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CHANCE News 3.16
(5 Nov to 10 Dec 1994)
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Prepared by J. Laurie Snell, with help from Jeanne
Albert, William Peterson and Fuxing Hou, 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 Data Base
http://www.geom.umn.edu/docs/snell/chance/welcome.html
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We've concluded that this is something the
casual user might see once every 27,000 years.
Intel spokesman John Thompson
commenting on the Pentium chip
division error.
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FROM THE INTERNET
David Griffeath's "Primordial Soup Kitchen."
Interacting particle systems is a branch of probability that
uses computer simulation both for understanding the
evolution of the processes and suggesting conjectures for
analytic results. These simulations result in color graphics
that are often also works of art.
David Griffeath has a web home page that provides examples
of his work and links to others working in this field.
David includes each week a "soup" and "recipe" from his
explorations. The soup is a color graphics snapshot of a
particle system and the recipe is a description of the
system that produced the "soup". Here is a recipe to give
you a taste of one of his soups.
The Cyclic Particle System.
A prescribed number of colors N are arranged cyclically in a
"color wheel." Each color can only be replaced (eaten) by
its successor (mod N). Cell x chooses a site y at random
from its four nearest neighbors in the two-dimensional array
(with wrap-around at the boundaries). If the color at y can
eat the color at x it does; i.e., site x is painted with the
color from y next time. From a completely random initial
configuration, this probabilistic interaction nucleates wave
activity that self-organizes into a very stable steady state
of spirals.
Check out these soups and also Rick Durrett's movie
for a model for the spread of measles. These and many
more interesting things can be reached from David's
homepage: http://math.wisc.edu/~griffeat/kitchen.html
<<<========<<
>>>>>==========>>
The Journal of Statistical Education is on the Web!
The address is:
http://www2.ncsu.edu/ncsu/pams/stat/info/jse/homepage.html
Volume 2 No.2 just came out. Read it on the web!
<<<========<<
>>>>>==========>>
FROM OUR READERS.
Joan Garfield contributed the following article.
Untrue Facts.
Minneapolis Star Tribune, 28 November 1994, p 1E
Sandra Y. Lee
The subtitle of this article, which was originally published
in McCall's Magazine, is "Intimidated by numbers and willing
to believe the worst, people too readily accept distorted or
even false statistics." Citing statistics such as "one in
four college-age women has been the victim of rape or
attempted rape", and "left-handed people die an average of
nine years earlier than right-handed people," this article
demonstrates that "many well-known statistics and studies
are distorted, misleading, or just plain false." Some of
the people quoted in the article are sociologist and survey
expert Judy Tanur, Cynthia Crossen, author of the recently
published "Tainted Truth: The Manipulation of Fact in
America"; and Christina Sommers, who discussed female-
victimization statistics in her book "Who Stole Feminism?"
In addition to statistics on rape and lefthandness, this
article attempts to address "facts" about domestic violence
increases on Super Bowl Sunday, drug abuse, alcohol abuse
and pregnancy as the biggest problems in public schools,
whether there is a link between drinking milk and diabetes,
whether baldness and birthdays cause heart attacks, and if
our parents had easier lives than we have.
A guide called "How to decipher the 'facts'" is offered,
that helps readers of research presented in the media focus
on the answers to six questions in determining what to
believe: Who was surveyed or studied? How many people were
surveyed and how many responded? How were the questions
worded? How was the problem defined? Who paid for the study?
Was the study published in a peer-review journal such as the
"New England Journal of Medicine?"
Discussion questions:
1. Which of the seven topics discussed have the most
reliable facts? Do you agree with the conclusions of the
author or experts cited regarding each topic?
2. What other questions do you think are important to ask in
determining whether or not to believe the results of a
research study.
<<<========<<
>>>>>==========>>
In the last Chance News we reviewed the book "The Social
Organization of Sexuality" based on a recent large sex
survey. In a discussion question, we asked for possible
explanations for the observation that the median number of
sex partners since age 18 was 6 for men and 2 for women.
