CHANCE News 4.13
(8 September 1995 to 30 September 1995)

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.

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

Reasonable doubt is not a mere possible doubt: because everything relating to human affairs, and depending on moral evidence, is open to some possible or imaginary doubt. It is that state of the case which, after the entire comparison and consideration of all the evidence, leaves the minds of jurors in that condition that they cannot say they feel an abiding conviction, to a moral certainty, of the truth of the charge.

California Supreme Court



Well, even we put too much trust in newspapers! We received several messages pointing out that the proportions for the colors for M&M's that we obtained from a newspaper article were not correct. Ann Watkins writes: I'm reading from a brochure called "Colors" sent to me in August by the Consumer Affairs Department, M&M/Mars, Hackettstown, NJ 07840, phone 908-852-1000.

On average, the new mix of colors of M&M's Plain Chocolate Candies will contain 30 percent browns, 20 percent each of yellows and reds and 10 percent each of oranges, greens and blues. For M&M's Peanut> Chocolate Candies, the ratio is 20 percent each of browns, yellows, reds and blues, 10 percent each of greens and oranges.

They explain that

While we mix the colors as thoroughly as possible, the above ratios may vary somewhat, especially in the smaller bags. This is because we combine the various colors in large quantities for the last production stage (printing). The bags are then filled on high-speed packaging machines by weight, not by count.

Roger Johnson noted that: Peanut Butter and Almond M&Ms were also given in the brochure (20 percent each of brown, yellow, red, green, blue), as well as percentages for holiday varieties. Prof. Johnson has written an interesting article about his experience with students testing the hypothesis that the percentages are as claimed ("Teaching Statistics", Spring 1993, Vol 15, No. 1, pp 2-4).

Tom Moore sent us the following item:

A user of Microsoft's Excel spreadsheet recently discovered that, if you enter one of the values 1.40737488355328, 2.81474976710656, and 5.62949953421312 as the contents of a cell, is immediately replaced with a different number (with 0.64, 1.28, or 2.56, respectively). This different number is both displayed and used in computations involving the cell. The bug affects both PC and Macintosh versions of Excel.

Microsoft has developed a WWW page about the bug, which contains the following passages, which I have juxtaposed to heighten the comic effect:

Question: What are the chances that I have been affected?

Answer: Although it is hard to have an exact number, we believe this will only affect a very small number of customers. In fact, based on our internal analysis the likelihood of any one of these sequence of digits appearing in a customer's spreadsheet is 1 in billions.

Question: How did you find out about this?

Answer: One of our customers actually found it.


How do you think Microsoft estimated the likelihood of one of the three sequences of digits appearing in a customer's spreadsheet? Do you think it was relevant to their calculations that the three numbers are 2^47th, 2^48th, and 2^49th with a decimal after the first digit? If not, should it have been?

Claude Steele has scores to settle.
The New York Times, 17 Sept. 1995, Magazine p. 45
Ehtan Watters

Inspired by "The Bell Curve", the University of Chicago School of Public Policy brought together an interdisciplinary group of scholars to discuss the topic: Why do African Americans score significantly worse on standardized test than whites?

This article gives an account of the ideas presented by Claude Steele, Stanford Professor of Sociology. It also discusses the lives and careers of the Steele brothers. Claude's brother Shelby Steele is a well-known conservative author. They are African American and identical twins.

Claude Steele believes that "whenever black students concentrate on an explicit scholastic task, they risk confirming their group's negative stereotype and that this extra burden, in situations with certain characteristics, can be enough to drag down their performance." Steele has carried out a number of experiments to support this thesis. The article describes one such experiment as follows:

Two groups of black and white Stanford undergraduates were given a test composed of the most difficult verbal- skills questions from the Graduate Record Exam. Before the test, one group was told that the purpose of the exercise was only to research "psychological factors involved in solving verbal problems", while the other group was told that the exam was "a genuine test of your verbal abilities and limitations."

The two groups had comparable S.A.T. scores. The black students in the group who thought they were just helping out in a research project, performed as well as the whites. However, those in the group who thought their abilities were being tested, performed significantly worse than the whites. In another experiment, two groups of black students with comparable high S.A.T. scores were given a test in which one group was asked to specify race and the other was not. The group that did not specify their race outperformed the group that did.

