But let us say a critic grants the existence of independent relationships between IQ and social outcomes after holding other plausible causes constant. How important are these “independent relationships”? Trivially so, says Stephen Jay Gould in his New Yorker review. The Bell Curve can safely be dismissed, he says, because IQ explains so little about the social outcomes in question—just a few percent of the variance, in the statistician’s jargon.
Here is the truth: The relationships between IQ and social behaviors that we present in the book are so powerful that they will revolutionize sociology. They are not only “significant” in the standard statistical sense of that phrase but are as well powerful in a substantive sense—often much more powerful than the relationships linking social behaviors with the usual suspects (education, social status, affluence, ethnicity). Not only are the attacks on these relationships unwarranted, but Herrnstein and I actually understate the strength of the statistical record. The story is complex but worth recounting because it tells so much about the academic response to The Bell Curve.
In ordinary multiple regression analysis, two statistics are of special interest. The first is the set of regression coefficients, one for each independent variable, explaining the magnitude of the effect each independent variable has on the dependent variable after taking the role of all the other independent variables into account. Each coefficient has a standard error, which may be used to determine whether the coefficient is statistically significant (i.e., unlikely to have been produced by chance). The second statistic of special interest is the square of the multiple correlation, R2, which tells how much of the variance in the dependent variable is explained by all the independent variables taken together.
One of the early topics about multiple regression that graduate students study is the different uses of regression coefficients and R2. If a coefficient is both large in a substantive sense and statistically significant, it is typically the statistic of main interpretive importance, while R2 is of secondary and sometimes trivial importance. Such is the case with the kind of analysis in The Bell Curve, for reasons we explain in Appendix 4. In all this, we treat our data as our colleagues around the country treat regression results every day. There is nothing controversial here, as evidenced by the fact that none of the quantitative social scientists who reviewed this part of the manuscript for The Bell Curve raised a question about our methods.
But that is not the end of the story. Herrnstein and I refer to the R2s in the introduction to Part II and in Appendix 4 as if they represent “explained variance”—and thereby we commit a technical error, falsely understating the overall explanatory power of our statistics. In logistic regression analysis with binary dependent variables, the kind of analysis we used throughout Part II, the statistic labeled R2 is an ersatz and unsatisfactory attempt to express the model’s goodness of fit. Most statisticians to whom I have talked since say we should have ignored it altogether. Stephen Jay Gould fell into the same error.
Once again, Gould’s criticism has been picked up by many others. It would be nice if a few respected professors would publicly point out that whatever else one might think about The Bell Curve, the criticisms about the small R2s in The Bell Curve are wrong. But this is unlikely to happen. Probably the allegation will quietly fade away as the academics who know the true story discreetly impart the news to those who do not.
The unfounded criticisms of the statistics in The Bell Curve that I have discussed so far will cause merely embarrassment among a few who both understand the issues and have the decency to be embarrassed. The real potential for backfire in the statistical critique of The Bell Curve comes from the attack on our use of socioeconomic status (SES).
Measures of SES are a staple in the social sciences. Leaf through the dozens of technical articles in sociology and economics dealing with issues of success and failure in American life, and you will frequently find a measure of SES as part of the analysis. A major purpose of The Bell Curve was to add IQ to SES as an explanatory variable. To avoid controversy, we deliberately constructed an SES index that uses the same elements everybody else does: income, occupation, and education. We did not have any reason for weighting any of these more heavily than the other, so we converted them to what are called “standard scores” and added them up to get our index, all of which would ordinarily have caused no comment.
But when it comes to The Bell Curve, a standard SES index suddenly becomes problematic. James Heckman notes ominously that we did not have income data for a large part of the sample.20 Arthur Goldberger looks suspiciously on the idea of standardizing the variables.21 Leon Kamin figures that probably the self-reports of income, education, and occupation are exaggerated in ways that falsely produce the relationships we report.22
My response to such criticisms is, “Fine. Let’s test out these potential problems.” Compare the results for the subsamples with and without income data. Do not standardize the variables; create some other scales, and use some other method of combining them. Examine the validity of the self-report data. If one does not like the idea of using an index at all, there is a simple solution: Enter the constituent variables separately, and ask directly how parental education, income, and occupation compete individually with the independent role of the child’s IQ.
As scholars are supposed to, Herrnstein and I checked out these and many other possibilities—the results we report were triangulated in numbing detail during the years we worked on the book—and we knew before publishing The Bell Curve what the critics who bother to retrace our tracks will discover: There is no way to construct a measure of socioeconomic background using the accepted constituent variables that makes much difference in the independent role of IQ.23 In the jargon, our measure of SES is robust and as valid as everyone else’s has been.
