CHANCE News 8.04

(25 March 1999 to 27 April 1999)


Prepared by J. Laurie Snell, Bill Peterson and Charles Grinstead, with help from Fuxing Hou, and Joan Snell.

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:

Chance News is distributed under the GNU General Public License (so-called 'copyleft'). See the end of the newsletter for details.

Chance News is best read using Courier 12pt font.


There are more worms unattached to hooks than impaled upon them; therefore, on the whole, says Nature to her fishy children, bite at every worm and take your chances.

William James


Contents of Chance News


Note: As we often do, we have left the best to the last so don't miss Dan Rockmore's essay on our visit to our local weather forecaster. You and your students will also enjoy Dan's commentaries on National Public Radio and Vermont Public Radio

Two corrections: In Chance News 8.03 in our discussion of interesting web sites we omitted the URL for David Lane's Rice Virtual Lab in Statistics.

Also we made an error in the URL for Elliot Tanis' homepage where there are illustrations showing applications of Maple in the teaching of probability and statistics.

Norton Starr sent us two items from the RSS News Forsooth! column for April 1999, page 14. (Vol. 26, #8)

Amy Starkey, a student, echoed the finding of the most recent MORI poll, which found that -4 per cent of Conservative voters were satisfied with Mr. Hague as leader.

The Times 4 February 1999

A decade ago, a hard-drinking Stenhousemuir fan convinced me he was just one Poisson curve short of a plausible reason why his club hadn't escaped from the bottom division in 70 years. But doubtless there was a Spearman's rank correlation to show they had been better than the glamour boys of Cowdenbeath all along.

The Guardian (sports supplement) February 1999

What are the chances of that!?!
The Washington Post, 4 April, 1999, B5
Richard Morin

Richard Morin's column, Unconventional Wisdom, for April 4 was devoted to our Chance project. You can read the article from the Chance web site so, rather than reviewing it, we will make some comments on how it came about. Richard Morin's weekly column in the Washington Post is like a Chance News for the social sciences and we often abstract his articles in Chance News. Thus he knew about our project and asked us for some of our favorite items from the news that we found particularly helpful in teaching a Chance course. We gave him such a list and he chose five for his column: the statistics of Shakespeare, the last breath of Copernicus, false positives, busting the bible codes, and lottery luck.

Morin did his own research on our stories and then wrote a draft of his column. He sent this to us and we went back and forth three times until we were both satisfied with the final version of the column.

Working with a science writer was a new experience for us. We were impressed with Morin's ability to transform our overlong explanations into shorter, livelier accounts designed to keep the interest of the reader, while at the same time giving an accurate presentation of the problem.

In his April 18th column, Morin also showed that a good science writer can even make his mistakes interesting. In his March 24th Unconventional Wisdom column, Morin wrote:

Improbable Probabilities

Want to do something that's probably never been done before -- something that's not illegal, expensive or kinky weird? Just get a standard deck of 52 playing cards and shuffle them well.

The chances are very good that the exact order of cards in your just-shuffled deck has never ever occurred before, said Virginia Postrel in a recent lecture titled "In Praise of Play" at the American Enterprise Institute.

That's because "an ordinary deck of 52 cards offers 10 to the 68th [power] possible arrangements [that's 1 followed by 68 zeros -- a really big number], which means that any order you happen to shuffle has probably never appeared before in the entire history of cards," said Postrel, who is the editor of Reason magazine.

Don't believe her? Here's one way to think about it. If 100 million card dealers each shuffled a deck of cards 1 million times a year for 1,000 years, they would exhaust no more than a quarter of the possibilities (10 to the 17th power) -- even if every shuffle produced a unique ordering, which is unlikely since all that shuffling would probably result in a few matches.

Still don't believe her? Start shuffling.

In his April 18th column Morin describes the e-mail he received about his math blunder (10^17 is a quarter of the 10^68 possibilities). Elementary school teachers wrote saying that their Algebra classes enjoyed finding that even adults can make mistakes with the laws of exponents. The youngest response came from a 12 year old, but Morin remarks his 15-year-old son was a gleeful close second. He received 73 e-mail messages in all, 14 of which had the subject field "Very Improbable Improbabilities" and another 7 "Impossible Probabilities".

The most original contribution was from Jim Hummel, professor emeritus of mathematics at the University of Maryland, who pointed out that the magnitude of Morin's mistake, 10^51, was Archimedes' estimate for the number of grains of sands in the universe presented in his article "The Sand Reckoner". (Reprinted in The World of Mathematics, edited by James K. Newman Vol. 1, p 420.)


