The Bell Curve: Intelligence and Class Structure in American Life
Page 80
In the Ree and Earles study, over all eighty-nine occupational schools, the average value of this square correlation was 58 percent (which corresponds to a correlation of .76). g, in other words, accounted for almost 60 percent of the observed variation in school grades in the average military course, once the results were corrected for range restriction. Even without a correction for range restriction, g accounted for over 20 percent of the variance in school grades on the average (corresponding to a correlation of .45).
27 Welsh, Watson, and Ree 1990.
28 Jones 1988. A similar analysis was performed for job performance but, because of the expense of obtaining special performance measures,’with a much smaller sample (1,545) spread across just eight enlisted job specialties (Ree and Earles 1991). The correlations with g in this study did not reach the extraordinarily high levels of predictiveness as for school grades, and the other cognitive factors were relatively more important for job performance than for school grades—points to which we shall return. But combining the results with the previously cited job performance study of air force personnel (Office of the Assistant Secretary of Defense for Force Management and Personnel 1989), the job predictiveness of AFQT for the specialties is correlated above .9 with the job predictiveness of g. Using the highest of the various correlations between job performance measures and g, the product-moment correlation is .97 and the Spearman rank-order correlation is .93. In other words, in predicting job performance, at least for these jobs and these performance tests, the validity of an AFQT score is virtually entirely explained by how well it measures g, per se.
29 Thorndike 1986. The comparison is between the predictiveness of the first factor extracted by factor analysis of the five cognitive subtests of GATB versus the regression-weighted subtest scores themselves, for cross-validating samples of at least fifty workers in each of the twenty-eight occupations.
30 Hawk 1986; Jensen 1980, 1986; Linn 1986.
31 For the linear relationship of cognitive ability, see Schmidt, Ones, and Hunter 1992. For the nonlinear relationship of job experiences see Blankenship and Taylor 1938; Ghiselli and Brown 1947; Taylor and Smith 1956.
32 Hawk 1970; Hunter and Schmidt 1982.
33 Humphreys 1968, 1973; Wilson 1983.
34 Seep. 66.
35 Butler and McCauley 1987.
36 McDaniel, Schmidt, and Hunter 1986.
37 Schmidt et al. 1988.
38 Maier and Hiatt 1985.
39 This story echoes the mixed findings for the learning of simple tasks in the psychological laboratory. Depending on which measures are used to predict performance and which tasks are being predicted, one can expect either to see convergence of performance with practice, or no convergence, or even divergence under some circumstances. See Ackermann 1987.
40 Schmidt et al. 1988. No data have yet tested the possibility that productivity diverges (the advantage enjoyed by the smarter employee increases with experience) in very-high-complexity jobs.
41 See also Schmidt et al. 1984.
42 See the discussion in note 15.
43 Burke and Frederick 1984; Hunter and Schmidt 1982; Hunter, Schmidt, and Judiesch 1990; Schmidt and Hunter 1983; Weekley et al. 1985. In the technical literature, the standard deviation of productivity measured in dollars is represented as SDy and has generally been estimated to average, over many different occupations, .4 times the average wage for the job. The corresponding figure as a proportion of the value of the average worker output is .2. Methods for estimating these distributions are discussed in the cited references, but they include such techniques as supervisor ratings of the dollar costs of replacing workers at various points in the distribution of workers, cost accounting of worker product, and scores on proficiency tests and at work sample stations.
44 Becker and Huselid 1992.
45 The more contemporary estimate would place this value at about $16,000 rather than $8,000. All the other dollar estimates of the benefits of testing mentioned in this section could similarly be doubled.
46 Hunter, Schmidt, and Judiesch 1990.
47 We use rounds numbers to make the calculations easy to follow, but these are in fact close to the current medians.
48 Hunter, Schmidt, and Judiesch 1990.
49 25,000 × .15 = 3,750; 100,000 × .5 = 50,000; 50,000/3,750 = 13.33.
50 100,000 × .5 × .6 = 30,000; 25,000 × .15 × .2 = 750.
51 There is another point illustrated by this exercise. Recall that a validity (correlation) “explains” only the amount of variance equal to its square; hence a validity of .4 explains only 16 percent of the variance, and this offers a temptation to dismiss the importance of intelligence as being of negligible economic consequences. And yet when we calculated the gains to be realized from an ability test that is less than perfectly valid as a predictor of proficiency, we multiplied the gain from a perfect test by the validity, not by the square of the validity. When trying to estimate how much of the value of a perfect selection procedure is captured by an imperfect substitute, the validity of the imperfect test is equal to the proportion of the value that is captured by it. A test with a validity of .4 captures 40 percent of the value that would be realized from a perfect test, even though it explains only 16 percent of the variance. Readers interested in the mathematical proof, which was first derived in the 1940s, will find it in Hunter and Schmidt 1982.
52 Two of the classic discussions of the conditions under which testing pays off are Brogden 1949 and Cronbach and Gleser 1965.
