CHANCE News 4.15
(21 October1995 to 16 November 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
Back issues of Chance News and other materials for teaching a
CHANCE course are available from the Chance Web Data Base.
Luck at its best is the residue of design.
Thanks to all that returned our questionnaire. We have added the questionnaire at
the end of this newsletter to give those who have not responded another chance to
Professor Nancy Reid at the Univerity of Toronto is teaching a Chance type course
and has put class by class accounts of what she is doing on the Web. Her address
Professor Reid has also permitted us to put her materials on our Chance Database so
you can also find them there by looking under "Chance Courses". You will find her
course notes a good source of Canadian chance issues. The American press and therefore
also our Chance News does not do justice to these issues.
We hope that others will make their materials available this way. We will be glad
1. Luck: The brilliant randomness.
2. Bible's word patterns suggest divine writing.
3. Technology on the Net.
4. Sony funds controversial ESP study.
5. Cholesterol-cutting drug prevents heart attacks.
6. 3 risk factors for breast cancer.
7. Ask Marilyn: Can computers generate random numbers?
8. 4.1 million awarded in implant case.
9. Proof of breast implant peril is lacking.
10. Weekly reader puffing for tobacco?
11. Solution to Shunhui's basketball problem.
Luck: The brilliant randomness of everyday life.
By Nicholas Rescher
237 pp. New York:
Farrar, Straus & Giroux.
We teach and write about chance as if we knew what it is. Yet we talk about luck
good and bad all the time and seldom ask what luck is and how it is related to chance.
In this book the well known philosopher Nicholas Rescher attempts to remedy this
Rescher's use of the term "luck" seems consistent with the definition in the Oxford
English dictionary: "the fortuitous happening of an event favorable or unfavorable
to the interest of a person". Thus luck combines a chance event with an effect on
an individual. We have good luck if the chance event helps us and bad luck if it hurts us.
Rescher writes: "Recognizing the prominent role of sheer luck throughout the role
of human affairs, this work will address such questions as: What is luck? How does
it differ from fate and fortune? What should our attitude toward lucky and unlucky
people be? Can we expect to control or master luck? Are people to be held responsible for
their luck? Should there be compensation for bad luck? Can luck be eliminated in
The only definitive answer you will find is "no" to the question: Can luck be eliminated
from our live? You may be disappointed on the first reading of this short book because
you don't get enough answers. However, you will start asking your own questions. For example, is there a law of large numbers for luck? You will find yourself
discussing the meaning of luck with your colleagues and students. Perhaps from this
you will get lucky and discover what luck really is.
1. Do you think a person's luck averages out through life?
2. Rescher argues that luck is democratic -- the poor are just as vulnerable to bad
luck as the rich? Do you agree?
3. Rescher states that "the life we come into is a matter of chance, but not of luck.
Do you agree?
Bible's word patterns suggest divine writing.
The Valley News, 3 Nov. 1995
An article in the October issue of "Bible Review" has renewed interest in research
by three statisticians, Doron Witztum, Eliyshu Rips and Yoav Rosenberg, published
in "Statistical Science" (1994, Vol, 9, No. 3, pp 429-438). These authors claim
to show that the book of Genesis contains information about events that occurred long after
it was written that cannot be accounted for by chance. The editors of the "Statistical
Science" comment that the referees doubted this was possible but could not find anything wrong with the statistical analyses. So they published it for the rest of us to
try to discover what is going on.
The authors chose 32 names from the "Encyclopedia of Great Men of Israel" and formed
word pairs (w, w') where w is one of the names and w' a date of birth or date of
death of the person with this name. We say a word w is "embedded" in the text if
it appears in the text at positions of an arithmetic sequence (not counting spaces) i.e.,
appears in the text seperated by intervals of fixed length of letters from the text.
For example, the word "has" is embedded in the sentence "The war is over." since
the letters h, a, and s occur in the sentence separated in each case by two letters. The
authors showed that the names and dates they chose appeared in Genesis (which is
not surprising) but the names were nearer their matching date than could be accounted
for by chance (p = .00002). All this was done using the Hebrew language.
