CHANCE News 4.08 (5 May 1995 to 7 June 1995)


Prepared by J. Laurie Snell, with help from William Peterson, Fuxing Hou and Ma.Katrina Munoz Dy, as part of the CHANCE Course Project supported by the National Science Foundation. Please send comments and suggestions for articles to jlsnell@dartmouth.edu

Back issues of Chance News and other materials for teaching a CHANCE course are available from the Chance Web Data Base.



79.48% of all statistics are made up on the spot.

John Paulos





Recall from the last Chance News that a reader wrote to Ann Landers to clarify the familiar but misleading statement that 1 in 8 women will get breast cancer. Her column closed with the statistics:

A 20-year-old women has a one-in-2,500 chance of developing breast cancer. At age 30, it's one in 233. At age 40, it's one in 63. At age 50, it's one in 41. At age 60, it's one in 28. At age 70, it's one in 24. At age 80, it's one in 16. And at age 95, it's one in eight.

Some of our readers remarked that it is far from clear what this means. We think we now understand where these odds came from and what they mean.

In 1991 the American Cancer Society announced that women's lifetime odds of getting breast cancer had risen to 1 in 9. The "New York Times" ran a story "Faulty Math Heightens Fears of Breast Cancer" (New York Times 15 March, 1992, Section 4 Page 1) criticizing the use of this statistic. This led to an article in the "Journal of the National Cancer Institute" which tried to give more meaningful statistics (Feuer et al, Journal of the National Cancer Institute. Vol. 85, 11, pp 892-897.)

Feuer and his colleagues argued that lifetime risks are hard to estimate and not too reliable. They felt it more meaningful to talk about the odds that a woman, free of breast cancer, will develop breast cancer, within a given number of years. They did this and provided a table of these odds. From their table you will find that the Ann Landers odds are the odds that a woman, free of breast cancer at a specific age, will get breast cancer in the next ten years. Thus Ann Landers should have written: A 20-year old women, free of breast cancer, has a one-in-2,500 chance of developing breast cancer by age 30 and similarly for the other odds given. With this interpretation all these odds accept the last one (age 95) agree with Feuer. Feuer's tables show that there is only a 1-in-100 chance that a women free of breast cancer at age 95 will develop breast cancer in her lifetime, so the odds of 1 in 8 for age 95 must refer to the famous 1 in 8 lifetime odds.

Feuer gives the lifetime odds of developing breast cancer for a given age and free of breast cancer. These odds are about 1 in 8 until age 60 when they start to decrease significantly.


At each successive decade from the 20's through the 80's, there is a greater chance of developing breast cancer in the next ten year. How can this be consistent with the statement that lifetime odds are about 1 in 8 through age 60?



We had several responses to the problem submitted by George Estabrook. Recall that his question was a variation on the familiar collector's coupon problem and could be described as an urn problem as follows:

In an urn you have balls of n colors with r balls of each color. How many draws do you have to make to be 95% certain of having one of each color? What is the expected number of draws until you get one of each color.

The most complete solutions were given by Roger Pinkham and Charles Grinstead. Using inclusion exclusion they observed that the answer to the first question could be obtained as follows:

Let p(m) be the probability of getting at least one picture of each player in a sample of size m. Then

p(m) = Sum{(-1)^j*C(n,j)*(nr - jr)^[m]/(nr)^[m], j=0..n}

where C(n,j)= n choose j and x^[r] = falling factorial, x(x-1)...(x-r+1).

The expected time to get all the balls for the first time is

(nr + 1)(1 - 1/P) where

P = (1 + 1/(r))(1 + 1/(2r)) ... (1 + 1/(nr)).

Note: The first part is Exercise 12 in Chapter 4 of Feller's book "An Introduction to Probability Theory and its Applications, 3rd Edition, Wiley 1950. Feller comments that for n = 13 and r = 4 it gives the probability a bridge hand has all 13 values and for n = 4 and r = 13 it gives the probability a bridge hand has all four suits.



Here is another contribution from our readers.

Ask Marilyn

Parade Magazine, 11 June, p 15.

Marilyn vos Savant

A reader writes:

I read that a sex survey said the typical male has six sexual partners in his life and the typical female has two. Assuming the typical male is heterosexual, and since the number of males and females is approximately equal, how can this be true?

