Is the Bell Curve Statistically Sound? (James Case, 01/95) Reprinted from SIAM News Volume

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Is the Bell Curve Statistically Sound? (James Case, 01/95) ========================================================== Reprinted from SIAM News Volume 28-01, January 1995 (C) 1995 by Society for Industrial and Applied Mathematics All rights reserved. ========================================================== Is The Bell Curve Statistically Sound? By James Case The Bell Curve: Intelligence and Class Structure in American Life. By R.J. Herrnstein and Charles Murray, The Free Press, New York, 1994, 845 +xxvi pages, $30. R.J. Herrnstein (now deceased) and Charles Murray knew very well that the mere mention of race in The Bell Curve: Intelligence and Class Structure in American Life would expose their work (and themselves) to severe criticism. They were not prepared, however, for the verdict of "guilt by association" rendered by (among others) ABC News, which likened The Bell Curve to the work of the "Professors of Hate" profiled in the oft quoted Rolling Stone article of October 24. Nor were they prepared to hear no fewer than three respected commentators on the MacNeil Lehrer NewsHour of October 28 denounce the book as a "political tract," rather than a scientific treatise, despite its strict conformance with accepted guidelines for the conduct of scientific inquiry.* Right or wrong, The Bell Curve is hardly the compendium of neo-nazi pseudoscience some make it out to be. Despite the clarity of its exposition, the book's contents are only partially accessible to technically unsophisticated readers, since the claims made and the evidence adduced are both statistical in nature. The claim is made, in particular, that intelligence is an effectively scalar quantity, measurable by standard IQ tests administered (sometimes in as little as 12 minutes) by trained examiners, and that scores so obtained during the high school or even junior high school years are unexcelled predictors of adult employment status and earning power. The authors express great confidence in the abstract measure of "general intelligence" proposed in 1904 by a former British Army officer named Charles Spearman, using the then still new concept of a correlation coefficient. As data from would-be intelligence tests began to accumulate, Spearman noticed that people who did well on one such test tended to do well on others, while those who did poorly on one tended to do poorly on all. Even when two tests were purposely designed to measure radically different cognitive skills, the correlation between scores remained positive. Although the correlations varied considerably in strength from one pair of tests to the next, they were (and continue to be) consistently positive. This convinced Spearman that differences between one intelligence and another are differences of degree, but not of kind, and motivated him to develop a scalar measure (and call it "g", for general intelligence) to quantify such differences. An analogy from the world of boxing might shed some light on the nature of g. All the measurements included in the "tale of the tape" before a prize fight of any consequence -- such as height, weight, and reach, along with circumferences at the chest (expanded and normal), neck, waist, thigh, wrist, ankle, fist, and bicep -- correlate positively with one another, at least to the extent that heavyweights tend to be larger in each dimension than middleweights, who tend to be larger in every way than lightweights. In consequence, Spearman's algorithm can be employed to determine an abstract scalar measure $b$ of "boxer size." Perhaps the fight game should replace its traditional weight classes with $b$-classes: Maybe young fighters could be better protected from injury that way. That still doesn't mean, however, that boxer size is a scalar quantity, or that the differences between two boxers of equal $b$ are unimportant. Spearman's method applies equally well to measurements of intelligence and boxer size and reveals no more about the one than about the other. Nevertheless, Herrnstein and Murray cite an extensive literature purportedly placing the essential correctness of Spearman's conclusions beyond reasonable doubt. They also point out that the current tests have largely been purged of the "cultural bias" once alleged to invalidate them: Twenty-five years have passed since the appearance of the report that made bias a sensitive issue (Arthur Jensen, 1969), and the problem never was as grave as advertised, say Herrnstein and Murray, nor, given time and good will, as hard to correct. For these and other reasons, Herrnstein and Murray tend to ignore the distinctions between g, IQ, and intelligence. Because others refuse to concede that those distinctions are unimportant, however, the abbreviation "IQtelligence" is used in place of "intelligence as measured by $g$" in the remainder of this review. The extent to which intelligence and IQtelligence are one and the same thing may never be known. Although $g$ is easily measured, attempts to define it and to observe it directly have never succeeded. Because even the most efficient intelligence tests include many questions, a high degree of "data compression" is undoubtedly possible without significant information loss. The Educational Testing Service achieves it by reporting just two scores (for verbal and quantitative abilities) on its oft defamed SAT test and three (for verbal, quantitative, and analytical skills) on its Graduate Record Examination. Both sets of scores are expressed on the familiar SAT scale, with its standard deviation of 100 about a mean of 500. Spearmanites further simplify the reporting process by combining scores from the different segments of a given intelligence test into a weighted average representing $g$, typically expressed on the IQ scale, where the standard deviation is 15 about a mean score of 100. Herrnstein and Murray justify (in part) their acceptance of g as a measure of intelligence by observing that little, if any, of the predictive power of intelligence testing seems to be lost by so doing. Although teenage IQ is not by itself a reliable predictor of success in engineering and other quantitative curricula, it does seem to predict adult employment status and earning power in today's increasingly complex world. The first of the four parts of The Bell Curve summarizes extensive evidence indicating that IQtelligence is (at least statistically) predictive. Part II explores the extent to which low IQ appears to predispose an individual toward poverty, failure in school, unemployment, illness, injury in the workplace, family problems, welfare dependency, and ineffective parenting, or a life of crime, incivility, and poor citizenship. Although these and other social ills have been studied extensively, IQ and its equivalents have often been omitted from the list of potential explanators, seriously compromising (at least in the opinion of Herrnstein and Murray) the validity of the conclusions reached. They stress that "years in school" and "highest degree earned" are inadequate proxies for IQtelligence. Part III digresses on racial issues, and a short Part IV discusses conclusions and policy prescriptions. Resting as it does on the still controversial statistical technique known as meta-analysis, the evidence