At the suggestions of a referee the authors tried the same tests using other Hebrew
works and even Tolstoy's "War and Peace" translated into Hebrew as controls. They
did not find any similar unlikely events in these controls.
The article in the "Bible Review' gives an interesting account of this research and
how it has been received. The authors first announced similar results in the "Journal
of the Royal Statistical Society A"., (155:1 1988, pp. 177-178) while commenting
on an article "Probability, Statistics and Theology" by D. J. Bartholomew. At his announcement
a public statement was made by well known mathematicians including H. Furstenberg
at Hebrew University and Piateski-Shapiro at Yale that these results "represented
serious research carried out by serious investigators."
(1) What do you think could be going on here?
(2) Do you think your name is embedded in Hamlet?
(3) The authors restrict themselves to words that are embedded in the text with separation
between letters at most a specified number D. They estimate the expected number
of times a word w is embedded in Genesis by taking the product of the relative
frequencies (within Genesis) of the letters constituting w multiplied by the total
number of equidistant letter sequences in the text having separation at most D. Is
the independence between letters assumed in this calculation reasonable?
Another Survey of Internet Users is Out.
The New York Times, 30 October 1995, Pg. D5
Peter H. Lewis
A comprehensive survey conducted by Nielsen Media Research has revealed that 10.8%
of the combined population, age 16 years or older from The United States and Canada,
had used the Internet in the last three months. The survey was conducted for Commerce
Net, a group of businesses interested in promoting electronic commerce.
The survey found that there are more Internet users than previously thought. Most
of the users, though, connect to the Internet from work, and not from home.
In recent months, other surveys have been carried out, but these have been on-line
surveys. The results from these surveys revealed a lower Internet population in
some cases, but a higher one in others. The Nielsen/Commerce Net survey is the first
reliable survey of Internet use because it employed statistically reliable methods to measure
Internet usage. Nielsen made random telephone interviews of 3000 households.
Some findings of the Nielsen survey:
1) 2.5 million adults have purchased goods/services over the Internet's World Wide
2) 35% of Internet users are women.
3) Of World Wide Web users, 25% had household incomes of at least $80,000 a year;
64% had at least 4 years of college; 51% listed themselves as professionals or managers.
4) More than 50% of Internet users were 35 years old or younger.
5) 62% of adult Internet users had access to it from home, but 38% did not.
These statistics indicate that the Internet is reaching mainstream popularity faster
than anticipated. Such a spread of Internet use could have positive ramifications
for businesses looking to branch out into cyberspace.
How many of the people that could not be reached by telephone were on the internet?
Sony funds controversial ESP study.
Los Angeles Times, 12 November, 1995, Pg. A30
Sony, the Japanese corporation that brought us the Walkman, is performing research
on paranormal phenomena. Among the topics being studied are the following: alternative
medicine, spoon-bending, X-ray vision, telepathy, and other forms of ESP.
Sony's "Institute of Wisdom" was founded in 1989. Researchers study psychics' brain
waves, pulse, temperature and skin conductivity but have not reached any solid conclusions.
A subdivision of the Institute, Extra-Sensory Perception Excitation Research, has worked with more than 100 subjects reported to possess ESP.
This effort is being led by Yoichiro Sako who is said to be a respected scientist.
One of Sako's experiments was to present subjects with two black plastic containers,
one with a small amount of platinum and the other empty. According to Sako: a certain
"supersensitive person" named T.I. was able to be right 70% of the time.
Apparently Sako believes that only people who already believe in paranormal phenomena
are qualified to conduct research into them.
According to another account, much of the research focuses on ki, the mysterious spiritual
energy that forms the basis of traditional oriental medicine. Based on the research,
Sony has developed the Pulse Graph. It is claimed to be able to diagnose diseases with a 20-30% success rate.
Some Japanese scientists, given the present interest in cults in Japan, are quite
unhappy about Sony treating this subject so seriously.
(1) Why do you think anyone cares whether Sony studies
ESP or not?
(2) How would you test if T.I. is really a supersensitive
Benefit to healthy men is seen from cholesterol-cutting drug.
