Disturbing as I find the anachronism of The Bell Curve, I am even more distressed by its pervasive disingenuousness. The authors omit facts, misuse statistical methods, and seem unwilling to admit the consequences of their own words.
Disingenuousness of content
The ocean of publicity that has engulfed The Bell Curve has a basis in what Murray and Herrnstein (New Republic, October 31, 1994) call “the flashpoint of intelligence as a public topic: the question of genetic differences between the races.” And yet, since the day of publication, Murray has been temporizing and denying that race is an important subject in the book at all; instead, he blames the press for unfairly fanning these particular flames. He writes with Herrnstein (who died just a month before publication) in the New Republic: “Here is what we hope will be our contribution to the discussion. We put it in italics; if we could we would put it in neon lights: The answer doesn’t much matter.”
Fair enough in the narrow sense that any individual may be a rarely brilliant member of an averagely dumb group (and therefore not subject to judgment by the group mean), but Murray cannot deny that The Bell Curve treats race as one of two major topics, with each given about equal space; nor can he pretend that strongly stated claims about group differences have no political impact in a society obsessed with the meanings and consequences of ethnicity. The very first sentence of The Bell Curve’s preface acknowledges equality of treatment for the two subjects of individual and group differences: “This book is about differences in intellectual capacity among people and groups and what these differences mean for America’s future.” And Murray and Herrnstein’s New Republic article begins by identifying racial difference as the key subject of interest: “The private dialogue about race in America is far different from the public one.”
Disingenuousness of argument
The Bell Curve is a rhetorical masterpiece of scientism, and the particular kind of anxiety and obfuscation that numbers impose upon nonprofessional commentators. The book runs to 845 pages, including more than 100 pages of appendices filled with figures. So the text looks complicated, and reviewers shy away with a knee-jerk claim that, while they suspect fallacies of argument, they really cannot judge. So Mickey Kaus writes in the New Republic (October 31): “As a lay reader of The Bell Curve, I’m unable to judge fairly,” as does Leon Wieseltier in the same issue: “Murray, too, is hiding the hardness of his politics behind the hardness of his science. And his science for all I know is soft.… Or so I imagine. I am not a scientist. I know nothing about psychometrics.” Or Peter Passell in the New York Times (October 27, 1994): “But this reviewer is not a biologist, and will leave the argument to experts.”
In fact, The Bell Curve is extraordinarily one-dimensional. The book makes no attempt to survey the range of available data, and pays astonishingly little attention to the rich and informative history of this contentious subject. (One can only recall Santayana’s dictum, now a cliché of intellectual life: “Those who cannot remember the past are condemned to repeat it”). Virtually all the analysis rests upon a single technique applied to a single set of data—all probably done in one computer run. (I do agree that the authors have used the most appropriate technique—multiple regression—and the best source of information—the National Longitudinal Survey of Youth—though I shall expose a core fallacy in their procedure below. Still, claims as broad as those advanced in The Bell Curve simply cannot be adequately defended—that is, either properly supported or denied—by such a restricted approach.)
The blatant errors and inadequacies of The Bell Curve could be picked up by lay reviewers if only they would not let themselves be frightened by numbers—for Herrnstein and Murray do write clearly and their mistakes are both patent and accessible. I would rank the fallacies in two categories: omissions and confusions, and content.
1. Omissions and confusions: While disclaiming on his own ability to judge, Mickey Kaus (in the New Republic) does correctly identify “the first two claims” that are absolutely essential “to make the pessimistic ‘ethnic difference’ argument work”: “(1) that there is a single, general measure of mental ability; (2) that the IQ tests that purport to measure this ability … aren’t culturally biased.”
Nothing in The Bell Curve angered me more than the authors’ failure to supply any justification for their central claim, the sine qua non, of their entire argument: the reality of IQ as a number that measures a real property in the head, the celebrated “general factor” of intelligence (known asg) first identified by Charles Spearman in 1904. Murray and Herrnstein simply proclaim that the issue has been decided, as in this passage from their New Republic article: “Among the experts, it is by now beyond much technical dispute that there is such a thing as a general factor of cognitive ability on which human beings differ and that this general factor is measured reasonably well by a variety of standardized tests, best of all by IQ tests designed for that purpose.”
Such a statement represents extraordinary obfuscation, achieved by defining “expert” as “that group of psychometricians working in the tradition of g and its avatar IQ.” The authors even admit (pp. 14–19) that three major schools of psychometric interpretation now contend, and that only one supports their view of g and IQ—the classicists as championed in The Bell Curve (“intelligence as a structure”), the revisionists (“intelligence as information processing”), and the radicals (“the theory of multiple intelligences”).
This vital issue cannot be decided, or even understood without discussing the key and only rationale that g has maintained since Spearman invented the concept in 1904—factor analysis. The fact that Herrnstein and Murray barely mention the factor analytic argument (the subject receives fleeting attention in two paragraphs) provides a central indictment and illustration of the vacuousness in The Bell Curve. How can authors base an eight-hundred-page book on a claim for the reality of IQ as measuring a genuine, and largely genetic, general cognitive ability—and then hardly mention, either pro or con, the theoretical basis for their certainty? Various cliches like “Hamlet without the Prince of Denmark” come immediately to mind.