53 These correlations cover the empirical range in two senses. First, they bracket the values found in the technical literature dealing with the predictiveness of intelligence. Second, they bracket the various occupations, as described by Hunter, Schmidt, and their colleagues. More complex jobs have higher correlations between intelligence and proficiency, but almost all common occupations fall in the range between .2 and .6. The graphs assume normality of the predictor and outcome variables and a linear relation between them. None of these assumptions needs to be strictly met in order for the figure to give at least an approximately correct account of the relationships, nor are there any known deviations from normality or linearity that would materially alter the account.
54 We estimate the percentile values by assuming that proficiencies are normally distributed.
55 Hunter and Hunter 1984; Schmidt, Mack, and Hunter 1984.
56 Hartigan and Wigdor 1989; Hunter and Hunter 1984.
57 The data for the following description come from Herrnstein, Belke, and Taylor 1990.
58 Hunter 1979.
59 Murphy 1986.
Chapter 4
1 Juhn, Murphy, and Pierce 1990; Katz and Murphy 1900.
2 Twenty-three percent for sixteen or more years of education versus 11 percent for twelve or fewer years, according to Katz and Murphy 1990.
3 Freeman 1976.
4 The wage decline in the 1970s for highly educated workers and in the 1980s for less educated workers could conceivably have been due to declines in the quality of college education in the earlier period and in primary and high school education in the later period or in corresponding changes in the skills of people at those levels of education, as reflected, for example, in the decline of SAT scores (Bishop 1989). Economists assessing this hypothesis have concluded that it could not have played a major role (see Blackburn, Bloom, and Freeman 1990; Juhn, Murphy, and Pierce 1990; Katz and Murphy 1990).
5 The dramatic growth of female work force participation would necessitate complex modeling to address for the labor force as a whole the question here dealt with just for men.
6 Comparing men with sixteen or more years in school to those with fewer than twelve years gives a 26.8 percent differential and to those with twelve years in school gives 29.8. Since each category is being compared to its own baseline, this calculation understates the size of the change in actual real wages.
7 In a slightly different approach to the data, Kevin Murphy and Finis Welch, restricting the
analysis to white workers, also found that more education had a shrinking wage benefit from 1963 to 1979, followed by a steeply rising benefit, but only for new workers. For experienced workers, the wage benefit for education did not decline during the earlier period, then rose more modestly thereafter. Work experience, in other words, dampened the wage benefit for education from the 1970s to the 1980s (Murphy and Welch 1989. See also Murphy and Welch 1993a, 1993b).
8 That intelligence is confounded with educational attainment is hardly a new idea. See Arrow 1973; Herrnstein 1973; Jencks et al. 1972; Sewell and Hauser 1975.
9 Juhn, Murphy, and Pierce 1990; Katz and Murphy 1990.
10 Public employment shielded workers, especially female workers, from the rising wage premium for education in the 1980s and the rising premium for unmeasured individual characteristics, presumably including intelligence. In the upper half of the wage distribution for highly educated workers, the ratio of federal to private wages declined from 1979 to 1988, even after corrections for race, age, and region of the country (Cutler and Katz 1991). The decline was especially large for women, perhaps because educated women were finding relatively more lucrative alternatives outside the government. For less educated workers in the lower half of the wage distribution, the ratio of federal to private wages rose during that interval, again especially for women. For state and local (as distinguished from federal) public employees, the rise in the ratio of public to private wages for less educated workers was larger still.
11 “Residual” in the regression analysis sense. After accounting for the effects of education, experience, gender, and their various interactions, a certain amount of real wage variance remains unexplained. This is the residual that has been growing.
12 Juhn, Murphy, and Pierce, 1990; Katz and Murphy 1990; Levy and Murnane 1992.
13 Juhn, Murphy, and Pierce 1990.
14 Diligence, or conscientiousness, is one noncognitive trait that appears to earn a wage premium (Schmidt and Ones 1992). Drive, ambition, and sociability have been examined by Filer (1981). None of these has been as well established as cognitive ability, nor do they appear to be as significant in their economic effects.
15 Blackburn and Neumark 1991.
16 Blackburn and Neumark 1991. This study used the National Longitudinal Survey of Youth (NLSY), a database described in the Introduction to Part II.
17 Lest we convey the false impression that we are suggesting that education per se is immaterial, once intelligence is taken account of, we note two ingenious studies by economists Joshua Angrist and Alan Krueger (Angrist and Krueger 1991a, 1991b). They examined wages in relation to schooling for school dropouts born at different times of year and for people with varying draft lottery numbers. Dropouts in many states must remain in school until the end of the academic year in which they reach a given age. For people who want to drop out as soon as possible, those born in, say, October will spend a year in school more than those born in January. Likewise, during the Vietnam era, people whose only reason for staying in school was to avoid the draft would get more schooling if they had low lottery numbers, making them more likely to be drafted, than if they had high numbers. In both populations, the extra schooling showed a wage benefit later on. These findings show effects of education above and beyond personal traits like intelligence, if we assume that intelligence is uncorrelated with the month in which one is born or the lottery number. In fact, human births are moderately seasonal, and the seasonality differs across races, ethnic groups, and socioeconomic status, which may mean that births are seasonal with respect to average intelligence (Lam and Miron 1991). No such complication confounds the study using lottery numbers. Even so, the generality of these findings for populations other than school dropouts and for people who stayed in school only to avoid being drafted remains to be established.
