation, but bare percentages alone are not sufficient to establish causation." Do you agree? 3. You are about to play a game of Russian Roulette. Two of the chambers of your 8-shooter are loaded. Unbeknownst to you, your roommate slips bullets into two more of the chambers. You die, and your family sues your roommate for wrongful death. The court rules in favor of your roommate, arguing that bare percentages alone are not sufficient to establish causation. How do you feel about this? 4. The spokesperson for the clinic said that "the Supreme Court decision reaffirms what we have always understood the medical malpractice statute to be." If this were your hospital how would you feel about this? <<<========<<

>>>>>==========>> College tries to make the grade mean something. Valley News, 15 October, 1994 Ellen Swain

As we have reported, Dartmouth (starting with this years' class) will put on a student's transcript, next to the student's grade for a course, the median grade for the course. This article provides student and faculty reaction at Dartmouth to this change as well as the opinion of people at other graduate schools, about how useful they will find this change. One student says: "I think it's a bad idea, because, unfortunately, it may increase competitiveness among students to the point where if you know that the average grade is an A minus or a B plus, you're going to try that much harder to get above the median in that class." Those involved in graduate admission seemed to think the additional information would be helpful to them. The director of career services at Dartmouth expects corporate recruiters to welcome the idea, remarking "Recruiters are always trying to quantify things." <<<========<<

>>>>>==========>> Study uncovers link of cancer to birth drugs. The New York Times, 22 September 1994, Pg. 22 Lawrence K. Altman

This article is a report of a study published in the Sept. 22 issue of "The New England Journal of Medicine". According to the article, women who are treated with infertility drugs have a risk of developing ovarian cancer that is 2.5 times that of women in the general population. The study examined a group of 3,837 women who had sought treatment for infertility between 1974 and 1986. Mr. Altman reports that "11 developed ovarian cancer, while the number expected from statistical calculations was 4.4." Curiously, Mr. Altman does not mention that some of the 3,837 women in the study did not take fertility drugs and that, in fact, two of the women with ovarian cancer were in this category. (See the article "Fertility drugs tied to ovarian tumors; Medical Notebook", Boston Globe, below, for additional discussion.) To put the 2.5 increased risk in perspective, the article points out that heavy smokers have a risk of lung cancer that is 10 times that of the general population. In addition, ovarian cancer is a rare disease, with a lifetime risk of 1.8 percent. By contrast, breast cancer has a lifetime risk of 12 percent. DISCUSSION QUESTIONS: 1. What do you think a "lifetime risk of 1.8 percent" means? How could you use this figure to determine the risk of developing ovarian cancer in the next 10 years for a woman who is 20 years old? How about 30 years old? 60 years old? 2. The article states that the study was "limited, primarily, by the small number of women with ovarian cancer." Explain. <<<========<<

>>>>>==========>> Fertility drugs tied to ovarian tumors; Medical Notebook The Boston Globe, 22 September 1994, Pg. 3 Judy Foreman

This brief article contains information that complements the Times article. For example, 9 of the 11 women who had ovarian tumors took the fertility drug clomiphene, which corresponds to a risk that is 2.3 times that of infertile women who did not take the drug. Moreover, those women who had taken the drug for at least 12 menstrual cycles were at the highest risk, and "women who have been exposed to fertility medications but have no family history of ovarian cancer are not at high risk." DISCUSSION QUESTIONS: 1. Which article provides more useful information for the public? 2. The study in the New England Journal states that there was "no increase in the risk associated with the use of clomiphene for less than 12 menstrual cycles" and that "similar proportions of short-term users (1 to 11 cycles, 50.0 percent) and long-term users (at least 12 cycles, 55.4 percent) became pregnant." Neither article noted these findings. Would you have included these figures? <<<========<<

>>>>>==========>> Avalanche survival chances. Nature, 6 October 1994, p.482 Letter from Martin Burtscher

The author analyzed mountain sports accidents in Austria since 1986. A previous article in Nature concluded that in an avalanche the depth of burial had no direct influence on survival chances. This author's data contradicts this assertion. Burtscher recorded the rescue outcome, burial time, and depth of burial for the 774 people caught in avalanches between 1986 and 1992. He did a stepwise logistic regression with rescue outcome as the dependent variable and burial time and depth of burial as independent variables. Burial time entered the model as step 1 and depth of burial as step 2, and its presence made significant improvement. DISCUSSION QUESTION: The author concludes his letter with the remark: Hence, when an avalanche begins, all measures helping to keep the skier on the surface increase the chance of survival. What measures do you think he has in mind? Would you have needed a study to suggest this advice? <<<========<<

>>>>>==========>> Is there logic in the placebo? The Lancet, 1 Oct 1994, p. 925 Peter Gotzche