Paul Campbell sent two references relating to this issue.
M.Morris, "Telling tales explains the discrepancy in sexual
partner reports", Nature 365:437-440.
Einon, D. (1994) Are Men More Promiscuous than Women?
Ethnology and Sociobiology 15:131-143.
<<<========<<
>>>>>==========>>
Mike Proctor sent a discussion on the ALLSTAT list about the
accuracy of the published odds on advertisements for the new
UK national lottery. In this lottery, six numbers are
chosen without replacement from a set of 49 numbers. You
win the jackpot if your choice of six numbers agrees with
the six chosen. You win some prize if you have at least
three of the six numbers chosen in your set. The discussion
centered around the following questions:
Discussion questions:
Assume that those who buy tickets choose their numbers at
random.
(1) If the advertisers say that they expect that 250,000
prizes will be given out, how many tickets do they expect
to sell?
(2) If you buy a single ticket, what is the probability
that you win the jackpot?
(3) Assume that 14 million tickets are sold. Estimate the
probability that the jackpot goes unclaimed. How likely is
it to be won by a single person? by exactly k people?
ARTICLES ABSTRACTED
>>>>>==========>> Ask Marilyn. Parade Magazine, 20 Nov 1994 Marilyn vos Savant
When I play in card games I like to shuffle the cards several times, but I'm often told that if I shuffle them too much they'll be returned to their original order. What are the odds of this happening with five to 10 shuffles? Teri Hitt, Irving, Tex. In her answer Marilyn considers both the case where Hitt means a perfect shuffle and an imperfect shuffle. For a perfect shuffle she correctly states the following relevant result: Some magicians are so deft with their hands that they can shuffle the cards "perfectly," meaning a shuffle in which the deck is exactly halved, and every single card is interwoven back and forth. If you do this eight times, the cards will be returned to their original position. About imperfect shuffles she says: A study shows that with ordinary imperfect shuffles, you need at least seven to make sure that the cards are randomly mixed. Six aren't quite enough, but eight aren't a significant improvement--although the mixing does improve with each shuffle. If we interpret Hitt's question in terms of imperfect shuffles then it is natural to consider the model of a binomial cut followed by a riffle shuffle introduced and analyzed by Gilbert, Shannon, Reeds, Bayer, and Diaconis. Discussions of their work by Charles Grinstead and Brad Mann can be found in teaching aids on the chance data base. This analysis provides a simple combinatorial expression for the probability that the deck will be back to the original order after k shuffles. Applying this result to 5 shuffles gives a probability of 3.21097 x 10^(-56) so this is probably not what Hitt had in mind. Marilyn assumes that if she meant imperfect shuffles she was more interested in being sure that they are well mixed and suggests that seven shuffles suffices. That "seven shuffles do not suffice" is shown by the following example: New Age Solitaire This fascinating game was introduced by Peter Doyle as a way of bringing home the fact that 7 ordinary riffle shuffles, followed by a cut, of a 52-card deck are not enough to make every permutation equally likely. Here is how John Finn describes the game. We start with a brand new deck of cards, which in America are ordered so that if we put the deck face-down on the table, we have Ace through King of Hearts, Ace through King of Clubs, King through Ace of Diamonds, King through Ace of Spades. Hearts and Clubs are the Yin suits, and Diamonds and Spades the Yang suits. We shuffle the deck of cards 7 times, then cut it, and then start removing and revealing each card from the top of the deck, making a new pile of them face-up (so if this were all we did, we'd just have the deck unchanged after going through it once, except that the deck would be lying face-up on the table). We start the pile for each suit when we discover its ace, and add cards of the same suit to each of these 4 piles, according to the rule that we must add the cards of each suit in order. Thus a single pass through the deck is not going to accomplish much in the way of completing the 4 piles, so having made this pass, we turn the remaining deck back over, and make another pass. We continue this until we complete either the two yin piles (hearts & clubs), or the two yang piles (diamonds & spades). If the yin piles get completed first, we call the game a win; it's a loss if the yang piles get completed first. If the deck has been thoroughly permuted (by having put the cards through a clothes dryer, say), then the yins and yangs will be equally likely to be