CHANCE News 5.10
(15 August 1996 to 7 September 1996)
Prepared by J. Laurie Snell, with help from Bill Peterson,
Fuxing Hou, Ma.Katrina Munoz Dy, and Joan Snell, as part of the
CHANCE Course Project supported by the National Science
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 site:
Note: The length of this Chance News is just chance fluctuation
and is unlikely to happen again.
Toute Penseé émet un Coup de Dés
(All Thoughts emit a Throw of the Dice)
-- Stéphane Mallarmé
Links to the web sites we listed in the last Chance News are now available on the
Chance Database under "Other Related Internet Resources". We provide here links to
sites we feel will be useful resources for those teaching an introductory probability
or statistics course such as course syllabi, data sets, applets and other statistics teaching
Most of our academic links are to materials from mathematics or statistics departments.
We would like to add similar sites from other discipline where statistics is taught,
such as sociology, psychology, economics, biology etc. Please send the URL's of any such sites you know about.
Here are four new sites just added to our list on our Chance web site.
Chance and Data in the News
You will find here a collection of chance type newspaper articles from the Australian
newspaper Hobart Mercury. These are grouped according to the five topics: Data Collection
and Sampling, Data Representation, Chance and Basic Probability, Data Reduction and Inference. Each topic starts with general questions for articles related to
this topic. In addition, each article has specific questions pertaining to it and
reference to related articles.
This is the homepage for Chance Magazine, a magazine of the American Statistical Association
published by Springer-Verlag. You will find summaries of recent issues, previews
of upcoming articles and columns, and information about how to subscribe to Chance Magazine.
This is the homepage of public health expert Steve Milloy.
It focuses on "junk science" issues with special emphasis on developments in the public
health research arena.
Target Risk: a book by Gerald Wilde
This is a book by Gerald Wilde. Wilde believes that people have a tendency to adjust
their behavior in such a way as to offset the overall effects of safety improvements.
He calls this "risk homeostasis". For example: stronger laws against "drunk driving"
do not appear to decrease the overall death rate due to automobile accidents. This
book is written in an informal and lively style and provides interesting insights
into risks we all face.
It never rains but it pours for the Meteorology Office men.
Daily Telegraph, 29 August, 1996, p.3
This report is based on an article by Robert A. J. Matthews in the current issue of
Nature (Nature, 29 August, p. 766).
Highfield says that, if the Meteorology Office forecasts a downpour, you should not
bother to take your umbrella. This despite the fact that the Meteorology Office
claims that short-range forecasts are now more than 80 percent accurate. Matthews
says that: "The accuracy figures are misleading because they're heavily biased by success
in predicting the absence of rain. The real probability of rain during a one-hour
walk, following a Meteorology Office forecast (of rain), is only 30%".
In the Nature article, Matthews uses current data from the weather service and carries
out a decision theory analysis assigning costs to the possible choices: taking or
not taking an umbrella, rain forecast or rain not forecast, it rains or does not
rain. He shows that, unless you attach an exceptionally heavy loss to getting wet, the optimal
strategy is to ignore the weather prediction and not take an umbrella on your walk.
(1) In the Nature article you find the following table giving the various outcomes
of forecast and weather over 1000 1-hour walks in London.
Rain No rain Sum
What is the P(rain|forecast of rain)?
Forecast of rain 66 156 222
Forecast of no rain 14 764 778
Sum 80 920 1000
What is the P(no rain|forecast of rain)?
(2) In the Daily Telegraph article you find the following comment:
The Meteorology Office chose its words carefully in response
(to the claim that you should not take an umbrella even
if rain is predicted). He (Matthews) may well be right
if you are looking at a showery situation. We would
maintain that, if we forecast a day of sunshine and
showers, and showers occur, the forecast is correct.
But we can't forecast whether rain falls on the high
street or not."
What do you think of this reply?
An article in the last Chance News (See Chance News 5.09 item 13) reported that the manager of the Iowa Cubs is upset
about his team giving up too many runs to the opposition with 2 outs. The author
of the article reported that, at the time he wrote the article, 39.8% of the total
runs the Cubs have given up occurred with 2 outs.
We asked if it is reasonable to assume that about 1/3 of the runs given up should
occur with 2 outs.
Hal Stern wrote:
There is a literature that models baseball as a
Markov Chain on 24 states (3 outs x 8 baserunner
configurations). One reference is Thomas M.Cover
and Carrol W.Keilers, "Operations Research", Vol.5
No.5, pp 729-740. If one puts in a guess at the
24 x 24 transition matrix and does a bit of work
you can compute the expected runs scored from any
situation. I did this choosing a transition matrix
for the 1989 season. The results were:
1989 AL statistics (approx 4 earned runs per game)
Expected # runs per half-inning with 0 outs = .09
1 out = .15
2 outs = .21
total = .45
proportion with 2 out = .47
1989 NL statistics (approx 4 earned runs per game)
Expected # runs per half-inning with 0 outs = .08
1 out = .135
2 outs = .19
total = .405
proportion with 2 out = .47
The analysis can be criticized on several grounds:
1- omits errors.
2- omits double plays, sacrifices, stolen bases.
3- assumes same transition matrix applies for
4- uses major league and not minor league stat
The resulting values seem higher than I would have
thought but do confirm that 1/3, 1/3, 1/3 is not
realistic at all. These results suggest the
Iowa-Cub pitchers have more problems with 0 and 1
out than they do with 2 outs.
What explanation can you give more runs being scored as the number of outs increases.
Norton Starr suggested the next article.
Degrees of separation.
Health, Sept. 1996 p. 16
Economists Jennifer Gerner and Dean Lillard of Cornell University analyzed data from
27,000 college students nationwide. After taking parents' income and education into
account, they found that children of separated or divorced parents were half as likely as those of married parents to attend one of the country's top 50 colleges.
Gerner is quoted as saying: "We knew that a divorce at home tends to lower a student's
grade point average and SAT scores, so we expected a difference, but not one this
large." She went on to say: "A divorce claims children's attention and emotional
energy, making it harder for them to concentrate on homework or join in activities such
as sports and drama - which can make or break a college application. Divorced dads
may also be less willing to spring for Ivy League tuitions."
(1) Starr remarks:
It seems to me that there are numerous rival explanations
here, or rather there are lots of possible confounding
factors. In particular, the factors that encourage
divorce are likely to damage the chances that a young
person will attend an elite school.
What factors that encourage divorce do you think Starr had in mind? What are some
other rival explanations or confounding factors?
(2) What is the difference between a "rival explanation" and a "confounding factor"?
Here is a discussion question without an article suggested by a conversation with
The "Iowa Electronic Markets" on September 9, 1996 offered a Clinton share for about
79 cents and a Dole share for about 21 cents. (You get a dollar back for each share
if your candidate wins). An article in the "Economist" (See Chance News 5.01) stated
that "Introduced in the 1988 election it (The Iowa Electronic Markets) easily out-performed
opinion polls as a guide to the eventual results in both the '88 and '92 election."
Peter remarked that you should not expect such a market to act as a poll.
What do you think about this?
Joan Garfield suggested this article last time and we forgot to put it in. We were
reminded of it when Beth Chance also suggested it.
