Prepared by J. Laurie Snell and Bill Peterson, with help from Fuxing Hou, Ma.Katrina Munoz Dy, Kathryn Greer, and Joan Snell, as part of the Chance Course Project supported by the National Science Foundation.
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By the blood of Crist that is in Hayles, Seven is my chaunce and thyne is cynce and treye.
=============================================================The Pardoner's Tale, Chaucer 1387
Notes: This issue was delayed because of our attempt to include the complicated issues raised in the recent news about recommendations for mammograms. We decided to report this separately in a Chance News Extra. If you cannot wait for this, you might want to look at the following articles:
The breast-screening brawl.
Science, 21 February, 1997, pp. 1056-1059
NCI reverses one expert panel, sides with another.
Science, 4 April, 1997, p. 27-29
New view sees breast cancer as 3 diseases.
The New York Times, 1 April, 1997, C1
Few heed shifts on mammograms.
The New York Times, 2 April, 1997, C8
The Winter issue of Chance Magazine just arrived and has a number of interesting articles. We will review one or two of these in the next Chance News. Of course, we hope you all subscribe to Chance Magazine. Information about Chance Magazine can be found on their web page.
We received the following note from firstname.lastname@example.org.
What are the chances that the first time that I tried yahoo's "random link" selection, it led me to your chance page? Weird but true...
From personal experience, we know the difficulty in maintaining a site suggesting good statistics web sites. Tor Tosteson brought to our attention one of the best we have seen called "Statistics on the Web." It is maintained by Clay Helberg.
Several readers pointed out that the "mystery" Powerball Lottery numbers 01 09 23 37 45, that occurred more often than should by chance, are not very mysterious: they are the corner points and the center point of the box in which you mark your five numbers. Here are the three remaining sets that we cannot explain:
01 03 09 30 34 05 06 16 18 23 02 05 20 26 43
Any suggestions? Our fascination with the data from the Powerball lottery led us to write a treatise on how you might use this lottery in a Chance course. It is available on the Chance web page under teaching aids.
Knuth's solitaire problem, mentioned in Chance News 6.04, was
solved by Charles Grinstead. It has a nice answer and you will be
proud of yourself if you solve it.
Donald Richards sent us the following contribution with the discussion questions he used in his class.
Pacific Rift, by Michael Lewis (published by W. W. Norton, 1993), is a very interesting little book, 128 pages long, about "why Americans and Japanese don't understand each other." On pages 21- 22, the following material appears:
Anyone who has seen one of the 17 (and counting) Japanese-produced Godzilla movies has also seen, in miniature, the Japanese view of the world. To a Japanese, the world is an accident waiting to happen -- to him. It is a collection of powerful, uncontrollable forces that are forever rising out of land and sea to squash Japanese executives flat as compact discs. This collective mental melodrama is not without some justification. As the Japanese never tire of telling, their country has had its fair share of earthquakes, typhoons, tidal waves, and volcanoes. For the last four centuries, Tokyo has been leveled by quakes every 70 or so years: 1633, 1703, 782, 1853, 1923.
(1) Estimate the year, and month, when Tokyo will next be "leveled" by a quake.
(2) How accurate is your estimate? That is, how much "confidence" do you have in your estimate?
(3) Would you buy land in Tokyo at this time? Would you
recommend that State Farm Insurance Company sell large amounts of
property insurance on Tokyo real estate during 1996? 1997? 1998?
Bill Peterson sent us the following note from Grant Gibson, one of his former Chance students:
Snapple is running a promotion where each bottle of Diet Snapple has a chance to win a free bottle. They list the odds as one in eight, and they're giving away something like four billion bottles of the stuff. Unfor- tunately, they aren't giving any to me. I buy one every now and then, but never thought much of the fact that I wasn't winning. After a while though, it started to get ridiculous. In fact, since I've been keeping track I have lost 25 times in a row. Drawing upon my superb probability skills, I figured the odds of this happening are about 4%. The thing is though, I haven't won yet, and I keep getting less and less lucky. It reminded me of the section we did on streakiness in the NBA.We decided to see how this works and bought a bottle and won the first time. But then, making chance work is our business.
Did Bill succeed in teaching Grant how to calculate the probability of getting a streak of 25?
A somewhat more substantial lottery has just been started by the Mars company using their M&M's. When you buy certain bags of M&M's you may find some gray candies. This is a signal that you may have won a million dollars or some lesser prizes consisting of large number of packages of M&M's.
If you do find a gray M&M, you will also find in the package a card, called the game piece, that looks like an instant lottery ticket. Scratch off the covering, and you could find a message saying you are an Instant Winner and specifying what you have won. Of course, more likely the card will not say this.
The first million dollar winner was a 19 year old college student Jason Rollman from our neighboring town of Enfield NH. He won before Mars even got to announce the contest, so they are providing another million dollar prize to go along with their official announcement.