Marilyn answers the question by first taking the opportunity to describe the difference between the mean, median and mode (a worthy task, no doubt), and then speculates that the solution to the paradox is that the word "typical" is being used to represent the mode, rather than the mean.

In fact, that isn't what's going on here at all. This sex survey data is certainly an interesting data set, which can make for lively discussion in class. We used a similar set of data based on the General Social Survey in our recent book "A Casebook for a First Course in Statistics and Data Analysis" (S. Chatterjee, M.S. Handcock and J.S. Simonoff, John Wiley, 1995). In a study of more than 3500 people, the mean number of lifetime female partners reported by male respondents is 11.7, while the mean number of lifetime male partners reported by females is 3.3. The median values are smaller, but similarly "out of balance," being 4 and 1, respectively. In fact, the modal values are right in line with each other, each being 1.

The observed discrepancy can't be explained by sampling bias, or from a systematic proportional overreporting by men or underreporting by women. In fact, for respondents that report fewer than 10 lifetime partners (which constitutes 82% of the sample), the distributions of lifetime partners reported by men and women are quite similar, suggesting that the noted discrepancy comes mostly from a small proportion of (mostly male) respondents reporting extremely large (and possibly inaccurate) numbers of lifetime partners. This suggests that there may not be a general tendency for "men to boast and women to hide," but rather a specific problem for more active persons. As nearly 80% of those who report 20 or more partners report in round numbers, there's a good chance that part of the problem is just the difficulty of accurate recall (for an interesting and insightful look at these issues, see "Telling tales explain the discrepancy in sexual partner reports," by Martina Morris in Nature 365:437-440 [1993]

Samprit Chatterjee

Mark S. Handcock

Jeffrey S. Simonoff

Note: For additional discussion of this problem see Chance News 3.16 and 4.03. In addition to the Morris reference, Paul Cambell recommended the article:
Einon, D. (1994) "Are Men More Promiscuous than Women?" Ethnology and Sociobiology 15: 131-143.



Milt Eisner suggested the following interesting article:

The Truth: In political Washington, statistics are weapons of war.

Washington Post, 4 June 1995, p W12

Peter Carlson

Carlson watches the T.V. program "Meet the Press" and hears Rep. Kaisch (R-Ohio) defending the Republican tax cut by saying: "Seventy-four percent of all the family tax relief goes to families below $75,000." A few minutes later White House economic advisor Laura Tyson says: "the Republican tax proposal has more than half going to families over $100,000. He wonders how this is possible. Then, while discussing Medicaid, Tyson says: "If you say I'm going to have it grow at 3 percent between now and 2002, that is equivalent to a 38 percent reduction in spending."

The author uses these examples and others to show how politicians on different sides of an issue find statistics, often relating to the same data, to bolster their case. He remarks: "Washington is a place where three government organizations calculate personal income in three different ways, thus producing three conflicting sets of numbers that can be extrapolated to create the conflicting statistics that are used to 'prove' conflicting political points."

The author attempts to settle the question of whether the Republicans' claim that Clinton's 1993 budget legislation produced "the largest tax increase in history" was correct.

He sought out experts and got answers like:

If you ask just in dollars what the tax increase is, then you can indeed make that statement. If you ask in terms of real dollars, constant dollars, then you would find other tax increases that were bigger. If you ask in terms of tax increases as a percent of GNP, you can find other ones that were bigger.

Needless to say the author had no trouble finding lots of other interesting examples of "how politicians can make just about any statistics work for them."


1. How can Tyson cast a 3% growth rate as a reduction?

2. Can the Tyson and Kaisch statements on who's getting tax relief be reconciled as two different calculations with the same set of numbers (as the author has done with the "largest increase in history question")? Or do you think one person is including categories that the other is not?

3. The governor of Massachusetts once proposed raising the state sales tax from 5% to 7%. He said that this was a small increase: only 2%. Comment.



Heart bypasses are safer, study shows. But a few hospitals fall below average.

The New York Times, 7 June 1995, B5

Elizabeth Rosenthal

Ever since 1990 New York State has collected data on the chance of a patient dying after bypass surgery in a particular hospital or with a particular surgeon. The raw number of deaths is adjusted to take into account the fact that some hospitals and surgeons take care of sicker patients than others do.