But there’s the rub: How valid have everyone else’s been? Until The Bell Curve came along, measures of SES similar to ours were used without a second thought. Now, suddenly, they are to be questioned. I doubt whether the questioning will be confined to just The Bell Curve. But there is not much room to improve such measures, for there is no way around it: SES is in fact dominated by occupation, education, and income. What we did in the book is, in effect, to throw down a challenge: Anyone who does not like the way IQ dominates this thing called “socioeconomic status” in producing important social outcomes should come up with another way of measuring the environment.
Such measures have been emerging over the past few decades. The HOME index we discuss in Chapter 10 is an example. But the social sciences have only scratched the surface. It is now broadly accepted, as it was not only a decade ago, that the presence of the biological father in the home has many important positive effects on children independent of SES. How much more might be understood if we could add to mere presence a good measure of competence. Suppose, for example, that one could create a good measure of the “competency of a father in the raising of a female child.” That might have a large independent effect on the girl’s chances of giving birth to a baby out of wedlock, whatever her IQ. Suppose that one could create a good measure of the “degree to which a young male is raised in an environment where high moral standards are enforced consistently and firmly.” I can imagine this having a major effect on the likelihood of becoming a criminal, independent of IQ.
But the same measures that compete with the importance of IQ are going to make starkly clear something that The Bell Curve has already suggested: The kinds of economic and social disadvantages that have been treated as decisive in recent discussions of social policy are comparatively unimportant. It may sound like an issue that concerns only social scientists. Far from it. If I were to nominate the biggest sleeper effect to emerge from The Bell Curve, it would be the degree to which the book undermines SES as a way of interpreting social problems, and with it the rationale for many of the social policies that came into vogue in the 1960s.
The Malleability of IQ
Raising the question of policy br
ings us to the last of my four examples of the potential backfire effect of attacks on The Bell Curve: the malleability of IQ. These attacks focused on Chapter 17. The cries of protest have been almost as loud as those directed to our chapter on race, and for the reason that Michael Novak identified: By arguing that no easy ways of raising IQ exist, we “destroy hope,” or at least the kind of hope that drives many of the educational and preschool interventions for disadvantaged youth.
Actually, we do express hope. Because the environment plays a significant role in determining intelligence—a point The Bell Curve states clearly and often—we say that sooner or later researchers ought to be able to figure out where the levers are. We urge that steps be taken to hasten the day when such knowledge becomes available. But in examining the current state of knowledge, we also urge realism. Speaking of the most popular idea, intensive intervention for preschoolers, we indeed conclude that “we and everyone else are far from knowing whether, let alone how, any of these projects have increased intelligence” (p. 409). We also predict that “many ostensibly successful projects will be cited as plain and indisputable evidence that we are willfully refusing to see the light” (p. 410).
This prediction has been borne out. Psychologist Richard Nisbett, for example, writing in The Bell Curve Wars, accuses us of being “strangely selective” in our reports about the effects of intervention and wonders if we were “unaware of the very large literature that exists on the topic of early intervention.”24 The “very large literature” of which we were unaware? The only study Nisbett mentions is a 1992 Pediatrics article about a program to provide special services to low birth weight babies. He describes the results as showing a nine-point IQ advantage at age 3 for participants in the intervention. Nisbett neglects to acknowledge the unreliability and instability of IQ measures at age 3. He fails to mention that two IQ measures were used, with the second one showing a gain of just 6.4 points. Most important, Nisbett fails to mention that a follow-up of the same project was published in 1994, when the children were age 5, old enough that IQ scores are beginning to become interpretable. The results? The experimental group had an advantage of just 2.5 points on one measure of IQ and two-tenths of a point on another—both differences being substantively trivial and statistically insignificant.25
There is one slender lead in this study. The 1994 follow-up broke down the results according to whether the babies were “lighter LBW [low birth weight]” (less than 2,000 grams) or “heavier LBW” (2,001-2,500 grams). That comparison showed a gain of 6.0 IQ points for the heavier LBW group on one IQ test and a 3.7 point gain on the other IQ test—not large gains but nevertheless significant. But with each bit of good news goes bad news: The lighter LBW sample showed a gain of only 0.6 point on one IQ test and a drop of 1.5 points on the other. This is the familiar story from Chapter 17: a little hope, as much disappointment, no breakthroughs.
The larger problem with those who claim that Herrnstein and I were too pessimistic is that they conflate improvements in educational achievement with improvements in cognitive ability. The distinction is crucial: Do we know how to take a set of youngsters with a given tested IQ and reliably improve their educational achievement? Yes. Do we know how to take a set of youngsters with a given tested IQ that would not (for example) allow them to become engineers, and reliably raise their cognitive functioning so that they can become engineers? No.
