!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!! CHANCE News 3.15 (16 Oct to 4 Nov 1994) !!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!! 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 email@example.com Back issues of Chance News and other materials for teaching a CHANCE course are available from the Chance Web Data Base in the Multimedia Online Document Library at the Geometry Center (http://geom.umn.edu/) or from the Geometry Center Gopher (geom.umn.edu) in Geometry Center Resources. ======================================= A career is nothing to leave to chance. American Statistical Association =======================================
>>>>>==========>> How did the polls do?
On Nov 8 the Hotline gave the results of the latest polls for the senate races together with margins of errors. We added the final vote and some idea of the errors in the polls. STATE ACTUAL LAST MARGIN POLL VOTE POLL OF ERROR ERROR ARIZONA Sam Coppersmith, D 40 30 3.5 .9 Jon Kyl, R 54 42 CALIFORNIA Dianne Feinstein, D 47 52 3.5 8 Michael Hunington, R 45 36 CONNECTICUT Joseph Lieberman, D 67 61 3.5 3.4 Jerry Labriola, R 31 24 DELAWARE Charles Oberly, D 42 37 3.1 1.8 William Roth Jr., R 56 53 FLORIDA Hugh E. Rodham D 30 28 3.5 0 Connie Mack, R 70 64 HAWAII Danel K. Akaka, D 72 No data Maria M. Hustace. R 24 INDIANA James Jontz, D 31 26 3.5 2.7 Richard M. Lugar, R 67 64 MAINE Thomas Andrews, D 37 29 4.4 2.7 Olympia Snowe, R 60 53 MARYLAND Paul S.Sarbanes, D 59 56 3.5 1.9 William Brock. R 41 36 MASSACHUSETTS Edward M. Kennedy, D 58 53 5 -.4 Mitt Romney, R 41 38 MICHIGAN Bob Carr, D 43 36 4.5 -4 Spencer Abraham, R 52 37 MINNESOTA Ann Wynia, D 44 38 4.2 -.2 Rod Grams, R 49 42 MISSISSIPPI Ken Harper, D 31 28 4 -.8 Trent Lott, R 69 60 MISSOURI Alan Wheat, D 36 29 3.5 4.2 John Ashcroft, R 60 58 MONTANA Jack Mudd, D 38 37 3.5 -4 Conrad Burns, R 62 51 NEBRASKA Bob Kerrey, D 55 58 3.4 6.7 Jan Stoney, R 45 36 NEVADA Richard H. Bryan, D 51 55 3.5 8.6 Hal Furman, R 41 31 NEW JERSEY Frank R. Lautenberg, D 50 47 3.5 4.5 Chuck Haytaian, R 47 37 NEW MEXICO Jeff Bingaman, D 54 47 4 1.3 Colin R. McMillan, R 46 38 NEW YORK Daniel P. Moynihan, D 55 60 3.5 2.3 Bernadette Castro, R 42 27 NORTH DAKOTA Kent Conrad, D 58 60 4.5 10.2 Ben Clayburgh, R 42 28 OHIO Joel Hyatt, D 39 34 4.2 .4 Mike DeWine, R 53 47 OKLAHOMA Dave McCurr y, D 40 40 3.5 -3.4 James Inhie, R 55 48 PENNSYLVANIA Harris Woflord, D 47 44 5.2 1.6 Rick Santnrum, R 49 43 RHODE ISLAND Linda J. Kushner, D 36 27 5 4.2 John Chafee, R 64 58 TENNESSEE Jim Sasser, D 42 42 3.5 -5.9 Bill Frist, 56 44 Jim Cooper, D 39 40 3.5 -7 Fred Thompson, R 61 47 TEXAS Richard Fisher, D 38 29 3 4.7 Kay Bailey Hutchison, R 61 57 UTAH Patrick A. Shea, D 28 24 4.2 0 Orin G. Hatch, R 69 59 VERMONT Jan Backus, D 41 37 5 0 James Jeffords,R 50 45 VIRGINIA Charles S. Robb, D 46 39 3.5 4 Oliver L. North, R 43 31 Other 11 WASHINGTON Ron Sims, D 45 41 3.5 -3.2 Slade Gorton, R 55 44 WEST VIRGINIA Robert C. Byrd, D 69 70 5 12.4 Stan Klos. R 31 16 WISCONSIN Herb Kohl, D 58 61 4.5 7.6 Robert Welch, R 41 32 WYOMING Mike Sullivan, D 40 38 4.5 -3.8 Craia Thomas. R 59 48 Note that you would have been correct every time except for Pennsylvania if you had just predicted the winner to be the person with the highest percentage in the poll. I don't have the similar figures for the governors races but I certainly lost my bet that the outcome for Cuomo would be within the margin of error! It is hard to say how you should determine the actual error in the poll, since these percentages do not add up to 100% because of undecided voters and other candidates. To make them comparable we normalized the percentages to add up to 100% for both the poll results and the final results. Using these normalized percentages, we determined the poll error as the difference between the predicted and the actual vote for the candidate who led in the poll. I hope this is not a fair way to judge the pollsters since about 1/3 of them did not fall in the margin of error and some are way off. I asked in a discussion question last time, at what stage the New York Times pollsters carry out their adjustments? I am told that the outfit in Connecticut only provides the pollsters with a random telephone sample for the state's telephones. The adjustments, demographic and others, appear to be made after the poll is taken. I am still not certain how all this is done. If anyone knows where the procedure is written down in all gory detail, I would appreciate knowing about it. DISCUSSION QUESTIONS (1) Is it fair to expect polls taken a few days before the election to accurately predict the outcome of the election? (2) What would a pollster say about our attempts to see if the final results fell within the margin of error of the poll? (2) Do you think that polls have a serious affect on the way people vote? (3) How do you think pollsters explain their being so far wrong in the governor's race in New York? (4) The Times says that Giuiani received the poll results saying that Cuomo had taken the lead before they were announced and this led him to announce his support for Cuomo. Do you think this will cause him to change his opinions about polls? <<<========<<