By the numbers.
The Country Chronicle, 26 June, 1996, p. 11
Sowell remarks: "One of the first things they teach in introductory statistics is
that correlation is not causation. It is also one of the first things forgotten."
To show this has been going on for a long time, Sowell gives two historical examples.
When Galileo invented the barometer he used water rather than mercury in the tube
so his barometer went up through the roof of his house. To help him tell height
of the water on a given day and hence whether the pressure was going up or down,
Galileo floated a wooden figure of a red devil on the water.
Galileo's neighbors noted that the red devil came out of the house on sunny days and
went back inside on rainy days. They attributed this correlation to sinister goings-on
with the devil and broke into Galileo's house and destroyed the barometer.
The second example occurred when the pioneers were settling the American northwest.
One group of pioneers brought measles which struck whites and Indians alike. The
doctor treated whites and Indians alike. The whites survived, but most of the Indians
died. The Indians noticed this and decided that the doctor was causing this by treating
the Indians differently than the whites and so they burned down the doctor's outpost,
killing him and many other whites. In fact, the correlation between race and dying
was caused by the fact that the Indians had no biological resistance to European diseases.
Bob Norman reported that, on our public radio station WVPR, Will Curtis stated that
the chance of dying as a result of a collision of the earth with a comet or asteroid
is greater than you might think, being about the same as dying by a plane accident
if you take one flight per year. Bob suggested that there could be problems in comparing
these probabilities. To see if we agreed with him we decided to find out how these
risks are estimated.
We found in the book "What the Odds Are" by Les Krantz, that, in 1991 (See Chance News 2.13 item 9), less than 1
in 1.6 million flights ended in deaths of passengers, crew or people on the ground.
We take 1 in 1.6 million as an estimate of the probability you will be killed on
your annual flight. This gives about a 1 in 25,000 chance of being killed in a lifetime assuming
if you fly once a year for 65 years.
The source of the oft quoted estimate of being killed by an asteroid or comet is an
article "Impacts on the Earth by asteroids and comets: assessing the hazard", by
Clark R. Chapman and David Morrison. (Nature, Vol 3l67, 6 Jan 1994, pp 33-40).
These authors estimate that a global catastrophe could be caused by asteroids in the
range .5 to 5 km. They estimate that an asteroid with diameter of about 1.5 km (about
a mile) would kill about 25% of the world's population. They call this a "nominal
asteroid" and estimate that it should occur about once in 500,000 years. They calculate
the risk of being killed in terms of the occurrence of a nominal asteroid. The current
world population is about 5.7 billion. Thus a nominal asteroid would kill about
1.9 billion people about once in 500,000 years. This would amount to about 3,800 deaths
per year. Thus your risk for a single year is about 1 in 1.5 million. The corresponding
lifetime risk for a 65-year span is 1 in 23,000.
Therefore, your yearly and lifetime probability of being killed by an asteroid (1
in 23,000) is about the same as being killed in an airplane accident (1 in 25,000)
if you fly once a year.
(1) Given an annual risk of 1 in 1.5 million how do you calculate the lifetime risk
for a 65-year span?
(2) We are now in a position to try to answer Bob Norman's questions. What problems
to you see in saying these two risks are comparable?
The Interrogator's fallacy.
Scientific American, September 1996, p. 171-175
The interrogator's fallacy is well-known to "Chance News" readers. It is the tendency
for the prosecutor to provide the jury with the P(innocent|evidence) when the expert
witness has provided P(evidence|innocent). This has been discussed most recently
in the case of DNA fingerprinting where the evidence consists of a match between the
DNA found at the scene of the crime and that of the accused. The FBI lab gives the
probability of a match given that the accused is innocent and the prosecutor uses
this as the probability that the accused is guilty given the match.
Stewart discusses this and a related example provided by Robert A. J. Matthews. Suppose
that you have assigned a probability of guilt and then given the additional evidence
that the accused has confessed. Does this increase the probability of guilt? The
answer is yes if Prob(confess| guilty) is greater than Prob(confess|innocent) and
no if Prob(confess|guilty) is less then Prob(confess|innocent). Of course this is
quite intuitive and you might wonder if the second alternative could occur. Matthews
suggests that it could in the case of a terrorist who has been hardened to not break down
under interrogation as compared to an innocent person who has not had experience
at being interrogated. For more on this see: Matthews RAJ, "The interrogator's fallacy"
Bull. Inst. Math. Appl. 1995; 31: 3-5.
Stewart uses these examples to illustrate the need for understanding conditional probability
and then goes on to do the usual thing of presenting paradoxical cases to persuade
you that you will never understand this concept. He chooses the well- known example of Mrs. Smith with her two children and the question of whether the Prob(two
girls|girl in the family) is 1/2 or 1/3 or some other number. Of course the point
he wants to make is that the answer depends on the context of the problem, but we
fear that this is not the point the readers come away with.
(1) It is fashionable to say that conditional probability is too hard for a first
statistics course. Do you agree?
(2) Here is the example Stewart gives. You know that Mrs. Smith has two children.
You see her in the garden with her two children and you see that one is a girl but
the other is hidden by their huge dog Otto. What is the probability that this second
child is a girl.
Randy White asked what we could make out of the following article.
ESPNET SportsZone, August 29, 1996
Rob Meyer says that, even though the Yankees were five games ahead of the Orioles,
in the AL East they aren't doing that much better. He writes:
When I run into something like this, the first
thing I like to do is check the Pythagorean formula,
a wonderful tool in that it combines high degrees
of both simplicity and utility. As defined by Bill
James, the Pythagorean formula states: "The ratio
between a team's wins and losses will be the same as
the square of the ratio of their runs scored and
Anyway, it works. If you run every major-league team
through the formula after the season, you'll find that
their records generally fall right in line with their
runs scored and allowed.
Except it's not working for the Yankees. Based on the
number of runs they've scored (662) and allowed (617)
through Wednesday, the Yankees should be not 72-53, but
67-58, which just happens to be Baltimore's record.
In case you're wondering, the Pythagorean formula works
out to 67-58, exactly, for the Orioles. So in essence,
the two AL East contenders are about as even as can be.
To understand all this we had to find out what the Pythagorean formula is. As Meyer
said, this is an empirical observation of Bill James. (See, for example, The "Bill
James Historical Baseball Abstract", 1988 p 293.) James provides data for the 24
major league teams in the 1984 season. Using his data we found a correlation of .857 between
the square of runs/runs allowed and actual wins/losses for these 24 teams, with best-fit
line y = .003x + 1.002x remarkably close to y = x.
The same idea has been applied to basketball, but now the power 2 is replaced by the
power 16.5. Dean Turcoliver compared the basketball version of the Pythagorean formula
to a simple probability model, in a paper "New measurement techniques and a binomial model of the game of basketball".
Turcoliver provides the data for the 27 NBA teams for 1990-91.
Using this data and fitting the actual percentage wins with those predicted by the
Pythagorean formula, using the power 16.5 yields a correlation of .99 and the best
fit-line y = .06 + .87x.