Steele calls this phenomena "stereotype vulnerability". He has carried out other similar experiments showing, for example, that stereotype vulnerability can negatively affect women who believe a given math test shows "gender differences". It also shows up in white men who took a difficult math test after being told that Asians tended to outperform whites on that particular exam.

Researchers at the conference, even including Charles Murphy, co-author of "The Bell Curve", felt this was very promising research. A paper co-authored with Joshua Aronson on these experiments is being published experiments this fall in the "Journal of Personality and Social Psychology".

This is a long and fascinating article both because of the description of Claude Steele's research and the reaction it made at the meeting and also because of the contrasting views of two identical twins.

"Aught" they "naught" be "zeros"?
The Dartmouth, 28 September 1995, p. 1
Jacqueline Rose

According to this article, diverse groups in the Dartmouth College administration have been trying to decide on the official name for next year's class and what members of this class should be called. A 32-member committee that oversees the College's official style could not decide on a name at a meeting this summer. Suggestions made were the "double aughts," the "aughties," the "naughts" and the "first decade". An informal survey conducted by the style committee placed the aughts at the top of the list. A spokesman for the college stated that the administration may let members of the class of 2000 name themselves.

A random survey of 20 students by "The Dartmouth" placed the "zeroes", with eight votes, as the students first choice. It was closely followed by the "2000s," which had seven votes.


(1) What is the margin of error for the survey carried out by the Dartmouth?

If you were a Dartmouth student in the current Chance course and wanted, for your final project, to settle this question by a serious survey, how would you design the survey?

The next item was contributed by Mathew Paymar, former U. of Minnesota Chance student.

Wording affects polls on affirmative action.
San Francisco Chronicle, 14 Sept. 1995, A17
Susan Yoachum

According to this article, more than three quarters of all California voters are aware of the ballot measure to be voted on in November 1996 that would roll back affirmative action in hiring, college admissions and contracting. However, a poll shows that voters' views depend on how the initiative is described.

When the words "affirmative action" were used by the polltakers, 32 percent were inclined to support the measure and 28 percent to oppose it. When the actual ballot measure, which includes the words "preferential treatment" and never mentions affirmative action, was read, the support for the measure jumped from 32 to 58 percent while only 33 percent said they would vote no.

These polls show also that support for cutting back on affirmative action differs greatly accurding to the race and age of the person being asked.

A more detailed discussion of the difference in the minds of the voters between affirmative action and preferential treatment and its effect on the California measure can be found in an article by pollster Louis Harris in the New York Times (New York Times, 31 July, 1995, A13)


Who do you think decides on the wording of issues that get put on the ballot? Who do you think should?

Study cites dangers in workplace from second hand smoke.
Chicago Tribune, 27 Sept. 1995, News p. 3
Associated Press

This is a report on an article in the current issue of the Journal of the American Medical Association (1995; 274: 945-951) on a large study on the effect of second-hand smoke. The researchers placed 25 fiber disks, treated to react to nicotine, at 25 workstations including various types of business and manufacturing facilities. The disks were left for a week in offices, cafeterias and production areas.

Nicotine levels ranged from 8.6 micrograms per cubic meter of air, in open offices where smoking was allowed, to 1.3 micrograms where smoking was restricted and .3 micrograms where smoking was banned. The levels in non-office areas were 2.3, .7 and .2 respectively.

The researchers stated, citing previous research, that exposure to an average of 2.3 micrograms of nicotine per cubic meter of air for eight hours a day over 40 years creates a lung cancer risk of three in 10,000.

A news release as well as the authors' abstract for this article can be found on the "Journal of American Medical Association" homepage http://www.ama-assn.org/ This AMA homepage will be a valuable resource for a chance course. It also provides a way to compare newspaper articles with the information given by the professional journals.

Global warming experts call human role likely.
The New York Times, 10 Sept. 1995, Section 1 p. 1
William K. Stevens

The Intergovernmental Panel on Climate Change (IPCC) was established to assess scientific information about climate change relevant for international and national policy formulation. The IPCC produced a 1990 Assessment Report and is currently preparing its Second Assessment Report, which will be completed in late 1995. They put a draft for review on the Internet with a statement that this report should not be cited or distributed.