first to get completed. Thus our expected proportion of wins will be 1/2. But it turns out that after 7 shuffles and a cut, we are significantly more likely to complete the yins before the yangs, so our proportion of wins will be greater than 1/2. John Finn and Jeanne Albert using True BASIC and Charles Grinstead using Mathematica have written programs to simulate New Age Solitaire. They can be found in teaching aids on the chance database. Running these programs shows that a casino could make about a 50% profit by offering this apparently fair game and shuffling seven times followed by a cut. This raises the question of how many shuffles are necessary to prevent the casino from making more than they now make on a game such as craps (about 1.41 percent) by taking advantage of the cards being imperfectly shuffled. We will try to answer this next time. <<<========<<
>>>>>==========>> Study: needle program reducing HIV infection rate. The Boston Globe, 27 October 1994, p9. Associated Press
The New York Times reported results of a two-year study on needle exchange, conducted by the Beth Israel Medical Center's Chemical Dependency Institute. Among the 2500 participants in the exchange program the infection rate was 2% a year, compared with a 4-7% rate for high-frequency intravenous drug users in general. DISCUSSION QUESTION: 1. Very little is said in the article about how participants were chosen. Can you think of any confounding variables, and ways that they might be controlled for? 2. The article notes that some critics have questioned whether needle exchange programs that work in smaller cities would work in New York City. What issues do you think these critics are worried about? <<<========<<
>>>>>==========>> Ask Marilyn. Parade Magazine, 27 November, 1994, p.13. Marilyn vos Savant
"Suppose a person was having two surgeries performed at the same time. If the chances of success for surgery A are 85%, and the chances of success for surgery B are 90%, what are the chances that both would fail?" Marylin gives correct answers assuming independence: 1.5% that both will fail, 8.5% that A will succeed and B will fail, 13.5% that B will succeed and A will fail. DISCUSSION QUESTIONS: (1) Explain why it is ridiculous to assume independence in this case. (2) Try to do your own analysis by making a plausible guess as to the dependence between these two events. (3) Do you think that Savant is trying to land a job with the FBI? <<<========<<
>>>>>==========>> Channeling and faith healing--Scam or miracle? Parade Magazine, 4 December 1994, p.14. Carl Sagan
A discussion of scientific arguments against alleged evidence for supernatural healing and other phenomenon, which concludes that most faith healing is delusion or scam. The following interesting calculation in included. Sagan notes that roughly 100 million people have visited Lourdes, France in the last 136 years, many in hopes of being cured of diseases that are untreatable with modern medicine. He states that the spontaneous remission rate for all cancers taken together is estimated to be one in 10,000 to one in 100,000. Supposing that no more than 1% of the visitors to Lourdes are there to treat their cancers, one would expect to have seen between 10 and 100 "miraculous" cures of cancer alone. Yet, Sagan notes, there have been only 64 miraculous cures of any kind authenticated by the Roman Catholic Church at Lourdes. DISCUSSION QUESTION: What do you think of the statistical analysis above? Is 1% a reasonable figure for the percentage of visitors to Lourdes seeking cancer cures? Seeking medical cures of any kind? <<<========<<
>>>>>==========>> There have been several recent articles in the British press about Britain's new National Lottery. Here is a sampling. Hackers join hunt for key to a fortune. The Sunday Telegraph, 13 November 1994, Pg. 7 Robert Matthews
This article describes how some lottery players hope to "beat the odds" by using computers to choose their six numbers. As the article points out, "Mathematicians agree that if the balls really are chosen at random, no scientific tricks can beat the system: by definition, randomness cannot be predicted." However, if there are irregularities in the balls or in the drum from which they are chosen, players hope to exploit such defects which could bias the pick toward certain combinations. The article describes software called "L25 JustLotto", marketed by Gemini Consultants, that uses Markov chain analysis in an attempt to predict future jackpot numbers from previous ones. While a correlation may exist between certain numbers, Dr. David Balding of Queen Mary Westfield College London comments "the problem is that you could never benefit from it, because the amount you'd pay out before you won would exceed your winnings." The article also mentions the potential for using neural-network based learning algorithms to spot patterns in past lottery jackpots. Such methods are being used to "beat the stock market, and are rumored to produce substantial returns." DISCUSSION QUESTIONS: 1. What do you think Dr. Balding means by his remark? 2. Do you agree that "by definition, randomness cannot be predicted."? 3. According to Professor David Bounds, recognizing patterns in past jackpot numbers won't help much since "any deviation from randomness is likely to be so small that it's going to take forever for it to show up in the data." What is the significance of this comment? <<<========<<