(1) Jason is studying for the ministry and the family are independent Baptists. His father said that, if he had spent his money on a lottery ticket, he would have been sinning. "The Lord doesn't approve of gambling, but a candy contest is something different." Do you think the Lord really makes this distinction?
(2) From the M&M homepage you find the prizes listed as:
Grand Prize: $1,000,000, awarded as an annuity payable as $50,000/year for 20 years, without interest. Odds 1:273,922,000.
(7,500) First Prizes: 365 coupons, each redeemable for 1 free single-size pack of "M&M's"® Chocolate Candies. Approximate Retail Value (ARV) $219.00 ea. Odds 1:36,523.
(32,500) Second Prizes: 180 coupons each redeemable for 1 free single-size pack of "M&M's"® Chocolate Candies. ARV $108.00 ea. Odds 1:8,429.
You are allowed to write in an get (as long as they last) a free game piece. Assuming that this cost you only the 32 cents for the stamp, and the prizes and odds of your winning are as given, what is your expected winning? What should you assume the million dollar prize anuitized is really worth? Should you take the value after taxes?
(3) If this is a lottery, how do they get around laws against
lotteries in certain states?
Alben Jones suggested the following data and article:
Special report: Gender equity in 1997.
USA Today College Sports
Title IX was designed to prevent gender discrimination in college sports. It is 25 years old and the newly enacted Equity in Athletics Disclosure Act requires colleges to make participation and financial data, related to sports, public. USA Today obtained this data from 303 of the 305 division I schools. On their web site, they provide some of this data and the conclusions they arrived at by analyzing it.
The good news is that the number of female athletes has increased 22% since 1992 and the bad news is that $1 is spent on women's college sports for every $3 spent on men's.
One of the ways that schools can be in compliance with title IX, is to have the proportion of athletes that are women essentially the same as the proportion of women in the undergraduate enrollment. "Essentially the same" has been interpreted to be within 5%. More than 90% of the Division I schools still do not meet this test.
While Notre Dame was not voted the number 1 team this year, it looks like they won the money sweepstakes. From the data, you see that their football revenues were $15,203,780 with expenditures of only $3,641,673.
(1) Colleges without football are four times as likely to pass the proportionality test than those with football. Some have suggested that a fairer way to assemble the numbers would be to leave football out of the equation. What do you think of this idea?
(2) The article discusses some difficulties in comparing the data because of different accounting methods for administrative and overhead costs. It is stated that:
At some institutions, administrative and overhead costs, which can be millions of dollars were divided between the men's and women's budgets. Other schools put administrative and overhead into a non-gender-specific budget.
What effect would this have on comparisons?
David Budescu sent the following contribution:
A Two-minute test for the AIDS Virus.
Maclean's, Feb 17, 1997, Health monitor, p, 70
An HIV blood-testing kit, developed by Octopus Diagnostics Research of Hantsport, Nova Scotia, reportedly can detect the virus that causes AIDS in a drop of blood in two minutes, while standard tests can take up to five days. Clinical studies of the test show that its rate of false positives--less than 2 percent-- is similar to other tests, but that it fails to detect HIV up to 5 percent of the time. Octopus has already contracted to provide half a million test kits to a Hong Kong distributor, and it is negotiating similar deals with other countries. The test is being considered for approval in Canada.
The standard test for the HIV virus is the Elisa test that tests for the presence of HIV antibodies. For every 1000 people tested who do not have the virus we can expect 998 people to have a negative test and 2 to have a false positive test. For every 1000 people tested who have the virus we can expect 998 to test positive and 2 to have a false negative test.
It has been estimated that 2 in every 1000 college students have
the HIV virus. Assume that, in a large group of college students,
100,000 are tested by the Elisa test. If a student test positive,
what is the chance this student has the HIV virus? Compare this
with the case of a positive test with the Octobus Diagnostic test.
Make the same comparison when the dealing with a population at
high risk where 5% of the population has the HIV virus.
The language of chance.
International Statistical Review, Vol. 65, No. 1, April 1997
Bellhouse, D.R. and Franklin, J
Formal probability is thought to have started in 1654 with the letters between Pascal and Fermat. However, examples of probability reasoning can be found well before this time but are few and far between. The authors want to see how widespread the ideas of chance were before 1654. They do this by looking at the English literature before this time. They feel that, if chance concepts are used regularly in the literature, even without the writer really understanding them, this would suggest that they were part of common knowledge at the time. For example, Tom Stoppard's play Arcadia uses concepts from chaos in a rather poetic way, reflecting the fact that this concept is more thoroughly understood by current mathematicians.