What is interesting about this article, besides the subheadline "But a few hospitals fall below average", is that a picture is included which shows, for each of the 31 hospitals, the death rate and the 95% confidence intervals. From this you can see that there are two hospitals that are significantly below the statewide rate of 2.71 and 3 that are significantly above this rate.

The state health commissioner comments that the survey based on 1993 data shows that the New York hospitals continue to improve and have lower death rates for by-pass surgery than does any other area of the country. However she cautioned that the latest statistics were not primarily intended to be used by patients in choosing a hospital or a surgeon but instead a tool to motivate or--embarrass--those with poor records to clean up their acts.


(1) How many statistically significant results would you expect in such a study of 31 hospitals even if the hospitals were all comparable? Could each of two hospitals that had statistically statistically significant higher rates reasonably claim they are one of these?

(2) A surgeon who had very high ratings cautioned that "It would be very misleading to publish a list in ascending order." Do you agree?



Breast cancer risk lower than thought by women in their 40's.

Chicago Tribune, 18 May 1995, News section p.7


A group of researchers headed by Dr. William Black at Dartmouth-Hitchcock Medical Center gave a survey to 200 women between 40 and 50 years of age who had had no history of breast cancer. The women were asked to estimate the probability that they will develop breast cancer and the probability of dying of it within 10 years, with and without screening. Their answers were compared to age specific risks given in the literature.

Respondents over-estimated their probability of dying of breast cancer within 10 years by over 20-fold. They over-estimated the risk reduction from screening by six fold and the absolute risk reduction by more than 100 fold.

Dr. Black attributed this, in part, to the famous 1 in 8 lifetime figure being interpreted also to apply to shorter periods. Also, people misinterpret these odds as the odds of dying of breast cancer rather than developing breast cancer.

An interesting aspect of the questionnaire was a series of questions to measure the numeracy of the respondents meant to judge the respondent's ability to estimate probabilities. One of the questions was:

Imagine that we flip a fair coin 1,000 times. Out of 1,000 flips, how many times do you think the coin would come up heads?

You had to say 500 to get it right. The other numeracy questions were consistency checks on answers. For example, was the respondent's answer to the question asking to estimate the probability of dying of breast cancer in the next 20 years greater than or equal to the answer to the question asking for the probability of dying of breast cancer in the next 10 years?

62% passed their numeracy test.


(1) If a coin is tossed 1000 times do you think that heads will turn up heads 500 times?

(2) Why are lifetime risks for breast cancer routinely given but not lifetime risks for heart attacks?



Pseudo-Opinion Polls: SLOP or Useful Data?

Chance Magazine, Spring 1995, pp 16-25

Dan Horvitz, Daniel Koshland, Donald Rubin,
Albert Gollin, Tom Sawyer, and Judith M. Tanur (editor)

"Science Magazine" occasionally runs polls of the form "fax-in-your-answer". The results of such polls have been published in "Science" with the comment that, while they were not statistically randomized polls, they do provide valuable information about how an admittedly self-selected group felt about an issue.

A number of (self-selected) statisticians wrote to the journal to complain that such polls were useless and a bad example for "Science" to set. The editor Dan Koshland wrote an editorial defending the polls. The issue was discussed at the 1994 AAAS meeting by the authors of this article. This article is an account of this discussion. Koshland defended the polls in a rather charming way. For example, he remarks: You might say, "Who are you, a midshipman, to argue with these admirals?" He then tells the following story:

An admiral on a battleship saw a light bearing down on him. He got on the scrambler radio and said "ship ahoy, ship ahoy, on collision course, turn 40 degrees north by northwest. This is Admiral Vanderbild calling. He expected instant action but instead got the reply " This is Midshipman Jones calling. Suggest you turn 40 degrees south by southeast." The admiral replied: "I don't think you understand. This is Admiral Vanderbilt and I am on a battleship and you better start heading 40 degrees north by northwest. The reply was: I am afraid you don't understand. This is Midshipman Jones and I am on a lighthouse, I suggest you turn.

Rubin concludes that such polls are o.k. for internal use but argues that, since editor of "Science" would not publish other researchers results based on such polls, they should not publish the results of their polls of this type. Gollin reviews the history of polling and concludes that such self-selected polls should be discouraged.

