The Bell Curve: Intelligence and Class Structure in American Life

by Richard J. Herrnstein

  40 The standard deviation squared times the heritability gives variance due just to genes; the square root of that number is the standard deviation of IQ in a world of perfectly uniform environments: = 11.6 A heritability of .4 would reduce the standard deviation from the normative value of 15 to 9.5; with a heritability of .8., it would be reduced to 13.4.

  41 If we take the heritability of IQ to be .6, then the swing in IQ is 24 points for two children with identical genes, but growing up in circumstances that are at, say, the 10th and the 90th centile in their capacity to foster intelligence, a very large swing indeed. A less extreme swing from the 40th to the 60th centile in environmental conditions would move the average IQ only 4.75 points. In a normal distribution, the distance from the 10th to the 90th percentile is about 2.5 standard deviation units; from the 40th to the 60th percentile, it is about .5 standard deviation units. If the heritability is .8, instead of .6, then the swing from the 10th to the 90th percentile would be worth 17 IQ points, from the 40th to the 60th, 3.4 IQ points.

  42 Burgess and Wallin 1943.

  43 Spuhler 1968.

  44 Jensen 1978. This estimate may be high for a variety of technical reasons that are still being explored, but apparently not a lot too high. For more, see DeFries et al. 1979; Mascie-Taylor 1989; Mascie-Taylor and Vandenberg 1988; Price and Vandenberg 1980; Watkins and Meredith 1981. In the 1980s, some researchers argued that data from Hawaii indicated a falling level of assortative mating for IQ, which they attributed to increased social mobility and greater access to higher education (Ahern, Johnson, and Cole 1983; Johnson, Ahern, and Cole 1980; Johnson, Nagoshi, and Ahern 1987). But the evidence seems to be limited to Hawaii. Other recent data from Norway and Virginia, not to mention the national census data developed by Mare and discussed in the text, fail to confirm the Hawaii data (Heath et al. 1985,1987). When intelligence and educational level are statistically pulled apart, the assortative mating for education, net of intelligence, is stronger than that for intelligence, net of educational level (Neale and McArdle 1990; Phillips et al. 1988).

  45 For a discussion of regression to the mean, see Chapter 15. The calculation in the text assumes a correlation of +.8 between the average child’s IQ and the midpoint of the parental IQs, consistent with a heritability of .6 and a family environment effect of .2. The estimate of average IQs in 1930 is explained in Chapter 1. The estimate for the class of 1964 (who were freshmen in 1960) is based on Harvard SAT-Verbal scores compared to the Educational Testing Service’s national norm study conducted in 1960, which indicates that the mean verbal score for entering Harvard freshmen was 2.9 SDs above the mean of all high school seniors—and, by implication, considerably higher than that for the entire 18-year old cohort (which includes the high school dropouts; Seibel 1962, Bender 1960). If we estimate the correlation between the SAT-Verbal and IQ as +.65 (from Donlon 1984), the estimated mean IQ of Harvard freshmen as of 1960 was about 130, from which the estimate of children’s IQ has been calculated.

  46 With a parent-child correlation of .8, 64 percent of the variance is accounted for, 36 percent not accounted for. The square root of .36, which is .6, times 15, is the standard deviation of the distribution of IQ scores of the children of these parents. This gives a value of 9, from which the percentages in the text are estimated.

  47 Operationally, Mare compared marriage among people with sixteen or more years of schooling with those who had fewer than sixteen years of schooling (Mare 1991, p. 23). For additional evidence of increasing educational homogamy in the 1970s and 1980s, see Qian and Preston 1993.

  48 Oppenheimer, 1988.

  49 DES 1992, Tables 160, 168.

  50 Buss 1987. For evidence that this phenomenon is well underway, see Qian and Preston 1993.

  51 In the NLSY, whose members graduated from high school in the period 1976-1983, 59.3 percent had obtained a bachelor’s or higher degree by 1990. In the “High School and Beyond” study conducted by the Department of Education, only 44 percent of 1980 high school graduates who were in the top quartile of ability had obtained a B.A. or B.S. by 1986 (Eagle 1988a, Table 3).