In the quote from Chaucer given above, you read that "seven is my chance and yours is three and five". Bellhouse and Franklin take this as evidence that it would have been known, as early as the fourteenth century, how to find the chance of a seven when two dice are thrown and, that the chance of getting a 7 is the same as getting either a three or a five.
The use of odds was common in the sixteenth century literature, particularly in the plays of Shakespeare. The authors state that, with the exception of an example by Greene in 1591 based on a card game, these odds corresponded to subjective probabilities. However, Evert Springhorn in his article, "The Odds on Hamlet", (The American Statistician, Vol. 24, No. 5, December 1970, pp. 14- 17), argues that the following occurrance of odds in Hamlet can be considered to be based on objective probability:
The King, sir, hath laid, sir, that in a dozen passes, between yourself and him,[Laertes] shall not exceed you three hits; he hath laid on twelve for nine.
Sprinchorn assumes that, to win the match, a contestant has to get three hits in a row. With this interpretation, and the assumption that the two contestants are equally matched, he shows that the probability that Laertes wins is .443 with corresponding odds very close to 9 to 12.
Of course the use of lots both in religion and in practical affairs goes back to biblical times. It is interesting that the idea that the fairness of random assignment in assigning pastures seemed to be appreciated, while, at the same time, it was believed that God could intervene if he did not like the way it turned out.
Lotteries were introduced in England in 1566. The authors comment that there was an understanding of the relative value of the chances of winning the various prizes but not even an order of magnitude understanding of the chances themselves.
Daston in his book "Classical Probability in the Enlightenment" gives the following description of how these the lotteries were carried out:
Players wrote their name and some "device" -- a proverb, a verse, an invocation to a saint--on a slip of paper, which was registered with a number at a central office. These were all put into an urn or leather sack. A second receptacle held an equal number of slips of paper, either blank or with a certain prize designated. A child (sometimes blindfolded) would draw out a name slip, an official would read aloud the device and the number, and the child would then draw a slip from the second urn, which the official would announce as either a blank or a prize.
Tickets were chosen, without replacement, until all the tickets were drawn. With the reading of the devices this could take as long as a month to complete.
In the 1566 lottery, Bellhouse and Franklin say that there were 400,000 tickets costing 10 shillings each and slightly over 29,500 prizes valued over the 10 shilling cost. Special prizes were available for those who bought more than one ticket. For example, if you bought several tickets and win three prizes in a row you win an extra 3 pounds, 6 pounds for 4 in a row, 10 for 5 in a row etc. The authors remark that it is a hard calculation, even now, to find the probability with 40 tickets of winning 3 in a row.
Bellhouse and Franklin conclude that the prevalence of chance concepts in the literature before 1654 suggest that there must have been a pretty widespread understanding of simple chance concepts.
Do you agree that the problem of finding the probability of
winning three prizes in a row when you buy 40 tickets in the 1566
British Lottery is hard? The authors estimated this probability
to be about 1 in 2.5 million. Can you see how they made this
Fire fight: Doctor whose study tied Joe Camel to kids goes on an odd journey.
The Wall Street Journal
21 February 1997, p1.
Suein L. Hwang
In 1988, a family doctor named Paul Fischer invented a picture matching game to investigate the effects of advertising on children. A set of 22 cards showed such famous symbols as McDonald's golden arches, Apple Computer's apple and Camel Cigarettes' Joe Camel. Depicted on a game board were pictures of a hamburger, a computer, a lit cigarette, etc. The game was tried on a sample of 229 children ages 3-6, who were recruited from nine day-care centers and an elementary school in the Augusta and Atlanta Georgia areas. One-third of the 3-year-olds and 91% of the 6-year-olds correctly matched Joe Camel with the cigarette. By comparison, less than 61% of the 6-year-olds identified the Marlboro man. Joe Camel turned out to be more readily recognized than the Pepsi logo.
Fischer's findings appeared in the Journal of the American Medical Association, and received wide coverage in the popular media. They became prime evidence in the federal government's call for further regulations on cigarette advertising. A California family law attorney filed suit against R.J. Reynolds (the manufacturer of the Camel brand), charging RJR with illegally promoting cigarettes in California and demanding that the company stop running Joe Camel ads. RJR attorneys subpoenaed Fischer's records, asking: "Must the public and defendants accept any and all scientific research as the absolute truth without the opportunity to critique, test, duplicate and learn the basis for the conclusions?" Fischer refused on the grounds that he had assured parents of the subjects that their children's names would never be released.
The article details a long sequence of legal maneuverings by the RJR, the Medical College of Georgia (where Fischer taught) and the state's attorney general. Ultimately, the data were ruled to be publicly available under the state's Open Records Act. By this time, however, Georgia law had been amended to protect the identities of the subjects.
(1) How do you think the 22 ad symbols were selected for the study? Wouldn't the Atlanta children have done better with the Coca Cola logo than with Pepsi since Atlanta is the home of Coca Cola?
