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Chance News 5.11

(8 September 1996 to 8 October 1996)


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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 Foundation.

Please send comments and suggestions for articles to
jlsnell@dartmouth.edu.

Back issues of Chance News and other materials for teaching a CHANCE course are available from the Chance web site:

http://www.geom.umn.edu/locate/chance

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My only hope is that at least it may stagger you in your certainties.
Darwin

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Contents Part 1

Contents Part 2

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Part 1

Alan Levine suggested the following segment from Jim Lehrer's
Sept. 25 PBS news program.

JIM LEHRER. Frequent drug use among teenagers is on the increase according to a report issued today. It was based on a survey by an Atlanta-based group called PRIDE, the Parents Resource Institute for Drug Education. The executive director said the use of most drugs was at the highest levels in nine years.

DOUG HALL, Executive Director, PRIDE: A high school classroom with 30 students--our studies show that 3.5 percent of the 12th grade tried heroin last year. That means that in every 12th grade classroom in America - every single classroom - one student, a 17 or 18 year old, had already tried heroin. Two had tried cocaine. Three had tried amphetamines. And nearly four had tried LSD, PCP, or some other hallucinogen.

Hall's first sentence was probably not transcribed exactly right but the rest of his remarks are exactly as stated in PRIDE'S official press released on their web site.

DISCUSSION QUESTIONS:

(1) What do you think of Hall's understanding of statistics?

(2) Do you think that Hall was suggesting that 10 students in every senior class of 30 students had tried one of the these drugs?
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Emil Freeman and Evan Fisher suggested the following three related letters to the editor of the "New York Times".

TWA Flight 800 crash, don't discount meteor.
The New York Times, 19 September 1996, A26
Letter to the editor by Charles Hailey and David Helfand

The writers refer to an earlier article about the TWA Flight 800 crash in which it is reported that "more than once, senior crash investigators have tried to end the speculation by ranking the possibility of friendly fire at about the same level as that a meteorite destroyed the jet." They feel that this must be based on a misconception of the probability that a meteorite would destroy a jet and write:

The odds of a meteor striking TWA Flight 800 or any other single airline flight are indeed small. However, the relevant calculation is not the likelihood of any particular aircraft being hit, but the probability that one commercial airliner over the last 30 years of high-volume air travel would be struck by an incoming meteor with sufficient energy to cripple the plane or cause an explosion.

Approximately 3,000 meteors a day with the requisite mass strike Earth. There are 50,000 commercial airline takeoffs a day worldwide. Adopting an average flight time of two hours, this translates to more than 3,500 planes in the air; these cover approximately two-billionths of Earth's surface.

Multiplying this by the number of meteors per day and the length of the era of modern air travel leads to a 1-in-10 chance that a commercial flight would have been knocked from the sky by meteoric impact.

DISCUSSION QUESTIONS:

(1) Do you believe that the authors' numerical assumptions are reasonable? What other assumptions have the authors have made in arriving at their "1 in 10 chance"?

(2) Assuming the authors' assumptions to be correct, try to determine the "chance that a commercial flight would have been knocked from the sky by meteoric impact". Do you obtain the same "1 in 10 chance" that the authors did?

(3) Could you estimate the chance that the TWA Flight 800 plane was hit by friendly fire? That any plane in the last 30 years was hit by friendly fire?
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Meteor and Plane Crash.
The New York Times, 24 Sept. 1996, A24
Letter to the editor from Guy Maxtone-Graham

Maxtone-Graham writes:

As any statistician can tell you, the outcome of past, random events has no bearing on future, unrelated random events. Toss a coin 10 times and the odds of getting heads or tails on the 11th toss are still 50-50.

Likewise, calculations based on the number of flights worldwide, the number of takeoffs per day and the number of years that commercial flights have thrived have no bearing on the question of whether a rock from outer space happened to enter the atmosphere to hit one particular airliner on July 17. The odds of such a freak accident downing a specific flight remain small, and the professors' conclusion that "the meteor impact theory deserves more considered attention" is difficult to suppor

DISCUSSION QUESTIONS:

(1) Do you believe there is anything that all statisticians would agree to?

(2) Do you agree with the argument expressed in this letter?

(3) In what has been called the "streak of streaks", Joe Dimaggio in 1941 got a hit in 56 successive games. Should you compute the probability that a typical player would achieve such a streak or that sometime in the history of baseball such a streak should occur? How would you estimate these probabilities?
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Meteors and numbers that count.
The New York Times, 28 September 1996, Section 1, page 22
Letter to the editor from Bill Grassman

Attempts to prove or disprove the probability that TWA Flight 800 was the victim of a meteor recall the tale of the business executive who, concerned that he might be on a plane with a bomb, commissioned a study to determine the odds of that happening.

When the calculations of flights per day, when and where the bombings had occurred and the normal flying patterns of the executive disclosed that the odds of his being on a plane with a bomb were 1 in 13 million, he asked for the probability of his being on a plane with two bombs. On learning that this increased the odds to 1 in 42 billion, he always carried a bomb with him. Statistics!