For his probability model, Turcoliver assumes a probability p that a team will score
2 points during a period when they have possession of the ball and a probability
q that they will allow 2 points to be scored when their opponent has the ball. (Note
the simplifications: the values p and q are constant for a given team and do not depend
on who the opponent is and all points scored are 2 points.)
For each team Turcoliver estimates p and q for this team from records of their games
throughout the season. Then the probability that this team will win a game can be
modeled as the outcome of tossing a p and a q coin about 100 times (a typical number
of possessions per game). The probability that the team wins is the probability that when
a p coin and a q coin are tossing 100 times the p coin gets more heads than the q
coin. This probability is taken as the predicted proportion of wins during the season
for the team.
Turcoliver tests this model for the 1990-1991 NBA season. Using his data, we found
a correlation of .98 between the predicted percentage of games won and the actual
percentage with best-fit line -.07 + 1.13x.
(1) Why do you think such a high power is needed for the Pythagorean formula for
(2) Could you modify Turcoliver's binomial model to give a model for baseball? for
Magnetic field exposure, breast cancer risk tied.
The Boston Globe, 20 August 1996, pA3
In the September issue of the journal "Epidemiology," Boston University medical researchers
report that women working near equipment that generate strong magnetic fields have
a 43% greater risk of breast cancer than women exposed to minimal radiation. Pre-menopausal women who worked around large mainframe computers had the highest risk--twice
that of women with no unusual exposure.
Overall, the risks identified were described as "modest" and the researchers are careful
to note that their estimates of exposure were quite crude. Using state cancer registries,
the study identified 6888 women diagnosed with breast cancer from 1988-1991. A comparison group was formed consisting of 9529 women of similar age and residence,
having no history of breast cancer. Interviews were used to determine each woman's
"usual occupation" during her lifetime, and an industrial hygienist ranked the jobs
for potential exposure to magnetic fields. Only 57 women with cancer and 65 women
from the comparison group fell into the "high exposure" category.
1. Compare the percentage of women having "high exposure" in the cancer and no-cancer
groups. What does this calculation have to do with comparing risks?
2. Does it seem to you that there are a large number of caveats and disclaimers in
this article? Do you think a study that finds relatively small risks using admittedly
crude measurement techniques should get this sort of headline?
Study's rate of business starts is greeted skeptically by some.
The Wall Street Journal, 23 August 1996 p1.
The National Federation of Independent Businesses (NFIB), the largest small-business
lobby in the nation, has reported that nearly 3.5 million businesses were started
in the US in 1995 and another 900,000 people bought companies last year. These estimates are based on a Gallup survey of 36,000 households
which asked people whether they had started or bought a business in the last 6 months.
About one-fifth of the respondents indicated that they had bought or started a business
employing at least one person besides themselves.
The NFIB figure for start-ups is 18 times greater than estimates by Dun and Bradstreet,
the traditional source for such statistics. A senior research fellow at NFIB says
that the findings don't contradict current thinking but are "simply more inclusive"
because more data were collected than in previous research. Dun and Bradstreet countered
that many people who start companies are in fact engaged in hobbies or part-time
occupations that have no significant commercial activity.
1. Can you reconstruct the reasoning whereby the 3.5 million figure was computed
from the responses reported?
2. What kinds of business activities do you suppose might be included NFIB's "more
inclusive" data collection in order to produce such a large increase over Dun and
Are athletes nearing the limit?
The Boston Globe, 19 August 1996, pC1
Are there limits to athletic performance? This article raises the question in the
context of Michael Johnson's dramatic performance in the 200 meters this year. In
the Olympic Trials he lowered the world record from 19.72 to 19.66 seconds. Then,
in his gold-medal winning race, he lowered it to 19.32 seconds. In a post-race interview,
he confidently stated that he could go still faster.
Gideon Ariel, a former computer science professor, has been studying the biomechanics
of athletes for almost 30 years, using computer models to analyze performance. In
1976, he projected what he considered to be the limits for the four track and field
events shown in the table below (which gives the 1976 and current world records along
with Ariel's projected limit).
1976 1976 current
According to Ariel, running the 100 meters any faster than 9.6 seconds would actually
tear muscles or break bones. While others have predicted a time of 9.15 sometime
after the year 2100, the article notes that such projections are based on current
statistical trends rather than physiology.
Event record projection record
100 meters 9.9 sec 9.6 sec 9.84 sec
Long Jump 29'-2.5" 29'-5" 29'-4.33"
High Jump 7'-6.5" 8'-10" 8'-0.5"
Shot Put 71'-8.5" 100' 75'-10.25"
The article lists a number of factors besides physiology that may contribute to future
records. Among these are equipment (the hard surface of the Atlanta track was said
to promote faster times), conditions (sprinters prefer warm humid weather, distance
runners prefer cooler) and advances in training techniques, and sports psychology.
1. In Atlanta, Canada's Donovan Bailey ran the 100 meters in 9.84 sec, establishing
a new world record. The article notes that over the last ten years, the record has
been bettered six times, starting at 9.95 sec. From this "statistical trend", when
would you estimate a time of 9.15 sec? What techniques do you think produced the statistical
projection of "somewhere beyond 2100" for this feat, reported in the article?
2. Suppose you wanted to investigate one of the other factors mentioned for improved
performance. For example, suppose you wanted to predict what Bailey could do at
the "ideal" temperature with the maximum allowable tailwind. How might you proceed?
Jane Millar suggested the next article.
The EPA's Houdini Act.
Wall Street Journal, 8 August, 1996, A10
Steven J. Milloy
In this op-ed editorial Milloy claims that the Environmental Protection Agency (EPA)
is "about to escape from the shackles of good science". This is going to be done
by a kind of Houdini Act that does away with the requirement of establishing statistical
significance before labeling such things as electromagnetic fields, dioxin, and second
hand-smoke as cancer risks.
Milloy does not state here what the Houdini act is and what his real complaint is.
Indeed, because he complained about the EPA switching from the more traditional
95% to 90% in the case of second-hand smoke, a reader in a letter to the editor to
the WSJ took Milloy to task for not realizing that the level of significance could reasonably
vary from situation to situation.
Fortunately Milloy has a more serious paper on this subject on his homepage (http://www.junkscience.com)
under "What's Hot". The real issue is that Milloy claims the old regulations REQUIRED
statistical significance and the new ones do not. The EPA disagrees with him. Who is correct will make an interesting discussion question.
According to the 1986 guidelines:
Three criteria must be met before a causal association can be inferred between exposure
and cancer in humans:
1. There is no identified bias that could explain the
2. The possibility of confounding has been considered
and ruled out as explaining the association.
3. The association is unlikely to be due to chance.
The 1996 guidelines propose:
A causal interpretation is enhanced for studies to the extent that they meet the criteria
described below. None of the criteria is conclusive by itself, and the only criterion
that is essential is the temporal relationship...
(1) Temporal relationship: The development of cancers
require certain latency periods, and while latency
periods vary, existence of such periods is generally
acknowledged. Thus, the disease has to occur within
a biologically reasonable time after initial exposure.
This feature must be present if causality is to be
(2) Consistency: Associations occur in several independ-
ent studies of a similar exposure in different
populations. or associations occur consistently for
different subgroups in the same study. This feature
usually constitutes strong evidence for a causal
interpretation when the same bias or confounding is
not also duplicated across studies.