>>>>>==========>> Birthdays blight hope of big lottery jackpots. No millionaires as more than a million share the first payout The Daily Telegraph, 21 November 1994, Pg. 5 Tim Butcher
The first National Lottery drawing produced 1,152,611 winners--those who matched at least three of the six jackpot numbers ranging from 1 to 49--which was more than five times the 200,000 winners expected by the lottery's organizers. This article discusses the impact of choosing low numbers, especially birthdays and anniversaries, many of which would be 31 or less, and, in particular, single digits. The first draw in fact produced the numbers 3,5,14,22,30, and 44. The article also mentions the enormous popularity of the first lottery--more than 24 million people bought 49 million pounds worth of tickets. DISCUSSION QUESTION: 1. How likely is it that five (or more) of the six numbers drawn are 31 or less? or that two (or more) of the six are single digits? <<<========<<
>>>>>==========>> Slim pickings in National Lottery. The Times, 24 November 1994, letter to the editor George Coggan
and the reply
No need to fear a lottery shortfall. The Times, 29 November 1994, letter to the editor The Director General of the National Lottery
Mr. Coggan is concerned about the possibility that, because people tend to pick low numbers, (see above article), there may not be enough money taken in from the sale of tickets to cover all the prize money. He points out that while the first lottery generated two single digit numbers, "sooner or later" a jackpot combination with three such numbers will come up. He estimates that, "if the number 7 had come up instead of say 44", there would have been a shortage of around 5 million pounds. In the reply, the Director General attempts to calm Mr. Coggan's fears by pointing out that, although in the first lottery there were many more 10-pound winners (those who matched three of the six numbers) than predicted, "it is just as likely that future draws will produce fewer than expected winners." The Director also cites "best advice" and observations of other lotteries in claiming that the chance is "extremely remote" that insufficient prize funds will be available in some future lottery. Finally, in a remark which almost makes the previous arguments unnecessary, the letter reads: "Your readers will be reassured to know, however, that I have not relied totally upon statistics or evidence from other lotteries. Camelot's [the lottery organizer's] license to operate the National Lottery also requires them to provide substantial additional funds by way of deposit in trust and by guarantee to protect the interests of the prize winners in unexpected circumstances." DISCUSSION QUESTIONS: 1. In the reply it is noted that since people generally don't pick their numbers randomly, "the number of the lower prizes can vary by up to 30 percent from the theoretical expectation." What does this statement mean? 2. Do you agree with the remark that future lotteries are just as likely to have a fewer-than-expected number of winners? If so, why is it significant? 3. How might you determine the chance which the Director General calls "extremely remote"? What information would you need? <<<========<<
>>>>>==========>> Forensic DNA typing dispute. Nature, 1 Dec 1994, p 398 Correspondence from R.C. Lewotin and Daniel L. Hartl
These are separate letters from the two well known biologists who started the current battle over the use of DNA fingerprinting in the courts by their articles in Science Magazine (Vol. 254 1745-1750, 1991 and Vol 260 473- 474, 1993. They are responding to the article by Lander and Budowie in Nature (Vol. 371, 735-738 1995) declaring the end of the controversy over the forensic application of DNA technology. They obviously do not feel that the war is over. Lewontin discusses three problems he feels are still to be dealt with: The first is laboratory reliability of DNA technology. He feels that this problem will not be resolved until the FBI and other laboratories agree to independent third-party quality control of their work. The second problem