DISCUSSION QUESTIONS:

(1) Do you think the writer is criticizing statistics for saying this is true or criticizing those who misunderstand statistics?

(2) How would you explain to your Uncle George what is wrong with the executive's reasoning that he should carry a bomb?
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Daniel Atlan found the following story on the front page of the 24 Sept. issue of "Le Monde". This story also appeared in the "Sunday Times".

Eurocrats bank on the stars.
Sunday Times, 22 September 1996, Home News
Nick Gardner and Jonathan Leake

The European Bank for Reconstruction and Development (EBRD) has been using astrological events to help it predict fluctuations in financial markets. Astrologers have claimed powerful links between the fluctuations in the financial markets and celestial events such as lunar eclipses.

Mark Curtis, the bank's treasurer, said the bank has a duty to investigate any method which appeared to give it an advantage when playing the market. The American trader and hypnotist Robert Krausz has been taken on as a special adviser.

The bank has carried out in-depth computer tests on astro- economic theories. The system compared past fluctuations in the money market with events such as lunar eclipses to see if there was a relationship. One of the most important findings claimed for the astrological system has been that markets become destabilised around the time of lunar eclipses. This means that financiers can buffer themselves against violent movements. Curtis emphasized that astrology-economics played only a small part in the banks investment policies.

The bank was founded five years ago to raise capital from its 60-member governments to provide loans to boost eastern European economies. In 1993 it was dubbed the "glistening" bank after revelations that it had spent far more on its headquarters in London than it had given out in loans.

DISCUSSION QUESTION:

What do you think the bank will be dubbed now?
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Study finds stunted lungs in young smokers.
The New York Times, 26 Sept. 1996, B10
Jane E. Brody

A study reported in the "New England Journal of Medicine" showed that lung development is impaired in teen-agers who smoke as few as five cigarettes a day.

The study involved 5,158 boys and 4,902 girls in six areas in the United States where environmental pollution was a particular concern. The children, aged 10 to 18, were given annual exams from 1974 to 1989. Their lung capacity was measured by seeing how much air they could get out after taking a deep breath and blowing out as hard as they could. From these measurements it was observed that children who smoked had less lung capacity than those who did not, and the amount less was directly related to the number of cigarettes smoked and how long they had been smoking.

The researchers also looked at asthma and wheezing and found that 25% of the nonsmoking teens had episodes of wheezing as compared to 56% of the boys who smoked from 5 to 14 cigarettes a day and 47% of the boys who smoked this many cigarettes a day.

It is stated that the better the lung functions in youth the healthier the lungs will be in later life.

DISCUSSION QUESTIONS:

(1) The authors concluded that lung damage due to smoking for girls was greater than it was for boys. What confounding factors might make it difficult to compare the effect of smoking on the lungs of boys and girls?

(2) The article states that every day 3,000 adolescents begin to smoke. Do you think that reporting studies like this one will help decrease this number?
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Incarceration is a bargain.
Wall Street Journal, 23 Sept. 1996,
Steve H. Hanke

The author states that a recent article by economist Steven D. Levitt (Quarterly Journal of Economics, May 1996) showed that violent crime would be approximately 70% higher today if our prison population had not increased since 1973, and property crime would be almost 50% more frequent. A graph is provided showing that an increase in prison population reduces all major categories of violent and non-violent crime. From this chart it is observed that on average about 15 crimes per year are eliminated for each additional prisoner locked up.

The author remarks that incarceration works and then asks if it pays. He quotes results from Levitt estimating that the average annual cost of incarceration is $30,000 a year while the annual amount of damage the average criminal would do if on the loose is $53,000.

DISCUSSION QUESTIONS:

(1) How do you think Mr. Levitt came to the figure that the average criminal would cause $53,000 damage annually?

(2) Hanke did not include those who are in jail for so-called consentual crimes such as drug offenders. Drug offenders have been estimated to be more than half the federal prison population. Why do you think he omitted these?

(3) How do you think that Levitt estimated how much more violent crime would have occurred if the prison population had not increased since 1973?

(4) In Levitt's article it is reported that one way to estimate the deterrent effect of having people in prison is to ask prisoners how many crimes they commit when not imprisoned. In a Wisconsin study this yielded a distribution of non drug-related crimes per year having median 12 and mean 141. What do you think the mode of this distribution was? How reliable do you think such statistics are?
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In the last Chance News I promised a review of another book that would be a valuable resource for teaching a Chance course or any introductory statistics course. Here it is:

A casebook for a first course in statistics and data analysis.
John Wiley, 1995
Samprit Chatterjee, Mark S. Handcock, Jeffrey S. Simonoff

This book provides a set of case studies from a variety of fields where statistical analysis is required to reach a meaningful decision. Each case describes the background of the problem, provides the data and poses questions that can be answered by statistical analysis. The cases fall into three categories: in the first category the case study is completely analyzed. In the second category the cases are not analyzed, but suggestions are made to guide the student in carrying out an analysis. In the third category the problem is described, the data provided, questions are posed, and the student is left to carry out the analysis.

