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CHANCE News 3.10
(10 July to 22 July 1994)
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Prepared by J. Laurie Snell, with help from Jeanne Albert
and William Peterson, as part of the CHANCE Course Project
supported by the National Science Foundation and the New
England Consortium for Undergraduate Science Education.
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 Mosaic at the Geometry Center
Mosaic(http://www.geom.umn.edu/) in their Online Document
Library.
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Statistics - a lot of numbers looking
for an argument. Mrs. W. Kilbride
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IN THIS NEWSLETTER
======================================= OTHER INTERNET SOURCES The new "Journal of Statistical Education" has just produced Volume 2 Number 1. As did Volume 1, it has some great articles. Here is the table of contents: JSE Volume 2 No 1 Table of Contents (Mackisack) What is the Use of Experiments Conducted by Students of Statistics? (Garfield) Beyond Testing and Grading: Using Assessment to Improve Student Learning (Ferris, Hardaway) Teacher 2000: A New Tool for Multimedia Teaching of Introductory Statistics (Eckert) Teaching Hypothesis Testing with Playing Cards: A Demonstration (Maxwell) A Coin-Flipping Exercise to Introduce the P-Value Teaching Bits: A Resource for Teachers of Statistics Datasets and Stories: (Hanley, Shapiro) Sexual Activity and the Lifespan of Male Fruitflies: A Dataset That Gets Attention Datasets and Stories: (McIntyre) Using Cigarette Data for an Introduction to Multiple Regression There are several news groups that discuss statistical problems. These include: sci.stat.edu (This is the edstat-l discussion group.) sci.stat.consult sci.math sci.skeptic The recent discussion on sci.stat.consult on several ways to explain regression to the mean was interesting. The discussion centered around the example of students who receive a high grade on the first exam and then regress to the mean on the second exam. Each writer gives a slightly different way of seeing why regression to the mean occurs for this example. The last writer points out that this example is rather special because the mean and variance of a student's grades are assumed to be the same on the two exams. He discusses the more general situation and also recommends reading Stigler's "History of Statistics" to see how Galton looked at regression to the mean. See "edstat-l discussion of regression on the mean." in the full text of articles on our Gopher or Mosaic. <<<========<<
>>>>>==========>> Sci.math quite often has amusing probability problems. A recent problem was to find the number of different ways you can order a dozen bagels from a mail-order bakery that sells 13 varieties of bagels. Most contributors get the answer Choose(24,12), or about 7.2 million, which is provided by Feller's stars and bars counting argument for the number of ways to put m indistinct objects (the bagels) into n distinct boxes (the varieties). Other ways to look at the problem were provided. For example, Ted Alpers gave this solution: Let Bagel(n,k) be the number of ways to buy n bagels from k varieties. Then (a) Bagel(n,1) =1, (b) Bagel(1,k) = k and (c) Bagel(n,k) = Bagel(n,k-1) + Bagel(n-1,k) (a) and (b) are obvious and (c) follows by considering the two cases: you have no plain bagels or you have at least one plain bagel. These conditions generate the Pascal Triangle rotated 45 degrees, giving the answer Bagel(n,k) = Choose(n+k-1,n-1). <<<========<<
>>>>>==========>> FROM OUR READERS Rich Guilfoyle suggested the following discussion on Public Radio about anti-lock brakes. The changing auto industry - part 3: National Public Radio, 6 July, 1994 Dan Charles.