  52 See Chapter 1.

  53 Authors’ analysis of the NLSY.

  54 Authors’ analysis of the NLSY.

  55 SAUS 1991, Table 17.

  Introduction to Part II

  1 Sussman and Steinmetz 1987. This is still a valuable source of information about myriad aspects of family life, mainly in America.

  2 For example, in the last ten years, out of hundreds of articles and research notes, the preeminent economics journal, American Economic Review, has published just a handful of articles that call upon IQ as a way of understanding such problems. The most conspicuous exceptions are Bishop 1989; Boissiere et al. 1985; Levin 1989; Silberberg 1985; Smith 1984.

  3 The criterion for eligibility was that they be ages 14 to 21 on January 1, 1979, which meant that some of them had turned 22 by the time the first interview occurred.

  4 Details of the Department of Defense enlistment tests, the ASVAB, are also given in Appendix 3.

  5 The test battery was administered to small groups by trained test personnel. That each NLSY subject was paid $50 to take the test helped ensure a positive attitude toward the experience.

  6 See Appendix 3 for more on the test and its g loading, and the Introduction for a discussion of g itself.

  7 Raw AFQT scores in the NLSY sample rose with age throughout the age cohorts who were still in their teens when they took the test. The simplest explanation is that the AFQT was designed by the military for a population of recruits who would be taking the test in their late teens, and younger youths in the NLSY sample got lower scores for the same reason that high school freshmen get lower SAT scores than high school seniors. However, a cohort effect could also be at work, whereby (because of educational or broad environmental reasons) youths born in the first half of the 1960s had lower realized cognitive ability than youths born in the last half of the 1950s. There is no empirical way of telling which reason explains the age-related differences in the AFQT or what the mix of reasons might be. This uncertainty is readily handled in the multivariate analyses by entering the subject’s birthdate as an independent variable (all the NLSY sample took the AFQT within a few months of each other in late 1980). When we present descriptive statistics, we use age-equated centiles.

  8 We assigned the NLSY youths to a cognitive class on the basis of their age-equated centile scores. We use the class divisions as a way to communicate the data in an easily understood form. It should be remembered, however, that all of the statistical analyses are based on the actual test scores of each individual in the NLSY.

  9 Regression analysis is only remotely related to the regression to the mean referred to earlier. See Appendix 1.

  10 Age, too, is always part of the analytic package, a necessity given the nature of the NLSY sample (see note 7).

  11 The white sample for the NLSY was chosen by first selecting all who were categorized by the interview screener as nonblack and non-Hispanic. From this group, we excluded all youths who identified their own ethnicity as Asian, Pacific, American Indian, African, or Hispanic.

  Chapter 5

  1 Ross et al. 1987. The authors used the sample tapes for the 1940 and 1950 census to calculate the figures for 1939 and 1949, antedating the beginning of the annual poverty statistics in 1959. The numbers represent total money income, including government transfers. The figure for 1939 is extrapolated, since the 1939 census did not include data on income other than earnings. It assumes that the ratio of poverty based on earnings to poverty based on total income in 1949 (.761) also applied in 1939, when 68.1 percent of the population had earnings that put them below the poverty line. Since government transfers increased somewhat in the intervening decade, the resulting figure for 1939 should be considered a lower bound.

  It may be asked if the high poverty percentage in 1939 was an artifact of the Great Depression. The numbers are inexact, but the answer is no. The poverty ra
te prior to the Depression—defined by the contemporary poverty line—was higher yet. (See Murray 1988b, pp. 72-73).

  2 See the introduction to Part II for more on the distinction between independent and dependent variables.

  3 Jensen 1980, p. 281.

  4 The observed stability of tests for children up to 10 years of age is reasonably well approximated by the formula, where r11 and r22 are the reliabilities of the tests on occasions 1 and 2, CA1 and CA2 are the subject’s chronological age on occasions 1 and 2, and r12 is the correlation between a test taken and retaken at ages CA1 and CA2. See Bloom 1964 for a full discussion.