To give a flavor of these case studies we describe the first one. It deals with eruptions of the "Old Faithful" geyser at Yellowstone National Park in Wyoming. Visitors visiting the geyser want to arrive at a time when they will not have to wait too long to view the geyser. The National Park Service erects a sign predicting when the next eruption will occur. How can they best predict the time between eruptions?

The authors provide data giving the time between eruptions and the duration of eruptions for August 1978 and August 1979. A histogram of the time between eruptions is found to be bi-model with peaks at about 55 minutes and 80 minutes. A scatter plot of time between eruption and duration of eruption shows that long eruptions tend to be followed by long intervals between eruptions, and short durations are followed by short times between eruptions. An explanation for this is given: eruptions of short duration leave hot water in the ground making it easier for the water to heat up for another eruption but for long eruptions most of the hot water in the earth is used up by the eruption requiring more heating for the next eruption.

The authors are led to a prediction rule that predicts that after an eruption of duration less than 3 minutes, one will have to wait about 55 minutes, and after an eruption of duration greater than 3 minutes the wait will be about 80 minutes. Data for August 1985 is provided and this rule is used to predict the time of the next eruption. This prediction is found to be within plus or minus 10 minutes about 90% of the time.

The authors have made good use of their web site to add new information about their cases and to provide additional case studies suggested by later work. For example, you will find here an analysis of the Old Faithful data by Donald Richter which shows that the tacit assumption made that the distributions of eruption times and times between eruptions are the same in August for different years, may not be completely justified and should be considered only as an approximation.

Faithful readers of Chance News (see Chance news 5.03) will recall that researchers at Yellowstone Park reported (The New York Times Feb 5, 1996, D1) that the average time between eruptions appears to be increasing through the years. Chatterjee and his co-authors wrote us about this:

The bi-modility has a direct effect on the question of lengthening average time intervals between eruptions. There are two obvious ways that the average time interval could increase, without changing the basic underlying pattern of eruptions: by a general shift upwards of the entire distribution, or by a change in the probabilities of a short time interval versus a longtime interval (with long intervals becoming more probable). Presumably these two different possibilities would have different implications from a geothermal point of view; so it would be interesting to see if either possibility (or what other possibility) describes the observed lengthening of the average time interval.

Thus we see how the web allows us to keep an interesting problem alive.
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Bob Griffen reminded us that the great Milwaukee "voucher battle" is still going on (See Chance News 5.09). Here is a recent article that describes the present state of this voucher battle.

Dueling professors have Milwaukee dazed over school vouchers.
Wall Street Journal, 11 October 1996, A1
Bob Davis

Since 1990, Millwaukee families of several thousand low-income families have been provided state-funded vouchers to allow them to take their students out of public schools and enroll them in private schools. The program has been watched closely as a model program designed to give poor children some of the advantages of children of wealthier families.

John Witte was selected by the state to track the progress of the program. In a series of annual reports he compared the progress of the voucher students to a control group chosen from the general Milwaukee school population. He found that voucher students did not advance faster than the control group despite the fact that the parents of the children felt that the private school atmosphere was much better for their children.

Harvard political scientist Paul Peterson was critical of comparing the progress of the voucher students to randomly chosen Milwaukee students. He carried out his own study by taking advantage of the fact that four private schools had more applicants than they had space for and so used a lottery to decide which to accept. Peterson compared the performance of those accepted and those not accepted and found that, while their performance in the first year was no better, it was significantly better on standardized tests after three years.

The issue has become highly political and, in fact, occurred in the last presidential debate. Dole is supporting the voucher plan, promising a $3 billion-a-year federal program to pay for scholarships to send low-and middle-income children to private schools. Clinton, while not opposing local voucher programs, would not support a federal voucher program with the "highly ambiguous" results in Milwaukee.

Peterson and Witte are carrying out a virtual duel over the statistical issues involved and you can find the data, the studies and their critiques of each other's work on the web page of the American Federation of Teachers.

DISCUSSION QUESTIONS:

(1) In his critique of Peterson's work, Witte writes:

The methodology employed by Peterson is one used primarily in controlled medical experiments. It is theoretically inappropriate for modeling educational achievement and, in its application to the MPCP, is very biased in favor of choice students. The method, to my knowledge, has never been used before in modeling educational achievement.

What do you think Witte means by: "It is theoretically inappropriate for modeling educational achievement"?

(2) Peterson says about Witte's study:

Mr. Witte stacks the deck against voucher students by comparing them with Milwaukee students generally. The latter students are whiter wealthier and more frequently live in two-parent families than voucher students--and thus more likely to perform better on standardized tests. Mr. Witte's efforts to make adjustments for the different groups are doomed because they are too dissimilar. The statistical controls that Mr. Witte used can't turn middle-income white students into lower-income blacks.