(3) Magnitude of the association: A causal relationship
is more credible when the risk estimate is large and
precise (narrow confidence intervals).
(4) Biological gradient: The risk ratio (i.e. the ratio
of the risk of disease or death among the exposed to
the risk of the unexposed) increases with increasing
exposure or dose. A strong dose response relationship
across several categories of exposure, latency, and
duration is supportive for causality given that
confounding is unlikely to be correlated with
exposure. The absence of a dose response relation-
ship, however, is not by itself evidence against a
(5) Specificity of the association: The likelihood of a
causal interpretation is increased if an exposure
produces a specific effect (one or more tumor types
also found in other studies) or if a given effect has
a unique exposure.
(6) Biological plausibility: The association makes sense
in terms of biological knowledge. Information is
considered from animal toxicology, toxicokinetics,
structure-activity relationship analysis, and short-
term studies of the agent's influence on events in the
carcinogenic process considered.
(7) Coherence: The cause-and-effect interpretation is in
logical agreement with what is known about the natural
history and biology of the disease, i.e., the entire
body of knowledge about the agent.
Did the 1986 guidelines require statistical significance? Do the proposed new guidelines
require statistical significance?
Here is another article on the issue of statistical significance, suggested by Allan
Psychologists divided over validity of statistical
Chronicle of Higher Education, 16 Aug. 1996, A12
This article reports that there is a hot controversy among researchers in Psychology
over the use of significance tests . Psychologist John Hunter is quoted as saying
"The significance test is killing off many of the benefits of research."
The American Psychological Association asked a group of researchers to look into this
problem and to suggest remedies if they see a real problem. The main criticism is
the obvious one that, if significance is required for success in publishing a paper,
then information is lost from experiments that indicated a positive result but did not
establish it. Of course, the current use of meta-studies is designed to help solve
this problem, but even there, the data may be hard to get if research that does not
establish significance is not taken seriously.
It is suggested that this is a bigger problem in Psychology than in other fields because
so much of the research in Psychology naturally lends itself to the standard statistical
Hit the lotto, buy a toaster.
The New York Times, 21 August, 1996, B1
New York Governor Pataki has ordered a change in the ads for the New York lottery.
He thought that the old ads were fostering false expectations and trying to lure
people into putting down a few dollars for a chance of winning big.
This article gives typical examples of the old ads:
Those adds by and large depicted such outrageously
funny moments as a lowly mail room clerk taking over
a large corporation after winning the jackpot and a
giddy toll taker waving motorists through for free as
he tosses his winnings into the change pocket.
and a new ad:
A news spot opens with a narrator solemnly announcing
that the lottery helps pay for education. The ad
then shifts to grainy black-and-white images of
students busily working at their desks and computer
terminals as the narrator volunteers for an educational
program that the lottery is helping sponsor. It all
ends with a warm message flashing across the screen
"The New York Lottery makes everyone a little richer."
Advertising experts say that it makes no sense to use less effective methods of advertising.
It will only mean less money for the worthy purposes that are being advertised.
Others wonder how the Governor can be so concerned about the possible harmful effects of lotteries ads given that he pushed through the new Quick Draw game that is
particularly likely to cause people to spend money they can ill afford because of
the ease of repeated plays.
(1) Does the Governor's actions seem hypocritical to you?
(2) Could a lottery ad suggesting you can get a new toaster be more effective than
one that encourages you to play the lottery to make you a millionaire?
Parade Magazine, 1 Sept. 1996, p 23
Marilyn vos Savant
Marilyn is asked the following question:
I've heard that you can take real data and
prove that people with bigger hands are better
at math. I could believe longer hands and the
piano, or even bigger heads and math. But
people with longer hands perform better at
math. Come on.
D. R., Columbia S. C.
Marilyn says it is true but in a misleading way. She says that you can even prove
that people with bigger ears are better at math. "Just take a random sample and measure
their ears and give them math tests and you will find a strong correlation."
Would Marilyn's answer convince your Uncle George?
For babies: bigger, better growth charts.
US News & World Report, 26 August 1996, p11
Pediatricians have been aware for some time that existing standardized height and
weight charts for children are inaccurate for the early months--most new infants
are ranked above average. (The article duly notes the parallel with Garrison Keillor's
Lake Wobegon, where all children are above average!). A study just published in the American
Medical Association's "Archives of Pediatrics and Adolescent Medicine" found that
a diverse group of 1574 Chicago infants was taller and about 7% heavier than the
standards at 1 month, but the differences was vanishing as the infants approached 1 year
Apparently it's not that today's infants are bigger, but rather that the old federal
benchmarks are inaccurate. They turn out to be based on a small group of infants
from Yellow Springs, Ohio, some born in 1929. The National Center for Health Statistics
is planning to have revised charts out next year.
1. In and of itself, does the fact that children are back on the charts by 1 year
mean that there could not have been an increase in birth weight during this century?
How do you think the latter was ruled out?
2. Speaking about the Yellow Springs data, the lead author of the Chicago study notes
that: "It was good quality data but not a representative sample." Is this statement
Technology in statistics brings 40 international experts together.
Ideal (Granada Spain), 24 July 1996
The University of Granada hosted an International
Conference on the Role of Technology in Teaching and
This article asks:
Who has not sometimes felt the desire to turn
the page when finding one of those huge
statistical graphs that fill reports, specialized
journals, and newsletters and provoke a state of
increasing perplexity in the subject?
It goes on to say that conference members feel that education is the answer to keeping
these people from turning the page.
Juan Godino, one of the organizers of the conference, explained that educational reformers
recommend that the teaching of statistical ideas begin at the very beginning of a
child's education. This is made possible by the development of computers and new
technological tools. The conference is devoted to learning how to make these tools effective
in the understanding of statistics.
Editors note: This was a great conference. The proceedings are being prepared by
Joan Garfield and will be made available on the web.
Debatable decisions: operations researchers cast their analytical eyes on an emotional
ORMS Today, August 1996 p24
At the spring national meeting of INFORMS (Institute for Operations Research and Management
Sciences) a discussion session was held on policies of affirmative action. The intent
was to see what perspectives the analytical modeling point of view could offer on this difficult social issue. ORMS Today presents here essays by the three main
panelists: Jonathan Caulkins of Carnegie Mellon University, Arnold Barnett of MIT
and Harold Pollack of Yale.
This is a long set of articles, and we will only highlight a few points here.
"Color Blind Policies Not Enough"--Jonathan Caulkins
Caulkins describes the need for affirmative action policies under four proposed assumptions
about the structure of society. For example, assuming that whites and blacks as
individuals might be equally racist, it does not follow that we will have equality
of opportunity, because whites hold a disproportionate share of influential positions.
Even assuming blacks and whites are equally powerful, Caulkins presents some simple
models to show why blacks would not be guaranteed equal opportunity.
His first model assumes that 10% of each race would discriminate if given the chance,
that everyone lives in integrated neighborhoods, and that everyone has eight neighbors.
The probability that any one neighbor of a white person discriminates is the probability that this neighbor is black (12.6%) times the probability that this person
is racist (10% by assumption). Thus the probability that at least one of a white
person's eight neighbors discriminates against him is given by
1 - [P(neighbor doesn't discriminate)]^8 = 9.6%
For a black, the corresponding figure is 51.9%.