This is the first of a series of articles on placebo. The author begins by trying to find a satisfactory definition of a placebo and a placebo effect. He concludes that this is not possible. He remarks that this should not discourage us from using them, any more than we should not use a chair just because we could not define a chair. Gotzche concludes that the present focus of interest in placebos should "switch from whether or not an intervention is a placebo, towards the magnitude of the effect and the choice of effect variable". He argues that untreated control groups as well as placebo-treated groups are needed in clinical trials. "Without them we cannot conclude, as is current practice, that an intervention is ineffective if no better than placebo." DISCUSSION QUESTIONS: (1) Why does the author conclude that, without untreated groups, we cannot conclude that an intervention is ineffective if no better than placebo? Do you agree? (2) What is wrong with the following definitions of placebo effect and placebo: The placebo effect is the difference in outcome between a placebo-treated group and an untreated control group in an unbiased experiment. Placebo is an intervention which is believed to lack a specific effect--i.e., an effect for which an empirically supported theory exists for its mechanism of action--on the condition in question, but which has been demonstrated to be better than no intervention. <<<========<<

>>>>>==========>> Study on Europe's wage rigidity calls standard labor theories into question. Wall Street Journal, 3 Oct 1994 Dana Milbank

Europe has had recently a higher unemployment rate than the United States and Japan. A theory used to explain this says that European wages are more rigid than those in the United State and Japan, in the sense that labor costs remain high even when unemployment rises. This in turn is thought to be caused by the high degree of unionization in Europe and high unemployment benefits. It has led to a style of labor politics (sometimes called the Reagen-Thatcher style) that recommends union busting and reducing unemployment benefits to combat unemployment. This theory has been challenged in a study carried out by two economists, David Blanchflower of Dartmouth College and Andrew Oswald of the London School of Economics. Using government wage and employment data for millions of workers in 15 countries, they showed that wage flexibility showed little variation across the globe. In each country, they found that doubling the local unemployment rate(within a region or industry) is associated with a drop in pay of roughly 10%. The study conflicts with the conclusions of many other groups including major banking interests that presumably were based on theories rather than on studies. The theory contradicted was not clear to me from the article so I asked Blanchflower. Here is his reply: The traditional supply-demand equilibrium that we teach our students says that if wages go up from equilibrium, unemployment increases. That is, higher wages go with higher unemployment with a fixed labor force. Workers in areas of high unemployment have to be compensated for the higher risk of unemployment -- hence wages and unemployment are positively correlated. Our stuff shows the reverse -- that they are negatively correlated with an elasticity of -0.1. Unemployment doubles and wages fall by 10%. It appears to be the same in all time periods and across all 16 of the countries we have looked at! It's as close to an economics law as we have ever seen. <<<========<<

>>>>>==========>> Exercise can reduce risk of breast cancer, study says. The Boston Globe, 21 September 1994, p1. Judy Foreman

A study published in the "Journal of the National Cancer Institute" gives evidence that exercise represents "an independent risk factor" for breast cancer. The study involved 1090 women, ages 40 and above. Of these, 545 were newly diagnosed with breast cancer, and the other 545 controls were cancer-free and otherwise similar in age, etc. Women who had exercised 4 or more hours per week throughout their reproductive years reduced their risk by more than 60% compared to inactive women. Women who exercised only 1 to 3 hours per week still had a 30% reduction in risk. Reseachers believe that cancer risk may be related to the number of menstural cycles a women has during her life in which ovulation occurs. The link is presumably due to hormonal fluctuations associated with ovulation. Other research has shown that adolescents who exercise regularly often have cycles without ovulation. DISCUSSION QUESTIONS: What do you think the term "independent risk factor" means here? How do you think the researchers arrived at the 60% reduction in risk for those who exercised 4 or more hours per week? <<<========<<

>>>>>==========>> Cardiac methods questioned. The Boston Globe, 21 September 1994, p3. Richard A. Kno

A Harvard Medical School study published in the Journal of the American Medical Association reports that doctors treating elderly heart attack victims could reduce their use of the most aggressive treatments by 25% without increasing patients' chances of dying. The analysis was based on examining nearly all of the 65-and-older heart attack victims treated under Medicare in 1987. Care given in the first 24 hours after the attack was found to be the most critical. Later invasive diagnostic tests and coronary 'replumbing' operations were often found to provide no benefit in terms of reduced mortality over the four year period following the attack. The actual statistical analysis uses a technique from economics called "instrumental variables estimation." As described in the article, the idea is to manipulate the data to mimic the random assignment of patients to treatment and control groups. Dr. Thomas Chalmers of the Dartmouth Medical School rejected the new method. He is quoted as saying "I don't believe a word of it. No matter how they manipulate things, they can't make up for the fact that randomized clinical trials are essential." DISCUSSION QUESTION: 1. What is the problem with a randomized control experiment in this context? 2. What do you think Dr.Chalmers has in mind to overcome such objections? <<<========<<