>>>>>==========>> Ask Marilyn. Parade Magazine, 6 November 1994, p10.
A reader asks Marilyn whether he was being "taken" in a dice game, where he bet on his throw of a single die coming out higher than an opponent's. The reader gives a symmetry argument that led him to think the game was fair: "If he [opponent] throws a 1, there are five numbers higher (2,3,4,5,6); but if he throws a 6, there are five numbers lower (1,2,3,4,5). If he throws a 2, there are four numbers higher; but if he throws a 5 there are four numbers lower. And if he throws a 3, there are three numbers higher; but if he throws a 4 there are three numbers lower. It looks the same to me..." Marilyn correctly points out that the reader's chances of winning were only five out of twelve. The above argument overlooks ties, on which the opponent wins. <<<========<<
>>>>>==========>> For one-time antagonists, DNA fingerprinting debate settled. The Boston Globe, 27 October, 1994, p11. Richard A. Knox
"The public needs to understand that the DNA finger- printing controversy has been resolved. There is no scientific reason to doubt the accuracy of forensic DNA typing results." The article cites these remarks by Eric Lander and Bruce Budowle made in their article in the current issue of "Nature". The remarks are particularly noteworthy because Lander had been a critic of the lack of scientific standards for DNA fingerprinting in earlier use. And Budowle, chief scientist for the FBI, has been a staunch defender of its use. The latest standards, however, use deliberately conservative assumptions about the possibility of a "four-point match" (match at four genetic loci), which can still provide odds of more than six million to one against accidental misidentification. These are based on the "ceiling principle" recommended by the 1992 report of the National Research Council which may be described as follows. If a population is made up of sub-populations with different gene frequencies, then the independence assumption cannot be assumed. The NRC proposed that gene frequencies be determined for the various possible sub- populations. Then, to estimate the probability for agreement at several sites, choose, for each gene, the highest frequency among all subpopulations and multiply these "worse case" probabilities. This is called the ceiling principle. The authors suggest that the independence computation could also be given in the trial, but with the understanding that the truth might well be somewhere in between this and the estimate given by the ceiling principle. James E. Stars, professor of law and forensic sciences at George Washington University, still criticizes the standards, maintaining that "it's not scientists who are supposed to give the benefit of the doubt. It's the jury and the law that are supposed to give the benefit of the doubt." DISCUSSION QUESTIONS 1. What do you think Stars meant by his remark? 2. Another report on this article asserts that a spokesman for the FBI once said that it had done six proficiency tests without an error and so its error rate was zero. How high an error rate could they have, in fact, and still have a reasonable chance for six tests in a row to be without an error? 3. Do you think this article was timed to affect the Judge's decision in ruling on the admissibility of DNA evidence in the Simpson trial? If so, is that bad? <<<========<<
>>>>>==========>> Science's role in courtrooms reassessed. The Boston Globe, 20 October 1994, p1. Anthony Flint
This article cites a number of recent cases in which scientific evidence plays a role in court decisions: if there is a 1 in 40,000 chance that the recovered DNA is not O. J. Simpson's, does this constitute reasonable doubt? [see preceding article]; which of the conflicting studies on cancer risk and cellular phones is to be believed?; does Gulf War Syndrome exist? The article reviews the Frye admissibility standard for scientific evidence and the 1993 Daubert v. Merrill Dow Pharmaceuticals case, after which the Supreme Court ruled that judges needed to be more active gatekeepers rather than leaving juries to sort out scientific claims. The article concludes with the following interesting quote, relevant to the previous article. With regard to DNA evidence, Albert A. Scherr of the Franklin Pierce Law Center notes: "When juries make their decisions, it's always been more like the decision of whether to marry someone. Relying on a number makes it a lot easier, and more like buying a house. If you put a number on reasonable doubt,--if you make the decision so quantifiable--you'll totally change the legal system." DISCUSSION QUESTION Do you think a number can be put on reasonable doubt? If so what number would be reasonable? <<<========<<
>>>>>==========>> Abortion tie to breast cancer risk is suggested. The Boston Globe, 27 October 1994, p9. Associated Press