This New York Times article is based on the report and starts off with the statement: "In an important shift of scientific judgment, experts, advising the world's governments on climate change are saying for the first time that human activity is a likely cause of the warming of the global atmosphere." The author remarks that: "Scientists say that a major reason for the change in view marked by the new report, in fact, is that a new generation of studies has enhanced their confidence in computer simulations of the atmosphere, creating a much better agreement between predicted patterns of climate change and those actually observed."

While the article suggests that there is now, for the first time, a general consensus that humans are to blame for the global warming, the author remarks that at least one expert, Richard Lindzen of M.I.T., does not have the same faith in the ability of computer models to estimate natural variability of the climate system on time scales of decades and centuries. He feels that there is "no basis" yet for saying that a human influence on the climate has been detected.

The draft report forecasts an increase in average global temperature of 1.44 degrees to 6.3 degrees Farhenheight by the year 2100 if there is no further action to curb emissions of greenhouse gases. The average global temperature is 5 to 9 degrees warmer now than in the last ice age.

Global warming is a very complex subject and one about which you can learn a lot from material available on the Internet. This report itself goes into a great deal of detail about the possible consequences of global warming, possible ways to prevent it etc. Even more basic information about what global warming really is, how it is measured, etc. can be found from climate change fact sheets.


Some commentators feel that the headline, and the first statement of the article, go further than what is said in the report. What the report actually said was:

Comparing the observed change in the global mean temperature with model simulations suggests that the observed increase over the last century (0.3 C - 0.6 C) is unlikely to be entirely due to natural causes and that a pattern of climatic response to human activities is identifiable in the climatological record.

Do you agree with these commentators?

Experts to review AZT role as the chief drug for H.I.V.
New York Times, 17 Sept. 1995, Section 1 p.1
Lawrence K. Altman

Anthony S. Fauci, director of the National Institute of Allergy and Infections Diseases, plans to convene a meeting with independent experts to decide whether AZT should continue to be the first choice for a drug to treat the H.I.V. virus.

This meeting was suggested by the results of a large study, reported this week, that compared the effectiveness of AZT and two other drugs, didanosine (ddI), and zalcitabine (ddC).

The study was carried out in 52 medical centers in the United State and involved 2,500 patients whose immune system had been moderately impaired as indicated by a CD4 count between 200 to 500 (normal count is 800-1200). Participants were randomly assigned to four groups, one receiving AZT alone, one ddI alone, one ddI and AZT, and one ddC and AZT.

AZT along was less effective than each of the other three treatments in preventing significant drops in CD4 counts, progression of infection to AIDS, and death.

One concern mentioned about the study was the large dropout rate. 53 percent of the subjects in the study did not complete it. One official state that "the premature withdrawal rate may have diluted the power to detect differences but does not appear to have negated the results and conclusions".


David Barr, director of treatment education in the Gay Men's Health Crisis in New York City, said that "the study suggested ddI is a better single drug to start with than AZT. But it does not answer the question whether ddI is better than nothing."Fauci confirmed that AZT had proved better than placebo in earlier studies but that ddI had never been compared with a placebo in a large study, even the one being reported.

(1) If drug A is better than drug B, and drug B is better than placebo, is drug A better than placebo? Why or why not?

(2) Are you concerned about the dropout rate in this study?

Roger Pinkham send the following note:

RSS News (Looks like a newsletter from Reading University)
Letters: Ernest Rudd, York

Mr. Rudd writes:

The newly formed York District has 29 wards, of which 8 elect one councillor, 18 two, and 3 elect three. In the recent elections in the two-councillor wards there were 55 pairs of candidates from the same party. In 49 cases, the candidate whose name came first in the alphabetical listing gained more votes than the other candidate, in three cases they both gained the same number of votes, and in the remaining three it was the second candidate who gained more votes.

For further information about this phenomenon, the writer invites us to read his paper Rudd E. (1977) The effect of alphabetical order of author listing on the careers of scientists.


A list of the members of the National Academy of Sciences can be found. Check out Mr. Rudd's theory.

Here's a contribution from our Milwaukee corespondent Bob Griffin:

Wisconsinites split on stadium plan, poll says.
Milwaukee Journal Sentinel, 9 Sept. 1995, 4A
Steve Walters

The future of major league baseball in Milwaukee has become an important issue in the city which once before lost a major league team, the Braves, to Atlanta. Bud Selig, the acting commissioner of baseball, owns the current Milwaukee team, the Brewers, and worked hard to bring baseball back to Milwaukee and to keep it there.