(1) Do you think there have ever been two careful shuffles that resulted in the same order of the cards?

(2) How many grains of sand would you estimate would be required to fill up the universe?

John Paulos' writes a column entitled "Who's Counting?" for ABC News on-line. You can find the current issue by going to ABC News Science Index

John's column appears the first day of each month. In this month's column, Weird Science, Paulos provides an April 1 news article thinly disguised as authored by Yiannis A. Paul (Yiannis is Greek for John). The article reports recent breakthroughs in parapsychology research, UFO's, numerology etc. Paulos then debunks his own article.

Alas, while fussing with this chance news, May 1 has come and John has a new column. In this column, Influencing Opinion, Paulos illustrate by examples how we are often unduly influenced by first impressions. He includes up-to-date applications such as: we are more influenced by the fate of refugees we see on television than those that we read about in the newspaper. He also includes some ideas from the Tversky school such as the "anchoring" effect.

In addition to Paulos' column, by going to the archives.

you will find "Chats with Paulos" where you can hear his response to questions, from those tuned in, on topics such as "Do You Believe the Polls". You will also find there a series "Profile and Puzzles" with John's favorite stories and puzzles.

In Chance News 8.03 we mentioned a web page where we find a list of about 300 rock stars who have died, along with the date of death, age at death, and cause of death. At the top of the page we read in large print:

Average Age at Death of Included Rock Stars 36.9 Years
Average Age at Death of Americans 75.8 Years

Readers Norton Starr and Ralph Blanchard reminded us that such samples are subject to obvious biases. One such bias is illustrated by the infamous "orchestra conductor" study (New York Times, 5 Dec. 1978, sec 3, p 1). In this study it was observed that the average lifetime of orchestra conductors of major orchestras was about 5 years longer than the life expectancy at the time of the study. The author of the study attributed this primarily to "work satisfaction" -- others suggested it was due to the exercise involved in conducting.

A simpler explanation was provided in a letter to the Times (J. D. Carroll, New York Times, 23 Jan. 1979, C2). Carroll noted that conductors of major orchestras are not appointed until they are about 30 years old. Thus, we should assume that the people in the sample had safely reached the age of 30. Then Carroll noted that the expected lifetime, given that a person has reached 30, was about the same as that found for conductors of major symphonies.

In the same way, a rock star would not be identified until reaching an age of about 16 at least; so, to avoid biasing the result, we should compare the average age of rocks stars with the expected lifetime of a 16-year-old.

As our readers observed, a much more significant bias results from considering only rock stars who have died by 1998. A rock star over 70 who died by 1998 would have to have been born before 1930. But a person born before 1930 would be thinking about a career before rock music had even been born. An extreme case of such a bias would be a college student finding the average age of death of his high school classmates who had died.

The reasons for death given for the rock stars certainly suggest that their average age of death is less than a random sample of the population. For example, of the 317 listed, 40 died of drug overdose, 36 committed suicide, 22 died by airplane accidents, and 18 were murdered. These do not seem to be typical risk factors. However, we asked ourselves how we could convincingly show that rock stars do die young.

We decided to do this as follows. For each rock star we associated a twin. We assumed that these twins, along with their rock star twin, reached age 16. We then simulated the age of death for these twins using an appropriate life table. A life table starts with 100,000 persons at birth and estimates how many of these would be alive after one year, after two years, after three years etc. Using this table we can find the conditional probability that a 16-year-old will die at age x. We simply find from the table the number of the 100,000 who are predicted to die between age x-1 and x and divide this by the number predicted to be still alive at age 16.

We used these conditional probabilities to simulate the age of death for our twins. We then selected those who had died by 1998 and computed their average age of death. We repeated this simulation a large number of times and estimate the average age of the twins to be 48 with a standard deviation of 2.2. Thus the 36.9 average age of death for the rock stars is significantly lower than their more typical twins. However, the average 48 years for the twins is a far cry from the 75.8 years listed for Americans.

Of course, life tables change from year to year. We used a life table for 1960 since this was a kind of mean value for the years that the rock stars were 16. However, we also tried other life tables and this did not significantly change the results. Our results were also not significantly changed by choosing other starting dates, for example, age 12 instead of age 16. However, if we ignore the "orchestra conductor" bias altogether and make the starting age 0, we get an average lifetime of 37.5 and standard deviation of 3.2 and so would not be able to reject the hypothesis that rock stars, on average, live less long than the general population.