18 Again from the NLSY. The sample chosen for this particular analysis was at least 30 years old, had been out of school for at least a year, and had worked fifty-two weeks in 1989 (from Top Decile Analysis). The median (as distinguished from the mean) difference in annual wages and salaries was much smaller: $3,000. A bulge of very-high-income individuals in these occupations among those with high IQs explains the gap between the mean and the median. For example, in these occupations, among those in the top decile of IQ, the 97.5th percentile of annual income was over $180,000; for those not in the top IQ decile, the corresponding income was $62,186.
19 The median wage for each occupation is the wage that has as many wages above it as below it in the distribution of wages in the occupation. A median expresses an average that is relatively insensitive to extreme values at either end.
20 A high IQ is also worth extra income outside the high-IQ occupations as we defined them. The wages and salaries of people not in the high-IQ occupations but with an IQ in the top 10 percent earned over $11,000 more in 1989 (again in 1990 dollars) than those with IQs below the top decile. The median family income of those in the top IQ decile who did not enter the high-IQ professions was $49,000, putting them at the 72d percentile of family incomes.
21 Solon 1992; Zimmerman 1992. Women are not usually included in these studies because of the analytic complications arising in the recent dramatic changes in their work force participation. The correlation is even higher if the predictor of the son’s income is the family income rather than just the father’s (Solon 1992). These estimates of the correlation between father and son income represent a new finding. Until recently, specialists mostly agreed that income was not a strong family trait, certainly not like the family chin or the baldness that passes on from generation to generation, and not even as enduring as the family nest egg. They had concluded that the correlation between fathers and sons in income was between .1 and .2—very low. Expert opinion has, however, been changing. The older estimates of the correlation between fathers’ and sons’ incomes, it turns out, were plagued by two familiar problems that artificially depress correlation coefficients. First, the populations used for gathering the estimates were unrepresentative. One large study, for example, used only high school graduates, which no doubt restricted the range of IQ scores (Sewell and Hauser 1975). Another problem has been measurement error—in the case of intergenerational comparisons of income, measurement error introduced by basing the analysis on a single year’s income. Averaging income over a few years reduces this source of error. Now, using the nationally representative, longitudinal data in the National Longitudinal Survey (NLS) and the Panel Study of Income Dynamics (PSID), economists have found the correlations of .4 to .5 reported in the text.
22 Solon 1992. For comparable estimates for Great Britain, see Atkinson, Maynard, and Trinder 1983.
23 U.S. Bureau of the Census 1991b, Table 32.
24 Herrnstein 1973, pp. 197-198.
25 For reviews of the literature as of 1980, see Bouchard 1981; Plomin and DeFries 1980. For more recent analyses, on which we base the upper bound estimate of 80 percent, see Bouchard et al. 1990; Pedersen et al. 1992.
26 Plomin and Loehlin 1989.
27 The proper statistical measure of variation is the standard deviation squared, which is called the variance.
28 Heritability is a concept in quantitative genetics; for a good textbook, see Falconer 1989.
29 Social scientists will recognize the heritability question as being akin to the general statistical model of variance analysis.
30 Plomin and Loehlin 1989.
31 Bouchard et al. 1990.
32 Estimating heritabilities from any relationship other than for identical twins is inherently more uncertain because the modeling is more complex, involving the estimation of additional sources of genetic variation, such as assortative mating (about which more below) and genetic dominance and epistasis. See Falconer 1989.
33 For a broad survey of all kinds of data published before 1981, set into several statistical models, the best fitting of which gave .51 as the estimate of IQ heritability, see Chipuer, Rovine, and Plomin 1990. Most of the
data are from Western countries, but a recent analysis of Japanese data, based on a comparison of identical and fraternal twin correlations in IQ, yields a heritability estimate of .58 (Lynn and Hattori 1990).
34 The extraordinary discrepancy between what the experts say in their technical publications on this subject and what the media say the experts say is well described in Snyderman and Rothman 1988.
35 Cyphers et al. 1989; Pedersen et al. 1992.
36 Cyphers et al. 1989; Pedersen et al. 1992.
37 Based primarily on a large study of Swedish identical and fraternal twins followed into late adulthood (Pedersen et al. 1992).
38 Plomin and Bergeman 1987; Rowe and Plomin 1981.
39 IQ is not the only trait with a biological component that varies across socioeconomic strata. Height, head size, blood type, age at menarche, susceptibility to various congenital diseases, and so on are some of the other traits for which there is evidence of social class differences even in racially homogeneous societies (for review, see Mascie-Taylor 1990).