is calculating probabilities when there is population heterogeneity and this is the subject of Hartl's letter. The third is the jury's ability to understand simple probability arguments. He does not feel that this can be resolved by a one-time instruction by a judge. (I guess we can all agree on that!) In his letter, Hartl points out that the 'interim' ceiling principle based on racial databases is a stop-gap measured intended to be replaced by a more refined method based on databases from diverse ethnic groups. He is not convinced that this will be carried out and fears that the ceiling principle itself will be dropped. He points out that differences in allele frequencies in ethnic groups have been shown to be statistically significant. He asserts that Budowie's argument to ignore substructure is based on the claim that these differences are not "forensically significant,". He wonders what that means and who decides if the differences are forensically significant. (1) In his letter Lowenten remarks that "it is common for people to believe that a 1 in 4 chance means that the event is bound to happen on the fourth trial." Do you think it is really that bad or did he mean to say that it is bound to happen in four trials? (2) In his letter Hartl remarks: "Statistical significance is an objective, unambiguous, universally accepted standard of scientific proof. When differences in allele frequencies among ethnic groups are statistically significant, it means that they are real." Do you agree? (3) Do you think the war is over? <<<========<<
>>>>>==========>> The poor quality of random numbers. Nature, 1 Dec 1994, p 403 John Maddox
Lerrenberg, Landau, and Wong (Phys. Rev. Lett. 69, 3382- 3384; 1992) reported that they had gotten some erroneous results from simulations related to the Ising model and suspected problems with the random number generator. Now Vattulainen, AlaNissila, and Kankaala (Phys. Rev. Lett. 73, 2513-2516; 1994) have shown that their errors can be traced to the random numbers used. They show that the random number generators of the type that were used fail to satisfy two simple tests. The first is called a "random walker" test. For an example of this test, carry out a two dimensional random walk at the origin and let it run for a thousand steps. Then record which quadrant it is in. Repeat this a large number of times and see if the proportions of times the walk ended up in each of the four quadrants are reasonably close to 1/4. For the second test produce 0's and 1's with probability 1/2 each and average successive groups of n. Then see if the proportion of times these averages are less than 1/2 is sufficiently near 1/2. That standard random number generators does not give reliable answers for questions about random walks was observed some time ago by David Griffeath and Bob Fisch when they were developing their award winning "Graphical Aids for Stochastic Processes" Discussion question: What kind of a statistical test would you use to see if the results of the two tests described are "sufficiently close" to the expected proportions? <<<========<<
>>>>>==========>> Study finds cholesterol-lowering drug may save lives. New York Times, 17 November, 1994, B11 Gina Kolata
As mentioned in previous issues of Chance News there has been a lot of controversy about the effect of using drugs to lower the cholesterol level of persons having a high cholesterol count. A number of previous studies appeared to show that drugs were effective in preventing heart disease but not in decreasing the overall death rate. To make matters more mysterious, the excess deaths in those who took the drugs seemed to be in non-disease related illnesses such as suicide and homicide or cancer. It is claimed that these problems have been settled by a large Scandinavian study involving 4,444 men and women age, 35 to 70, with heart disease and having moderate to high cholesterol levels. In this study, half were given the cholesterol-lowering drug, simvastatin. The others were given a placebo. The subjects were followed for a median of 5.4 years. Those given the drug had their cholesterol level decrease by an average of 30 points and had a death rate 30 percent lower than those in the control group. There were essentially no side effects from the drug and there was no difference in the deaths in the two groups from other causes including suicides or cancer. Experts predict that this study will result in a significant increase in the use of drugs for lowering cholesterol levels for those with known heart problems and high cholesterol. For those with high cholesterol and no heart problems the situation is more complicated. Only about 40% of those with high cholesterol levels die of heart disease, and there is no good way to predict