(2) From the description in the article, don't you think you could conduct a similar study without seeing Fischer's records? Why do you think RJR felt it was so important to have the original data?
See also the next story for a related discussion.
Clean-air researchers pressured to show data.
The Boston Globe, 04 March 1997, pA1
In Chance News 6.02, we posed a discussion question about evidence linking air-borne particulates to deleterious health effects. Douglas Dockery and Joel Schwartz of the Harvard School of Public Health are the authors of a key research project called the "Six Cities Studies", which has been widely cited for proof that fine particles can kill people. The research looked at residents of six communities over a 16-year period, tracking deaths against the level of fine particles in the air. Dockery and Schwartz found a 26 percent higher death rate in the dirtiest city, Steubenville, Ohio, compared to the cleanest city, Portage, Wis.
Since proposed new EPA regulations may cost up to $20 billion annually, Dockery and Schwartz find themselves under increasing pressure from Congress industry groups to release their raw data. So far they are resisting, citing confidentiality of the test subjects.
This is not the first time the study has been criticized. In response to earlier concerns, the EPA in 1994 hired the Health Effects Institute of Cambridge to re-analyze Six Study data. The institute found death levels associated with elevated levels of soot and dust, as reported in the original Harvard study. But it also found that other kinds of pollution, such as carbon monoxide in engine exhaust, could be causing some deaths. Some new critics are suggesting that even high humidity might be responsible for some of the deaths.
Dockery and Schwartz, with the backing of Harvard, say they will continue offering access to the raw data only on a case-by-case basis to researchers who come to Cambridge. "Anybody who wants to come and analyze this data can," said Dockery. "We have not been willing to just throw it out there and put in on the web."
Do you think that any data used to support public policy decisions
should be a matter of public record? What are the pros and cons?
Left-handedness: Sinister origins.
15 February 1997, p80
About 10% of men and 8% of women are left-handed, and archaeological evidence indicates that these percentages have been stable for thousands of years. By contrast, in species of mammals other than humans, right paw and left paw dominance seems to be evenly split. Noting that there are observed disadvantages to left-handedness in humans--for example, left-handers tend to be shorter and older at puberty than right-handers, and by some accounts they don't live as long--the article raises the question of why left-handedness has persisted in the population.
In the December edition of the "Proceedings of the Royal Society", French evolutionary biologist Michel Raymond and several colleagues present their hypothesis that left-handers have persisted because they have an advantage in fighting. The researchers studied college athletes at the University of Lyons and also world-class competitors, and found that left-handers tend to be over-represented in sports where an opponent is confronted directly, such as fencing, boxing, baseball and tennis. The effect is not found in sprinting or swimming, where contestants compete against the clock.
The findings for world-class athletes were the most striking. For confrontational sports, the lefty effect becomes stronger as the playing distance between opponents decreases. For example, 16.7% of world's top tennis players are left-handed. But from 1979- 1993, 33% of the men's world foils competitors were left-handed; for those who reached the quarterfinals of competitions, the percentage was 50%. By contrast, in sports which involve the hands, but where there is no tactical advantage to left- handedness, no lefty effect was found. For example, about 10.7% of discus, javelin and shot-put champions are left-handed, which is comparable to the population percentage.
The researchers suggest that, because of the predominance of right-handedness, right-handers are used to fighting with right- handers. As long as left-handers are comparatively rare, they have the advantage of hitting from unexpected directions. This might confer an evolutionary advantage that balances the disadvantages of left-handedness noted earlier. According to the article, this squares with a legend about the design of medieval castle stairs, which were said to wind clockwise as a defense mechanism. Attackers mounting the stairs were forced to fight with their right arms tight to the wall.
Previous studies on the disadvantage of being left-handed have been full of methodological problems. How does this study seem to you?
Parade Magazine, 30 March 1997, p. 15
Marilyn vos Savant
Marilyn appears to want more of the good press she got with the Monty Hall problem. She gives several of the responses to her solution to the "two children" problem similar to those she got for her solution to the Monty Hall problem. Here is one of the these letters:
I am stunned at your abandonment of good sense in your response to a reader who wrote: "A woman and a man (unrelated) each have two children. At least one of the woman's children is a boy, and the man's older child is a boy. Do the chances that the man has two boys equal the chances that the women has two boys?
You wrote that it's more likely the man has two boys. I can only conclude that you felt your readers were getting frustrated by your superior abilities, so you decided to raise our collective self-esteem by exhibiting the logical skills of a second-grader who has had too many turns on the teeter-totter.
Yorktown Heights, NY.
After providing us with a couple other such letters, Marilyn goes through the usual calculation to show that her original answers: 1/3 for the women and 1/2 for the man are correct.