What do you think of this criticism?
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Full House.
Harmony Books
Stephen Jay Gould

It is always fun to find a "best seller" that is full of statistical concepts. Full House is a popular version of several of Gould's previous works. Those who teach Chance are familiar with two of these: Gould's delightful article "The Median is not the Message" (Discover Magazine June 1985), and Gould's explanation of why there are no more .400 hitters in baseball told by him on the "Against All Odds" video.

In the "Discover" article Gould describes how he reacted to the news he received in 1982 that he was suffering from abdominal mesothelioma, a rare and serious cancer with a median mortality of 8 months after it is diagnosed. Gould describes how he cheered himself up by realizing the distribution of lifetimes for those diagnosed with his disease could not have a left tail of more than 8 months and probably had a very large right tail. He assumed that he was far out in this tail. Evidently he was.

In "Against All Odds", Gould explained the disappearance the .400 hitter by observing that, while the average batting average for the past 100 years remained around .260, the standard deviation of this average continually decreased. Ty Cobb's .420 batting average in 1911 was 4.16 standard deviations above the mean batting average and Ted Williams' .406 batting average in 1941 was 4.21 standard deviations above the mean for that year. Thus while the .400 hitters seemed to disappear after Ted Williams, because of the decrease in the standard deviation for the average batting average, George Brett's .390 batting average in 1980 was 4.03 standard deviations above the mean. Thus his .390 batting average represented a comparable exceptional average.

Gould argues that the batters are, in fact getting better; but so are the pitchers and fielders. So this improvement does not show up in their batting averages. We should not be measuring excellence by the batting average but rather by how many standard deviations the players average is above the mean of the batting averages. Gould explains the decrease in standard deviation by the fact that players in every position are getting near the limit of what is possible so there is less room for variation.

Thus, the theme of this book is that it is misleading to look at a single attribute of a system such as maximum values but, rather, you have to look at the "full house".

In both examples, variation is effected by boundaries that are imposed. In the first example, Gould's additional lifetime after being diagnosed must be at least 0. In the baseball example there are physiological limits to how good the players can get.

To get into the spirit of his main example, evolution, Gould looks at a drunkard's walk example. He gives an example of random walkers something like this. Consider a lot of random walkers who move on the integers, making one step to the right or left with equal probabilities. If they ever reach 0 they disappear (0 is a bar). Start 100 such random walkers at 10. Then the distribution of their positions after 100 steps will have mean about 10 but will have a right tail that is much longer than the left tail (limited to 10). When I carried out a simulation of this experiment, the mean position was 10.6, the mode was 10 and the right tail of the distribution extended to 32 achieved by just one of the random walkers.

To show what this means for evolution, Gould considers the case of single-celled protozoans called planktonic forams. Evidently these forams occur in fossils, and their evolution has been studied through millions of years. It has been observed that, over time, their body size appears to increase. This increase has been explained by Darwin's concept of "survival of the fittest" in terms of an advantage for larger bodies. However, Gould's argues that this does not really fit into Darwin's scheme of things and the apparent increase in size can be accounted for even with no tendancy for size to increase by the existence of a left barrier just as in the case of the random walkers.

Gould looks at a study done by W.C. Parker at Florida State University which followed the descendants of 342 species of forams. The laboratory procedures to study forams sieve out forma with size less than a certain minimal size. Thus when following the changes in size of descendants of a given species, if a change results in a size smaller than this minimum size, this species will disappear just like our random walker did upon reaching 0.

Parker showed that the distribution of the changes in sizes from one generation to the next is symmetric with no preference for being larger or smaller. In other words these changes looked like the changes of our random walker with no preference for going to the right or left. Thus, just as for our random walker, the mean of the distribution of size should remain about the same. But as time goes on, the distribution of size will have a large right tail, making it appear that something is causing the forams to be getting bigger when, in fact, it is just a natural consequence of statistical variation in a random process with a barrier.

Well, from this example it is only one step to conclude that the same kind of argument can be used to explain the apparent increase in complexity or intelligence in the human species. This increase has nothing to do with adapting to our environment but rather to the fact that there is a limit to how dumb or simple a species can be but not to how smart or complex it can become. Thus starting from a bacteria, over a long time, random variations in species have produced some very intelligent forms of life. We are lucky enough to be on this right tail of the distribution of many random walkers. We started as bacteria and the mode intelligence after all these millions of years of evolution is still that of bacteria providing Gould further evidence that he is on the right track.

DISCUSSION QUESTIONS:

(1) A 1992 study of abdominal mesothelioma still gives the median mortality time to 12, 10, or 8 months, depending on the state at which it is diagnosed. What might have been the source of Gould's good fortune?

(2) Gould suggests that, while the mode should stay the same, the mean would increase in his model for the size of forams. Should the mean increase if his random model with a barrier is correct?

(3) From p. 175: `If we could replay the game of life again and again, always starting at the left wall and expanding thereafter in diversity, we would get a right tail almost every time, but the inhabitants of this region of greatest complexity would be wildly and unpredictably different in each rendition---and the vast majority of replays would never produce (on the finite scale of a planet's lifetime) a creature with self-consciousness. Humans are here by the luck of the draw, not the inevitability of life's direction or evolution's mechanism.'