Caulkins introduces his second example by noting that, in 1991, 13.5 million of the
125 million workers in the US were black, or roughly 1 in 9. He then considers the
hypothetical situation where nine equally qualified candidates (8 white, 1 black)
apply for nine jobs, which all agree rank in desirability from 1 (most desirable) to 9 (least).
If blacks are discriminated against, so that the black gets the worst job, then
the average job rankings for whites and blacks will be 4.5 and 9 respectively. If,
on the other hand, the hiring is colorblind, the expected rankings become 5 for each
group. Finally, under an aggressive policy that award job 1 to the black candidate,
the averages are 5.5 and 1. The point is that the presence or absence of discrimination has a much more pronounced effect on the minority group.
Finally, even in a model where no one is racist, existing inequalities can create
a "trapping state." Because race is easily observed and is correlated with job-relevant
characteristics, it may be rational to discriminate statistically. The resulting
reduction in opportunity could discourage minorities from investing in their human capital,
thereby perpetuating the problem.
Fill in the details in the calculations for the first example.
"Building Equal Opportunity on a Firmer Footing"--Arnold Barnett.
Barnett noted for the discussion panel that he would be "comfortable" arguing presenting
either side of the questions; here he has been selected to make the case against
affirmative action. He clarifies this to mean he will argue against "extreme" affirmative action, which he defines as preferential treatment based on ethnicity or gender
that routinely results in the selection of less qualified individuals. His first
proposition is that such action may be widespread in the US. He presents, for example,
mean SAT scores for four groups of undergraduates admitted to Berkeley in fall of
Mean Score (400-1600)
He notes that these are consistent with national data indicating an average white-black
difference of 182 points among students entering 26 prestigious colleges in 1990-91.
He adds that non-Asian minority students have much lower graduation rates than whites. While these data are open to various interpretations, Barnett points out that
they certainly do not support claims that differences in academic qualifications
suggested by the entrance data become irrelevant once students enroll.
His second proposition is that the number of individuals who perceive they have suffered
under affirmative action may greatly exceed the number who actually suffer. The
(1) "I would have gotten that job had I been a member
of a minority group", and
(2) "I would have gotten that job had it not been for
are not equivalent, though they might initially appear to be. For example, even though
one's qualifications might have met some reduced threshold a minority candidate who
got a desirable job, it does not follow that one would have beaten out all qualified non-minority candidates. The first interpretation allows many more people to feel
they have suffered reverse discrimination. Even though this perception is inaccurate,
Barnett wonders if, in a pragmatic sense, we can afford the bitterness resulting
from extreme affirmative action, because it may harden attitudes against other more desirable
His third proposition is the case for affirmative action, recently enunciated in a
1995 report prepared for President Clinton, contains weak analytical reasoning.
For example, the report states that "the average income for Hispanic women with college
degrees is less than the average for white men with high school degrees." While it is
initially striking, this comparison unfortunately fails to control for key variables.
It does not take age into account--there may be proportionately few Hispanic college
graduates who have had time to advance in their careers. Also, it does not consider
whether the women enter careers such as school teaching that (rightly or wrongly)
pay less than some blue collar jobs.
In his second proposition, Barnett suggests that we may sometimes
need to change policy in light of an emotional reaction to a policy's effect, even
if that reaction is based on a flawed (analytically speaking) perception of what
has actually happened. Would you agree?
We do not normally review books but three recent books are so obviously useful to
supplement a Chance course that we feel that we should mention them.
A Casebook for a First Course in Statistics and Data Analysis
Samprit Chatterjee, Mark S. Handcock, and Jeffrey S. Simonoff
Wiley, New York, 1995
Unfortunately, this is such a good book that someone ran off with our copy so we are
unable to give a detailed description this time. However, for now we encourage you
to read the find review of this book by Judith M. Tanur in the Winter 1996 issue
of "Chance Magazine". See also Chance News 4.08 and 5.03 for a discussion of examples from
Workshop Statistics: Discovery with Data
Allan J. Rossman
Available from Jones and Bartlett in North America
and Springer outside North America.
Rossman states that "Statistics is the science of reasoning from data." He has based
his book on this belief and his philosophy that students learn statistics by doing
Rossman envisions the classroom as a laboratory where the instructor gives occasional
explanations of basic ideas but mostly helps the students in a co-operative learning
experience. The basic ideas of statistics are learned in terms of exploring data
sets either provided by the text or generated by the students. Activities guide them
in their explorations. Emphasis is placed on students learning to effectively communicate
their findings. The data sets provided are from a variety of fields of study and
many represent issues of current interest to students such as: student's political views,
hazardness of sports, and campus alcohol habits.
The book is organized by subject into six units each of which has several subunits.
Each subunit has the following items
- Overview: a brief introduction to the topic,
emphasizing its connection to earlier topics.
- Objectives: a listing of specific goals for
students to achieve in the topic.
- Preliminaries: a series of questions to get
the students thinking about the issues and
applications to be studied and sometimes to
collect relevant data.
- In-class activities: the activities that guide
students to learn the material of the topic.
- Homework activities.
The first two units introduce descriptive statistics and standard graphical displays
of data and exploratory data analysis. The third unit deals with randomness and the
last three with statistical inference. The students are assumed to have a computer
or calculator available for their explorations.
The exploratory statistics units give the student a wonderful opportunity to try lots
of different and interesting ways to look at the data, starting with a few basic
graphics techniques such as stem-leaf plots, box-plots, histograms and scatter diagrams.
The tools for inference and test of hypothesis provided are limited to the standard
normal, t-test and binomial tests. It might be better, having described statistics
such as the sample mean, sample standard deviation or the chi-squared statistic,
to have the students obtain, by simulation, the approximate confidence intervals, or p-values.
Then, for example, if they were given the activity to design an experiment to determine
if a fellow student can tell the difference between Pepsi and Coke they could explore different designs instead of being limited to the independent trials model suggested
for Fisher's famous "tea testing experiment." They might even choose the design
that Fisher used.
The use of the "bootstrap method" would also allow more adventuresome explorations.
The instructor might have to help with some of the simulations but, after all, that's
On the other hand, what makes this such a great book is that the author has limited
himself to make it possible to get over the basic concepts of statistics at a reasonable
level and to make a course based on the book very teachable. The book can also be
used as supplementary material to liven up a more traditional course. In either case,
Rossman's book shows that student's first introduction to statistics can be made
the exciting experience it should be.
Editors (Snell's) comment: Here are some comments on the Rossman book from the biased
point of view of a probabilist.
As Rossman dramatically demonstrates, it is a lot more interesting and instructive
to introduce statistical concepts in terms of real data related to serious issues.
This presents a challenge to we who write probability books to discuss basic concepts
of probability in terms of experiments and data corresponding to significant problems
rather than the traditional experiments of tossing coins, rolling dice and drawing
balls out of urns.
Of course, as a probabilist we were disappointed that there is essentially no discussion
of basic probability concepts such as conditional probability and expected value.