New York Times, 16 Nov. 1995, A1
Jane E. Brody
This article describes the outcome of a study reported in the current issue of the
"New England Journal of Medicine" on the effectiveness of the cholesterol-lowering
drug pravastatin in preventing heart attacks. The study was supported by a grant
from the Bristol-Myers Squibb Company, which makes pravastatin and sells it under the name
The study involved 6,595 apparently healthy men in Scotland between the ages of 45
and 64. The researchers found that over five years those treated with parvastatin
suffered 31 percent fewer nonfatal heart attacks and at least 28 percent fewer deaths
from heart attacks than a comparable group of men who received a placebo.
The cholesterol levels of the participants at the beginning of the study averaged
272 milligrams per deciliter of blood serum with at least 115 milligrams of harmful
low-density liporotein cholesterol (LDL) which is the form that clogs up arteries.
Those receiving paravastatin lowered their total cholesterol by an average of 20 percent
and LDL cholesterol by 26 percent. Their protective high-density lipoprotein cholesterol
(HDL) was increased by an average of 5%.
Previous studies have show that drugs to lower cholesterol are effective for men with
a previous history of heart disease, but this is the first study to show that drugs
to lower your cholesterol are helpful in preventing heart attacks for men who do
not already have a heart problem.
An accompanying editorial comments that these drugs are expensive, costing about $800
a year per person. The editorial suggested pursuing less expensive solutions such
as using certain kinds of margarine that have been shown to have a ability to lower
Results from related studies suggest that similar benefits from the drug might be
found for women.
(1) Should we be nervous that the study was supported by the company that makes the
(2) The article reports that the drug did not appear to have serious side effects.
It is stated that: "The most common side effects of parvastatin, seen in the placebo
group as well, included a mild skin rash and gastrointestinal upset". Should something
that occurs also in the placebo group be called a side effect?
(3) Why do you think the researchers limited their study to men?
Study: 3 factors cause almost half the cases of breast cancer in U.S.
Atlantic Journal and Constitution, 15 Nov. 1995, 2D
A study published in the current issue of the "Journal of the National Cancer Institute"
reports on the first study that uses a probability sample to study risk factors for
The researchers consider three factors that have generally been thought to be risk
factors for breast cancer: not having a baby or waiting until after age 19 to have
one, having a moderate or high income and having a family history of breast cancer.
The study involved 7,508 women ages 25 to 74, beginning in 1971. By 1987, when the
study ended, 193 had developed breast cancer. The results of the study suggested
that 41 percent of the risk is linked to the three factors considered.
(1) The article states that it was estimated that 29 percent of the breast cancer
cases were attributable to not having a baby, or waiting until after age 19. An additional
19 percent were linked to having a moderate or high income, and 9 percent were linked to an inherited predisposition for breast cancer. What does this really mean?
(2) The article comments that: "Weaknesses in the study include the small number
of women having no risk factors, relatively few breast cancer cases, and the need
to add weight, statistically, to some population groups. Such deficiencies reduce
the 'statistical power' of studies, because small changes can cause large leaps in percentages."
What does all this mean?
(3) Just looking at information given here, can you say anything sensible about the
probability that a women will get breast cancer? If you had the actual data could
Parade Magazine, 29 Oct. 1995, p. 18
Marilyn vos Savant
A reader writes:
From what I understand, computers do exactly
what you instruct them to do. If so, how can
a computer generate random numbers? How does
someone write one set of instructions that would
produce a different answer every time? It seems
like an impossible task.
Michael H.G. Ho,
Sagamore Hills, Ohio
Computer programs don't generate numbers randomly,
but the results can be used as random numbers.
That's because they're likely to be "more random"
than any other random number generator you can name,
such as a deck of cards, or the fellow at the desk
next to yours. After all, how can anything be truly
(1) How would you have answered the reader's question?
(2) How can anything be truly random?
$4.1 Million Awarded in Implant Case; Dow Chemical Facing.
Prospect of More Suits.