Congressman Tom Sawyer describes his own use of such polls and defends their use. It is a lively discussion and in the end the participants agreed to disagree.


1. Koshland points out that Gallup considers a 60% response to a survey a good response and so even these polls might have an element of self-selection. Do you think this is a serious problem for Gallup polls?

2. Most of us participate in self selected polls -- we write our congressmen, sign petitions etc. If we happen also to be statisticians should we feel we are not being true to our profession?

3. One example of the self-selected polls reported in "Science" was the reporting of 200 responses to questions relating to the 1993 special issue on women in "Science". Only 30 men who responded. One result given was the proportion of those responding who felt that there is a female style for doing science. The results were not given by gender. How do you feel about this?



The Law of Averages.

Chance Magazine, Spring 1995, pp 26-31

Ann E. Watkins

I confess that I never really believed people think that a coin owes some heads if it has come up tails several times in a row. After reading this article I am prepared to believe they do. Watkins has found a wonderful collection of newspaper quotes to show the many variations on misconceptions of the law of averages.

She starts with the "it is due" interpretation.

Announcer Chick Hearn notes that Perkins had made the last six out of six free throws and concludes that the law of averages works for the opposition.

Dear Abby: My husband and I just had our eighth child. Another girl. Even the doctor told me that the law of averages were in our favor 100 to 1.

The next version is that things will average out over a moderate length of time.

The law of averages is what baseball is all about. It is the leveling influence of the long season. A 250 hitter may hit 200 or .300 for a given period but he will eventually level off at .250.

Watkins observes that this interpretation is even blessed by the definition of the "law of averages" in the Oxford English Dictionary.

Other interpretations discussed are: everyone or almost everyone is average, rare events should not happen in succession, and if we wait long enough even impossible events can occur.

Editor's note: Bernoulli, the author of the law of large numbers, did not have such a pessimistic view of his readers. Before presenting his proof he writes:

Further, it cannot escape anyone that for judging in this way about any event at all, it is not enough to use one or two trials, but rather a great number of trials is required. And sometimes the stupidest man--by some instinct of nature per se and by no previous instruction (this is truly amazing)--knows for sure that the more observations of this sort that are taken, the less the danger will be of straying from the mark.

At the conclusion of his proof Bernoulli writes:

Whence, finally, this one thing seems to follow: that if observations of all events were to be continued throughout all eternity, everything in the world would be perceived to happen in fixed ratios and according to a constant law of alternation, so that even in the most accidentally and fortuitous occurrences we would be bound to recognize, as it were, a certain necessity and, so to speak, a certain fate.


(1) If heads turns up 100 times in a row what odds would you give for heads turning up on the next toss?

(2) A story in the "New Yorker" related what life was like the day that the law of large numbers was repealed. If this happened, how would it affect your life?



Women are becoming equal providers.

The New York Times, 11 May 1995, A27

Tamar Lewin

A new survey by Louis Harris & Associates Inc. has found that working women are providing about half of their families' income.

More than 50% of the employed women surveyed--both single and married women--said they provided at least 50% of their household's income. 18% said that they were their household's sole provider. Among married women, 48% said they provided half or more of the family income.

The survey is based on telephone interviews with a representative national sample of 1,502 women ages 18 to 55, conducted last November and December, for which the margin of sampling error is plus or minus 3 percentage points. Two-thirds of the women are employed outside of the home at least part time.

According to Bureau of Labor Statistics data on earnings by married women who worked full time throughout 1993, women contributed a median of 41% of the family's income. Howard Hayghe, an economist at the bureau, said, "Certainly, women are a major source of family income. And in 1993, women earned more than men in 23% of the married-couple families where both spouses worked."

Although women overall are providing such a large chunk of the family income, 64% of the women in married-couple households in the survey said their husband's jobs offered more financial security than their own jobs.

Employed outside the home or not, 9 out of 10 women said that it was their responsibility to take care of the people in their families.

On some of the questions, the women's answers were compared to those of a group of 460 men. For instance, when asked what makes them feel successful, 51 % of the women mentioned the quality of their work and 7% mentioned the paycheck. Men, however, cited the quality of their work just as often, but 26% talked about their paycheck.