What do you think Gould means by a `vast majority'? How do you suppose Gould carried out this computation? Is self-consciousness merely a matter of large brain capacity?

(4) Look closely at Figure 27 on p. 165, which Gould says is taken from Stanley's work. Notice that all the big rightward jumps in the picture originate on the right side of the picture. Why? If there is a mean tendency for offspring to increase in complexity, does this invalidate Gould's central contention (p. 162) that size increase `is really random evolution away from small size, not directed evolution toward large size'?
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Ask Marylin
Parade Magazine, 15 Sept 1996, p. 24
Marylin vos Savant

Marylin is asked:

Say I have two dozen pickles--labeled No. 1 through No. 24--in a jar. I pull out a pickle at random, note the number and replace the pickle in the jar. Then my friend pulls out a pickle at random. What are the chances that she will pull out a higher- numbered pickle than I did?

Paul Joseph, Houston Texas

Marylin observes that the chance that you obtain the same number is 1/24. If you don't get the same number, you have an equal chance that your number is smaller or bigger than the first number. Thus the answer is 23/48. Marylin remarks that her answer would be different if you tell her the outcome of the first choice.
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Part 2

NOTE: At the end of this Chance News you will find a call for papers for the Fifth International Conference on Teaching Statistics - ICOTS-5 - to be held in Singapore, June 21-26, 1998.

Interesting web sites: COLLEGEBALL.COM

This is a "for fun" football pool. Each week about 18 of the leading college games are picked. Your instructions are:

Make your picks for each game by clicking on the radio button next to the team. Assign a unique confidence value for the pick from 1-18. 1 is the highest confidence and 18 is the lowest. Use each confidence value only once!

Point spreads are not used. Suggested strategies for this pool are given. For an interesting example of strategy in football pools with point spreads, see "The Evil Twin strategy for a football pool"
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It's election time and you may want to follow the tracking polls. You can find these at the following sites:

PoliticsNow

AllPolitics

Gallup

And don't forget our favorite "The Iowa Electronic Markets" where you can play the futures market for real money. You can buy a share of Dole today for about 8 cents.
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Milt Eisner suggested the next two articles. The full text of these articles can be found on the Washington Post homepage. They only keep articles there for two weeks.

Tails Over Heads.
Washington Post, 13 Oct 1996, C1
William Casey

Ever since January 1985, William Casey has been collecting all the coins that he sees on the ground wherever he goes (coins includes bills). He has established a data base containing information about these coins. In this article he discusses several aspects of his collection which now contains 11,902 coins. He reports, for example, that 51.5% of the coins were found with tails up. He provides a bar graph showing the distribution of coins found by month, with January yielding the most and September the fewest. Casey plans to continue collecting coins until Dec. 31, 1999.

DISCUSSION QUESTIONS:

(1) Casey wonders why 51.5 percent of his coins were found tails up. Is this a significant difference from chance? If so, what explanations might you give him?

(2) Casey also asks: why is the average mint date 1985 for Philadelphia pennies but only 1983 for those from Denver? What would you have to know to decide if this difference is significant?

(3) Do you have any idea why January should be the best month for finding coins?
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The next three articles are a series based on a survey by the Washington Post, Harvard, and the Kaiser Foundation.

A nation that poor-mouths its good times.
Washington Post, 13 Oct 1996, A1
Richard Morin and John M. Berry

This article discusses the difference between the actual performance of the U.S. economy (as reflected in statistics) and the public's perception of the economy. The article's title indicates that the former is pretty good while the latter is pretty bad. The authors surveyed 1511 Americans with the following open questions:

The article reports "according to government statistics, unemployment is at a seven-year low. Inflation is at its lowest level in three decades. The federal budget deficit has declined to about $109 billion this year from $290 billion in 1992. The economy is creating millions more jobs than are being lost to downsizing, mergers, business failures or foreign competitions."

On the other hand, from the survey, we learn that "the average American thinks the number of jobless is four times higher than it actually is. Nearly 1 in 4 believes the current unemployment rate tops 25 percent--the proportion of Americans who were estimated to be out of work is as it was at the worst of the Great Depression. They believe that prices are rising four times faster than they really are and that the federal budget deficit is higher, not lower, than it was five years ago. And 7 in 10 say there are fewer jobs than there were five years ago."

The article discusses problems this disparity makes for politicians creating public policy.

DISCUSSION QUESTIONS:

(1) Do you think the average American should know the answers to the four questions listed above?

(2) Why do you think there is such a disparity between what the public thinks and the government reports?
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Prosperity imbalance.
Washington Post, 14 Oct. 1996, A1
Clay Chandler and Richard Morin

This second article in the series reports that the survey and other data show that people are divided into distinct groups: those who have trouble meeting their bills and see little hope for a life without financial woes and those who are well off and have no financial problems. The gap between these groups has increased significantly in recent years. The main factor in deciding who is in each group is education. The family income of a family with a college diploma increased 28 percent in inflation-adjusted dollars from 1974 to 1994 while incomes of high school graduates increased just 3 percent and incomes of those without a high school diploma shrank more than 10 percent.