This is a discussion with W. D. Smith, test driver for General Motors, and Charles Hurley, vice president, Insurance Institute for Highway Safety, on the increased safety brought about by anti-lock brakes. Mr. Smith demonstrates that in a situation where the front wheels are on a wet, slippery surface, the back wheels are on a dry surface, and the brakes must be slammed on, the car will spin around with ordinary brakes but not with anti-lock brakes. Mr. Hurley comments that studies they have carried out have failed to find a reduction in fatal injuries in cars equipped with anti-lock brakes, and the same is true for injury data. They began looking about three years ago and are surprised to have not found the sought-for effect. Hurley suggests that since the situations in which the brakes really make a difference are sufficiently rare, it just does not show up in the statistics presently available. A spokesman for General Motors feels that the drivers may not know how to use the brakes properly. People still tend to pump them which is the wrong thing to do. They might also drive more recklessly because they feel that they have a lot more braking power. While Hurley believes anti-lock brakes are a safety feature, he feels that marketing them as a super brake is irresponsible, and they don't have the safety value of air bags or of just buying a bigger car. He remarks that Insurance companies offer discounts for those who have anti-lock brakes despite the fact that the statistical evidence collected so far fails to support a decrease in accident rates. DISCUSSION QUESTION: What can the Insurance Institute for Highway Safety do to try to solve this mystery? <<<========<<
>>>>>==========>> MORE NEWS ARTICLES The Numbers Game Newsweek Magazine, 25 July, 1994, p56 Jerry Adler
Inspired by the appearance of Chynthia Crossen's and Christina Hoff Summers' recent books, this article discusses the problem of the wide disparity in statistics reported in the press relating to a specific issue. For example, Time Magazine says that there are 4 million American women assaulted by a "domestic partner each year" and Newsweek says that the number of women beaten by "husbands, ex-husbands and boyfriends" was 2 million a year. Estimates of homelessness range from 223,000 to 7 million, etc. The article explains how some of these differences occur. TFor example, the numbers can vary due to different definitions (when should a child be counted as a hungry child?), or because of different estimation methods. Of course, these numbers are usually mentioned by an advocate who chooses the number optimally to make a point. The author feels that such numbers are over emphasized and the real point should be made that, for example, too many women are battered. DISCUSSION QUESTION The author states that researchers at magazines such as Newsweek "by and large consider their job done when they find a number that can be attributed to a credible source." Do you think this is sufficient? If not, what else should they do? <<<========<<
>>>>>==========>> Despite awareness of risks, more in U.S. are getting fat.
New York Times, 17 July, 1994, Sec 1 Page 1 Marian Burros
An ariticle in the July 19 issue of the Journal of the American Medical Association reports the results of the most recent of a series of studies, conducted about once each decade, to determine the relation between diet and health. These are large surveys carried out by interviews of randomly chosen individuals accross the country. One result of the most recent survey is that "the number of overweight adults that had remained stable at about a fourth of the adult population from 1960 through 1980 had suddenly jumped to a third of all adults between 1980 and 1991." The article states that the report adds additional support for health and nutrition professionals who feel that the governement, the medical profession, and the insurance companies should devote more resources to this problem, and in particlar, combat the huge resources that the food industry spends on advertising ($36 billion a year) to entice people to eat. DISCUSSION QUESTION: This article states that "for purposes of the study, obesity was defined as being 20 percent or more above a person's desireable weight." That is about 25 pounds for an average (5-feet 4-inch) woman, and 30 pounds for an average (5-feet 10-inch) man. The Guardian article states that obesity is determined by a person's body-mass-index, which is your weight divided by the square of your height. If the body-mass-index is used, why do you square the height? Does this make overweight independent of height? <<<========<<
>>>>>==========>> Women versus the biologists: an exchange The New York Review of Books, 14 July, 1994 pg. 54 C. Davison Ankney, R.C. Lewontin