who these are. The drug simvastatin is expensive, costing between $650 and $1,000 dollars a year. It is felt that further studies are needed to determine the value of the drug for those who do not have a heart condition. Discussion questions: (1) Should we be concerned that the study was sponsored by Merck, the company that makes simvastatin? (The article states that it was carried out independently in several countries) (2) The investigators said that for every 100 people who took simvastatin, nine would have been expected to die of heart disease, but only four did. Similarly, 21 would have been expected to have a non-fatal heart attack, but only seven did. How do you think they arrived at these conclusions? <<<========<<
>>>>>==========>> Disputing 4 studies, new research supports x-rays as cancer screen. The New York Times, 30 Nov 1994, B11 Jane E. Brody
There have been four major studies that seemed to show that annual chest X-rays were not effective in lowering cancer mortality rates for smokers and former smokers. These four studies, three in the United States and one in Czechoslovakia, involved about 38,000 middle-aged men who smoked. The studies were judged by the "mortality rate", which is the number of cancer deaths during the time period observed divided by the total number in the group followed. The studies did not show a significant difference in mortality rates between those screened and those not screened. This failure to show an overall mortality benefit led the American Cancer Society to recommend against X-ray screening for lung cancer. Now oncologist Dr. Gary Strauss has re-examined the data. Strauss used a different statistic called the "fatality rate" to evaluate the result. The fatality rate is the number of cancer deaths divided by the number of cancers detected in the group followed. Using this statistic, Strauss found a significantly higher fatality rate in the controls than in those screened. Discussion questions: (1) The article remarks that there are 46.3 million current smokers and 43.5 million former smokers in the United States. Do you think that the cost of screening should be taken into account in considering recommending annual X-ray screening for all in these two groups? (2) Survival time can appear to be longer when a cancer is detected earlier and this is called "lead time bias". Could this be a problem with judging the outcomes of a screening study by mortality rates? How about by fatality rates? <<<========<<
>>>>>==========>> Psychic powers: what are the odds? New Scientist, 26 November 1994, Pg. 34 John McCrone
This enjoyable article describes the recent psychokinesis research of Robert Jahn, whose work is "currently the most respected of PK studies because of its scale and sophistication...." Jahn, a professor of engineering at Princeton, runs the Princeton Engineering Anomalies Research (PEAR) laboratory but, as the article makes plain, within mainstream academic circles he is not exactly revered for this work. Several experiments are described, but by far his most extensive study has involved over 100 subjects who together have logged over 14 million trials of the following experiment: each subject attempts to psychically persuade an electronic random number generator to produce more heads or more tails in a series of 200 "coin flips". According to the article, the results are "tiny but highly significant. The size of the effect is about .1 percent, meaning that for every thousand electronic tosses, the random event generator is producing about one more head or tail than it should by chance alone." Naturally, the article contains a description of attempts by skeptics, including members of the Committee for the Scientific Investigations of Claims of the Paranormal (CSICOP), to evaluate or even discredit Jahn's work. In particular, an experimental subject who is believed to be a member of the PEAR staff apparently participated in 15 percent of the 14 million trials but was responsible for half of the total "successes". Jahn's beliefs about possible explanations for his results have also come under fire. The article says that he does not think that there is a "mental interference with a physical event but something much more subtle--a distortion of the laws of statistics themselves....the subjects somehow distort the 'probability envelope' of an outcome." DISCUSSION QUESTIONS: 1. The subjects in Jahn's coin flipping experiment sit and watch "a cumulative line rising or falling on a computer screen" which charts their progress in producing more heads or more tails. As a precaution, the subjects are required to move the line up for half the time, and down for half the time. Why do you think this is necessary? What kind of behavior would you expect for the line if the subjects were causing no effect? 2. The article says that "there is only a 1 in 5000 chance that Jahn's results are a statistical fluke." How do you think they determined this figure? What does it mean? <<<========<<