with which the authors seek to establish the correlation between teenage IQtelligence and adult status and earning power demands scrutiny. In use since 1904, when Karl Pearson grouped data from the British military to conclude that the then current practice of vaccination against intestinal fever was ineffective, the technique did not become commonplace until the 1980s. Today, meta-analysis is prominent in medical research and is becoming more so in the social sciences, due in part to its 1992 endorsement by the National Research Council. It is designed to illuminate the not uncommon situation in which scores or even hundreds of costly studies of a given issue have already been made, by a host of different investigators, using a variety of different approaches, without achieving actionable consensus. Meta-analysis represents an attempt to replace the blue ribbon committee approach to building such consensus with something more scientific. The idea is to treat the existing studies as data to which the tools of statistical inference may be applied. Yet meta-analysis remains a controversial method of inference which has sparked controversy in every field to which it has been applied: Few investigators, it has been suggested [1], possesses the statistical expertise to conduct and interpret meta-analysis. That said, it does appear that postadolescent IQ has indeed become an excellent predictor of adult "employment status" and/or earning power. The authors of The Bell Curve point out, in summarizing the findings on which that conclusion presently rests, that whereas the year 1900 found the top 10% of American IQs scattered almost uniformly throughout the workforce (if not on the farms where half the population still lived, then in stores, churches, factories, bicycle shops, and the like), the second millennium will find them highly concentrated in science, medicine, the law, top management, and a handful of other more or less prestigious occupations. As the social and financial barriers that once restricted entry into the more desirable occupations have fallen, members of what Herrnstein and Murray term the "cognitive elite" have come to all but monopolize them. Readers of The Bell Curve will, of necessity, learn much about this cognitive elite. In addition to spending more years in school than most, and receiving better grades, say the authors, members "watch far less television than the average American. Their movie-going tends to be highly selective. They seldom read the national tabloids that have the nation's highest circulation figures or listen to the talk radio that has become a major form of national communication for other parts of America." They are also, even at an early age, more politically inclined than average. None of this means that "the cognitive elite spend their lives at the ballet and reading Proust. Theirs is not a high culture, but it is distinctive enough to set them off from the rest of the country in many important ways." Members tend, in particular, to live in virtual isolation from nonmembers. As columnist Mickey Kaus puts it, "I entered a good Ivy League college in 1969. I doubt I've had a friend or regular social acquaintance since who scored less than 1100 on his or her SAT boards." Isolated or not, members of the cognitive elite tend to earn substantially more than other Americans. The figure shown here, which appears on page 516 of The Bell Curve, provides historical perspective. As shown in the figure, whereas median family income rose rather steadily to a 1973 peak, then leveled off at a somewhat lower level, the fraction of American families with income in excess of a hundred thousand 1990 dollars has continued to climb (with some irregularities). Their new-found riches, Herrnstein and Murray allege, tend to bring the political interests of the cognitive elite into alignment with those of the already affluent. The following established tendencies seem likely, say the authors, to persist and to aggravate existing social frictions: - An increasingly wealthy and isolated cognitive elite. - A merging of the cognitive and the affluent elites. - A deteriorating quality of life for people excluded from the upper reaches of the cognitive ability distribution. The latter effect, which is partially documented by the figure, is a direct consequence of the other two. Unchecked, say Herrnstein and Murray, "these trends will lead the US toward something resembling a caste society, with the underclass mired ever more firmly at the bottom and the cognitive elite ever more firmly anchored at the top, restructuring the rules of society [italics added] so that it becomes harder and harder for them to lose. . . . Like other apocalyptic visions, this one is pessimistic, perhaps too much so. On the other hand, there is much to be pessimistic about." The last remark would seem to explain why The Bell Curve was written in the first place. Herrnstein and Murray knew full well that they would be accused of racism, bigotry, and intellectual dishonesty, just as Arthur Jensen was some 25 years ago, for saying many of the same things. Yet as they (and apparently the electorate) interpret current events, the nation is in an alarming decline, due in large part to inadequate leadership and public policy. The forces of darkness are advancing on every front, and the authors genuinely believe that the measures they propose will help stem the tide. Many of the policy reforms proposed by the authors have to do with education. They think it extraordinarily unwise, for instance, that "only one tenth of 1 percent of all the federal funds spent on elementary and secondary education go to programs for the gifted." After all, they say, "The people who run the United States -- create its jobs, expand its technologies, cure its sick, teach in its universities, administer its cultural and political institutions_are drawn mainly from a thin layer of cognitive ability at the top." Since the 1960s, however, "while a cognitive elite has become increasingly segregated from the rest of the country, the quality of the education they receive has been degraded." Would they not run things better if they were better educated? Would they not become the philosopher kings Plato sought to train? The Bell Curve has more to say about the nature and causes of the nation's current decline, and contains more food for thought, than even a lengthy synopsis can hope to convey. At a guess, the book's most lasting contribution will be its documentation of the nation's increasing stratification according to IQtelligence and/or wealth, and its shrill warning against any alliance of the cognitive and affluent elites. The individual agendas of these groups transcend traditional party lines, and together they constitute an even greater menace than Herrnstein and Murray seem to realize: Each group reinforces the other's instinctive arrogance by lending its prestige to the never-ending quest of every elite to "restructure the rules of society" to its own advantage. References [1] Charles C. Mann, Can meta-analysis make policy?, Science, 266 (November 11, 1994), 960-962. [2] William Overton, Creationism in schools: the decision in McLean versus the Arkansas Board of Education, Science, 215(February 19, 1982), 934-943. James Case is an independent consultant who lives in Baltimore,

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