Not surprisingly, the people in these two groups have very different attitudes about the state of the U.S. economy even though, the economy appears to be in good shape.

DISCUSSION QUESTION:

Why do people with a college education fare so much better today than they did thirty years ago?
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Great divide: economists vs. public.
Washington Post, 15 Oct. 1996, A1
Mario A. Brossard and Steven Pearlstein.

This last article in the series compares the opinions of economists about the economy with those of the general population. Opinions of the economists were obtained from a survey of 250 economists from a random sample of members of the American Economic Association. The opinions of the general public were obtained from the Post/Harvard/Kaiser study.

There is a wide disparity between the opinions of the general public and the economists. For example: 35% of the economists feel that, in the past 20 years, family incomes have been going up faster than the cost of living while only 11% of the public believe this. 39% of the economists feel that most of the new jobs being created today pay well as compared to only 16% of the public who believe they do. 50% of the economists but only 24% of the public feel the average standard of living will increase over the next five years. 50% of the economists believe that trade agreements have helped create more jobs while only 17% of the public believe this.

The article discusses the many reasons for this difference. For example, it is stated that the public tends to look locally at what is happening in the country and the economists look globally. The economists see that trade agreements lead to less expensive goods while the public sees the local cobbler goes out of business.

DISCUSSION QUESTIONS:

(1) How do you think the economic status of the average economists compares with that of the average person in the general survey? If different, would that explain some of the differences in their answers?

(2) Should the President, in proposing public policy, be more influenced by the opinions of the economists or by the opinions of the public?
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College board revises test to improve chances for girls.
New York Times, 2 October, 1996, B8
Karen W. Arenson

In an agreement with the Office of Civil Rights, the College Board will add a multiple-choice test on writing to its Preliminary Scholastic Assessment Test (PSAT). This test will include questions involving the structure of language and standard written English. The PSAT test is taken by high school juniors and is the main determinant in awarding the National Merit Scholarships.

This followed a complaint filed with the Education Department in 1994 by civil rights activists who said that girls tend to score lower on the PSAT than boys, even though their high school and college grades were better.

Each year more than a million high school juniors take the PSAT tests. About 55% of these are girls. Those in the top 15,000 scores, of which about 60% are boys, automatically become National Merit semifinalists. The students then submit grades, extracurricular activities, recommendations and essays; and about 14,000 are chosen as finalists.

In 1989, a Federal District Court in Manhattan ruled that the New York Regents Scholarships discriminated against girls because they were based on SAT scores. When New York State relied on standardized test, girls won 43 percent of the scholarships. A year after the court ruling, when grades were also taken into consideration, the girls won 51% of the scholarships.

DISCUSSION QUESTIONS:

(1) A spokesman for the College Board denied that the test in its present form is biased against women. What does it mean to say that the PSAT test is biased against women?

(2) A spokesman for the College Board said about the writing test to be added that "Women tend to do better than men on this test, about two or three points better on a high score of 800". Do you think that will significantly help the women to get National Merit Scholarships?

(3) From the 1996 Profile of College-Bound seniors we find that the following statistics:

Verbal SAT      Males       Females



Mean             507         503



Standard         112         109

Deviation



Percentiles

75th             580          580

50th             510          500

25th             430          430





Math SAT        Males       Females



Mean             527          492

Standard         115          107

Deviation



Percentiles 

75th             610         560

50th             530         490

25th             450         420
These statistics are based on the 1,084,725 students who took these tests any time during their high school years through March 1996. If the student took it more than once the most recent score was used.

(1) Why do you think there is such a large difference between the mean math scores for men and women?

(2) Is there significant less variation in the women's scores than in the mens? If so, can you explain this?
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Use of daily election polls generate debate in press.
New York Times, 4 Oct. 1996, A24
James Bennet

On Saturday the latest CNN/USA Today Gallop tracking poll showed only a 9-point difference between Clinton and Dole. A CNN commentator reported that "the race has closed. This single digit lead is half of what it was earlier this month." On Tuesday it showed a 25-points difference, and another CNN reporter stated that "Mr. Clinton's domestic political standing is strong, he has opened up his largest lead since the poll began in September."

Sharp changes are newsworthy but are they significant?

These daily reports put pressure on the candidates spokesmen to explain the sudden changes. For example, did a foreign crisis bolster the President?

Experts compare watching the daily tracking to watching the daily Dow Jones average and explaining, after the fact, what made it go up today or go down.

DISCUSSION QUESTIONS:

(1) Would it help to report an average the last three days' polls?

(2) The margin of error for the Gallup poll is 4 percentage points. How much of a gap could there be between two successive days' results for the polls still to be within their margin of errors?
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Misreading the gender gap.
New York Times 17 Sept. 1996, A23
Carol Tavris

The author lists several examples of supposed gender gaps which disappear when a relevant trait is controlled for.