A study in the Journal of the National Cancer Institute reports that the annual risk of breast cancer for a 40- year-old women is 0.6 per 1000 among women who have had an abortion, as compared to 0.4 per 1000 for women who have not. Higher risk was associated with abortions performed when women are younger than 18 or older than 30. The risk was not found to be associated with number of abortions or number of live births or miscarriages. These findings were base on interviews with 845 breast cancer patients and 961 healthy women of the same age group. This is another example of a kind of study that epidemeologists call "case control studies". In the last Chance News, we asked how the relative risk is determined in such a study. I confess that I did not know the answer but it appears to be as follows: The "relative risk" of an abortion for breast cancer is: P(breast cancer|abortion)/P(breast cancer|no abortion) This can be written as the product of the two terms: P(abortion|breast cancer)/P(no abortion|breast cancer) and P(no abortion)/P(abortion). We can estimate P(abortion|breast cancer) by the proportion of the breast cancer cases who say they had an abortion. We estimate the P(abortion) by the proportion of the control cases who said they had an abortion. (This is reasonable if the incidence of breast cancer in the population is realtively small) From these we can estimate the two terms whose product estimates the relative risk. DISCUSSION QUESTION (1) The findings are preliminary, and a co-author of the report said it would be "premature" for women to make any abortion decision based on the study. Do you think the difference found in the study is large enough to be taken seriously? (2) Other reports on this study described the outcome of the trial by saying that the risk of breast cancer for women under 40-years old who had an abortion was 50% higher than for a women who had not had an abortion. Is that consistent with the information given in this report? Which method of reporting the results do you think is most informative? (3) A commentator on this study remarked that the small difference could be due to errors from the interview process. She suggested that a person who had had cancer would be more apt to admit having an abortion than one who did not. Why might this might be true? (4) In an observational study the relative risk is directly estimated from the outcome of the study. How might you think of this case control study as an observational study? <<<========<<
>>>>>==========>> Extracting the truth from statistics. The Boston Globe, 17 October 1994, p11. Gordon McKibben
This article describes a report by Arnold Barnett of MIT Sloan School of Management, called "How Numbers are Tricking You" which appeared in Oct issue of MIT Technology Review. Barnett says the ideal way for readers to be better served by numbers is to use the newspaper as a prod for future research--assuming the newspaper gives the source. Even when this is not possible, common sense is called for. [This almost sounds like a plug for a CHANCE course!] Barnett cites an example of ambiguity from an Associated Press story which appeared in the Globe last spring [and in Chance News], reporting that outbursts of anger can double your risk of heart attack. Since the conclusion was based only on interviews with recent heart attack victims, Barnett wonders about healthy people who get angry. Might not they benefit from letting off steam in a way that reduced their heart risk? The author gives the readers lots of good advice about how to handle articles that include statistical analysis, concluding with: "Don't be frightened by statistics, just apply common sense." DISCUSSION QUESTION The article gives a number of cases where people have challenged the Globe's use of statistics. One example is the following: An editorial plugging handgun controls, mentioned that deaths by firearms exceeded 38,000 a year. A reader suggested it would have been helpful to mention that the number is more than twice the one usually given because it includes 18,526 suicides. Do you agree? <<<========<<
>>>>>==========>> Discovery that AIDS can be prevented in babies raises debate on mandatory testing. New York Times, 3 Nov 1994, B14 Gina Kolata
The current New England Journal of Medicine reports the result of the study that was stopped early, showing that, when a pregnant women who has the HIV virus takes AZT, it helps prevent the virus being passed on to the child. The study involved 477 pregnant women infected with the HIV virus. Half were given the AIDS drug AZT and the other half a placebo. Only 8.3% of the children of women who took the drug were infected with the virus as compared to 25.5 percent of the children of women who had the placebo. Editorials in the NEJM recommend that HIV testing of pregnant women be encouraged but should be voluntary. Experts are quoted on both sides of the issue of mandatory testing of pregnant women. On the one hand it seems likely that this would save the lives of many of the children; but on the other hand, to be effective, this would require also mandatory treatment for the mother which to some, is a significant violation of civil rights. DISCUSSION QUESTION (1) In New York State, a group has been set up to make recommendations to the Governor relating to this issue. What would your recommendation be? (2) Studies of the effectiveness of AZT in extending the life of those who have the HIV virus have not been very encouraging. Should this make a difference in considering mandatory treatment of the mother in an attempt to save the child? <<<========<<