Admittedly, factor analysis is a difficult and mathematical subject, but it can be explained to lay readers with a geometrical formulation developed by L. L. Thurstone in the 1930s and used by me in Chapter 7 of The Mismeasure of Man. A few paragraphs cannot suffice for adequate explanation, so, although I offer some sketchy hints below, readers should not question their own IQ’s if the topic still seems arcane.
In brief, a person’s performances on various mental tests tend to be positively correlated—that is, if you do well on one kind of test, you tend to do well on the others. This result is scarcely surprising, and is subject to either purely genetic (the innate thing in the head that boosts all scores) or purely environmental interpretation (good books and good childhood nutrition to enhance all performances). Therefore, the positive correlations say nothing in themselves about causes.
Charles Spearman used factor analysis to identify a single axis—which he called g—that best identifies the common factor behind positive correlations among the tests. But Thurstone later showed that g could be made to disappear by simply rotating the factor axes to different positions. In one rotation, Thurstone placed the axes near the most widely separated of attributes among the tests—thus giving rise to the theory of multiple intelligences (verbal, mathematical, spatial, etc., with no overarching g). This theory (the “radical” view in Herrnstein and Murray’s classification) has been supported by many prominent psychometricians, including J. P. Guilford in the 1950s, and most prominently today by Howard Gardner. In this perspective, g cannot have inherent reality, for g emerges in one form of mathematical representation for correlations among tests, and disappears (or at least greatly attenuates) in other forms that are entirely equivalent in amounts of information explained. In any case, one can’t grasp the issue at all without a clear exposition of factor analysis—and The Bell Curve cops out completely on this central co
ncept.
On Kaus’s second theme of “cultural bias,” The Bell Curve’s presentation matches Arthur Jensen’s, and that of other hereditarians, in confusing a technical (and proper) meaning of bias (I call it “S-bias” for “statistical”) with the entirely different vernacular concept (I call it “V-bias”) that agitates popular debate. All these authors swear up and down (and I agree with them completely) that the tests are not biased—in the statistician’s definition. Lack of S-bias means that the same score, when achieved by members of different groups, predicts the same consequence—that is, a black person and a white person with an identical IQ score of too will have the same probabilities for doing anything that IQ is supposed to predict. (I should hope that mental tests aren’t S-biased, for the testing profession isn’t worth very much if practitioners can’t eliminate such an obvious source of unfairness by careful choice and framing of questions.)
But V-bias, the source of public concern, embodies an entirely different issue that, unfortunately, uses the same word. The public wants to know whether blacks average 85 and whites 100 because society treats blacks unfairly—that is, whether lower black scores record biases in this social sense. And this crucial question (to which we do not know the answer) cannot be addressed by a demonstration that S-bias doesn’t exist (the only issue treated, however correctly, by The Bell Curve).
2. Content: As stated above, virtually all the data in The Bell Curve derive from one analysis—a plotting, by a technique called multiple regression, of the social behaviors that agitate us, such as crime, unemployment, and births out of wedlock (treated as dependent variables), against both IQ and parental socioeconomic status (treated as independent variables). The authors first hold IQ constant and consider the relationship of social behaviors to parental socioeconomic status. They then hold socioeconomic status constant and consider the relationship of the same social behaviors to IQ. In general, they find a higher correlation with IQ than with socioeconomic status; for example, people with low IQ are more likely to drop out of high school than people whose parents have low socioeconomic status.
But such analyses must engage two issues—form and strength of the relationship)—and Herrnstein and Murray only discuss the issue that seems to support their viewpoint, while virtually ignoring (and in one key passage almost willfully and purposely hiding) the other factor that counts so profoundly against them. Their numerous graphs only present the form of the relationships—that is, they draw the regression curves of their variables against IQ and parental socioeconomic status. But, in violation of all statistical norms that I’ve ever learned, they plot only the regression curve and do not show the scatter of variation around the curve, so their graphs show nothing about the strength of the relationship—that is, the amount of variation in social factors explained by IQ and socioeconomic status.
Now why would Herrnstein and Murray focus on the form and ignore the strength? Almost all of their relationships are very weak—that is, very little of the variation in social factors can be explained by either IQ or socioeconomic status (even though the form of this small amount tends to lie in their favored direction). In short, IQ is not a major factor in determining variation in nearly all the social factors they study—and their vaunted conclusions thereby collapse, or become so strongly attenuated that their pessimism and conservative social agenda gain no significant support.