Davison Ankney, a professor of zoology at the University of Western Ontario, is responding in this letter to an article by Lewontin entitled "Women Versus the Biologists" that appeared in the New York Review on 7 April, 1994. The article itself is a fascinating discussion and review of seven books, each authored or co-authored by Ruth Hubbard, about whom Lewontin says: "No one has been a more tireless and influential critic of the biological theory of women's inequality." Ankney's letter is in response to Lewontin's review of the book "The Politics of Women's Biology", which, as Lewontin writes, "discusses the history of claims for a biologically determined cognitive difference between the sexes." The passage in Lewontin's article which seems to be the basis for Ankney's letter reads: Women's brains have been claimed to be smaller than men's, although actual measurement shows them to be a bit larger in proportion to body size, and, anyway, no one has ever found a correlation between brain size and human cognitive abilities. Ankney states that both of these assertions are "patently false", and describes his own 1992 study of 1,261 adults which he claims "showed, unequivocally, that after statistically controlling for differences in body size, men's brains average about 100 grams (8 percent) heavier than those of women." Ankney also insists there is in fact a positive correlation (+0.2) between head size (+0.4 if brain volume is used), and various cognitive abilities, although he admits that these relations have been found independently in men and women, and that while "women have proportionately smaller brains than do men, [they] apparently have the same general intelligence test scores." Lewontin in turn responds to Ankney in his own letter, where he claims that Ankney's paper was a re-analysis, without access to the original data, of a study which found that after body size adjustment there was no consistent difference in brain size between the sexes. He then explains why he thinks Ankney erred: instead of correcting for body size in determining each subject's brain size and then averaging all these corrected values, Ankney apparently favored taking "ratios of group averages". Lewontin also points out that it is by no means clear what a correct measure of "body size" should be. DISCUSSION QUESTIONS: 1. Lewontin tries to make a distinction between 1) first determining brain size relative to body size in each subject and then averaging the resulting brain to body size ratios, and 2) first averaging brain sizes, and then correcting for (presumably the average) body size. How do you think these two methods of analysis differ? Which do you think yields a better description of "average brain size"? 2. Lewontin criticizes a study on the connection between brain size and function cited by Ankney for using a small, "non representative" sample. He claims that the adults in the sample had an average IQ score of 118, while in the general population only one person in seven has a score above 116. Why do you think he says that such a study "cannot be taken too seriously"? <<<========<<
>>>>>==========>> The new mythology. The National Review, June 27, 1994 Christina Hoff Summers
This article is adapted from Summers' book, Who Stole Feminism?, Simon and Schuster 1994. Summers begins by listing some "alarming" statistics which she claims have been propagated by the press,(especially women), but which are nevertheless untrue: 150,000 girls die of anorexia each year! 40% more women are battered on Super Bowl Sunday! Women get paid 59 cents on the dollar! She sums up, "When feminists quote statistics, reach for your common sense." The majority of the article is spent debunking these claims. Summers describes how she traces down the "source" of the incorrect statistic and attempts to explain how the apparently false information could end up being spread throughout the media. For example, she writes that "on November 4, 1992, Deborah Louis, President of the National Women's Studies Association, sent a message to the Women's Studies Electronic Bulletin Board: 'According to [the] last March of Dimes report, domestic violence (vs. pregnant women) is now responsible for more birth defects than all other causes combined.'" She then recounts how she called the March of Dimes (who "denied any knowledge" of such a report), along with several journalists who had used the information in their own newspaper articles. Eventually, the incorrect information is traced back to a misunderstanding of a remark made by a child-care specialist describing March of Dimes research. Summers writes that according to that research, the "truth" is that "more women are screened for birth defects than are ever screened for domestic battery," not that battery causes birth defects. (See also: Birth defects and the environment in this issue of Chance News.) What particularly upsets Summers is that the statistics she quotes were so readily accepted by journalists and other "experts". She asks, "Where were the fact-checkers, the editors, the skeptical journalists?" She doesn't stop there, however. "Why," she asks,"are certain feminists so eager to put men in a bad light?" She then goes on to suggest that much of this "misinformation" is purposely used by "certain feminists" for their own agenda. (For more on this topic, see the review of Cynthia Crossen's book, Tainted Truth: the Manipulation of Fact in America, in the most recent Chance News.) DISCUSSION QUESTION: What do you think of Ms. Summers remark: "When feminists quote statistics, reach for your common sense."? What information would you want to have before deciding on the truth of her implication that feminists are purposely misusing statistics ? <<<========<<
>>>>>==========>> Birth defects and the environment.