>>>>>==========>> Heart ills and high cholesterol may not be linked in old age. The New York Times, 2 November 1994, C12 Gina Kolata
A study being published in the "Journal of the American Medical Association" reports that high cholesterol for men and women over 70 seems not to affect the chance of a heart attack or dying of heart disease or, for that matter, of anything else. They followed 997 men and women from 1988 to the end of 1992. A third of the women and a sixth of the men had high cholesterol levels. This result is found to be a bit surprising, given other studies that show that high cholesterol is a risk factor for heart disease in middle-aged men and women. One explanation is high cholesterol does not affect the arteries for some and those for which it does have been, to some extent, selected out before reaching their 70's. DISCUSSION QUESTION Snell has higher than average cholesterol level but will be 70 in January. Should he go back to eating hot fudge sundaes after his birthday? <<<========<<
>>>>>==========>> High doses of a heart drug are found to be dangerous. The New York Times, 17 October 1994, A14 Lawrence K. Altman
Two studies, designed to test the effectiveness of the drug heperin routinely used to treat heart attacks, were stopped (in April) early when it was noticed that high doses of the drug were causing lethal bleeding in some of the patients. Doctors are just now being publicly alerted to this danger. Authors of the study explain that the delay was caused by concern about their work being peer-reviewed and also to allow for a careful presentation that would not discourage physicians from using the drug in moderate amounts. On the other hand, the delay was criticized because it was known that doctors were at times using doses larger than those that had been found to produce unacceptable results. DISCUSSION QUESTION Do you think the delay in publicizing this result was justified? <<<========<<
>>>>>==========>> A More Perfect Union. Washington Post, 30 Oct 1994, Book World p x1 Charles C. Mann
This is review of the following two books coming out of the sex survey we reported in the last chance news. SEX IN AMERICA A Definitive Survey By Robert T. Michael, John H. Gagnon, Edward O. Laumann and Gina Kolata Little, Brown. 300 pp. $ 22.95 THE SOCIAL ORGANIZATION OF SEXUALITY Sexual Practices in the United States By Edward O. Laumann, John H. Gagnon, Robert T. Michael and Stuart Michaels University of Chicago. 718 pp. $ 49.95 The first book is a carefully written account of the survey but with a minimum of technical statistics and obviously aimed at the best selling list. The second book is a more technical report of the survey but also written with the intent of being read by the non-expert. Indeed, it is, in many ways, a fine primer on survey sampling. The authors discuss in detail how they went about making the decision on the nature and the size of the sample they chose, how they decided between a telephone survey, interviews, written forms etc. They also discuss possible biases and how they planned to check for these. Like the "Bell Curve," they often take the time along the way to explain in quite simple terms the statistical techniques they use to determine sample sizes, look for correlations etc. This reviewer does a good job of highlighting some of the inevitable problems in a study of this kind. Because of the withdrawal of federal support the researchers had to decrease the size of the sample from the proposed 20,000 to about 9,004. They had to eliminate 1,141 because they belonged to empty buildings. Again for financial reasons they had to limit the study to English speaker adults between 18 and 59. This eliminated another 3,514. Of the remaining 4,369 households, the researchers interviewed people in 3,432 of them with a response rate of 78.6 percent. One more for financial reasons, they chose not to cover people in institutions such as college dormitories, military barracks or prisons which might cause problems with the use of their survey for AIDS policies, which was one of their main objectives. The reviewer comments on the obvious difficulties of telling if people are being truthful. The researchers asked for written responses for some of the people interviewed and checked them with the interview but he is not convinced that this is much of a check. The book itself gives a careful discussion of all these problems but does put a bit of a positive spin on them. The reviewer concludes that "The National Health and Social Survey represents a mountain of hard work, but its findings should be greeted with more skepticism than its authors would like." DISCUSSION QUESTIONS (1) In discussing possible biases in their survey in the the more technical book, the authors state that: "Only 6 percent of the interviews took place with the spouse or other type of sex partner present, and an additional 15 percent had other people present ... These 'others' were overwhelmingly likely to be children or stepchildren of the respondent... When interviewed alone, 17 percent of the residents reported having two or more sex partners in the past year, while only 5 percent said so when their partners were present during the interviews." After discussing how they looked into this potential problem, the authors remark: "On the basis of these bivariate analyses, we cannot conclude that the presence of others caused the reporting differences in the sense of suppressing the truth." What else could cause the difference? (2) The authors list seven possible explanations for the fact that the median number of sex partners since age 18 was 6 for men and 2 for women and comment on which they feel is most likely. See if you can come up with some of their explanations and which is most likely. <<<========<<
>>>>>==========>> The Bell Curve. Intelligence and Class Structure in American Life by Richard J. Herrnstein and Charles Murray Free Press, 845 pp. $30.00
I promised last time to try to say what is in this book but my review is getting as long as the book so I will give only Part I this time and continue next time.
INTRODUCTION Tests to measure intelligence (called cognitive ability here) play a central role in this book. Thus, in their introduction, the authors discuss the history and the controversies surrounding attempts to measure intelligence. Modern theory traces its beginnings to Spearman. Spearman noticed that performances on tests attempting to measure intelligence were positively correlated. To explain this, he postulated the existence of a single variable that he called g which is a persons general intelligence. It is a quantity like height or weight that a person has and that varies from person to person. When you take a test to measure intelligence your score is a weighted sum ag + bs + e of the factors g , s, and e with g your general intelligence, s a measure of your intelligence relating to this particular test and e a random error. If you take several different tests, g is common to all of them and causes the positive correlation. The magnitude of a tells you how heavily the test is "loaded" with general intelligence -- the more the better. This simple model is only consistent with a very special class of correlation matrices (those with rank 1) and so had to be generalized to include more than one kind of g. This led to the development of factor analysis as a mathematical model for what is going on. It also led to the development of IQ tests to measure intelligence. The controversies over the use of IQ began when it was proposed that they be used to justify sterilization laws in an attempt to eliminate mental retardation, and immigration laws to favor the Nordic stock. It continued when Arthur Jensen suggested that remedial education programs (begun in the War on Poverty) did not work because they were aimed at children with relatively low IQ, largely inherited and therefore difficult to change. Then followed debates over whether differences in IQ were due mostly to genetic difference or to differences in environment culminating in Stephen Jay Gould's best seller "The Mismeasure of Man". Gould concluded that "deterministic arguments for ranking people according to a single scale of intelligence, no matter how numerically sophisticated, have recorded little more than social prejudice." While the authors admit that Gould's ideas still reflect a strong public sentiment about IQ tests, they feel that it bears very little relation to the current state of knowledge among scholars in the field. Finally, the authors discuss current attempts to understand intelligence, describing three different schools. THE CLASSICIST: intelligence as a structure. This school continues to extend the work of Spearman using factor analysis and assuming, as Spearman did, that some kind of general intelligence is associated with each individual. Workers in this school continue to try to understand the physiological basis for the variables identified by factor analysis and to improve methods of measuring general intelligence. THE REVISIONISTS: intelligence as information processing. This school tries to figure out what a person is doing when exercising intelligence, rather than what elements of intelligence are being put together. A leading worker in this field, Robert Sternberg writes: "Of course a tester can always average over multiple scores. But are such averages revealing, or do they camouflage more than they reveal? If a person is a wonderful visualizer but can barely compose a sentence, and