We confess that we would have agreed with Marilyn, but, previous remarks of our colleague Peter Doyle and the convincing discussion of this problem in the next article, have, at last, convinced us that the problem
Given that a family has two children and one is a boy, what is the probability the other child is a boy?
is just not a well-posed problem.
The next article, suggested by Ruma Falk, relates to Marilyn's problem.
Ambiguities and unstated assumptions in probabilistic reasoning.
Psychological Bulletin, 1996, Vol. 120, No. 3, 410-433
Raymond S. Nickerson
Nickerson revisits all the famous conditional probability problems that have led people to conclude that conditional probability is just too hard to teach. These include variations on the problem just discussed in the Marilyn vos Savant column, the Monty-Hall problem, the three prisoner problem, the three drawer problem etc.
The author feels that arguments about solutions to these problems arise because reasonable people can interpret them in different ways and get different answers. Thus, they are not difficult, rather just not well posed.
He builds on the work of Bar-Hillel and Falk in their article "Some teasers concerning conditional probabilities", Cognition, 1982, 11, 109-122.
He makes good use of the famous Mr. Smith problem from the Bar- Hillel-Falk paper:
Mr. Smith is the father of two children. We meet him walking along the street with a young boy whom he proudly introduces as his son. What is the probability that Mr. Smith's other child is also a boy?
A reasonable person might get the answer 1/2 to this problem assuming that Mr. Smith is equally likely to choose a daughter to go for a walk with if he has a boy and a girl. Another person might not be willing to make this assumption and would get an answer that depends on the probability Mr. Smith would pick his son for the walk if he has to choose between his son and daughter.
If Mr. Smith happened to say: "Let me introduce my son Sebastian," then another reasonable person would say that the answer also depends on the probability that a family names a son Sebastian. Come to think of it, we might demand to know if the probability that Mr. Smith would "proudly" introduce his daughter is the same as the probability that he would "proudly" introduce his son."
Once you have settled on a well-posed problem, a simple tree diagram easily solves the problem. It is also increasingly popular to use simple contingency table arguments for these kinds of problems, emphasizing the frequency interpretation.
(1) Do you agree that the Marilyn vos Savant problem, as it relates to the woman, is not well posed? Is the problem, as it relates to the man well posed?
(2) You are asked the problem:
A coin is tossed twice and at least one head turns up. What is the probability that two heads turned up?
Give three different ways that the information that a head turns up might have been obtained. What is the answer in each case?
(3) How do you decide if a problem is well posed?
US counts future inmates: 1 in 20 born today to face prison, study says.
The Boston Globe, 7 March 1997, A3
According to Justice Department figures, nearly 1.1 million men and women were imprisoned in a state or federal facility at the end of 1995. If incarceration and death rates remain constant, then about 5 percent of US residents born today will spend time in a state or federal prison at some point during their lives. This projection is based on what is likely to happen to a hypothetical population of newborns over their lifetimes.
Broken down by sex, the figures indicate that 9 percent of the prisoners will be male and 1.1 percent female. For minority males, the chances of spending time in prison are much greater. At current levels of incarceration, a black male in the United States today has a greater than 25 percent chance of going to prison during his lifetime. For Hispanic males the chance is 16 percent, whereas for white males it is 4.4 percent.
(1) Should Dartmouth students think that 5% of their classmates are bound for prison? In what ways is the 1 in 20 figure from the headline a useful summary?
(2) What distortions might result from considering the chance of
spending time in prison "at some point in one's life"?
16 March 1997, p25
Marilyn vos Savant
A reader sent the following inquiry:
"On Thursday, June 6, 1996, I sat down to play bridge with some other ladies. The first hand was cut, and then I dealt. We each picked up our hands and discovered to our great surprise that I had 13 clubs, one opponent had 13 hearts, my partner had 13 diamonds, and the other opponents had 13 spades. We're all in our 60s and 70s, and we never heard of even one person receiving 13 cards of one suit, much less all four. We wondered if it was a joke, but the lady who brought the deck swore it was not. Do you have any idea what the odds are of such an occurrence?"
Marilyn answers that four perfect hands are likely to occur once in 2,235,197,406,895,366,368,301,559,999 deals (about 1 in 2235 septillion). She notes that, if indeed it was not a trick, then poor shuffling might be to blame. But she cites a result from N.T. Gridgeman in the "American Statistician" saying that even if 100 million people played 10 hands of bridge every day and shuffled the cards poorly, a perfect deal would still occur only once every three centuries.
(1) Can you reproduce Marilyn's 1 in 2235 septillion figure?
(2) How do you suppose Gridgeman modeled "poor shuffling"?
