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 wisdom.

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.

Chance Magazine

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.

Junk Science

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
Roger Highfield

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 
Forecast of rain 66 156 222
Forecast of no rain 14 764 778
Sum 80 920 1000
What is the P(rain|forecast of rain)?
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 every player
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 Peter Doyle.


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
Thomas Sowell

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?

Mathematical Recreations
The Interrogator's fallacy.
Scientific American, September 1996, p. 171-175
Ian Stewart

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

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 allowed."
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 basketball?

(2) Could you modify Turcoliver's binomial model to give a model for baseball? for football?

Magnetic field exposure, breast cancer risk tied.
The Boston Globe, 20 August 1996, pA3
Richard Saltus

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.
Michael Selz

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 Bradstreet's figure?

Are athletes nearing the limit?
The Boston Globe, 19 August 1996, pC1
Barbara Huebner

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
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"
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.

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 association.

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 considered.

(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 causal relationship.

(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 Rossman.

Psychologists divided over validity of statistical significance tests.
Chronicle of Higher Education, 16 Aug. 1996, A12
Christopher Shea

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 significance tests.

Hit the lotto, buy a toaster.
The New York Times, 21 August, 1996, B1
Raymond Hernandez

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?

Ask Marilyn
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 of age.

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 contradictory ?

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 Learning Statistics.

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 issue.
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 1993.
      Mean Score (400-1600)
Asians 1293
Whites 1256
Hispanics 1032
Blacks 994
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 two statements

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 policies.

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 this book.

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 it.

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

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 co-operative learning.

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?

Activity-based statistics.
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 activity.

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 behavior?

Sedentary lifestyle looms large as death risk.
USA Today, 1D, 17 July 1996
Doug Levy

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.

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 cholesterol level."

New study questions radon danger in houses.
The New York Times, A15, 17 July 1996
Associated Press

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 radon.

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
Maggie Fox

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 1.3%.

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

Wickham writes:

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 other examples.


(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
Associated Press

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 proper CPR.
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 explains:

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 hour.

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, (esource@esource.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 why.

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 story.


(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
Chip Brown

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)