Ralph Blanchard also remarked that biases could occur in the selection of the rock stars. For example, if the choice was influenced by news reports, mediocre rock stars might get included because they died tragically but not be included if they just went on living a long time (and were still mediocre).

Ralph also wrote:

Similar pitfalls in analysis can occur when looking at mutual fund history but with opposite bias. By looking at all mutual funds returns over the last 10 years, using data from the funds themselves, the return will be biased high, as it will tend to not include those with bad returns that were shut down.

A similar gross error in mortality analysis was done by animal rights activists calculating mortality for captured dolphins. Their analysis compared average life in captivity by taking the time from capture to the study's end date, and comparing that to normal "in the wild" estimated dolphin life span. The sample ignored those years of life before capture and made no allowance for years of life after the report ended.


At the web site The Dead Rock Stars Club we find another list of dead rock stars. This list has about 1000 entries and includes dead rock stars, dead people who have been associated with rock stars and dead people whose music helped influence and create rock. This includes, in particular, blues musicians, many of whom performed well before rock was born. For most on the list the date of birth, date of death and cause of death are given.

We considered the 841 for which we could determine the age of death and found their average age of death to be 50 years. Why did we get such a bigger number in this case? How do you think the average age of death of the blues musicians would compare with that of the rock musicians? Could you answer this using this database? If so, try it out and let us know the results.

Kent Morrison wrote us about Richard Dawkins' new book: Unweaving the Rainbow (Houghton Mifflin 1998). While recommending the book he suggested that Dawkins may have made a subtle mistake in the famous birthday problem. Dawkins writes:
If you have a roomful of only 23 people, mathematicians can prove the odds are just greater than 50 percent that two of them will share the same birthday. Two readers of an earlier draft of the book asked me to justify this astonishing statement. I have every sympathy with people who are phobic about mathematical formulas, so I'll spell out an approx- imation in words.

Dawkins then goes on (page 153) to show that there are 253 ways to choose pairs of people from a group of 23. Each of these pairs has probability 364/365 of not having the same birthday. He then remarks that raising 364/365 to the power 253 gives a number very close to .5. Thus the probability of at least one pair having the same birthday is also close to .5. Dawkins makes no mention of independence or lack thereof.

Actually, this approximation is a good way to show that the result should not be considered surprising. We have 253 chances for a match, each occurring with probability 1/365, so the expected number of matches is 253/365 = .7. Hence it is not surprising that the probability of a match is greater than .5

This discussion is in a chapter on coincidences, and Dawkins does a nice job of explaining why we seem to experience so many coincidences and how they can be explained away. He even gives a Darwinian explanation for our willingness to be impressed by apparently uncanny coincidences.

Dawkins also has an interesting discussion of experiments by Skinner in which he taught pigeons and rats to become good statisticians. Dawkins explains why he believes that all animals, to some extent, behave as intuitive statisticians choosing a middle course between type 1 and type 2 errors. Dawkins remarks that, like most of us, he can never remember which is type 1 and which is type 2 and so calls them "false positive" and "false negative" instead.

Dawkins gives us the example of a fish trying to decide whether to snap at a worm which may or may not be at the end of a fisherman's hook. He suggests that in this case the fish might even choose the strategy of going for the worm every time. To back this up he quotes the remark of the philosopher and psychologist William James:

There are more worms unattached to hooks than impaled upon them; therefore, on the whole, says Nature to her fishy children, bite at every worm and take your chances.


(1) What advice would you give to Mr. Fish?

(2) Is "false positive" and "false negative" a reasonable alternative name for type 1 and type 2 errors (or should this be type 2 or type 1 errors)?

Profiling debate hinges on issue of experience vs. bias
The New York Times, 9 April, 1999
Jodi Wilgoren

Safir defends frisking policy before a panel of skeptics
The New York Times, 20 April, 1999
Michael Cooper

Whitman says troopers used racial profiling
The New York Times, 21 April, 1999
Iver Peterson

Driving while black
The Washington Post, Aug. 16, 1998
John Lamberth

The first article discusses the issues involved in profiling -- the use of race and ethnicity as clues to criminality. The fatal shooting two months ago of Amadou Diallo, an unarmed West African immigrant, by four white New York officers has led to federal and state investigations into police behavior in New Jersey and New York.