(3) One of the great old professors at Dartmouth used to get
about one call a year late at night saying: "I'm playing bridge
and I just got a hand of all hearts. What is the chance of that
happening?" He always replied: the same as any other hand and
hung up. Was this a good answer? Should there be such an event
about once a year in a town of about 10,000?
Census plans to insure full count of minority members and poor.
The New York Times, 12 March 1997, A15
The Census Bureau plans to make changes in the next census that are intended to address concerns that minorities and the poor have been undercounted in the past.
Census 2000 involves an important change in the type of scientific sampling the bureau will use to account for people who cannot be surveyed directly. Originally, the bureau planned to count at least 90% of the households in each county and then use statistical sampling to estimate the number of people missed. For Census 2000, however, the bureau would use sampling to estimate only after trying to count 90% of the households in a census "tract" -- an area of several square blocks that is far smaller than a county.
The move to tract-by-tract sampling has been endorsed by minority groups, such as the Congressional Black Caucus, who argued that relying on countywide sampling could lead to over representation of white, suburban communities. If census-takers could reach 90% of the households in a county without doing much counting in the inner city, they might neglect the rest of the count.
To insure better counts, the Census Bureau announced that it would assign workers to visit a list of households that did not respond to mailings, instead of letting them choose the ones they visit, to bring their totals to 90%. Home visits will be more extensive in those tracts where the initial response, by mail, falls below 90%.
Censuses affect Federal aid to states and cities. The 1990 Census severely undercounted members of minority groups, especially in large cities such as New York, and prompted a coalition of cities to sue.
The Census Bureau relies on Congress to give it sufficient funding
to carry out its job. Do you think this permits Congress to exert
too much influence on its technical decisions on how to best carry
out the census?
A Study alters criteria in rating universities, and Stony Brook soars.
The New York Times, B12, 19 March 1997
A new study, "The Rise of American Research Universities: Elites and Challengers in the Postwar Era" (Johns Hopkins University Press), by Hugh Davis Graham, a Vanderbilt University professor, and Nancy Diamond, a graduate student in public policy at the University of Maryland at Baltimore County, proposes that ratings of universities based on reputation understate the quality of some universities while overstating others.
The study used conventional criteria like publications and research money but avoided criteria based on reputations. It also gave smaller colleges a handicap: the scoring was averages per professor, not totals, which give bigger campuses an advantage. The study also used the following five criteria divided by the total number of faculty members: Federal grants for research and development, the number of journal articles published by its faculty members, the number of articles published in a smaller number of prestigious journals in science and technology and in the social and behavioral sciences, and awards in the arts and humanities. The data covered 25 years -- 1965 to 1990.
The study found the State University of New York at Stony Brook to be the third-best public research university in the nation, behind the University of California at Berkeley and Santa Barbara and ahead of the University of Michigan. Among private institutions, Brandeis University tied for ninth place with Johns Hopkins while Stanford led the list.
(1) The influential National Research Council rankings uses similar data but also asks thousands of professors to vote on which programs are best. Do you agree that this is too much like awarding Oscars and can do more harm than good?
(2) Brandan Maher, who was co-chairman of the NRC 1995 rating,
challenged the adjustment for size commenting: "The question is
would you rather go to, a small hospital like Southern
Massachusetts or a large one like Massachusetts General? What do
you think of this argument?
Can Mozart Make Maths Add Up?
New Scientist, 17 March 1997, p. 17
Study finds piano lessons boost youth's reasoning.
Los Angeles Times, 28 Feb. 1997, A3
Thomas H. Maugh II
Musical Mathematics: Researchers think Lessons May Aid
Milwaukee Journal Sentinel, 4 April 1997, p. 1.
Readers of Chance News will remember the controlled study showing that college students did better on an I.Q. test when they listened to Mozart's Piano Sonata in D for 10 minutes right before taking the test. (See Chance News 2.17.) This experiment was carried out by Frances Rauscher and Gordon Shaw at the University of California, Irvine. The effect noticed in this study wore off within an hour of taking the test. These researchers now have carried out additional research on preschoolers in the hopes of discovering more lasting effects of music.
Their new study involved 78 3 and 4-year olds at three preschools. These children were randomly divided into four groups: the first received daily singing lessons and two 15-minute piano lessons a week, the second received only the singing lessons, the third received 15 minute daily computer training, and the final group received no training at all.
At the beginning of the study, the students were given four tests of mental ability, including one that measures spatial-temporal reasoning. In this test, students might be shown a picture of an animal broken into 5 pieces and asked to re-assemble it or shown a simple geometric figure and asked to match it with one of a group of similar figures.
At the beginning of the study, all the students scored at the national norm on the tests. At the end of six months, those receiving the piano lessons scored an average of 34% higher on the test for spatial-temporal ability, while children in the other groups showed no improvement on any of the tests. The results of this research are published in the February issue of the Journal of Neurological Research.