We think that it is a mistake to separate statistical reasoning and probabilistic
reasoning so completely. After all, the greats such as Laplace, Fisher and Galton didn't;
so why should we?
Schaeffer, Gnadiseken, Watkins, Witmer
"Instructor Resources" available from Springer-Verlag
"Student Guide" available from Jones and Bartlett
Under an NSF grant, the authors developed and tried out a large number of activities
suitable for an introductory statistics course. In the "Student Guide", the authors
give almost an encyclopedia of the activities they developed and tested. In the "Instructor's Resources", they provide these activities and discuss the art of using them
in a statistics course.
In the Student Guide, each activity starts with a "scenario" which, in most cases,
tells the student a real-world situation relevant to the activity. Then the objectives
of the activity and a question that it will answer are given. Next, detailed instructions are given for carrying out the activity. Then students are given some "wrap
up" questions and possible extensions of the activity.
The "Instructor Resources" provides the pages from the "Student Version" relating
to each activity. It starts each discussion of an activity with general remarks about
where and how it might be used in a statistics course. It then specifies what the
students need to know and the materials needed to carry out the activity. Sample results
from previous experiences with the activity are provided. Finally, you will find
sample assessment questions to see what the students have learned from doing the
There are many more activities than one would use in a single course, allowing instructors
to pick those most suited to their own course. It is also possible to construct an
interesting statistics course using primarily some of these activities.
The activities include a few old favorites, such as the German tank problem and standing
coins on end, but, at least for us, most of them were new. We were pleased to see
that a number of activities aimed at learning probability concepts are provided.
Strangely, the important concept of conditional probability is again missing. It must
have taken real will-power to omit the infamous Monty Hall problem, and we can appreciate
not including this, but, surely, the activity of having students discover the probability of AIDS given a positive test would have been appropriate.
The activities range from very simple to somewhat complex. For example, to illustrate
the idea of bias we find the very simple activity of asking the students to estimate
the length of a piece of string 45 inches long. The distribution of the student's
estimates will be centered near the more natural length of 36 inches.
To introduce the idea of trying to tell the effect on the outcome of an experiment
of one factor when two factors affect the outcome, the authors describe a delightful
but more complicated "frog activity". Students begin by constructing a frog from
a square piece of paper. The students are randomized according to the four different possibilities
of size and weight of paper and then they experiment to see how far their frogs will
jump. We confess we did not believe jumping frogs could be constructed from a square piece of papers and so, with some difficulty and some help from my son, We followed
the instructions and were delighted to find that our frog did indeed jump quite well.
(We will try to put a video on the web version of our frog jumping.)
If you used some of these activities and the students enjoy them as much as we did
the "frog activity" your course cannot fail!
Butterflies on the street.
The New York Times, 19 July 1995, A27
John Allen Paulos
Paulos remarks that the recent volatility in the stock market reminds him of an experiment
he carried out in one of his probability classes some time ago.
He put a box at the top of his exams that were given twice a week. He told the students
that anyone who checked a box would be given an extra 10 points with the proviso
that if more than half checked the box the students would all lose 10 points.
Paulos reports that the number of students checking the box increased until they were
finally penalized and after this dropped significantly. Then, for the rest of the
semester, the proportion of the students who marked the box oscillated between 25
and 40 percent.
Paulos remarks that it is not surprising that researchers at the Santa Fe Institute,
in their study of the behavior of stock market investors using concepts from chaos
and complexity, are considering scenarios like the one he described.
Paulos observes that concepts from chaos such as the "butterfly effect" -- small changes
can cause large deviations in future behavior -- would help explain some of the problems
in getting reliable estimates for the deficit and other economic projections.
(1) Can you think of other situations where people have to make decisions like those
made by the students in Paulos' class? What would occur to you if you were asked
you to think of a situation where you have thought: "but what if everyone did that?"
(2) Can you think of a game or other devise to study the behavior of people faced
with the kind of decisions that Paulos' students had to make.
(3) Can you think of a way to study this kind of behavior through a game or experiment
that could be repeated enough times to see if there is some kind of long run consistent
Sedentary lifestyle looms large as death risk.
USA Today, 1D, 17 July 1996
A new study in an issue of the "Journal of the American Medical Association" devoted
to sports medicine has found that being unfit is nearly as large a risk factor for
death as smoking. The study followed 25,341 men and 7,080 women for eight years.
The study found that men who were among the 20% least fit had a 52% greater chance
of dying during the study period. The least fit women had a 110% greater risk of
Death risk from all causes was 41% lower among moderately fit, nonsmoking men than
among low fit, nonsmoking men. For nonsmoking, moderately fit women, their mortality
risk was 55% lower than low fit women.
Dr. Fraser Bremner of Loyola University Medical Center summed up the findings: "If
you're fit, you're going to live longer, and you're going to offset the impact of
bad habits, like smoking, and risk factors like hypertension and having a high blood
New study questions radon danger in houses.
The New York Times, A15, 17 July 1996
A new radon study conducted in Finland at the Finnish Center for Radiation and Nuclear
Safety have failed to connect indoor radon exposure with lung cancer. The study
raises uncertainties about public health warnings that the colorless, odorless gas
is responsible for as much as 10% of lung cancer in the United States. The study analyzed
residential exposure to radon for 1,055 lung cancer patients and compared that with
the radon exposure of 1,544 people without lung cancer.
Radon is a gas that forms from the decay of uranium and radium in soil and rocks.
When inhaled, the gas can leave radioisotopes in the lungs and, over time, the low
levels of radiation damage the lungs and cause cancer. The debate arises not from
the fact that radon causes lung cancer, but from the uncertainty of what is the level of
risk from low-dose exposures.
The Environmental Protection Agency first issued warnings about radon in the 1980's,
after studies linked it with lung cancer among hard-rock miners who were exposed
to high levels. The EPA then used these levels to extrapolate what level in homes
would be hazardous. They estimated that 10% of American lung cancer cases were caused by
The EPA recommends that homeowners with at least 4 picocuries per liter of air of
radon should install vents or fans to prevent the gas from accumulating. The Finnish
study, however, was done in an area of high levels of radon at which some levels
were at 10 picocuries per liter of air. The study found no link between high radon levels
and lung cancer.
Further international radon studies are being done and will eventually be combined
to get a better picture of radon hazard in homes. Current North American radon research
is underway in Connecticut, Iowa, New Jersey, and Utah.
Regimen of painkillers holds risks, study says; Can mask serious gastric complications.
Boston Globe, 23 July 1996, A3
Richard A. Knox
A new study by Stanford University researchers has found that millions of arthritis
sufferers who take daily painkillers are at risk of sudden and potentially fatal
bleeding. There were no mild warning symptoms of stomach problems for 4 out of 5
patients who suffered serious gastric complications while taking common analgesics for arthritis.
Individuals who took antacids or acid-blocking pills such as Tagamet, Zantac, or Pepcid,
to prevent stomach damage from their arthritis medication, actually had more than
twice as many episodes of serious gastric complications as arthritis patients who
took the stomach drugs only when they had symptoms. By suppressing heartburn and other
warning signals, these drugs increase the chance of gastric complications because
they create a false sense of security for the patient and physician.