The Washington Post, 29 October 1995
Last spring, Dow Corning filed for bankruptcy as a result of
lawsuits brought by women who alleged their health had been
ruined by company's silicone breast implants. Fearing they
would be denied compensation, some women sought to sue the
parent company, Dow Chemical. Now a Nevada jury has now
ruled that Dow Chemical must pay an Elko, Nevada women $3.9
million in damages. This is the first time the parent
company has been held responsible for the damage allegedly
caused by the implants. Health complaints have ranged from
chronic fatigue and muscle pain to connective tissue
disorders and rheumatic diseases, though a series of
scientific studies have been unable establish any links to
The plaintiff's attorneys argued that Dow Chemical had done
studies of other uses of silicone in industry and
agriculture, and knew of problems that should have been made
public. Dow Chemical attorneys denied this claim. They
maintain that the plaintiff's symptoms are consistent with
traumatic stress disorder and fibrmyalgia unrelated to the
implants, and that she sought medical attention for the
implants only after seeing an attorney.
Robert Gordon, attorney for a New York law firm representing
5000 other women seeking compensation is quoted as saying:
"It's an amazing verdict. The jury saw that there is a lot
of good science backing this up." What good science do you
think the jury saw?
[See also the next story.]
Proof of a breast implant peril is lacking, rheumatologists say.
The New York Times, 25 October 1995
Mere days before the above verdict was announced, The
American College of Rheumatology issued a formal statement
saying that there was no evidence that silicone breast
implants cause the diseases attributed to them, and stated
that the FDA and the courts should stop acting on the basis
of anecdotal evidence. (In 1992, the FDA imposed a
moratorium on use of the devices until the alleged health
risks were investigated.) The article notes that since an
estimated 1 million American women have received implants, it
should be expected by chance alone that thousands would
become ill with connective tissue and rheumatic diseases.
Some doctors disagree with these conclusions, and have
testified in court that the devices cause a new type of auto-
immune disorder. But Dr. Sam Ruddy, departing president of
the ACR said there was no scientific evidence to support
this. Instead, there are "collections of cases with no
(1) Describe how a controlled study would be conducted. For
follow-up reading, you might look at J. Sanchez-Guerrero,
et. al.(1995) , Silicone breast implants and the risk of
connective-tissue diseases and symptoms. New England Journal
of Medicine 332: 1166-1170.
(2) If you were a woman with implants, what type of
potential ailments would convince you to have them removed?
Would the prospect of minor muscle aches be enough, or would
you need an established link to connective tissue disorder?
(Bear in mind that no surgery is risk-free.)
(3) Assume that you already suffer on of these ailments.
Before having them removed what proof would you require that
the implants--and not something else--was responsible for
Weekly reader puffing for tobacco?
Washington Post, 2 Nov. 1995, p C1
A University of California study found from 1989 to 1994, 68%
of the Weekly Reader's articles on smoking included the
tobacco industry's views, while only 38% carried a clear
anti-smoking message. A competing weekly, Scholastic News,
contained industry views 32% of the time and included anti-
smoking messages 79% of the time. As an explanation for the
difference, the article points out that the Weekly Reader was
bought in 1991 by K-III Holdings, a subsidiary of the former
majority owner of RJR Nabisco.
K-III spokesman David Adler rejected the finding, saying "The
Weekly Reader is probably more influential than any other
entity in discouraging kids from smoking." But UC Medical
Professor Stanton Glantz, author of the study, said that 62%
of the tobacco-related articles published before the K-III
purchase presented a no-smoking message, compared with 24%
after the purchase.
Solutions to the Basketball problem.
We received two solutions to our basketball challenge. Recall that Shunhui wanted
to divide ten basketball players into two teams of five by having the players toss
coins (by hand or fist). He wanted to minimize the number of coins tossed. Ben Tilly
and Charles Grinstead each described a method that is very likely best possible (expected
number of tosses 7 3/21) but not too practical. Ben then proposed a quite efficient
"practical" method. Here are their solutions.
The Grinstead-Tilly optimal solution.
There are 126 ways to divide the players into the two teams. We want these to occur
with equal probability. Identify the possible teams with the dyadic expansions for
the numbers from 0 to 125. Toss a coin 7 times. If the outcomes provide the dyadic
expansion of a number from 0 to 125, choose the corresponding team. If not, keep repeating
this process until you do get a number between 0 and 125. Each time you repeat it
you need only 6 tosses since you can use the last digit of the previous number to
determine the outcome of a coin toss.