>>>>>==========>> Is a bitter winter on the way? Or did the almanac cry wolf? The New York Times, 11 December 1994, Ideas & Trends William K. Stevens
In response to The Old Farmer's Almanac's prediction of a snowier than normal winter for most of the Northeast this year, this article asks the question, "Just how trustworthy are long-range forecasts?" The answer varies with the type of indicator forcasted (temperature, for example, which is the simplest to predict), and with the time period over which the prediction extends. "Two weeks ahead is generally taken as the limit" for "precision" forcasts, while the Weat her Service's 6-to-10 day temperature forcast accuracy rates range from 75 percent in winter, 65 percent in summer, and lower for spring and fall. According to the article, "since forecasters would be right 50 percent of the time just by chance, 'all the knowledge that's put into the forecast squeezes out another 10 or 15 percent in the winter and much less in the summer', said Fred Gadomski, a meteorologist at the Penn State Univ weather communications group." In particular, the article states that "to make accurate daily forcasts months or a year ahead, as several almanacs try to do, is impossible", according to many meteorologists. Instead the Weather Service tries to forcast the weather relative to what is "normal" for a given region. That is, they give probabilities that a particular part of the country will experience above-normal, normal, or below-normal precipitation or temperature for the upcoming month or season. Determining these probabilities is greatly facilitated this season by the return of El Nino, the marked warming of surface temperatures in the Pacific. Accompanying the article are two maps of the U.S. with bands indicating the probability that given regions will experience warmer-than-normal temperatures and precipitation for the winter months December, January, and February. So, what can the Northeast expect? The maps indicate a 55 percent chance for above normal temperatures in most of New England (except norhtern Maine, which shold see below normal temperatures), and a 50 percent chance for above normal percipitation. DISCUSSION QUESTION: 1. Considering the difficulties mentioned in making long-range predictions, how do you think the Weather Service determines what is "normal" weather for a given region? 2. Do you agree that "forecasters would be right 50 percent of the time just by chance?" <<<========<<
>>>>>==========>> Binge drinking linked to campus difficulties. The Boston Globe, 7 December 1994, Pg. 1 Richard A. Knox
A survey of nearly 18,000 students at 140 four-year colleges and universities in the U.S. has found that half the men and 39 percent of the women identify themselves as so-called "binge" drinkers--at least five drinks in a row during the last two weeks for men, four in row for women. Perhaps more significantly, the Harvard School of Public Health study found that this drinking appears to have an adverse effect on the non-binge-drinking students at these institutions. The study is the first of its kind to examine college and university alcohol consumption rates on a national scale. The article reports that almost nine out of ten students at the institutions that comprise the top 30 percent of alcohol consumption rates said they had been subjected to a variety of abuse which they attributed to their alcohol-drinking classmates. These abuses included unwanted sexual assaults, other physical assaults, property damage, and interruption of study or sleep. Interestingly, the study concluded that college policies to reduce drinking by under-age adults have had little effect, and Robert Sherwood, Dean for student development at Boston College, states that setting the legal drinking age at 21 and not 18 has created or at least exacerbated existing problems. DISCUSSION QUESTION: What questions would you want to ask the researchers about their survey design? How reliable do you think the study is? <<<========<<
>>>>>==========>> The Bell Curve - continued. Part II: Cognitive Classes and Social Behavior