The risk of ulcers among arthritis patients is 15 times the general population's rate
-- of 30 million arthritis sufferers, 15% have ulcers. Of the 1,900 people in the
study, 42 were hospitalized for gastrointestinal problems and 34 of them had no warning episodes.
The study was funded by G.D. Searle and Co, which is making a drug to counteract the
stomach-damaging effects of arthritis anti-inflammatory drugs. Current medication
depletes prostaglandins (produced by the stomach which protect the stomach lining)
while simultaneously reducing prostaglandins in arthritic joints, where they cause inflammation.
Study blames cot deaths on smoking parents.
Reuters World Service, 25 July 1996
Peter Fleming of the Royal Hospital for Sick Children in Bristol and his colleagues
have finished a two-year study on sudden infant death syndrome (SIDS) in three regions
of England using 195 babies who died and 780 who did not.
Published in the "British Medical Journal," the study found that parents who smoke
during pregnancy and after birth could be responsible for more than half of cot deaths
(SIDS). They found that 62% of the mothers of babies who died smoked, as compared
to 25% of mothers of babies who lived. Babies of fathers who smoked were also slightly
more likely to die.
The researchers, working for the British Foundation for the Study of Infant Deaths,
also researched other factors for cot death. They confirmed earlier findings that
babies laid down in the supine position were at least risk of dying from SIDS. Other
factors that increased SIDS were the side sleeping position; loose bedding, such as
duvets; and bed sharing by mothers who smoke (routine bed sharing with parents two
or more nights a week was commoner among babies who died, 26%, than controls, 14.2%).
The exact cause of cot death is unknown. SIDS kills more babies in Britain than anything
else, but rates of death due to SIDS vary widely around the world.
(1) What confounding factors might you want to consider in this study?
(2) All of the data appearing in the article
are given above. How do you think the 61% figure (for the
potential reduction in crib deaths) was arrived at?
Dart throwers beat pros and industrials.
Wall Street Journal, 7 Aug. 1996, C1
Nancy Ann Jeffrey
The darts extended their streak to 6 consecutive wins over the pros and the Dow Jones
Industrial Average, in this ongoing contest sponsored by the "Wall Street Journal."
In this latest six-month period, the stocks chosen by the darts had an average gain
of 2.6%, while the pros has an average loss of 8.6% and the Dow an average gain of
This makes the current score pros 44, darts 31. Against the Dow the score is pros
38, Dow 36. The pros have had an average six-month gain of 10.1%, compared with
5.7% for the darts and 5.9% for the Dow.
Do you have enough data here to determine if the pros lead over the darts is significant?
If so is it?
World events keep hitting close to home.
Union Leader (Manchester NH), 21 July, 1996, A1
Shawne K. Wickham
It seems to happen every time. First comes word of
some event, all too often a tragedy, that attracts
international attention. And shortly thereafter
comes the news: There's a New Hampshire connection.
Many examples of this are provided, such as the death of Concord school teacher Christa
McAuliffe in the Challenger explosion,
Bernard Goetz choosing the Concord N.H. police station in which to surrender, the
pilot of the Pan Am Flight 103 crash living in Kensington N.H., and, most recently,
at least five of the 230 passengers killed in the crash of TWA flight 800 having
ties to New Hampshire.
Wickham asks why this is the case, saying: that "After all, we're a tiny state, ranking
41st in population."
Paul Brockelman, professor of philosophy and religious studies at the University of
New Hampshire, says that one fairly obvious explanation is that: "We are a pretty
educated and cultural population. We've got a lot of creative people here, bright
people, and therefore they're involved in things. We have ambitious people, so they're all
over the world. And that translates into a higher probability that New Hampshire
folks will end up in dramatic situations." Brockelman also suggested that we don't
react as deeply to world events that have not touched New Hampshire.
James Baumgartner, professor of mathematics at Dartmouth and a former teacher of the
Dartmouth Chance course, is not convinced that New Hampshire figures more prominently
in world events than other states. He points out that most people probably have
connections to many states, which increases the probability that any small state will
have connections to a big news event. In addition, one should consider other factors.
The fact that TWA flight 800 originated from New York increases the chance that there
will be passengers from New Hampshire. In the end, he suggests that New Hampshire's
appearance of a special fate may be just a "coincidence."
The author of the article appeared not to be convinced and proceeds to list numerous
(1) Which professor's argument do you find more convincing.
(2) What do we mean when we say that something is a "coincidence."
(3) 230 people are killed by a new form of "killer bees." Assuming that these 230
people were chosen randomly from the U.S. population, how would you find the probability
that 5 or more are from New Hampshire?
Bob Griffin, who teaches science writing sent us the following discussion of an article
that he has used.
Bystanders' CPR efforts often backfire, study says
Milwaukee Journal Sentinel, 27 December 1995, p. 6A
The lead (first) paragraph reads:
Chicago -- Bystanders who attempted CPR on cardiac
arrest victims got it wrong more than half the time,
reducing patients' already slim chances of survival,
a study found.
Notice that the clear implication of the headline and of the first paragraph is that
people who try to do CPR on a heart attack victim, and who do it improperly, are
doing worse for the victim than if they had done nothing at all. That is pretty
important advice, advice with ethical and legal implications, as well as implications for
the life of the poor victim.
The news item was based on an article by Gallagher, Lombardi & Gennis that appeared
in the Dec. 27, 1995, issue of the Journal of the American Medical Association (JAMA
1995; 274:1922-1925) entitled "Effectiveness of Bystander Cardiopulmonary Resuscitation and Survival Following Out-of-Hospital Cardiac Arrest."
The brief AP news story quotes one of the article's authors, John Gallagher of the
Albert Einstein College of Medicine in New York, as stating that improperly administered
CPR "does not seem to be any better than no CPR." The story concludes by stating:
Gallagher looked at 2,071 cases of cardiac
arrest in New York City over six months and
found that 662 of the patients were given CPR
by a bystander. In 357 cases, the CPR wasn't
done properly, and these patients' rate of
survival was one-third that of people given
An abstract of the JAMA article, available via the Internet, briefly explained the
research method and basic findings of the study. Emergency hospital personnel who
arrived at the scene of a cardiac arrest had recorded whether any bystander had attempted
CPR on the victim and, if so, whether the technique they used was "effective," that
is, whether it was performed according to medical guidelines. The patient "survived"
if he or she left the hospital afterward to come home alive. The researchers also
controlled for some other factors which might affect the outcome of the study. The abstract
Overall, 30 of the 2071 patients who experienced a cardiac arrest survived. 662 (32%)
received bystander CPR. The survival statistic for those receiving CPR was 19 out
of 662 compared to 11 out of 1405 who did not receive CPR. The bystander CPR was
judged to be effective in 46% of cases. Of those patients who received effective bystander
CPR, 14 out of 305 survived (4.6%) compared with 5 out of 357 (1.4%) who received
CPR judged to be ineffective. This gives an odds ratio of 3.4 for survival with effective compared to ineffective CPR. This odds ratio persisted after controlling for variables
such as initial cardiac rhythm, time elapsed before CPR was initiated and time elapsed
before advanced life support (ALS) was initiated.