  5 After age 10, the correlation of test scores will usually fall between the product of the reliabilities of the two tests and the square root of their product. Thus, for example, the correlation of two measures of IQ after age 10 when both tests had reliabilities of .9 may be expected to fall between .81 and .9. Since the best IQ tests have reliabilities in excess of .9, this is tantamount to saying that the stability of scores is quite high. Following are some sample reliabilities as reported in the publisher’s test manuals. WISC = .95, WAIS = .97, Wonderlic Personnel Test = .95. The reliabilities of some of the major standardized achievement tests are also extremely high. For example: ACT = .95, SAT = 90+, California Achievement Tests = .90-.95, Iowa Test of Basic Skills Composite = .98−.99. For a longer list of reliabilities and an accessible discussion of both reliability and stability, see Jensen 1980, Chap. 7.

  6 Is there reason to think that, had the test been administered earlier, at age 7 or 8, the results would have turned out differently? The answer, with some reservations, is no. We would observe the normal level of fluctuation in tests administered at ages 7 and 20, with some individuals scoring higher and some lower as they grow up. The correlations between a person’s IQ obtained at age 7 and social behavior in adulthood would support the same qualitative conclusions as those based on an IQ obtained at age 20. The correlations using the younger scores would be smaller, because they measure the adult trait of intelligence less reliably than a score obtained later in life. See Appendix 3 for a discussion of changes in IQ among the members of the NLSY sample.

  7 Himmelfarb 1984.

  8 E.g., Ryan 1971.

  9 For a few words about regression analysis, see the Introduction to Part II and Appendix 1. In fewer words still, this is a method for assessing the independent impact of each of a set of independent variables on a dependent variable. The specific form used here is called logistic regression analysis, the appropriate method for binary dependent variables, such as yes-no or female-male or married-unmarried.

  10 We eliminate students to avoid misleading ourselves with, for example, third-year law students who have low incomes in 1989 but are soon to be making high incomes.

  11 Note a distinction: Age has an important independent effect on income (income trajectories are highly sensitive to age), but not on the yes-no question of whether a person lives above the poverty line. It is also worth noting that age in the NLSY is restricted in range because the sample was all born within a few years of each other.

  12 The imaginary person is sexless.

  13 We refrain from precise numerical estimates of how much more important IQ is than socioeconomic background, for two reasons. First, they are not essential to the point of this discussion. Second, doing so would get us into problems of measurement and measurement error that would needlessly complicate the text. It seems sufficient for our purpose to note that IQ has a greater impact on the likelihood of being poor than socioeconomic background, as those variables are usually measured.

  14 The 1991 poverty rate for persons 15 and over was 11.9 percent, compared to 22.4 percent for children under 15. U.S. Bureau of the Census, 1992, Table 1.

  15 For an analysis of the demographic reasons and some measurement issues, see Smith 1989.

  16 U.S. Bureau of the Census 1992, Table C, p. xiv.

  17 U.S. Bureau of the Census 1992, Table C, p. xiv.

  18 Eggebeen and Lichter 1991; Smith 1989.

  19 Given childless white men and women of average age, socioeconomic background, and IQ, the expected poverty rates are only 1.6 percentage points apart and are exceedingly low in both cases: 3.1 and 4.7 percent, respectively.

  20 The relationships of IQ to poverty were statistically significant beyond the .01 level for both married and unmarried women. Our policy throughout the book is not routinely to report significance statistics, but at the same time not to present any relationship as being substantively significant unless we know that it also is statistically significant.

  21 An entire draft of the book was written using a different measure of IQ. As described in Appendix 3, the armed forces changed the scoring system for the AFQT in 1989. The first draft was written using the old version. After discussing the merits of the old and new measures at length, we decided to switch to the new one, because, for arcane reasons, it is psychometrically superior. The substantive effects of this change on the conclusions in the book are, as far as we can tell, effectively nil. All of the analyses have also been repeated with two versions of the SES index, and many of them with three. Again, the three versions yielded substantively indistinguishable results. But each of the successive versions of the SES index was, in our judgment, a theoretically more satisfying and statistically more robust way of capturing the construct of “socioeconomic status.”