Herrnstein and Murray actually admit as much in one crucial passage on page 117, but then they hide the pattern. They write: “It almost always explains less than 20 percent of the variance, to use the statistician’s term, usually less than 10 percent and often less than 5 percent. What this means in English is 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.” Despite this disclaimer, their remarkable next sentence makes a strong causal claim: “We will argue that intelligence itself, not just its correlation with socioeconomic status, is responsible for these group differences.” But a few percent of statistical determination is not equivalent to causal explanation (and correlation does not imply cause in any case, even when correlations are strong—as in the powerful, perfect, positive correlation between my advancing age and the rise of the national debt). Moreover, their case is even worse for their key genetic claims—for they cite heritabilities of about 60 percent for IQ, so you must nearly halve the few percent explained if you want to isolate the strength of genetic determination by their own criteria!
My charge of disingenuousness receives its strongest affirmation in a sentence tucked away on the first page of Appendix 4, page 593, where the authors state: “In the text, we do not refer to the usual measure of goodness of fit for multiple regressions, R2, but they are presented here for the cross-sectional analysis.” Now why would they exclude from the text, and relegate to an appendix that very few people will read or even consult, a number that, by their own admission, is “the usual measure of goodness of fit.” I can only conclude that they did not choose to admit in the main text the extreme weakness of their vaunted relationships.
Herrnstein and Murray’s correlation coefficients are generally low enough by themselves to inspire lack of confidence. (Correlation coefficients measure the strength of linear relationships between variables; positive values run from 0.0 for no relationship to 1.0 for perfect linear relationship.) Although low figures are not atypical in the social sciences for large surveys involving many variables, most of Herrnstein and Murray’s correlations are very weak—often in the 0.2 to 0.4 range. Now, 0.4 may sound respectably strong, but—and now we come to the key point—R2 is the square of the correlation coefficient, and the square of a number between 0 and 1 is less than the number itself, so a 0.4 correlation yields an r-squared of only 0.16. In Appendix 4, then, we discover that the vast majority of measures for R2, excluded from the main body of the text, have values less than 0.1. These very low values of R2 expose the true weakness, in any meaningful vernacular sense, of nearly all the relationships that form the heart of The Bell Curve.
Disingenuousness of program
Like so many conservative ideologues who rail against a largely bogus ogre of suffocating political correctness, Herrnstein and Murray claim that they only seek a hearing for unpopular views so that truth will out. And here, for once, I agree entirely. As a card-carrying First Amendment (near) absolutist, I applaud the publication of unpopular views that some people consider dangerous. I am delighted that The Bell Curve was written—so that its errors could be exposed, for Herrnstein and Murray are right in pointing out the difference between public and private agendas on race, and we must struggle to make an impact upon the private agendas as well.
But The Bell Curve can scarcely be called an academic treatise in social theory and population genetics. The book is a manifesto of conservative ideology, and its sorry and biased treatment of data records the primary purpose—advocacy above all. The text evokes the dreary and scary drumbeat of claims associated with conservative think tanks—reduction or elimination of welfare, ending of affirmative action in schools and workplaces, cessation of Head Start and other forms of preschool education, cutting of programs for slowest learners and application of funds to the gifted (Lord knows I would love to see more attention paid to talented students, but not at this cruel and cynical price).
The penultimate chapter presents an apocalyptic vision of a society with a growing underclass permanently mired in the inevitable sloth of their low IQ’s. They will take over our city centers, keep having illegitimate babies (for many are too stupid to practice birth control), commit more crimes, and ultimately require a kind of custodial state, more to keep them in check (and out of our high IQ neighborhoods) than with any hope for an amelioration that low IQ makes impossible in any case. Herrnstein and Murray actually write (p. 526): “In short, by custodial state, we have in mind a high-tech and
more lavish version of the Indian reservation for some substantial minority of the nation’s population, while the rest of America tries to go about its business.”
The final chapter then tries to suggest an alternative, but I have never read anything so feeble, so unlikely, so almost grotesquely inadequate. They yearn romantically for the “good old days” of towns and neighborhoods where all people could be given tasks of value and self-esteem could be found for all steps in the IQ hierarchy (so Forrest Gump might collect the clothing for the church raffle, while Mr. Murray and the other bright folks do the planning and keep the accounts. Have they forgotten about the town Jew and the dwellers on the other side of the tracks in many of these idyllic villages?). I do believe in this concept of neighborhood, and I will fight for its return. I grew up in such a place within that mosaic known as Queens, New York City, but can anyone seriously find solutions (rather than important palliatives) to our social ills therein?
However, if Herrnstein and Murray are wrong about IQ as an immutable thing in the head, with humans graded in a single scale of general capacity, leaving large numbers of custodial incompetents at the bottom, then the model that generates their gloomy vision collapses, and the wonderful variousness of human abilities, properly nurtured, reemerges. We must fight the doctrine of The Bell Curve both because it is wrong and because it will, if activated, cut off all possibility of proper nurturance for everyone’s intelligence. Of course we cannot all be rocket scientists or brain surgeons (to use the two current slang synecdoches for smartest of the smart), but those who can’t might be rock musicians or professional athletes (and gain far more social prestige and salary thereby)—while others will indeed serve by standing and waiting.
The Mismeasure of Man Page 40