(1) Based on the story, would you try CPR on a heart attack victim if you were not
thoroughly trained in CPR? Based on the abstract of the actual research, would you
try it? Why?
(2) What small table could you construct that would show the most important comparison
among the three main classes of victims (those not given CPR, those given ineffective
CPR, and those given effective CPR)?
(3) What information should the reporter have considered and included in the story
to make the meaning clear? Would that have changed the lead paragraph and headline?
(4) Why did the researchers include the control variables that they did? Were they
appropriate? Are there other control variables that you might include, given the
opportunity to have access to those data?
Shunhui's air conditioner question (See Chance News 5.07 item 9) finally answered.
As you may recall, Shunhui reported that the "engergyguide" on his new air conditioner
estimated that it would cost him $40 a year to operate. (Recall that the energyguide
is a yellow label that the Federal Trade Commission requires every manufacturer of
air-conditioners to install on their appliances.) Shunhui asked: "What does this mean
and how is it estimated?"
Since this cost is the same on every machine of this model sold, it must be some kind
of national average. We started with the problem of finding the average cost of
electricity. In the last Chance News, we described two methods used to estimate this
average price. By either method, the average price was found to be about 8 cents per kilowatt
In the meantime our son, who is in the energy business, gave us an excellent reference
that provides the additional information needed to answer Shunhui's question. This
is the review "Room air conditioners: "A guide to window and through-the-wall units"
Tech Updates, 5 March 1996. Unfortunately, this guide is available only to members
of E. Source, INC, (email@example.com).
To find the amount of electricity used per hour you need to know the air-conditioner's
cooling capacity and it's energy efficiency ratio (EER).
The cooling capacity is the amount of heat removed per hour measured in British thermal
units (Btu). This capacity is indicated on the machine.
The energy efficiency ratio (EER) is the ratio of the rate of heat removal in British
thermal units per hour (Btu/h) to the rate of energy input in Watts per hour (W/h).
Its value is on the energyguide.
Shunhui's air-conditioner has a capacity of 5000 Btu/h and an EER of 10. Thus it
will use 500 watts or 1/2 kilowatt per hour and cost 4 cents per hour to run. The
average use nationally is 750 hours per year, so the cost per year would be 750x.04
or 30 dollars. This is pretty close to the 40 dollar estimate that Shunhui found on his energyguide,
so this is our guess as to how this number was arrived at.
We were told by a representative of the Federal Trade Commission this number is put
on the energyguide just to allow comparison between different air-conditioners.
He said it would be meaningless to try to do better than this. Here is one reason
A study in New Jersey showed that the operating times of nearly identical room air
conditioners ranged from 2.5 to 1,557 hours. And they consumed from 1.2 to 1,048
kWh during the cooling season monitored. Thus, the variation in the way that individuals
use an air-conditioner would make it rather meaningless to suggest that it is possible
to estimate their annual cost for an individual customer. Here are two scatter plots from their paper showing that there was no correlation between outdoor temperature and hours the air conditioner was run for occupied apartments. For unoccupied apartments there was a linear relation between outside temperature and hours run when the thermostat was set at a moderate setting.
The "Tech Update" article does provide a map showing estimates for the average number
of hours air conditioners are used for different parts of the country. For New Hampshire
this is about 200 hours. So if Shunhui is an average user in New Hampshire, it should cost him only $8 a year to operate his new air-conditioner.
Of course, all the above assumes that Shunhui chose an air-conditioner that is reasonable
for the size of the room that he is using it in -- and how to determine this is another
(1) If you had an old air-conditioner, how could you decide if it pays to buy a new
one? Do you think it would pay if you live in New Hampshire? How about if you live
in southern Florida?
(2) The article states that people have a misconception of how an air conditioner
works, evidenced by the fact that, if asked what they do when they start up their
air-conditioner when the room is very hot, they say things like "We set the thermostat
to maximum cool when we first turn it on, then adjust to a more economical level." What
is wrong with this?
(3) Would it be better to give on the energyguide the cost of running your air-conditioner
per hour using an average cost for electricity then to give the average yearly cost?
We put the following article last as a reward to anyone who gets this far. It is
a great article and was suggested by Jeanne Albert.
They laughed at Galileo too.
The New York Times, 11 Aug. 1996, sec 6, p 41 Magazine Desk
Dean Radin is director of the Consciousness Research Lab at the University of Nevada at Las Vegas. Rabin is one of the leading researchers in parapsychology and also one of the most colorful. This article is about Rabin and about the way that research in his field is treated by scientists.
Radin does experiments quite similar to those carried out at the Princeton Engineering
Anomalies Research (PEAR) lab. The Princeton Lab was also the subject
of an article in the Magazine section of the New York Times (Questions for the cosmos,
New York Times, Magazine Desk, 26 Nov. 1989, Stephen Fishman) Those who study the effect of humans on influencing the outcome of the toss of a coin feel that you
have to toss lots of coins to have the effect show up. A typical PEAR experiment
has a machine toss a coin 200 times and record the number of heads and then repeat
this for a sequence of trials. Subjects attempt to influence the outcomes so that the numbers
produced in 1000 trials will have a significantly higher sum (or significantly lower
sum) than should occur by chance. In a typical experiment the subject is asked to
do 3 series of 1000 trials. In one they try to make the outcomes too large, in another
too small and in the third to have no influence. (it is claimed that even having
no influence is hard).
The lab has a variety of machines to give the subject a choice of ways to influence
the random outcomes. My favorite was the one where you chose two pictures -- I chose
a lion and a wave. You are then presented with a series of pictures with 200 pixels
chosen randomly from the two pictures. You try to make your picture more or less prominent
out by pure thought.
Rabin's version of this experiment has the subject try to get a mechanical device
to go to the M&M's and pick up one for you getting there more quickly than it would
if left to its own random steps.
Rabin tries other kinds of experiments. In one of these he has a "healer" massages
a doll made out of Play-Doe, hair and personal effects to resemble the patient It
is claimed that this caused the patient's blood flow and electrodermal activity to
increase. Another experiment showed that the millions of people watching climatic moments
of the O.J. Simpson trial and the Academy Awards affected a random number generator.
(1) The article states that 145 million Americans think they've had a psychic experience.
Can that many people be wrong?
(2) With a few notable exceptions statisticians are not inclined to study the data
produced by those who do research is psychotherapy. Why do you think this is?
(3) At Princeton we gave Linda, our co-teacher, 10 to 1 odds that if she was a subject
for the standard PEAR experiment she could not establish a significant results at
the 95% level. What would be a reasonable criteria to set for her to win the bet.
(4) In fact, we forgot to set the criteria for Linda to win. It turned out that Linda's
low series was lower than guessing but not significant so. Her neutral series was
also lower than chance but again not significantly so. However her high series was
so low that it would have been significantly low if it had been a low series. This
made the total of her three sums significantly low. Would we have won the bet by
the criteria you established in question (3)? Should we have won it?
(5) Go to the Rabin's virtual laboratory
and play the virtual slot machine. What is the expected value of your winning if
you have no influence over the wheels? Be a subject for the precognition experiment and desribe how you thought the experiment came out.
Please send comments and suggestions for articles to
CHANCE News 5.10
(15 August 1996 to 7 September 1996)