The expected number of tosses required for this algorithm is 7 2/21. You cannot do
better than log(126) to base 2 rounded up (i.e. 7) so this is no doubt the best you
Here is Ben Tilly's suggestions for the best "practical solution".
The basic strategy for dividing n people into a group A of k people and a group B
of n-k people goes as follows. At each stage there are four groups, U, A, B and the
odd person out. At the start everybody except one person is in group U, and at the
end everybody will be divided between A and B.
Now at each stage you have everybody in group U flip, dividing that into H and T.
You will move one or both of these two groups into A or B subject to the following
1) If possible you move the larger of H and T down. If there is a tie, then you move
2) Whichever group gets moved down gets moved into the one which is closest to being
full if that is possible, otherwise it moves into the one which is farther from being
full. (You can prove that the smaller of H and T can always move into the one which
is farthest from being full.) If there is a tie then you move it into A.
3) If it is possible to move the rest of U into the other one, then you do so, put
the odd person in on the one that is not full and you are finished. Otherwise you
go to the next stage with the group that did not move down now playing the role of
U and the odd person out remaining unchanged.
It can be shown that this procedure takes 2n+O(sqrt(n)) flips to finish, and it finishes
in approximately log_2(n) stages. Improvement iii) listed below does not produce
a significant savings. To the best of my knowledge any other version of this gives
too little extra savings for the increased effort.
Now for n=10 and k=5 you can make the following improvements.
i) In step 2 you have the group moving down move into the one which is farthest from
being full at all points. (The opposite choice is better for large n, but not for
ii) If you see an obvious way to divide people into teams at any time, you take it.
iii) At each flip there is no need to have everybody flip, instead one person each
time is arbitrarily declared a head. If there is a tie in step 1 then one flip breaks
the tie. (You can do this in general, but the saving is only about log_2(n) since
you save about one flip per stage.)
For 10 people this algorithm has an expected value of just under 10 and a half flips
to divide them equally, and it is almost always finished in at most 2-3 stages. (Later
stages go faster since fewer people are involved.)
(1) How practical is Ben's solution?
(2) Why the change of strategy in i)?
(3) If you had a strategy for which the expected number of tosses would be less than
7 you would have to have at least one situation where you reached a decision after
6 tosses. Why is this impossible?
Please send comments and suggestions for articles
CHANCE News 4.15
(21 October 1995 to 16 November1995)
To: Readers of Chance News
From: J. Laurie Snell
We are exploring ways to obtain support for the continuation
of our e-mail Chance Newsletter and our Chance Database on
the Web when our NSF grant runs out this year. For this we
have to make a case that we are doing something worthwhile.
To help with this, we would appreciate your answering the
short questionnaire below and return it to us at your
1. Using the Chance Newsletter: Have you used the Chance
Newsletter in your teaching or other professional activities?
___ no, not at all.
___ yes, a little.
___ yes, often.
___ yes, very often.
If yes, how have you typically used Chance news? (check all
___ for class discussions of items in the news involving
___ as examples of how statistics are used in the real world.
___ as part of the class reading assignment.
___ to share items with colleagues.
___ other (please describe).
2. Using the Chance Database: Have you used materials on the
Chance Database on the Web in your teaching or professional
___ no, not at all.
___ yes, a little.
___ yes, often.
___ yes, very often.
If yes, how have you typically used the Chance database?
(check all that apply)
___ to search for articles on a particular statistical topic.
___ to obtain the full text of an article abstracted.
___ for ideas on teaching particular statistical topics.
___ to access teaching resources such as evaluation.
instruments, project guidelines, video summaries, etc.
___ other (please describe).
3. Teaching a Chance course: Have you taught, or are
planning to teach, a Chance-type course (a quantitative
literacy course based on current events in the news that
use concepts from probability or statistics)?
___ yes, I've taught one.
___ yes, I'm planning to teach one in the near future.
___ I'd like to teach a Chance course but don't have the
freedom or flexibility to do so in my department.
___ unsure if I'll teach one or not.
___ no plans to teach one.
If you have any general comments about usefullness
of the Chance News or Chance Database or ways to
improve them, please add these here. Thanks for your help.