In Milwaukee, the current economic problems of baseball have meant that the team has asked the state and some local county governments to help them construct a new stadium which, they believe, will increase attendance and revenue in the future. Without revenue enhancement, it is quite possible that the team could move from the city. The governor and some state legislators have proposed that the new stadium be funded primarily through a .1 percent sales tax increase in Milwaukee and neighboring counties such as Waukesha County. The plan is contentious, in some segments of the populace, due to bad feelings about major league baseball brought on by the recent players' strike. The newspaper has been campaigning strongly in favor of a new stadium, and the state legislature, at the time of this story, was just about to start considering the funding plan.

This news story starts with the headline: "Wisconsinites split on stadium plan, poll says: Results offer little guidance to legislators."

The lead paragraph states: "Slightly more Wisconsin residents favored the new Milwaukee Brewers stadium funding plan than oppose it, but neither side had a majority in the first statewide poll released on the issue."

The article then reports that an independent research firm had found, in a statewide survey of 600 Wisconsinites with a reported 3.5 percent margin of error, that 47.7 percent of the respondents favored the plan, 44.3 percent opposed it, and the rest were either undecided or did not care.

The article then reported on opinions in the two counties, Milwaukee and neighboring Waukesha, that would be more strongly affected by the plan. "Residents of Milwaukee County, who would have to pay slightly higher sales taxes to build the stadium, supported it," the story said, and reported the figures as 51.7 percent in favor and 42.5 percent opposed. In Waukesha County "the margin of support was less," the story said, with 48.6 percent in favor and 45.9 percent opposed.


(1) The headline states that Wisconsinites are split on the stadium plan while the story says that slightly more people favor the plan than oppose it. Given the survey's margin of error, which of those two statements is more accurate?

(2) The story states that, in Milwaukee County, 51.7 percent favor the plan and 42.5 percent oppose it. In Waukesha County, 48.6% favor the plan and 45.9 percent oppose it. A check of census data indicates that about 20 percent of the state's residents live in Milwaukee County and about 6 percent live in Waukesha county. Assuming a probability sample of the state's population, how many of the 600 survey respondents are likely to reside in Milwaukee County? In Waukesha County? What is the margin of error for the percentages of those in favor and opposed in each of those two counties? How would you interpret the results in those counties based on those margins of error?

Of chimps and mutual funds.
The Gazette (Montreal), 19 Sept. 1995, F4
Ron Chalmers

Burton Malkiel, a Princeton University professor, has argued that a blindfolded chimpanzee, throwing darts at a board can pick stocks as well as mutual-fund managers. In fact, when mutual funds report their track records, they warn that past performance is not a guarantee of future returns.

Many financial analysts, however, disagree with Malkiel's argument. As a result, Malkiel did a study of U.S. mutual fund performance in the June 1995 issue of the "Journal of Finance". He studied year-by-year returns of funds, including those that subsequently disappeared or merged with other funds. By ignoring defunct funds, studies tend to exaggerate the average performance of all funds.

Here is what Malkiel found:

(1) In the 1970s, a fund that was above average one year had a 65 percent chance of being above average the next year.


(2) In the 1980s, an above average fund only had a 52 percent chance of repeating the next year.

The author of this article, Ron Chalmers, did a similar study of Canadian equity funds' performance. In Sept. 1994, 81 of the funds he examined were above average in the preceding 12 months, and were still around in Sept. 1995. In Sept. 1995, 40 were still above average and 41 were below average.

Chalmers concludes, just as Malkiel originally did, that the performances in one period do not help at all in predicting mutual fund performance for the next period. Using a dart board to pick stocks is just as good as hiring a mutual fund analyst.


(1) How convincing do you find Malkiel's observations about the performance of mutual funds?

(2) Do Malkiel's observations take into account the fact that funds claim to be different in the amount of risk involved, volatility of the stocks involved, etc.?

Pros Top Darts in selecting stock winners.
Wall Street Journal, 13 Sept. 1995, C1
Georgette Jasen

In this ongoing contest between the experts and the darts, the four pros easily won with a strong boost from technology stocks. Their average investment gain was 26.7 percent (helped by pro John Bogle Jr. choosing Seagate Technology which had a 78.4 percent gain), compared to 11.4 percent for the portfolio of four stocks chosen by throwing darts. The Dow Jones average rose 15.3 percent during the period of this contest which was from March 6 to Aug. 31.