The new study also confirmed that education plays a key role in improving women's lives. Among women who were college graduates, 95% said that things were going at least fairly well, as compared with only 3% of women who had not completed high school.

Colleen Kearst, executive director of the Whirlpool Foundation, the sponsor of the study, summed up the finding of the survey: "Women are the new providers. They have firm roots in both worlds of work and home. This study calls for an end to the debate over whether women should or shouldn't work."


The survey found that more than 50% of employed women, single or married, provided at least half of their household's income. Among married women, 48% reported providing at least half of their family's income. Do these two figures seem consistent (shouldn't a far larger percentage of single working women be providing at least half their household's income)? What else do you need to know?



Ask Mr. Statistics.

Fortune Magazine, 29 May 1995, p 175

Daniel Seligman, Ronald B. Lieber

Mr. Statistics looked at the "The New York Times" during a typical five days April 19-23 to see if the Times writers had improved their treatment of numbers since being chastised by Max Frankel (See Chance News 4.05). He gives the following examples to suggest that there are still some problems:

April 19: Marian Burros offers, as evidence that single malt Scotch whisky is becoming very popular in the United States, that shipments have risen 9% in the last five years. This is a 1.7% growth rate in a period when U. S. consumption of consumer goods was expanding at a rate of around 4%.

April 20: Judith Dobrzynski, writing about diversity in the workplace, uses a 1987 Hudson Institute study stating that, between 1988 and 2000, white males would account for only 12% to 15% of those joining the work force. Mr. Statistics asserts that these percentages were the result of a copy-reading error and the correct percentages are well known to be about 40%.

April 21: Maria Newman writes: "Of the city's 3,805 buses, some 2,537 are used exclusively to transport special education students. Mr. Statistics suggests over precision.

April 21: Jane Brody discusses the new theories that mild exercise is not enough. The Center for Disease Control and Prevention estimated that, if every person who is currently sedentary would walk, work around the house, dance or do something comparable for 30 minutes a day, there would be an annual decline in deaths of about 250,000 a year. Mr. Statistics suggests that they were talking about extended lives rather than this many fewer deaths per year.

April 23: Lois Gould remarks that the odds against winning the lottery are up to 18 million to 1 and then says that a mathematician calculated this to be the same as a poker player getting four royal flushes in a row, all in spades and then getting up from the card table, meeting four strangers all with the same birthday -- odds that Mr. Statistics calculates as 1.2 octillion times greater than 18 million to 1.


(1) Why does Mr. Statistics think Jane Brody is wrong saying that the CDC predicted that exercise could lead to an annual decline in deaths of about 250,000 a year? Do you agree?

(2) Does Mr. Statistics have the odds correct for the probability problem stated by Lois Gould?



The Simpson trial Day 69-Part 18 DNA discussion.

CNN Transcript, 11 May 1995

The press did not widely report the DNA discussion in the Simpson trial. When it was mentioned, it was reported that the issue of validity of DNA testing has been pretty well resolved and so the defense concentrated on lab errors instead. However, as this days testimony shows, Peter Neufeld did raise the obvious statistical issues relating to DNA testing. Here are a few of the questions and answers relating to this.

Peter Nuefeld: And, likewise, if the band was smaller than 10,000 and was only, let's say, 9,600 base pairs, under your system's imprecision, you would still declare a match between the 9,600 base pair band and the 10,000 base pair band. Is that correct?

Robin Cotton: That's right.

Peter Neufeld: I take it, Dr. Cotton, that to arrive at a frequency of one in 170-million people, you did not test the blood of 170-million people.

Robin Cotton: That's obviously correct. We tested for the database, the size ranges from about 150 to 325. If you add all the people in the database up, all three racial groups, it comes to around 500 to 600.

Robin Cotton: There are 240 people in MS1, 238 for MS31, 223 for MS43, 200 for G3 and 146 for YNH24.

Peter Newfeld: And would you agree that to go from a database of 250 African-Americans in Detroit to a number of one in 170-million to one in 1.2-billion, you had to make certain assumptions about the independence of these different genetic characteristics?

Peter Neufeld: Now, Dr. Cotton, would you agree, however, that they are based on a number of assumptions, one of which, you said, is that different genetic markers are inherited independently of one another?