The recent aggressive strategy, adopted in New York and to some extent nationally is aimed at casting a wide net in an attempt to find illegal drugs and guns. Only a "reasonable suspicion" is required for the police to stop-and-frisk. On the highway, state troopers can only stop a car for a traffic violation but there are so many such violations that the trooper has to use discretion in deciding which cars to stop.

The police argue that it is a statistical fact that blacks and Hispanics are over-represented in prisons and with convictions on serious charges, so it is not surprising that they are stopped more often. Critics like the ACLU make the argument that this is a self-fulfilling prophecy. By stopping and investigating a higher proportion of minorities, there will be a higher proportion convicted and the circle will go on.

There have been no nationwide studies analyzing the rate of stops and searches by race, but several narrower surveys have turned up results that have been called "too outrageous to be coincidence."

In the second article New York Police Commissioner Howard Safir, at a City Council hearing, defends the department's Street Crime Unit from allegations that it stops people because of their color.

Mr. Safir said: The racial and ethnic distribution of the subjects of stop-and-frisk reports reflects the demographics of known violent crime suspects as reported by crime victims. Similarly the demographics of arrestees in violent crimes also correspond with the demographics of known violent crime suspects.

Replying to the suggestion that police were threatening people's civil liberties, Safir replied: Your suggestion that we do racial profiling is not true. What we do is we take the victim's description of the perpetrator and that's what we use to look for perpetrators."

The third article reports that New Jersey Governor Christine Todd Whitman and her Attorney General have conceded, for the first time, that some state troopers did use profiling to single out black and Hispanic drivers on the highway. The report is an interim report which studied actions of troopers in two of the state police barracks.

Courts have ruled that profiling is illegal under the Fourth Amendment's protections against unreasonable search and seizure. It is expected that this report will result in a number of appeals of previous court rulings.

The New Jersey report found that troopers from the Moorestown and Cranbury barracks stopped 87,489 motorists along the New Jersey Turnpike during the 20 months ending in February. 59.4 percent were white, 27 percent black, and the rest Hispanic, Asian and "other." Of 1,193 vehicle searches during a slightly longer period, 77.2 percent were for cars driven by blacks or Hispanics, and 24.1 percent by whites. When charges were filed, 62% were against blacks and 6 percent "other." 10.5 percent of the cars of whites searched produced arrest or seizure of contraband, usually drugs or weapons, and 13.45 percent of minority-driven vehicles produced arrest or seizure of contraband.

In the last article, Professor John Lamberth, a psychologist at Trinity University, relates his experience in providing statistical evidence for two court cases regarding profiling, one in Maryland and the other in New Jersey. In each case Lamberth carried out studies to see if police stop-and-search black motorists at a rate disproportionate to their numbers on the highway. Each study had drivers go 5 miles above the speed limit and record the number and racial composition of the drivers who passed them, in violation of the speed limit, as well as those whom they passed and so were not in violation of the speed limit.

He found that the same proportion of black and white drivers violated the speed limit. He also verified that, indeed, the majority of the drivers -- over 90% -- were in violation of the speed limit, giving the police a great deal of discretion in whom they stopped. And both studies showed that the troopers used this discretion to stop a significantly higher proportion of black drivers than white drivers. You can see details of the Maryland study.


(1) What can, and can you not, conclude from the data given from the New Jersey report when you are not given the proportion of drivers on the highway who were black? What more could you conclude if you were given this information? (Lambert's study found that about 15% of the drivers on the highway were black)

(2) The first article reports that police experts say that young officers, when they hit the streets, often with veteran officers, develop a "sixth sense," the instinctive ability to sniff out situations or isolate individuals who seem potentially unsafe. Do you think that this "sixth sense" could be established by a statistical experiment? How would you design such a study?

(3) Read the report of the Maryland statistical study and comment on the design of the experiment. Were the results of this study consistent with the findings reported in the New Jersey report?

Study questions gene influence on male homosexuality
The New York Times, 23 April 1999, A18
Erica Goode

based on

Male Homosexuality: Absence of linkage to microsatellite markers at Xq28
Science 23 April, 1999, 665
Rice, et al.