>>>>>==========>> Ask Marilyn. Parade Magazine, 25 September 1994, p21. Marilyn vos Savant

Question: Let's say my friend puts six playing cards face- down on a table. He tells me that exactly two of them are aces. Then I get to pick up two of the cards. Which of the following choices is more likely? (A) That I'll get one or both of the aces (B) That I'll get no aces Marilyn solves the problem by enumerating the C(6,2) = 15 cases for choosing two cards and counting those favorable to given probability 9/15 for (A) and 6/15 for (B). <<<========<<

>>>>>==========>> Sampling errors in political polls. Teaching Statistics, Autumn 1994, pp. 71-73 Zhigniew Kmietowicz

A typical poll result gives three proportions: the proportion p(A) of the voters who favor candidate A, p(B) who favor candidate B and p(U) who are undecided. The newspaper then gives one margin of error. This might lead the reader to believe that this margin of error applies to all three percentages: the leader, say p(A), the candidate who is behind, P(B), and even how much of a lead A has, p(A)-p(B), which is often the most interesting quantity. Since all three of these quantities have different variances it is interesting to see how hard it is to get more accurate information about the margin of error. In this note the author shows that this is quite easy. He also discusses the use of these formulas in determining confidence intervals and for testing hypotheses. DISCUSSION QUESTIONS: (1) Let n be the number of people sampled, P(A), P(B), and P(U) the true proportions of voters who favor A, favor B and undecided respectively. Assume that P(U) = 0. What is the variance of p(A) and of p(A)-p(B). What is the largest these variances can be? (2) Assume now that there are undecided voters in the population you are sampling. Find the variances for p(A), p(B) and p(A) - p(B). <<<========<<

>>>>>==========>> The 1994 campaign: New York governor; deep discontent with Cuomo strengthens Pataki, Poll shows. The New York Times, 5 Oct 1994, A1 Kevin Sack

This is a good time of year to discuss polls, and this is an interesting article to use for this purpose. This poll showed Pataki holding a lead of 44 percent to 41. the article remarks: "The distance between Mr. Pataki and Mr. Cuomo is within the polls' margin of sampling error of plus or minus three percentage points, meaning that either candidate could actually be ahead." The percentages by regions were: New York City Cuomo 66% Pataki 25% Suburbs Cuomo 36% Pataki 47% Upstate Cuomo 34% Pataki 51% showing the need for adjustments by regions. Here is the official description of how the poll was carried out: How the Poll Was Conducted. The latest New York Times/WCBS-TV News Poll of New York State is based on telephone interviews conducted from Thursday to Sunday with 1,552 adults throughout the state. Of these, 1,148 said they were registered to vote. The random sample of telephone numbers was provided by Survey Sampling of Fairfield, Conn. Within each household, one adult was randomly designated as the respondent. The results have been weighted to take into account household size and number of telephone lines at the residence, as well as to adjust for variations relating to region, race, sex, age and education. In addition, results about respondents' intended votes in November have been weighted by the statewide distribution of actual ballots in recent elections from New York City (31 percent), its suburbs (24 percent) and the rest of the state (45 percent). According to statistical theory, in 19 of 20 cases, the results based on such samples will differ by no more than 3 percentage points in either direction from what would have been obtained by seeking out all registered voters in New York State. The potential sampling error for smaller subgroups is larger. For example, results based on residents of New York City would be plus or minus 4 percentage points. In addition to sampling error, the practical difficulties of conducting any opinion survey may introduce error into the poll. Differences in the wording and order of questions, for instance, can lead to somewhat varying results. A New York Daily News/WNBC-TV poll conducted Oct 9-12 by Lou Harris surveyed 805 "probably" voters with a 3.4% margin of error and found Pataki 48% Cuomo 39% Golisano 4% giving Pataki a significant lead. This promises to be an interesting election to follow. DISCUSSION QUESTIONS: What article says that "The distance between Mr. Pataki and Mr. Cuomo is within the polls' margin of sampling error of plus or minus three percentage points, meaning that either candidate could actually be ahead." Is the writer saying anything here? Why do they care how many telephone lines there are coming into a house? How do you think they carry out the adjustments for the different regions: New York City, the suburbs, and rest of the state? !!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!! CHANCE News 3.14 (22 Sept to 15 Oct 1994) !!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!! Please send suggestions to: jlsnell@dartmouth.edu >>>==========>>|<<==========<<< >>>==========>>|<<==========<<<