  Regarding the specific analysis of the role of gender and marital status in mediating the relationship between IQ and poverty: Originally, the analysis (and the graphic included in the text on page 138) was based on married/unmarried, men/women. Then we looked more closely at women and their various marital situations, then at those marital situations for women with children. All of the poverty analyses were conducted with two measures of poverty: the official definition (represented in this book), and a definition based on cash income obtained from sources other than government transfers. We decided to present the results using the official definition to avoid an extra layer of explanation, but we have the comfort of knowing that the interpretation fits both definitions, except for a few nuances that are not important enough to warrant a place in this concise an account. We have conducted some of these analyses for age-restricted samples, to see if things change for older cohorts in ways that are not captured by using age as an independent variable in the regression equation. Throughout all of these regression analyses, we were also looking at cross-tabulations and frequency distributions to try to see what gnomes might be lurking in the regression coefficients. Finally, we duplicated all of the analyses you see with and without sample weights, to ensure that there were no marked, mysterious differences in the two sets of results. There were undoubtedly other iterations and variations that we have forgotten over the last four years.

  None of this will be surprising to our colleagues, for the process we have described is SOP for social scientists engaged in complex analyses. But for nonspecialists, the story is worth remembering. It should make you more skeptical, insofar as you understand that such enterprises are not as elegant and preordained as authors (including us) sometimes make it sound. But the story can also give you some additional confidence, insofar as, when you find yourself wondering whether we considered such-and-such an alternative way of looking at the data, the chances are fairly good that we did.

  22 In passing, it just isn’t so for blacks either. The independent roles of poverty and socioeconomic status are almost exactly the same for blacks in the NLSY as for whites. See Chapter 14.

  Chapter 6

  1 Kronick and Hargis 1990.

  2 For a discussion of definitional issues in measuring the dropout rate, see Kominski 1990.

  3 Most people get their high school degrees or equivalences later than at the age of 17, so the figure on page 144 implicitly overestimates the proportion of dropouts in the population as a whole, at least for recent times. In 1985, the U.S. Government Accounting Office estimated that 13 percent of the population between the ag
es of 16 and 24 could be characterized as school dropouts, which amounted to 43 million people (cited by Hahn and Lefkowitz 1987; Kronick and Hargis 1990). Dropout rates in some locales may differ markedly from the national averages. In Boston, for example, dropping out of the public schools (as distinguished from losses due to transferring out of the school system) has recently risen above 45 percent (Camayd-Freixas and Horst 1987).

  4 In 1990, the percentage of persons ages 25 to 29 who had completed four years of high school or more was 85.7 percent, higher than the plotted “graduation ratio,” which is based on 17-year-olds (National Center for Education 1992, Table 8).

  5 Quoted in Clignet 1974, p. 38. See Chapter 22 for additional discussion.

  6 Tildsley 1936, p. 89.

  7 These numbers represent an unweighted mean of the six studies of ninth graders and the nine studies of students who were either seniors or graduates. When sample sizes are taken into account, the (weighted) means for the two groups are 104.2 and 105.5 (Finch 1946, Table I, pp. 28-29). This may understate the degree of difference between the dropout and the high school senior. Other studies indicate that within any given school, a statistical relationship existed between IQ and the likelihood of finishing high school. In urban areas, the size of the correlation itself could be substantial. In one of the best such studies, Lorge found for the city of New York in the 1930s that the correlation of IQ with highest completed grade was +.66 (Lorge 1942). Some of the individual studies of specific high schools conducted during that period reviewed by Finch also showed larger differences. But those studies tended to be subject to a number of technical errors. Even giving substantial weight to them, the difference between the mean IQ of the high school dropout and youths who made it to the senior year during the 1920s was considerably less than half a standard deviation (7.5 IQ points). Perhaps children who dropped out before the ninth grade had somewhat lower IQs, so that: the overall difference between diploma holders and dropouts was larger than the difference between ninth graders and twelfth graders. The data on this issue for the first half of the century are fragmentary, however.