In 1993 Dean Hamer, a geneticist at the National Cancer Institute, carried out a study which seemed to suggest the existence of a "gay gene." Hamer considered 40 pairs of homosexual brothers. He found that 33 of the 40 pairs shared a particular sequence of genetic code on their X-chromosome in an area called Xq28. A man gets this genetic code from one of two versions of his mother's X- chromosome chosen at random so there is a 50% chance that the brothers share the sequence of code that the Hamer group identified. This lead Hamer to the conclusion that there was a gene that influences sexual preference.

A second study in 1995 carried out by Mamer's group found similar evidence for a link but the effect was smaller.

Now Canadian researchers, led by Dr. George Rice at the University of Western Ontario, considered 52 pairs of homosexual brothers and failed to duplicate the results of Hamer.

Hamer claims that the Canadian team did not find the gene linkage because the families of the brothers they studied were not representative of those likely to have an X-linked gene. He says that, by design or by chance, those considered had a high level of homosexuality on the father's side of the family. Thus, these would not be a natural group to consider in looking for evidence of a gay gene that can only be obtained from the mother.

Dr. Rice said that the study's participants were "totally random." He explained that only 48 families were included because it was not possible to get blood samples from the rest. He also asserted that the families in their study were not very different from those studied by Hamer.


(1) What do you think of Rice's explanation statement that his participants were "totally random"?

(2) What would you conclude from three studies of about 50 subjects each, in which the first was highly significant, the second slightly significant and the third not significant at all?

(3) In Hamer's study the aim was to find a region in the DNA on the X-chromosome that was common to the brothers more often than should be expected by chance. Is this a little like the problem of interpreting a cancer cluster?

Finance and Economics: A la mode
The Economist, 20-26 March 1999, p 80

The inflation report projections: understanding the fan chart
Bank of England Quarterly Bulletin, Feb. 1998, 38, pp. 30-37
Britain, E., Fisher, P.G. and Whitley

Asymmetric density forecasts of inflation and the Bank of England's fan chart
National Institute Economic Review, January, 1999, 106-112
Kenneth F. Wallis

Like the Federal Reserve in the United States, the Monetary Policy Committee (MPC) of the Bank of England sets interest rates to achieve the Government's target for inflation (currently 2.5%). Starting in 1993 the MPC gave their inflation forecast by a chart which provided the inflation rate for the past 5 years and their forecasts for the for the next two years. To indicate the reliability of their forecasts, they provided the average errors for previous predictions for each time in the two year time interval. By 1996 they recognized problems with this kind of chart. Even with the indications of the average errors the specific predictive values were given more importance than warranted by the uncertainty involved. In addition the estimate of the error, based on past experience, did not properly take into account knowledge of the economy at the time the forecast was made.

In 1996 the MPC decided that, rather than representing their estimate of inflation at a future date by a single number, they would represent it by a probability distribution. Such a proposal has been suggested by weather experts to replace specific forecasts for the maximum and minimum temperatures for the next five days.

They considered using normal distributions for this purpose but realized that the appropriate distribution might well be skewed since alternative outcomes for economic factors might effect the inflation rate more in one direction than the other.

To allow for skewed distributions they considered a class of distributions called 'two piece normal' introduced by S. John (Communications of Statistical Theory and Methods, 11(8), 879,885 ,1982). Such a distribution is obtained by combining the left half of a normal density with mean m and variance s1 with the right half of a normal distribution with the same mean m and standard deviation s2 and normalize the resulting function to obtain a continuous density. The result is a bell shaped curved skewed to the right if s2 > s1 and to the left if s1 > s2. The MPC chose to parameterize these distributions by the three parameters: the mode, the standard deviation and the skewness measured by the mean - the mode.

The MPC then estimates these three parameters to determine distribution for the inflation one year into the future and two years into the future. They base these parameter estimates on computer models for the economy, variation in previous estimates, and their subjective probabilities for the various economic events that could occur to influence the inflation rate as well as other relevant statistical data they had.

They then obtain distributions for other times by interpolation. Then they consider how the forecasts determined by these preliminary distributions agree with what they really think will happen. If they don't look right, minor changes are made in the parameters and this process is continued until they are satisfied that the resulting forecasts accurately represent their state of knowledge.

They presents their results by a chart called a "fan chart" constructed as follows. The inflation rate for the previous five years is plotted with time on the x-axis and rate of inflation on the y-axis and a horizontal line is drawn at 2.5% representing the target.