another person can write glowing prose but cannot begin to visualize the simplest spatial images, what do you really learn about those two people if they are reported to have the same IQ?" THE RADICALS: the theory of multiple intelligences. This school led by Howard Gardner, rejects the notion of a general g and argues instead for seven distinct intelligences: linguistic, musical, logical- mathematical, spatial, bodily-kinesthetic, and two forms of "personal" intelligence. Gardner feels that there is no justification for calling musical ability a talent and language and logical thinking intelligence. He would be happy calling them all talents. He claims that the correlations that lead to the concept of g come precisely because the tests are limited to questions that call on these two special aspects of intellegence. Herrnstein and Murray consider themselves classicist and state that, despite all the apparent controversies, most workers in the field of psychometrics would agree with the following six conclusions that they feel are consequences of classical theory. (1) There is such a thing as cognitive ability on which humans differ. (2) All standardized tests of academic aptitude or achievement measure this general factor to some degree, but IQ tests expressly designed for that purpose measure it most accurately. (3) IQ scores match, to a first degree, whatever it is that people mean when they use the work intelligent or smart in ordinary language. (4) IQ scores are stable, though not perfectly so, over much of a person's life. (5) Properly administered IQ tests are not demonstrably biased against social economic, ethnic, or racial groups. (6) Cognitive ability is substantially heritable, apparently no less than 40 percent and no more than 80 percent. The authors stress that IQ tests are useful in studying social phenomena but are "a limited tool for deciding what to make of any individual." THE DATA USED IN THIS BOOK Throughout the book the authors make use of data from the National Longitudinal Survey of Youth (NLSY) started in 1979. This was a representative sample of 12,686 persons ages 14 to 21 in 1979. This group has been interviewed annually and the authors use the data collected through 1990. REVIEWER NOTE While this study was meant to follow labor trends, a number of other groups used the subjects for their studies. One of these provided the IQ data necessary for this book. The army had been using a test called the Armed Services Vocational Battery (ASVB) since 1950 to help in the selection of recruits and for special assignments. It had been suggested that the volunteer army was selecting a group less well qualified than the Army obtained by the draft. To check this they decided to administer the ASVB to the sample chosen for the NLSY. This study was called the Youth Profile and was administered by the National Opinion Research Council. The results showed that the volunteer army was getting a higher quality army, as measured by these tests, than the draft, but at the same time found significant differences between the performance of various ethnic groups. A study of these differences and a summary of explanations for them are provided in "The profile of American youth : demographic influences on ASVAB test performance" by R. Darrell Bock and Elsie G.J. Moore. It is interesting to compare their analysis with that of the authors of this book. The ASVB has ten subtests which vary from tests you might find on an IQ vocational test, such as automobile repair and electronics. The Armed Forces Qualification Test (AFQT) is made up of the four subtests of the ASVB: word knowledge, paragraph comprehension, arithmetic reasoning, mathematical knowledge. The authors show in an appendix that this test has the properties of a very good IQ test . In particular, they found that over 70% of the variance on the AFQT could be accounted for by a single factor, g, which they identify with general intelligence. CHAPTER I. COGNITIVE CLASS AND EDUCATION 1900-1990 In this part the authors provide a number of graphs that show there is a cognitive sorting process going on in education. While many more students are going to college, a higher and higher proportion of the really bright students are going to a few select schools. We see graphs that exhibit the following: (1) In the twentieth century the prevalence of college degrees increased rather continuously from 2% to 33%. (2) From 1925 to 1950 about the same percentage (55%) of the top IQ quartile of the high school graduates went to college. Starting in 1950, this percentage increased dramatically from 55% to over 80% in 1980 (3) In 1930 the mean IQ scores for all those attending college were about .7 standard deviations above the mean and those attending Ivy League and Seven Sisters colleges were about 1.3 standard deviations above the mean. In 1990 the mean IQ for all attending college had remained about same a .8 standard deviations, while the mean IQ for the Ivy League and Seven sisters mean had increased to 2.7 standard