Rauscher discussed her work in an interview on NPR (Talk of the Nation Science Friday, April 4, 1997.) This is a very interesting interview and we recommend that you listen to it if interested in this topic.
Rauscher suggested that the piano keyboard helps children learn in three ways: ³With the piano keyboard, the children are able to see their hands on the keyboard and learn spatial relationships on a one-on-one fashion. And they¹re also able to hear those relationships as they play the note, and they can feel them if they get motor feedback. So what you¹re doing is: you¹re in a way teaching these spatial relations through three different modalities.²
However, Rauscher is quick to note that listening to music WHILE doing, say, a math problem may or may not help. The experiment had music played for the students BEFORE the tests, not during, so as to prevent distraction. Thus, the effect of listening to music while actually doing work is unknown.
Rauscher believes that these experiments could have a lasting effect on how children are taught in school and also could be a strong support for increasing music lessons in school. If music can help create brighter, more intelligent minds, the cutbacks in money for the arts in education would probably be decreased considerably.
Professor Rauscher has a new grant to continue her research in the head start program and in the schools themselves. One part of this new research is described in the Milwaukee Journal Sentinel article. Rauscher is at the University of Wisconsin Oshkosh and is working with teachers at Magee and Wales elementary schools to experiment with their kindergarten students.
Two 20-student Kindergarten classes get 20 minutes of piano lessons each week, while other classes (the control group) get none. The program has run for 2 months and preliminary results show that children with the piano lessons scored an average of 36% higher in activities requiring ³spatial reasoning skills" similar to those used by Rauscher and Shaw in their study.
Wales music teacher Mary Anne Zupan was the key player in bringing the 5-year experiment to the Kettle Moraine District. She read about Rauscher¹s research and sought permission to try out the program. Zupan says, ³There¹s tons of anecdotal evidence that kids in music do better. We love to see the science holding up all the intuition and instinct we¹ve had.² Each room has 10 keyboards in it for use. The study has found that one-on-one teaching is not necessary for improved scores. The children not only have the structured lessons, but also are allowed to practice or play whenever they have some free time.
You can see this class in action on the April 16 NBC "Today" show in a segment on "Music and Intelligence".
(1) What do you think it means to say that: at the beginning of the study, all the students scored at the national norm on the tests?
(2) The researchers originally recruited 111 children from three preschools: one an inner city school for children of single mothers and two that served middle class families. 23 children dropped out during the study and were not counted in the analysis. Could this have biased the results?
(3) The L.A.Times article states that the research was sponsored
by grants from, among others, the National Piano Foundation and
the National Assn. of Music Merchants. Could this bias the study?
Do guns prevent crime? Another look.
The Washington Post, C5, 23 March 1997
Two University of Chicago economists, John R. Lott, Jr. and David Mustard, claim that allowing citizens to carry concealed weapons would prevent thousands of rapes and murders annually while producing no significant increase in accidental deaths.
The two economists analyzed county-level crime data collected by the FBI in ten states that passed "carry" laws between 1977 and 1992. They compared the crime rates before and after the laws took effect, and then estimated what the impact would have been if every state in the country had similar statutes. Lott and Mustard estimate that the annual "benefit" from easing concealed weapons laws is $5.74 billion in savings from hospital expenses, lost earnings and other costs of violent crime. They also postulate that if the country had adopted right-to-carry concealed handgun provisions in 1992, at least 1,414 murders and over 4,177 rapes would have been avoided. They published their results in the January 1997 Journal of Legal Studies.
Skeptics of Lott and Mustard's work, however, abound. Daniel Nagin and Dan Black at Carnegie-Mellon looked at the same data and found discrepancies. While the annual murder rate did go down in 6 of the 10 states, it went up for the other four. Rape dropped in five states but increased in the other five. Black claims that, if the benefits arise from the concealed weapons laws, then the impact should not vary by such huge margins from state to state. They also pointed out that all of the benefits of concealed weapons disappear when Florida is taken out of the analysis.
(1) What would you conclude from the fact that when you take out the state with the biggest effect, you lose significance?
(2) What more would you like to know about the study to decide if
allowing concealed weapons prevents crimes?
A safe prediction: The next economic forecast will be wrong.
US News & World Report, 3 March 1997, p58.
James K. Glassman
Glassman ponders the question: Why would anyone ask an economist to predict anything? He cites a survey conducted a year ago by the Bloomberg Business News, in which 24 leading economists were asked to predict how much the GDP (gross domestic product) would grow in 1996. The highest estimate of the group was 3.1%, and the average was 2.0%. But the GDP actually grew 3.4%! It turns out that the economists also had trouble forecasting growth for the previous year, only that time 85% of them missed on the high side. Glassman goes on to say that the average guess for 1996--2%--was exactly the growth for the previous year. He suggests that economists fear standing out, so they just guess that things will pretty much stay the same.