Then for each times t in the next two years they look at the density of the distribution they have chosen for this time. They start with the mode and move down on either side of the density until they reach two points a(t) and b(t) the same distance below the mode such that 10% of the area under the curve lies between a(t) and b(t). Another characterization of the interval (a(t),b(t)) is that it is the smallest interval that contains 10% of the probability distribution. They plot a(t) and b(t) for the two years into the future and color the region between these two lines dark red. They are forecasting a 10 percent chance that the inflation rate will lie in this region.

Then starting at the points where they stopped for the 10 percent area they move further down each side of the density until they reach points c(t), d(t) such that 20% of the area under the graph lies between c(t) and d(t). They then plot the functions c(t) and d(t) getting two more curves. They color the bands between the 10% curves and the 20% curves a slightly lighter color of red. They continue this process for 30, 40, 50, 60 ,70,80 and 90 percent each time representing the bands between them a slightly lighter color of red. The bands get wider as time increases because of the increased variation in the distributions as time increases. This makes the shaded area fan out which explains the name "fan chart."

The MPC provides this fan chart in their quarterly Inflation Report. If you look at the most recent report presented on Feb. 12, 1999 you will see that, at the time the report was published, the inflation rate was very near the 2.5 percent target. The fan chart indicates that one year later there is a 90% chance that it will lie in the interval (2.3, 3.5)) and after two years there is a 90% chance that it will lie in the interval (1,4).

The Economist article is based on the article by Kenneth Wallis, a well known British economist. Wallis is critical of the MPC use of the mode and their choice of intervals.

Let (r(t),s(t)) be the interval chosen so that there is a 50% chance that the inflation rate will lie in this interval at time t. Wallis feels that there should then be a 25% chance that the inflation rate will be less than r(t) and a 25% chance that it is greater than s(t). This will not be true for the method for choosing the intervals used by the MPC unless the distribution at time t is symmetric.

To make this the case, Wallis recommends using the median as the central value rather than the mode and choose the intervals as the usual symmetric quantiles to determine the fan chart. He illustrates the difference by using the data in the August 1997 report and comparing the two fan diagrams that you would get using the mode or the median. The latter tends to suggest a greater variation in the future inflation than the former. To see this in more detail he gives a comparison of the intervals for the two year predictions for the two methods:

                MRC method

Prob.      Lower     Coverage   Upper      Prob 
below      limit                limit      above

 3.6       1.01         90       5.12       6.4
 7.2       1.34         80       4.54      12.8
10.8       1.56         70       4.15      19.1
14.5       1.74         60       3.84      25.4
18.1       1.89         50       3.58      31.7
21.8       2.03         40       3.34      38.1
25.3       2.15         30       3.12      44.5
28.9       2.27         20       2.91      50.8
32.4       2.38         10       2.70      57.4

          Method proposed by Wallis

 5         1.16         90       5.30        5
10         1.52         80       4.75       10
15         1.76         70       4.39       15
29         1.96         60       4.10       20
25         2.14         50       3.86       25
30         2.31         40       3.65       30
35         2.46         30       3.46       35
40         2.62         20       3.27       40
45         2.78         10       3.10       45

Note that for the MRC method there is a much higher probability (6.4%) of being above the 90 percent interval than below it (3.5%). For Wallis' method these probabilities are each 5%. Since the MRC intervals are the smallest that can be chosen to include 10% of the area, the intervals chosen by Wallis' method will be bigger in general. For example the 90% interval has length 4.11 for the MRC method and 4.14 for Wallis's method. This will suggest higher possible inflations rates using Wallis's method and this is clearly illustrated by looking at the two fan charts.

The Economist points out that the 10% interval for the MRC method (2.38,2.70) includes the target rate of 2.5 while the 10% interval using the Wallis' method (2.78,3.10) does not include the target rate of 2.5. They remark that this could be considered an important difference.


(1) Suppose you wanted to use the mean as your central values. How would determine your intervals in this case?

(2) Do you think Wallis has a point?

(3) In a speech John Vickers, Chief Economist at the Bank of England, asks the following question: Suppose you ask yourself how much worse is it to miss the target by 1.2% rather than .6%. Possible answers include:

(a) four times as bad (quadratic loss function)
(b) twice as bad (linear loss function)
(c) equally bad (perfectionist)
He suggests that if the answer is (a) you should use the mean, if it is (b) you should use the median and if it is (c) you should use the mode. Why?


Bob Griffin is professor of journalism and the director of the center for Mass Media Research at Marquette University. He is also a frequent contributor to Chance News. He called our attention to the following book in which he contributed a chapter.