deviations above the mean. Since these graphs display standardized scores, the authors spend some time explaining the concepts of mean and standard deviation in the test and provide a more complete discussion in an appendix. The authors express the fear that the clustering of the high IQ students in a small number of colleges will make them isolated from and unaware of the real world. CHAPTER 2. COGNITIVE PORTIONING BY OCCUPATION The point of this chapter is that jobs sort people by cognitive ability in much the same way that colleges do. A group of twelve professions: accountants, architects, chemists, college teachers, dentists, engineers, lawyers, physicians, computer scientists, mathematicians, natural scientists, social scientists are considered to be "high-IQ professions". The mean IQ of people entering these professions is said to be about 120, which is cutoff point for the top decile by IQ. The authors provide a graph showing that, until 1950, about 12% of the top IQ decile were in these jobs. Then the percentage significantly increased, reaching about 38% in 1990. They link this to education with another graph showing that the proportion of the CEO's with graduate training remained around 10% until 1950 when the proportion increased dramatically to about 60% in 1976. Combining these observations the authors conclude that, at mid-century, the bright people were scattered throughout the labor force but, as the century draws to a close, a very high proportion of these people are concentrated within a few occupations paralleling the cognitive portioning by education. CHAPTER 3. THE ECONOMIC PRESSURE TO PARTITION This chapter is devoted to showing that IQ is a good predictor of job performance. It is the first use of correlation, and an appendix devoted to explaining the concept of correlation is available for the reader not familiar with this concept. The authors discuss a number of studies showing that the correlation between IQ and job performance is typically at least .4 and often more. They point out that the military offers huge data sets for these studies, since everyone in the military must take the ASVB tests (and hence also the AFQT IQ test ) and members of the military attend training schools where they are measured for "training success" at the end of their schooling, based on measures that amount to job assessment skills and knowledge. In these studies, the average correlation between IQ and job performance is about .6. By looking at the high correlation between the g factor for the IQ test and job performance, they conclude that the g factor is the key to success in these jobs. Modern studies in the civilian population are typically done by meta-analysis of small studies leading to results similar to those found in the military studies. An exception was in a report of the National Academy of Sciences "Fairness in Employment Testing", which reported a correlation of only about .25. The authors suggest that this is because researchers for this study did not apply corrections for restricted range which they feel was appropriate for the purposes of their study. (Restricted range means that your sample did not include reasonable numbers from the entire range of possible scores). When these corrections are made they say that the correlation would increase to around .4, consistent with other studies. The authors also compare various predictors for job performance and report the results of a study that showed that the highest correlation between a predictor and job performance rating was the cognitive test score (.53) followed by biographical data (.37), reference checks (.26), education (.22), interview (.14), college grades (.11) and interest (.10). The chapter concludes by remarking that the Supreme Court decision of Griggs v. Duke Co. in 1971, which severely limited the use of IQ tests for job selection, is costing the American economy billions of dollars. REVIEWER NOTE. The main issues referred to in the Griggs v. Dude decision is the possibility of so-called "disparate- impact" lawsuits. These are lawsuits that challenge employment practices that unintentionally but disproportionately affect people of a particular race, color, religion, sex or national origin. The supreme court has twice changed the ground rules set up in the Griggs v. Duke decision. The current rules related to these suits are governed by the Civil Rights act of 1991. According to this law, if a plaintiff shows that a specific part of the employment practice disproportionately affects a particular group, then the employer must be able to demonstrate that the employment practice or criterion in question is consistent with a business necessity (whatever that means). In order to prove disparate impact using statistical comparisons, the comparison must be with racial compositions of the qualified people in the work force, not the racial composition of the entire work force. When multiple employment criteria are required and it can be argued that they cannot be separated, then the