U.S. News & World Report, 18 July, 1994, pg. 14
This article is a brief summary of a study recently published in the New England Journal of Medicine on the causes of birth defects. The study, conducted in Norway and based on 22 years of Norwegian birth records, found that women who had one child with a particular birth defect were much more likely (11.6 percent) to have a second child with the same defect, provided the father of the two children was the same. Not surprisingly, if the second child has a different father the increased risk of birth defects is somewhat lower, (7.3 percent). But what did come as a surprise to researchers is that, even with the same father, if the mother moved to a different town the risk dropped even further, to 5.1 percent above the normal risk. Thus "familial birth defects also have a strong non-genetic component that could stem from changes that women make in their workplace, diet, or natural environment when they move." According to an article on the same research from the Chicago Tribune, 11 July, 1994, of the more than 150,000 babies born with birth defects in the United States each year, most of the known causes are specific genetic mutations. However, the cause of most birth defects (about two thirds of all cases) is still a mystery. DISCUSSION QUESTION: How would you design a study to test the environmental causes hypothesis for birth defects? <<<========<<
>>>>>==========>> Air quality survey finds a haze of lingering smoke
The Boston Globe, 17 July 1994, p1. Usha Lee McFarling
This article discusses results of a month-long air quality survey by the Globe, which found that so-called nonsmoking areas often contain alarming levels of smoking byproducts. The data were obtained by using pumps to draw air through filters for 1/2 hour periods, and then subjecting the filters to lab analysis for nicotine content. The key measure here is micrograms of nicotine per cubic foot of air. Some examples: U. Mass. Boston cafeteria smoking section 11.4, nonsmoking section 10.2, border of smoking/nonsmoking sections 14.5; Boston Globe smoking room 16.7, walking past smoking room 1.1, office separated by wall from smoking room 0.3; Fenway Park (during game) 2.3. Worst case: a reading of 70 was obtained in a nonsmoking seat next to the smoking section of an airplane. The conclusions are that smoke carries (not surprisingly) and therefore even designated nonsmoking areas may not offer much relief from exposure. According to Mary Beth Smuts, an indoor pollution specialist at the Boston EPA office: "There are very few environmental contaminants where you have hundreds of millions [of people] exposed. Virtually all of America is exposed to secondhand tobacco smoke. That's a public health issue." DISCUSSION QUESTION: The article contains a data display of measured nicotine levels (micrograms nicotine per cubic meter of air), which includes the following entry: "Considered safe by EPA: 0." Do you think this is realistic? <<<========<<
>>>>>==========>> Risk of indirect smoke is debated: tobacco companies dispute EPA report.
The Boston Globe, 17 July 1994, p1. Usha Lee McFarling
The EPA report says that secondhand smoke each year causes 3000 lung cancer deaths in US nonsmokers, more than 150,000 cases of pneumonia and bronchitis in infants, and aggravates asthma in up to 1 million children. Most of the tobacco companies' criticism has focused on the lung cancer figure. The article asserts that most of the medical community agrees with the EPA. Harvard Medical School epidemiologist Julie Buring is quoted as saying: "There seems to be a very consistent increased risk [from secondhand smoke]." Buring notes, however, that a nonsmoker's risk of getting lung cancer is so low that doubling it still leaves the total risk quite low. But Katherine Hammond, a U. Mass expert on environmental tobacco smoke (and the inventor of the measuring device used in the study described in the preceding article) asks why nonsmokers should want to bear any unnecessary risk when there is no benefit. DISCUSSION QUESTION: Although an individual's increased risk is small, when that risk is applied to the population at large it apparently translates into 3000 deaths a year. Assuming we accept these figures, which do you think is the more appropriate measure for the present public policy debate over proposed smoking bans? <<<========<<
>>>>>==========>> Life in US is becoming less risky, studies say.