Robin Cotton Yes, but what I'm saying is that there is data to back up that assumption, and therefore it is not really an assumption at this point.

Peter Neufeld: All right, Dr. Cotton, has there been controversy in the past about that very point?

Robin Cotton: Yes.


(1) Do you think that the genetic trait of hair color is independent of eye color. How would you test this?

(2) If you were on the jury of the Simpson Trial what more would you want to know about the way the 1 in 170 million probability for a match was obtained?

(3) In his new book "A mathematician reads the newspaper" John Paulos considers an case where the probability of a match was given of 1 in a million in a city of 3 million. He suggests that there should be about 3 people with the same DNA on the loci considered and so a suspect with a match has only a 1/3 chance of being guilty. Is this reasonable?

(4) What odds would you assess to you have an identical twin that you did not know you had?



Throwing 'Curves'

OR/MS Today, June 1995, p10.

Harold O. Davidson

This is yet another review of "The Bell Curve", which the author (a retired partner from the Ernst and Young consulting firm) identifies as a review of a review: he takes exception with many of the comments in Arnold Barnett's review (OR/MS, February 1995--abstracted in Chance News 4.03). In particular, he is upset with the implication that the use of mathematical modeling in the book puts it in the domain of Operations Research. Says Davidson: "I challenge the premise that one can be adequately 'informed' about a particular application by knowledge of the mathematics that may have been used."

Concerning probability, Davidson writes: "Probability has nothing to do with the actual phenomenon, but can be used to quantify ignorance in the sense that he prediction of heads or tails on a particular toss has only a 50% chance of being wrong. On the other hand, with a good model of the phenomenon and precise control of the 'launch,' the chances of a correct prediction would be 100 percent (barring calibration errors, etc.). However, since there's no good economic reason for creating the model and launch apparatus, we're stuck with probability."

He also notes that, while Barnett purports to find flaws in Herrnstein and Murray's analytical methodology, his review is primarily judgmental. In critiquing the Bell Curve's statistical appendix, Barnett wrote: "What is not sure, is that people can learn much statistics from this appendix." Davidson wonders whether the authors really expected it to be a tutorial. He proceeds to dispute Barnett's claim that the use of standard deviations

and centiles is uninformative without discussion of the means of the distributions. He says when a young M.D. acquaintance of his recently scored in the 92th percentile on his board certification exams, his parents knew exactly what that meant.


1. What do you think of Davidson's characterization of probability?

2. How much more medicine does the young doctor know than someone who scored in the 70th percentile? How much more of the test did he correctly complete?



Amid Inconclusive Health Studies, Some Experts Advise Less Advice.

The New York Times, May 10 1995, C12

Gina Kolata

Every year a torrent of health studies, health advice, health warnings, and health tips deluge the public. A number of public health experts and medical researchers are insisting that the public should be told not just what the latest study says but also what it does not say, and how certain it is that the conclusion is correct.

The recent host of conflicting health studies illustrate the problem.

(a) In February, the Centers for Disease Control and Prevention issued a statement saying any exercise, even moderate activity, was good. versus Last month, a study by Harvard University researchers concluded that only people who exercise regularly and strenuously would live onger.

(b) The relationship of diet and heart disease has been held up to question. (1) A recent study found no evidence that eating fish protects against heart disease, contradicting a widely held but poorly substantiated belief that fish contains some specifically heart-healthy component. (2) A recent review of studies on low-fat diets found no evidence to support the national goal of reducing dietary fat to 30% of calories as a way of reducing heart disease rates.

(c) Last year, the purported link between antioxidant vitamins and cancers was also questioned. (1) A large study of smokers found that those who took vitamin E and beta carotene had the same lung cancer rate as those who did not take the vitamins.(2) A second study found that vitamin C, vitamin E, and beta carotene offered no protection against pre cancerous growths on the colon.

The problem, said Dr. Jules Hirsch, is that some researchers and officials have overstated the case for healthful habits, reasoning that the public wants advice. Many people, he said, want to hear that there is a magic set of foods that will protect them from heart disease or cancer or obesity, or that modest exercise will prolong their lives. "It's such an attractive thing to be able to do something for yourself," Dr. Hirsch said. But as advice proliferates: "it's gotten all out of proportion to the facts of the matter."