We continue our attempt to describe what is in this lengthy book. This has become less necessary with the appearance of a review by someone who has read the book. This review is by Stephen Jay Gould and appeared in the November 28 issue of the New Yorker Magazine (Page 139). However, we shall not give up quite yet. Part II is almost entirely based upon the National Longitudinal Survey of Youth (NLSY). Recall that this study began in 1979 and follows a representative sample of about 12,000 youths aged 14 to 22. It provides information about parental socioeconomic status and subsequent work, education, and family history. It also had IQ information because, in 1980, the Department of defense gave the participants their battery of enlistment tests to see how this civilian sample compared with those in the voluntary army. In part II the authors seek to see how IQ is related to social behavior. They limit themselves to non-Latino whites to avoid the additional variation of race which they treat in Part III. Their method is to carry out a multiple correlation analysis with the independent variables being cognitive ability and the parents socioeconomic status (SES) (based on education, income, and occupational prestige) and a dependent variable which, in the first chapter, is poverty. The next seven chapters replace poverty successively with education, unemployment, illegitimacy, welfare dependency, parenting, crime, and civil behavior. IQ scores are standardized with mean 100 and standard deviation 15 and NLSY youths are divided into 6 groups corresponding to intervals determined by the 5th, 25th, 75th, and 95th percentiles. Those in these six groups are labeled very dull, dull, normal, bright, very bright. In the same way the NLSY youths are also divided into six groups by the 5th, 25th, 75th and 95th percentiles using the SES index and labeled very low, low, average, high, very high. The authors find that the percentages in poverty for each of the six socioeconomic groups, going from very low to very high are 24, 12, 7, 3, 3. The percentage in poverty for each of the six IQ classes, going from very dull to very bright, are 30, 16, 6, 3, 2 They observe the similarity of these percentages and turn to multiple regression to attempt to see which is more directly related to poverty. For this they carry out a logistic regression with the independent variables age, IQ, and SES, and dependent variable poverty. Giving IQ and SES, age has little effect so they concentrate on IQ versus SES. To do this they plot two curves on the same set of axes, an IQ curve and an SES curve. The IQ curve considers a person of average age and SES and plots the probability of poverty as IQ goes from low to high. The SES curve considers a person of average age and IQ and plots the probability of poverty as SES goes from low to high. The IQ curve shows about 26% probability of poverty for very low IQ decreasing to about 2% probability of poverty for very high IQ. The SES curve indicates about 11% probability of poverty for very low SES score and decreases to about 5% probability of poverty for very high SES score. Thus fixing SES and varying IQ has a significant effect on poverty but fixing IQ and varying SES does not have much effect on poverty. It is argued that this shows that IQ is more directly related to poverty than is socioeconomic status. This same procedure is carried out in the subsequent chapters to show that being smart is more important than being privileged in predicting if a person will get a college degree, be unemployed, be on welfare, have an illegitimate child etc. There are some exceptions to this but the general theme of part II is that it is IQ and not socioeconomic status that is important in predicting these social variables. Little in said about variation while discussing these examples but in the introduction to part II the authors remark that "cognitive ability will almost always explain less than 20 percent of the variation among people, usually less than 10 percent and often less than 5 percent." (They give all the regression details in an appendix). "Which means that you cannot predict what a given person will do from his IQ score. On the other hand, despite the low association at the individual level, large differences in social behavior separate groups of people when the groups differ intellectually on the average." Discussion questions. (1) What is the basis for the author's argument that, "even though cognitive ability explains only a small percentage of the variation among people, large differences in social behavior separate groups of people when the groups differ intellectually on the average"? (2) In the introduction to part two the authors state that "We will argue that intelligence itself, not just its correlation with socioeconomic status, is responsible for group differences. ". What statistical evidence would allow the authors to conclude this? !!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!! CHANCE News 3.16 (5 Nov to 10 Dec 1994) !!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!! Please send suggestions to: jlsnell@dartmouth.edu >>>==========>>|<<==========<<<
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