The Bell Curve: Intelligence and Class Structure in American Life by Richard J. Herrnstein, Charles A. Murray
Authors: Richard J. Herrnstein, Charles A. Murray
Tags: United States, General, science, Social Science, History, Psychology, Sociology, Political Science, Education, Life Sciences, Genetics & Genomics, Educational Psychology, Intelligence Levels - United States, Nature and Nurture, Intelligence Levels - Social Aspects - United States, Intellect, Intelligence Levels
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all, the relation between IQ scores and job performance is weak, and, second, whatever weak relationship there is depends not on general intellectual capacity but on the particular mental capacities or skills required by a particular job. 3
There have been several reasons for the broad acceptance of the conclusions President Bok drew. Briefly:
A Primer on the Correlation Coefficient
We have periodically mentioned the “correlation coefficient” without saying much except that it varies from −1 to +1. It is time for a bit more detail, with even more to be found in Appendix 1. As in the case of standard deviations, we urge readers who shy from statistics to take the few minutes required to understand the concept. The nature of “correlation” will be increasingly important as we go along.
A correlation coefficient represents the degree to which one phenomenon is linked to another. Height and weight, for example, have a positive correlation (the taller, the heavier, usually). A positive correlation is one that falls between zero and +1, with +1 being an absolutely reliable, linear relationship. A negative correlation falls between O and −1, with −1 also representing an absolutely reliable, linear relationship, but in the inverse direction. A correlation of O means no linear relationship whatsoever. 4
A crucial point to keep in mind about correlation coefficients, now and throughout the rest of the book, is that correlations in the social sciences are seldom much higher than .5 (or lower than −.5) and often much weaker—because social events are imprecisely measured and are usually affected by variables besides the ones that happened to be included in any particular body of data. A correlation of .2 can nevertheless be “big” for many social science topics. In terms of social phenomena, modest correlations can produce large aggregate effects. Witness the prosperity of casinos despite the statistically modest edge they hold over their customers.
Moderate correlations mean many exceptions.
We all know people who do not seem all that smart but who handle their jobs much more effectively than colleagues who probably have more raw intelligence. The correlations between IQ and various job-related measures are generally in the .2 to .6 range. Throughout the rest of the book, keep the following figure in mind, for it is what a highly significant correlation in the social sciences looks like. The figure uses actual data from a randomly selected 1 percent of a nationally representative sample, using two variables that are universally acknowledged to have a large and socially important relationship, income and education, with the line showing the expected change in income for each increment in years of education. 5 For this sample, the correlation was a statistically significant .33, and the expected value of an additional year of education was an additional $2,800 in family income—a major substantive increase. Yet look at hownumerous are the exceptions; note especially how people with twelfth-grade educations are spread out all along the income continuum.
For virtually every topic we will be discussing throughout the rest of the book, a plot of the raw data would reveal as many or more exceptions to the general statistical relationship, and this must always be remembered in trying to translate the general rule to individuals.
The variation among individuals that lies behind a significant correlation coefficient
The exceptions associated with modest correlations mean that a wide range of IQ scores can be observed in almost any job, including complex jobs such as engineer or physician, a fact that provides President Bok and other critics of the importance of IQ with an abundant supply of exceptions to any general relationship. The exceptions do not invalidate the importance of a statistically significant correlation.
Restriction of range.
In any particular job setting, there is a restricted range of
There have been several reasons for the broad acceptance of the conclusions President Bok drew. Briefly:
A Primer on the Correlation Coefficient
We have periodically mentioned the “correlation coefficient” without saying much except that it varies from −1 to +1. It is time for a bit more detail, with even more to be found in Appendix 1. As in the case of standard deviations, we urge readers who shy from statistics to take the few minutes required to understand the concept. The nature of “correlation” will be increasingly important as we go along.
A correlation coefficient represents the degree to which one phenomenon is linked to another. Height and weight, for example, have a positive correlation (the taller, the heavier, usually). A positive correlation is one that falls between zero and +1, with +1 being an absolutely reliable, linear relationship. A negative correlation falls between O and −1, with −1 also representing an absolutely reliable, linear relationship, but in the inverse direction. A correlation of O means no linear relationship whatsoever. 4
A crucial point to keep in mind about correlation coefficients, now and throughout the rest of the book, is that correlations in the social sciences are seldom much higher than .5 (or lower than −.5) and often much weaker—because social events are imprecisely measured and are usually affected by variables besides the ones that happened to be included in any particular body of data. A correlation of .2 can nevertheless be “big” for many social science topics. In terms of social phenomena, modest correlations can produce large aggregate effects. Witness the prosperity of casinos despite the statistically modest edge they hold over their customers.
Moderate correlations mean many exceptions.
We all know people who do not seem all that smart but who handle their jobs much more effectively than colleagues who probably have more raw intelligence. The correlations between IQ and various job-related measures are generally in the .2 to .6 range. Throughout the rest of the book, keep the following figure in mind, for it is what a highly significant correlation in the social sciences looks like. The figure uses actual data from a randomly selected 1 percent of a nationally representative sample, using two variables that are universally acknowledged to have a large and socially important relationship, income and education, with the line showing the expected change in income for each increment in years of education. 5 For this sample, the correlation was a statistically significant .33, and the expected value of an additional year of education was an additional $2,800 in family income—a major substantive increase. Yet look at hownumerous are the exceptions; note especially how people with twelfth-grade educations are spread out all along the income continuum.
For virtually every topic we will be discussing throughout the rest of the book, a plot of the raw data would reveal as many or more exceptions to the general statistical relationship, and this must always be remembered in trying to translate the general rule to individuals.
The variation among individuals that lies behind a significant correlation coefficient
The exceptions associated with modest correlations mean that a wide range of IQ scores can be observed in almost any job, including complex jobs such as engineer or physician, a fact that provides President Bok and other critics of the importance of IQ with an abundant supply of exceptions to any general relationship. The exceptions do not invalidate the importance of a statistically significant correlation.
Restriction of range.
In any particular job setting, there is a restricted range of
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