Women are more likely to believe in horoscopes and psychics. (Not if you control for the number of math and science classes a person has had. What appears to be a gender gap is a science gap.)

Men are more likely than women to express anger directly and abusively. (Not if you control for the status of the individuals involved. What appears to be a gender gap is a power gap.)

Now everyone is talking about the gender gap in the current Presidential race. According to the most recent New York Times/CBS News poll, women prefer Clinton to Dole by 61% to 33%.

Conservatives explain this gap by saying that women tend to be more sentimental, more risk-averse and less competitive than men, while liberals claim that women are more compassionate and less aggressive than men, and thus attracted to the party that will help the weakest members of society.

Tavris rejects both of these explanations claiming "affluent women have never shown an especially tender-hearted sympathy toward their sisters in poverty" and making similar remarks about the other supposed differences.

She suggests that the gender gap in the political situation is largely an experience gap. If their husband has left them they may have been saved by welfare. More women than men are taking care of aging, infirm parents. More single mothers than single fathers are taking care of children on their own etc. Tavris remarks: "For women to perceive the Democrats more responsive than the Republicans to these concerns is neither sentimental nor irrational. It stems from self interest."

DISCUSSION QUESTIONS:

(1) Can you think of other gender gaps that might disappear when you control for a relevant factor?

(2) Do you agree with the author's explanation for the gender gap in politics?
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Michael Olinick provided the following story, which he heard on NPR and tracked down the transcript on Nexis/Lexis.

NPR Weekend Edition Sunday (10:00 am ET)
18 August 1996, Transcript # 1189-6
The following puzzle was read on the air by Will Shortz: ...This week's challenge is a logical puzzle by Terry Stickels [sp], who has written a 365-day puzzle calendar for 1997 called Mind Bending Puzzles. There are four colored balls in a bag; two red, one black, and one blue. If you draw two balls at random, and then you're told that one of them is red, what is the likelihood that the other ball is also red?"

Listeners were encouraged to mail solutions on a post-card to Weekend Edition Sunday Puzzle at NPR.

DISCUSSION QUESTION: What is the probability?
------------------------

NPR Weekend Edition Sunday (10:00 am ET)
25 August 1996, Transcript # 1190-6
LIANE HANSEN, Host: This is Weekend Edition; I'm Liane Hansen. And joining us is puzzle master Will Shortz...Well, I tell you, we are all confounded by last week's challenge...We've been talking about it pretty much up until the point of this broadcast.

SHORTZ: Well, it stumped a lot of people. It was from a 1997 calendar by Terry Stickels [sp] called Mind-Bending Puzzles....The likelihood is 20 percent, or one chance in five, and here's why. There are only six combinations of balls; red one and red two, red one and black, red one and blue, red two and black, red two and blue, and black and blue. Now, since you were told that one of the balls was red, you can ignore this last combination. There are five combinations left that have red in them, only one of which has two reds, so the odds are one in five.

LIANE HANSEN: We had about 600 entries this past week, in spite of the-the challenge, and the fact that a lot of us are probability impaired...

Our winner is Susan Ehrhardt, and she lives in Oswego, New York; and, Susan, first of all, I have to thank you very much for giving us some visual aids to Will's puzzle. You actually drew the combinations that came up. Nice going, Susan.....What do you do there in Oswego?

SUSAN EHRHARDT: I'm a veterinarian.

LIANE HANSEN: Oh. How long did it take you to come up with the answer to this puzzle?

SUSAN EHRHARDT: Well, I've had statistics courses, so it's-it was a second, so-

LIANE HANSEN: A second, she says [laughs].

SUSAN EHRHARDT: But I'm not probability impaired.

DISCUSSION QUESTION: A second?!

--------------------
NPR Weekend Edition Sunday (10:00 am ET)
1 September 1996, Transcript # 1191-5
LIANE HANSEN: .....you know, Will, people are still talking about those balls--

WILL SHORTZ: Uh-huh.

LIANE HANSEN: -from two weeks ago.

WILL SHORTZ: I- I had a feeling that would happen.

LIANE HANSEN: So what are we gonna do?

WILL SHORTZ: Well, I have written a fuller explanation of the solution to that statistics puzzle from two weeks ago, and you can get it by sending us a self-addressed stamped envelope, or by going to the Weekend Edition Web page on the Internet, either way.

The URL is http://www.npr.org/programs/wesun/puzzle_archive.html

Included there is a response to questions by many listeners who wondered why the answer isn't 1 in 3. They reason that, given one of the balls being red, the other ball by elimination must be red, black, or blue. Thus, the odds of the second ball being red are 1 in 3.

DISCUSSION QUESTION: What is wrong with the argument for 1 in 3?

Editor's comment: This kind of problem also interested Lewis Carroll whose Pillow-Problem number 5 was:

A bag contains one counter, known to be either white or black. A white counter is put in, the bag shaken, and a counter drawn out, which proves to be white. What is now the chance of drawing a white counter?