The Boston Globe, 18 July 1994, p1. Betsy A. Lehman
According to the article, studies show that life for most Americans is safer than it was a decade ago, this in spite of perceptions people may have based on media coverage of disasters. For example, the Boston press recently had extensive coverage of the death of a local firefighter, and national news had coverage of the deaths of 14 people in Colorado's wildfires. Nevertheless, the decade-long trend in fire-related fatalities is downward. In 1983, 113 firefighters and 5920 civilians were killed by smoke and flames; the corresponding figures for 1992 (latest year available) were 75 and 4730. The article's general assertion that life is getting safer is based on interviews with representatives of federal agencies and officials from private consumer and worker safety groups. All cited improvements in technology, stricter voluntary and government standards, and education campaigns as factors contributing to decreased levels of risk. <<<========<<
>>>>>==========>> Health Sense: What the UV index doesn't tell us.
The Boston Globe, 18 July 1994, p25. Betsy A. Lehman
For Boston and 57 other cities, the National Weather Service report now includes an ultraviolet radiation index. This article cautions that, while the warnings--with their numerical risk ratings from 0 to 15--sound very definitive, the scientific evidence behind the ratings is not as definitive as data on smoking, seat belts, or drinking and driving. The American Cancer Society estimates there will be 32,000 new cases of melanoma this year, with 6900 resulting in death. By contrast, there will be more than five times as many cases of lung cancer, and more than 20 times more lung cancer deaths. Furthermore, while there is a well-established link between smoking and lung cancer [as long as you're not talking to the president of a tobacco company], the data on melanoma are much less well understood. While bad sunburns during childhood are associated with increased incidence of melanoma, it is not known whether adult sun exposure is a risk factor. According to Dr. Robert Stern, a dermatologist at Beth Israel Hospital in Boston, "...the scientific evidence would suggest that, once you're 18 or 20, sun exposure habits are not going to greatly influence your risk of melanoma." For children, "what patterns of exposure, what wavelengths, how much protection would make a difference...I think it's a huge guess." Does this uncertainty mean that warnings should not be issued? Dr. Howard Koh, the director of cancer prevention and control at Boston Univ. Medical Center, views this as a classic health care challenge: At what level of risk, and at what level of proof, should the entire population be told how to behave? DISCUSSION QUESTIONS 1. Do the numbers in the second paragraph above mean that lung cancer is 20 times as deadly as kidney cancer? If not, what do they mean? 2. The article notes that telling people to stay out of the sun might have an impact on otherwise healthy exercise patterns. Should this kind of concern also be part of the debate on warnings? <<<========<<
>>>>>==========>> Finally, here are some less formal notes from our Boston Globe reporter Bill Peterson. The following is from an article you won't find in Nexis/Lexis, but it is characteristic of the type of comment I've been seeing more and more frequently with polls. This particular example comes from our local paper, The Addison County Independent. The article "Addison survey shows split on school issues", by Peter Conlon, reports on a recent mail- in survey on full-day kindergarten conducted by the paper, which generated 23 responses (9 for, 7 against, others suggesting cutting the number of days or scrapping kindergarten altogether to cut costs). The article notes: "The survey, though unscientific, prompted a wide variety of insights from voters." The article goes on to quote some of the respondents. Similar notes I've read in other papers or heard in TV news about polls say: "This is not a scientific poll, but represents a sampling of reader/viewer opinion." My concern is that "represents" sounds too much like "representative" and "sampling" is too close to "random sample." Does anyone else get the feeling they're trying to make the results sound comparable to a statistically designed poll without doing the work? (I also can't help imagining the subtext: Isn't it just the picky old scientists who would quibble with these results? These are the voices of your fellow citizens, after all.) Do you think journalists would write something like "Experience with this polling format suggests that these responses reflect predominantly the views of the most ardentproponents of each position. Extreme caution should be used in trying to infer from these the sentiments of the voting population at large?" !!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!! CHANCE News 3.10 (10 July to 22 July 1994) !!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!! Please send suggestions to: jlsnell@dartmouth.edu
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