The professionals now lead 38 to 25 in the 63 contests since the contest began in July 1990. Comparing investment performance over the entire period, the pros had an average gain of 9.5 percent, the darts 4 percent and the Dow Jones, 4.9 percent.


(1) Is the number of times the professionals are ahead statistically significant?

(2) Do you think it matters that the professionals are not using real money when they pick their stocks?

Women give weight study a pounding.
Los Angeles Times, 24 Sept.1995, A1
Terence Monmaney

A new Harvard study has found that, in a health survey of more than 100,000 middle-aged female nurses, the lowest mortality rate was observed among women who weighed at least 15 percent less than the U.S. average.

The study, directed by Dr. JoAnn E. Manson of the Women's Hospital in Boston, tracked 115,195 nurses who were 30 to 55 years old in 1976. The researchers sorted all the women into seven weight categories ranging from very thin to extremely obese. To emphasize the role of body weight, they targeted their survey towards women who neither smoked nor had gained a lot of weight since adulthood.

The study found that, compared with the thinnest women, those who weighed successively more had higher mortality rates. For instance, a 5'5" woman's added mortality risk is 20 percent at 122 pounds and 60 percent at 170 pounds. They also found that the skinniest women had lower mortality rates than even women with average weights.

The most important finding of the study is the following: Losing weight isn't as important as keeping it off. The lowest death rate of all was among middle-aged women who gained no more than 20 pounds since young adulthood.

According to Susan E. Hankinson, a co-author of the study, the 20 percent figure of increased mortality risk is not statistically significant. She said that the mathematical techniques the researchers were compelled to use made it necessary to round off the risk factor to 20 percent. The added risk conferred by a small amount of fat may be more or less than 20 percent.

The study doesn't take into account muscle to fat ratio. Muscle weighs more than fat, and because of this the Harvard study may give an inflated death risk to women who have high muscle to fat ratios and therefore weigh more than the guidelines suggest.

Many experts, while citing the study as perfectly sound, have urged people to disregard the finer points of the findings and to concentrate on the bigger lifestyle picture. Dr. David Williamson, an epidemiologist at the U.S. Centers for Disease Control and Prevention, advised against concentrating on pounds and emphasized healthful habits like not smoking, walking a lot, and eating healthily.


(1) What did Susan Hankinson mean by "the mathematical techniques the researchers were compelled to use made it necessary to round off the risk factor to 20 percent"?

(2) The article states that "the risk that a nonsmoking young or middle-aged woman will die in a given year is so small that a 20 percent rise verges on the imponderable. The jump in odds translates roughly to a rise from 10 in 10,000 to 12 in 10,000." Is this a good way to explain the risk of being 20 percent over the recommended weight? Do you think they mean any 20 percent increase in weight?

Linking technology and health groups to find best cure.
The New York Times, 24 Sept. 1995, A32
Holcomb B. Noble

A group that includes some of the nation's largest employers (AT&T, Pepsico, etc.) along with Federal and state insurance-purchasing agencies, is pushing health maintenance organizations to feed massive databases of patient records into computers to determine the most effective treatments for a broad range of major illnesses. These employers argue that such a database would help them pick the HMO that provides the best quality health care for the best price.

Nine medical conditions, with more to be added on later, were picked for the study. These nine are depression, coronary-artery disease, asthma, breast cancer, diabetes, hypertension, low back pain, arthritis, pregnancy and maternity care.

Most of the time medical studies have focused on the efficacy of a new or refined treatment. Once these treatments have been approved and become part of accepted practice, however, they are rarely compared with the efficacy of alternative treatments.

Private employers and government insurance pools pay the largest shares for health insurance and are unable, under the current system, to assess if what they are paying for is quality health care. Companies are pushing the study because they see potential savings in future health insurance costs. For instance, Dwight McNeill, information manager for GTE Laboratories in Waltham, Massachusetts, said that his company could potentially save up to $25 million a year if they convert 75 percent of their employees and 25 percent of their retirees from an average HMO. to a high quality one.


What do you think of this use of medical records?

Please send comments and suggestions for articles to


CHANCE News 4.13
(8 September 1995 to 30 September 1995)