DISCUSSION QUESTION:
And what is the answer to Lewis Carroll's problem?
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Ask Marilyn.
Parade Magazine, 22 September 1996, p.20
Marilyn vos Savant

Blaise Pascal, a scientist and philosopher, posed a decision problem for atheists, sometimes called 'Pascal's Wager.' If you were an atheist, how would you respond?
Glenn Niblock,
San Diego, Calif.

Pascal's argument is that, if God does not exist, one loses relatively little by believing in him, whereas there is a tremendous loss in failing to believe in him if he really does exist. Weighing these alternatives, a rational man
should gamble that God exits.

Marilyn asserts that the wager contains two important assumptions: (1) God exists and (2) If he exists, believing in him brings eternal life. She notes that the argument can be adapted to reason that a religion that promises eternal life to the faithful is better than one which promises, for example, only a few days of life after death. And a religion that promises eternal life plus some other benefits would look even more attractive. In other words, the best bet would be to join the religion that makes the most promises.

DISCUSSION QUESTIONS: Do you agree with Marilyn?
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Boys' club.
Athletic Business, May 1996, p9
Rick Berg

The article is a bit dated, but pertains to a current issue at Middlebury, where our athletic director is retiring and we are conducting a national search for his replacement. One of the members of the search committee forwarded this article to me (Bill Peterson) for comment. The article notes that most Division I-A Athletic Directors (ADs) are male, former players and former coaches, even though college presidents report that none of these credentials are requirements for the job.

Toni Wyatt, a professor of sport management at Appalachian State University, surveyed Division A-I presidents to learn what they think is important in an AD, and compared the results with the profiles of those who actually get hired. Some of his findings:

Prof. Wyatt speculates that football experience is more important to presidents than they might like to admit. The survey also finds the following demographic profile: 96.2% of presidents and 98% of ADs are male; 92.5% and 97.9% are white.

DISCUSSION QUESTIONS:

(1) Do the data mean that presidents are simply saying one thing and doing another? What other information would you like to have to evaluate the hiring practices?

(2) What do you make of the football connection?
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NOTE:
The Fifth International Conference on Teaching Statistics - ICOTS-5


Place Nanyang Technological University, Singapore,
Dates June 21 - 26, 1998.

Theme Statistical Education - Expanding the Network

Contacts

Chair IPC Brian Phillips (bphillips@swin.edu.au
Fax + 61 9819 0821)

Chair LOC Teck-Wong Soon (twsoon@singstat.gov.sg)

Singapore contact Lionel Pereira-Mendoza (pereiraml@am.nie.ac.sg)

WWW site www.nie.ac.sg:8000/~wwwmath/icots.html



CALL for PAPERS


If you are interested in presenting a paper at ICOTS-5 please submit an abstract, 300 - 500 words, of the paper you would like to be considered as soon as possible but before Dec. 18, 1996 to the relevant topic convener whose name and email is listed below or the IPC Chair. You will then be put in touch with the appropriate session organizer.

Note: Because of the limited number of speakers who can be accepted for each session, people whose abstracts are not accepted for the session they nominate may be referred to organizers of other relevant sessions and/or the contributed paper or poster sessions.

Topics

1. Statistical education at the school level (Elementary level, secondary level, teacher training, local teachers) Lionel Pereira-Mendoza pereiraml@am.nie.ac.sg

2. Statistical education at the post-secondary level (Introductory statistics, mathematical statistics, design and analysis of experiments, regression and correlation, Bayesian methods, categorical data analysis, sample survey design and analysis) Richard Scheaffer scheaffe@stat.ufl.edu

3. Statistical education for people in the workplace (Statistical consultancy, continuing education, distance education, total quality) Kerstin Vannman kerstin.vannman@ies.luth.se

4. Statistical education and the wider society (Statistical Societies, statistical literacy, publications, legal contexts, journalists, informed society) Anne Hawkins ash@maths.nott.ac.uk

5. An international perspective of statistical education (African region,Asian region, Spanish speaking , Other developing regions,) James Ntozi isae@mukla.gn.apc.org

6. Research in teaching statistics
(Junior levels, senior school levels, post-secondary levels, probability) Joan Garfield jbg@maroon.tc.umn.edu

7. The role of technology in the teaching of statistics (Software design,teaching experiments, graphics calculators, visualization, research,multi-media and WWW)
Rolf Biehler rolf.biehler@post.uni-bielefeld.de

8. Other determinants and developments in statistical education (Cultural/historical factors, learning factors, assessment, gender factors, projects/competitions)
Guiseppe Cicchitelli pino@stat.unipg.it

9. Contributed papers
Shir-Ming Shen hrntssm@hkucc.hku.hk

10 Poster sessions
Peng Yee Lee leepy@am.nie.ac.sg


Note: Anyone who wants to run a special session such as a special interest group discussion, a demonstration/training session should contact the IPC Chair for consideration.
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Please send comments and suggestions for articles to
jlsnell@dartmouth.edu.

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CHANCE News 5.11

(8 September 1996 to 8 October 1996)


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