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
CHANCE News 4.13
(8 September 1995 to 30 September 1995)
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
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
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
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 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
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
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
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
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
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
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
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
Of chimps and mutual funds.
The Gazette (Montreal), 19 Sept. 1995, F4
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
(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
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
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)