In related examples of botched forecasts, Glassman notes that the Congressional Budget Office had predicted the 1996 federal deficit would be $170 billion; the actual figure was $107 billion. Despite faith in human stock-picking expertise, for 11 of the past 12 years, the Vanguard Index 500 (a fund investing in the S&P 500 Stock Index) has outperformed a majority of managed funds. Glassman says his favorite example is a 1943 prediction of US population for the rest of the century, prepared for President Roosevelt by a panel of social scientists. The 1943 population stood at 132 million, and the panel forecast the maximum population for 1990 as 168 million. The actual number was 249 million. It turns out they got life expectancy about right, but missed the baby boom completely.
Noting that most of the world now seems to realize that it is impossible for any government to gather enough accurate data to plan economic activity, Glassman wonders why we still can't resist asking the experts what will happen next.
Psychologists Kahneman and Tversky used the phrase "anchoring
and adjustment" to describe people's tendency to make estimates by
using a readily accessible number and then adjusting from there.
(One famous example involved a simulated quiz show, where
contestants' guesses about the percentage of African countries in
the United Nations was found to be influenced by the spin of a
wheel setting the prize for a correct answer.) How does this
relate to Glassman's hypothesis about economists simply not
wanting to stand out?
TWO CORRECTIONS TO CHANCE NEWS 6.03, 6.04
In Chance News 6.03 we misquoted remarks sent to us by Elliott Weinstein about the SAT math question that was graded wrong. Recall that the problem was:
Directions: The following question relates to two quantities: one in Box A and one in Box B. You are to compare the two quantities and on the answer sheet fill in oval
A if the quantity in Box A is greater, B if the quantity in Box B is greater, C if the two quantities are equal, D if the relationship cannot be determined from the information given. Consider the sequence: 1, a, a^2, a^3,...,a^n The median of the Box A sequence if n is Box B a^(n/2) a positive even integer
What Elliott actually wrote was:
First, it's interesting that Box A specifies that n is positive, even though from the description of the problem this is totally unnecessary. (Unnecessary information often puzzles a test-taker.)
Second and more important, it is not really possible to compare the two boxes when n is odd, which still is a possibility for Box B; for then Box B (a^(n/2)) is well- defined, but Box A (the median of the sequence if n is a positive even integer) is not defined at all. Again, puzzling information complicating the task for a test-taker. I'm surprised this wasn't pointed out.
Editor: One way or the other, I guess we all agree it was a
pretty stupid question.
Paul Alpert sent the following note about the article on prostate cancer describing the difficulty in getting volunteers for a controlled study. Some of his remarks apply generally to reading accounts in the news.
March 5, 1997
There is at least one error of fact in item #7 of Chance News 6.04 (2/21 to 3/4/97). Dr. Joseph Oesterling is not at the University of Minnesota but is at the University of Michigan; this error appeared in all the press releases. Furthermore, Dr. Patrick Walsh, a urologic surgeon, is always cited on any article dealing with prostate cancer despite his extremely biased views regarding the efficacy of surgery over watchful waiting or radiation treatments. Except for urologists trained under him, it would seem that his statistics for cure (and avoiding incontinence and impotence) are considered laughably out of line with what other surgeons are able to obtain. Dr. William Catalona, again as everyone familiar with the disease knows, has too much personal capital invested in surgery and the PSA blood test and steadfastly refuses to believe that there is any other conceivable treatment. Several of those on our listserve have made efforts to inform these two men that the numbers they cite are seriously out of wack but to no avail.
On February 13, 1997 I sent you a message regarding the basic flaw in the study, namely its irrelevance:
This study was a milestone in prostate cancer treatment because there had never been a properly randomized experiment. Right after it was funded, a new (version of an old) treatment emerged which according to many is just as good as surgery and almost totally without its side effects of impotence and incontinence.
The study, therefore, without considering internal implantation of radioactive seeds (brachytherapy) promises to be totally irrelevant. What does this suggest about experimental design in an environment in which new treatments are created more rapidly than old treatments can be evaluated?
I am rehashing this because one of the principles of statistics is that context is very important. With respect to prostate cancer, more and more of the lay public, victims and otherwise, are learning that newspaper articles, journal articles and medical doctors are often misleading, often by accident and ignorance but sometimes because of a vested interest. Without this knowledge, any discussion is likely to be beside the point.
P.S. For what it's worth, I just wrote a book review of eight books on prostate cancer; the review will appear shortly in the "Journal of Scientific Exploration." I have an e-mail version in case someone is interested. As an interesting aside, Dartmouth is the place which contains the leading advocates for watchful waiting.
Editor's comment: This review contains a wealth of inform- ation about the current status of alternatives treatments for prostate cancer.
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