Communicating uncertainty
Lawrence Erlbaum Associates, New Jersey, 1999
Edited by Sharon Friedman, Sharon Dunwoody, and Carol Rogers

This book "examines how well the mass media convey to the public the complexities, ambiguities and controversies that are part of scientific uncertainty."

Chance News readers will enjoy reading Bob's chapter since he talks about the kinds of problems that we worry about but from the point of view of someone whose job is to educate future journalists. He begins by cautioning journalists to not rely too much on anecdotes even though they are story tellers. He then goes on to give a series of case studies based on articles that appeared in major newspapers and deal, in one way or the other, with uncertainty. He uses these to illustrate ways to convey the uncertainty accurately as well as the many ways that uncertainty can be and is conveyed inaccurately in the news.

In the other chapters you will have a chance to learn also how scientists, social scientists and science writers think about uncertainty. There are a number of common themes that come through. One is that the natural inclination of newspapers to concentrate on new news, does not lend itself to looking at the big picture of a series of studies and trying to make sense out of them. This leads the public to think that uncertainty just means that a study today will tell them to eat asparagus and another tomorrow will tell them not to eat asparagus.

That it is possible to write a successful series on a complex topic is wonderfully illustrated by Pulitzer Prize-winner Debra Blum's chapter on her experience writing a series of articles on the biology of behavior for the Sacramento Bee.

Sociologist Steven Zehr, in his chapter, comments that, the fact that journalists often feel compelled to get other points of view on a study to provide a balanced presentation, often suggests more uncertainty than there actually is in the study. This would be particularly true in an area such as parapsychology.


(1) What other areas do you think would be susceptible Steven Zehr's concern?

(2) If you were a science writer, how would you explain the uncertainty in mathematical models such as those used for studying global warming? Would this be harder for a science writer than explaining the uncertainty in a clinical trial?

Recall that in Chance News 7.11 we described an attempt by the Royal Statistical Society to develop a Richter scale of risk. We presented some examples of where various risks would fit on scale as proposed by the RRS group.

The data used for the risks was British data and Richard Morin asked us how the UK results would compare with those using US data. We worked this out and, in the process, learned about the difficulty of obtaining appropriate data for this risk index.

Our first attempt to find the risk of travel by train came out to make travel by train about 100 times as risky in the US as in the UK. This did not seem reasonable. We discovered that the problem was that the US government data considered train deaths to be not only passenger deaths but also deaths caused by a train hitting cars at a crossing or by people walking on the tracks. There are about 1000 deaths a year in these last two categories while only a dozen or so passengers are killed in a year by train wrecks. Once we limited ourselves to actual passenger deaths the risk came out comparable for the two countries.

Using information from the 1998 edition of "Statistical Abstracts for the United States" and the 1998 edition of "Transportation in American Report" provided by the Eno Transportation Foundation, and with help from Rosalyn Wilson at Eno, we think we got it pretty well straightened out.

Recall that the Risk Magnitude (RM) is essentially the probability of being killed in the miles traveled or period of time considered sometimes discounted. The Risk Factor is a logarithmic scale defined by RF = 8 + log(RM). Here is the comparison for the two countries:
                		RM          RF

100-mile rail journey                .000000022      .3
1000 mile flight                     .0000005       1.7
100-mile car journey                 .0000008       1.9
Homicide (new-born male)             .00038         4.6
Lifetime car travel(new-born male)   .0032          5.5


100-mile rail journey                .000000088      .9
1000 mile flight                     .00000087      1.9
100-mile car journey                 .00000117      2.1
Homicide (new-born male)             .003395        5.5
Lifetime car travel(new-born male)   .00457         5.7


Where do you think the risk of bicycles fall on this scale? How about space travel?

About a year ago we went with our colleague Dan Rockmore to visit our local weather forecaster Mark Breen to see how weather is really predicted. (Breen starred in "Local Forecasting" in the Chance Lecture Series.) We hoped to write something that might be useful for a Chance course. We have not gotten far with this project, but Dan wrote a brief account of the visit right after we got back. It was such a great experience that it occurred to us that his account might inspire others to visit their weather predictor so here it is:

Our local weather forecaster at work
Dan Rockmore

We wake up at 4:30 AM at the Fairbanks Motor Inn. Check out, grab some complimentary coffee, get in the car and make our way into town. We park in front of the Fairbanks Museum in St. Johnsbury and walk down the steps at back and enter the basement. First greeted by a stuffed owl in a small wildlife display, we turned the corner to find our favorite NPR weather forecaster, Mark Breen, about to construct the day's forecast. Mark gets up at 3:30 AM on mornings on which he forecasts, giving himself time for some exercise and breakfast before driving into work.