I will venture two broad statements on this issue. First, in the critiques to date, no one has pointed to a credible study showing evidence of significant, long-term effects on IQ scores that we do not consider in The Bell Curve. Second, our account of the record to date is, if anything, generous. The two major intensive interventions for raising the IQ of children at high risk of mental retardation, the Milwaukee Project and the Abecedarian Project, have come under intense methodological criticism in the technical literature. We allude to the controversy on pp. 407-409, but in neither case is the evidence so clear that it was appropriate for us to come down hard on the “no-effect” conclusion, so we do not. If we err, it is in the direction of giving more credit to the interventions than is warranted.
But just as we predicted, many others are nominating “programs that work” that we mysteriously failed to consider. I am sure that some of them do work—for goals other than raising IQ. We would be the last to suggest that education cannot be made better, for example, or that the socialization of children cannot be improved. But in The Bell Curve we talk about a particular goal: improving the cognitive functioning of human beings over the long term. On that score, the record remains as Herrnstein and I describe it: Yes, it can be done, but apparently only in modest amounts for most children, usually temporarily, and inconsistently.
In this instance, I have reason to hope that the unintended effect of the attacks on The Bell Curve will be to crystallize a debate that has long needed crystallizing. The cry that “Herrnstein and Murray are too pessimistic” is going to force a great many claims to be laid on the table for examination. Howard Gardner’s review in American Prospect took us to task for not citing Lisbeth and Daniel Schorr’s book, Within Our Reach, for example. I would be delighted to join in a rigorous look at the programs they describe and see whether we find among them hard evidence for long-term improvement in cognitive functioning.26 Let us bring up all the other nominees for inspection as well. In short, I hope that academicians and politicians alike use the furor over The Bell Curve finally to come to grips with how difficult it is, given the current state of knowledge, for outside interventions to make much difference in the environmental factors that nurture cognitive development.
A few weeks after The Bell Curve appeared, a reporter said to me that the real message of the book is, “Get serious.” I resisted his comment at first, but now I think he was right. We never quite say it in so many words, but the book’s subtext is that America’s discussion of social policy since the 1960s has been carried on in a never-never land where human beings are easily changed and society can eventually become a Lake Wobegon where all the children are above average. The Bell Curve does indeed imply that it is time to get serious about how best to accommodate the huge and often intractable individual differences that shape human society.
This is a counsel not of despair but of realism, including realistic hope. An individual’s g may not be as elastic as one would prefer, but the inventiveness of the species seems to have few bounds. In The Bell Curve, we are matter-of-fact about the limits facing low-IQ individuals in a postindustrial economy, but we also celebrate the capacity of people everywhere in the normal range on the bell curve to live morally autonomous, satisfying lives, if only the system will let them. Accepting the message of The Bell Curve does not mean giving up on improving social policy but thinking anew about how progress is to be achieved—and, even more fundamental, thinking anew about how progress is to be defined.
The verdict on the influence of The Bell Curve on policy is many years away. For now, the book may have another useful role to play that we did not anticipate. The attacks on it have often read like an unintentional confirmation of our view of the cognitive elite as a new caste, complete with high priests, dogmas, heresies, and apostates. But the violent response, unpleasant as it has been in the short run, is essential if The Bell Curve is to play its constructive role in the long run. The social science that deals in public policy has in the latter part of the twentieth century become self-censored and riddled with taboos—in a word, corrupt. Only the most profound, anguished, and divisive reexamination is going to change that situation, and it has to be done within the profession. Perhaps starting that reexamination will be The Bell Curve’s most important achievement.
Charles Murray
Washington, D.C.
20 June 1995
Appendix 1
Statistics for People Who Are Sure They Can’t Learn Statistics
The short explanations of standard deviation (page 44), correlation (page 67), and regression (page 122) should be satisfact
ory for people who are at home with math but never took a statistics course. The longer explanations in this appendix are for people who would like to understand what distribution, standard deviation, correlation, and regression mean, but who are not at home with math.
DISTRIBUTIONS AND STANDARD DEVIATIONS
Why Do We Need “Standard Deviation”?
Every day, formally or informally, people make comparisons—among people, among apples and oranges, among dairy cows or egg-laying hens, among the screws being coughed out by a screw machine. The standard deviation is a measure of how spread out the things being compared are. “This egg is a lot bigger than average,” a chicken farmer might say. The standard deviation is a way of saying precisely what “a lot” means.
What Is a Frequency Distribution?
To get a clear idea of what a frequency distribution is, imagine yourself back in your high school gym, with all the boys in the senior class in the school gym assembled before you (including both sexes would complicate matters, and the point of this discussion is to keep things simple). Line up these boys from left to right in order of height.
Now you have a long line going from shortest to tallest. As you look along the line you will see that only few boys are conspicuously short and tall. Most are in the middle, and a lot of them seem identical in height. Is there any way to get a better idea of how this pattern looks?
The Bell Curve: Intelligence and Class Structure in American Life Page 66