But much of the fervently repeated health advice "is ludicrous," said Dr. Donald Loura, chairman of preventive medicine and community health at the New Jersey Medical School in Newark. With the proliferation of guidelines and advice, he said: "we are grotesquely overselling to the American people." And he cautioned: "The danger of that is that they will not believe the stuff we have that's documented."

These experts do not think that everything the American public has been told is questionable. Cholesterol levels are linked to heart disease risk and indirect evidence strongly suggests that people with high cholesterol levels who reduce them, whether by very low fat diets or drugs, do protect themselves from heart disease. Studies have proved that those who already have heart disease and lower their cholesterol levels with drugs reduce their risk of dying from heart attacks or strokes.

High blood pressure does pre-dispose people to strokes and heart attacks, and people with high blood pressure should take drugs to reduce it. And what often sounds like the most boring, prosaic recommendations -- to wear seat belts when riding in an automobile, to wear a helmet when riding a bicycle or Rollerblading and to refrain from smoking cigarettes -- are among the best documented, most effective health advice for the greatest number of people.

The confusion comes in, said Dr. Walter C. Willett, a professor of epidemiology and nutrition at the Harvard School of Public Health, because often little distinction is made in public health advice between firmly grounded facts and wishful thinking. As a result, when studies come out contradicting conventional wisdom, many people throw up their hands, concluding that they cannot believe anything scientists say.

For example, Dr. Willett said, the recommendation to eat a 30% fat diet to protect against heart disease is not based on facts. Research has not proved that there is an ideal amount of fat to be aimed for in the diet. This was apparent even in a pivotal study in the search for dietary advice, the Seven Countries Study, which was published in 1980.

The study correlated heart disease rates with dietary fat in different countries and found that heart disease rates tended to be lower in areas where less fat was eaten. But, Dr. Willett noted, it also found that the lowest heart disease rate was in Crete, where the diet was 40 percent fat. It may depend on what kind of fat is eaten, Dr. Willett said, but much more research needs to be done on that question.

Dr. Willett said cancer prevention was another example "where we've given a lot of strong advice without good data to back it up." He said that the link between high-fat diets and cancer was tenuous at best. Studies within populations have repeatedly failed to find a relationship between fat intake and cancer incidence. And comparisons of populations in different countries may neglect other factors contributing to low cancer rates.

For example, Dr. Willett said, in rural China, where the population eats little fat and has a low breast cancer rate, people also have limited amounts of food in general and the average age of menarche is 18. The later the onset of menstruation, the lower the cancer rate.

Some public health experts said it might be better simply to tell the public where the uncertainties are, to emphasize the limits of studies that compare populations or that lack control groups, and to say that, if a hypothesis is unproven, then people will have to weigh the evidence themselves and decide what they want to do.

But that approach can backfire, as the National Cancer Institute learned last year when it decided to withdraw its advice that women in their 40's have mammograms, telling them instead that they should look at the data and decide for themselves. The institute concluded that there was no evidence that women under 50 benefited from mammograms, but that younger women might choose, as individuals, to have the breast cancer screening test anyway.

That decision set off a firestorm of criticism from those who wanted the institute to take a firm stand. Some said the institute should have flatly told younger women not to have mammograms. Others, equally adamant, wanted the institute to stand by its previous recommendation that younger women have the tests.

Dr. Fletcher, who headed a panel that evaluated the mammogram evidence for the cancer institute, agreed that there was a danger in going against the tide and declining to give guidelines when the evidence was not there. But, Dr. Fletcher said: "I don't see any way around that. I think we have to keep working to educate the public and tell them what we know and what we don't know."

The message Dr. Fletcher would like to see is that science is incremental. "People want to know about scientific advances, and I think we should tell them," Dr. Fletcher said. "But we should communicate the level of our certainty." The problem now, Dr. Fletcher said, is that "we tend to communicate more certainty than we have."


1. When Dr. Fletcher suggests: "But we should communicate the level of uncertainty" who do you think she feels should do this, the researchers, the science writers or who?

2. Assuming that you want to comply with Dr. Fletcher's recommendation, what language would you propose for expressing degrees of certainty? Is there an obvious quantitative rating?


CHANCE News 4.08

(5 May 1995 to 7 June 1995)


Please send suggestions to: jlsnell@dartmouth.edu