Mark takes us behind the partition dividing his and Steve Maleski's workspace. A small Macintosh computer is perched on a desk, which itself is amid the general clutter associated with many research offices (including our own!). Of course not all offices have an old barometer on the wall. We greet each other and sit down to begin the forecast. Laurie and I panic quietly as we realize there is no coffee in sight.

I guess that I figured that we'd be poring over faxed data sheets and weather maps, information which would be proprietary to the weather community, but no, instead we sit down in front of the Mac, fire up Netscape and hit the web. At the first stop we quickly access the output of a particular weather model. We get the projected weather for Glens Falls, Albany, Burlington, Lebanon... Mark moves quickly through these and other pages, including satellite data, raw data, NWS reports, telling us about the numbers and graphs we're seeing; never writing anything down. He comments that the output doesn't completely jive with the strong, gusty wind that he felt at the top of the hill where his home is. This will have to be accounted for.

Laurie and I barely have time to figure out what it is we're looking at, and of all the things we look at, only the initial model data is printed. After 20 minutes or so of this relaxed talk and data collection, we hear the muffled ring of a phone. Mark lets it ring 7 or 8 times and then opens the door to a closet which contains the phone as well as a bit of broadcasting equipment. It's the first radio station calling for a weather forecast - Mark chats a bit with the dj and then all of sudden he's in the booth giving a report! No script, just riffing on the numbers from the one piece of printout. We are completely impressed; incredibly fast assimilation of all of this data.

This is the rough format of the following two hours. More web surfing, more numbers, charts. Charts showing cloud cover with dots of increasing diameter. Pretty hard for us to read. Comparison of different model outputs. The model output is sometimes in the form of snapshots of projected weather flow over the country. For these, a series of these are loaded through netscape allowing Mark to access them quickly from the cache, making cheap "movies" of the projected weather over the day. Mark compares a few of these, also watches another movie from another site. This one indicates rain moving into the area. Using a wax pencil, Mark makes an X on the screen where the front begins, how far it moves after 4 hours and then projects that in about 4 more hours (given the direction of the prevailing winds) that the storm will be in our area around noon. Determining the time of the rain seems to be the main focus of the forecast today.

The data is augmented by email and phone calls from radio listeners who like to send in their own weather observations. The phone calls are great. They range from quick local temperature/wind speed reports to longer chats, comments on conditions for planting tomatoes or going fishing -- "No, I put my tomatoes in the woodshed before I came in - might want to wait a day on that". It seems like anyone can call just to find out if today is a good day for a picnic. Mark is unflappable, answers all the calls with his trademark "Gooood Morning!", doesn't rush anyone, even though there are still forecasts to come.

Finally Lisa Peakes from Vermont Public Radio calls to the booth. Mark schmoozes a bit and then sits down for the extensive VPR forecast. They give him about 5 minutes to talk about the weather -- a huge amount of time. For this forecast he takes one extra piece of information in with him -- satellite output for the local area. Again, it is all ad-libbed, a synthesis of the web data, a few local observations with cues from the few pieces of printout that he takes into the booth. Very impressive -- the forecasts are so smooth we had been sure that they were scripted. It seems that all of the writing happens after the forecasts. Then the "Eye on the Sky" web page needs to be updated and some measurements are recorded. We go outside, check on some of the equipment (the museum is an official NWS site). We check the humidity (uses human hair in the equipment), observe the cloud cover (a 4 out of 10, with probably a 5 for opaqueness).

Now we're done. Mark will update the web page -- he proceeds by modifying yesterday's page since yesterday's forecast should give a head start on today's weather. In fact, the frequent phenomenon of "persistence" often implies that today's page won't differ too much from yesterday's. No "verification" is performed, that is, the comparison of yesterday's forecast with today's weather. After all, people just want to know what's going to happen next...

Chance News
Copyright © 1998 Laurie Snell

This work is freely redistributable under the terms of the GNU General Public License as published by the Free Software Foundation. This work comes with ABSOLUTELY NO WARRANTY.


CHANCE News 8.04

(25 March 1999 to 27 April 1999)