FEATURE ARTICLE
The Role of Intelligence in Modern Society
Are social changes dividing us into intellectual haves and have-nots? The question pushed aside in the 1970s is back, and the issues are far from simple
Earl Hunt
Psychometric Views of Intelligence
In popular discussions of intelligence, including The Bell Curve, the term generally refers to scoring well on tests that have been developed to measure mental ability as psychologists have come to see it. I shall refer to this
emphasis on test scores as the psychometric view of intelligence. Its core belief is that individual differences in human cognition can be adequately measured by performance on intelligence tests, and that intelligence itself can therefore be defined by variations in test scores, across people. This notion was expressed most pungently when the psychologist Edwin Boring (1923), in a public debate with the columnist Walter Lippman, said that "intelligence is what the intelligence test measures." It turns out that that statement is not quite so arrogant or self-serving as it sounds. To see why we have to look at what intelligence tests are and how intelligence measures are inferred from test scores.
Although it is not always clear in our everyday use of language, scientists distinguish carefully between a conceptual variable and its operational definition?the way that it is measured. Physicists distinguish between mass as a concept and scale readings as data to be analyzed. In the best of situations there is a clearly understood link between the two. Physicists can provide a theory of the relation between a scale's movement and the mass of the object being weighed. The relation between the data for and
the concept of intelligence is not at all like the relation between scale readings and mass, because in psychometrics the concept is inferred from the measuring instrument, rather than having the measurement technique dictated
by the concept.
Most intelligence tests do not measure just one thing, in the sense that a scale measures only the gravitational attraction between an object and the earth. Instead, intelligence tests are made up of a number of component
subtests, in which people are asked to perform different cognitive tasks. The test score is supposed to measure the common thread that runs through performance on the subtests. For instance, the widely used Wechsler Adult
Intelligence Scale (WAIS) contains subtests that evaluate a person's vocabulary, short-term memory, arithmetical ability, world knowledge and several other specific skills. The Scholastic Achievement Test (SAT), which is a widely
used college-screening test, and the Armed Service Vocational Aptitude Battery (ASVAB), which is used to screen military recruits, are organized in somewhat
the same way. Instead of thinking of these tests as cognitive yardsticks measuring intelligence the way a real yardstick measures length, it is better to think of an intelligence test as a sort of mental track meet, in which
cognitive ability is inferred by combining subtest scores, just as athletic ability can be inferred by combining the scores in a decathlon.
This brings us to the question of how the subtest scores are to be combined. Although there is some variation from test to test, the formal basis for test combination is a statistical procedure called factor analysis. Suppose
that an intelligence test consists of K subtests. (To continue the analogy to the decathlon, K is usually 10 or 12.) A person's scores on the subtests can be represented by a K-dimensional vector. The
collective scores of all people in the group can be thought of as a swarm of points in a K-dimensional space. Factor analysis attempts to reduce the K-dimensional space to a smaller P-dimensional space,
where P is less than K and the axes defining the dimensions are orthogonal, or at right angles to one another. Unless the scores of two of the original tests are perfectly correlated, this always entails some loss of accuracy. The loss can be measured, so we can determine how much of the variation in the original K-space lies along a particular dimension in the reduced P-space.
To get an intuitive idea of factor analysis, imagine buying a hot dog with pimientos embedded in it. The hot dog is a three-dimensional object, so it takes three dimensions to specify the exact location of each pimiento. However, you can locate a pimiento reasonably accurately by saying where
it is along the long axis of the dog. In factor-analytic terms the pimientos are the data from each person, and the three dimensions of the hot dog represent the individual tests. The long axis of the hot dog would be the first factor to be extracted and would capture most of the variation between pimiento locations. If we apply factor analysis to test scores, instead of hot dogs, the first factor accounts for most of the variation between people just as the length of the hot dog accounts for most of the positioning of the pimientos. But instead of saying "length of hot dog," we say "general intelligence."
There are two objections to this argument. One is that when the data are reduced from the K-dimensional to the P-dimensional space, the orientation of the orthogonal dimensions in the P-dimensional
space is arbitrary. To see this, consider the hot-dog example again. Although locating pimientos can be reduced from a problem in three dimensions to a problem in one dimension, the one dimension does not have to point exactly
along the long axis of the hot dog. It could be rotated to any angle at all, excepting at a right angle to the long axis, and the pimientos could still be located with equal accuracy.
This fact led one critic of the idea of general intelligence, Stephen Jay Gould (1983) to argue that factor analysis is not an appropriate way of defining the variables underlying test scores, because one solution is statistically as a good as another. Gould was wrong. There are statistical methods (which were well known to specialists at the time) that make it possible to compare
the goodness of fit of one factor-analytic solution to another. When these methods are applied, investigators virtually always find a highly reliable first factor. The case for general intelligence, the unitary IQ score, is
far from trivial. However, there are alternative explanations for the data, based on the idea that there are different types of intelligence, even when one restricts oneself to the notion that intelligence is what the tests
measure. To understand what they are, we need to delve into factor analysis a bit more.
Suppose that the statistical variation in the data can be reduced from K dimensions (the original test space) to P orthogonal dimensions. This is only possible if the K original tests are positively correlated,
which they virtually always are. In this case there will also be a solution in M dimensions, where P is less than M is less than K, in which some of the M dimensions are not orthogonal to each other. (In psychological terms, if two abilities are statistically unrelated to each other, the dimensions representing them will be orthogonal.) Now, suppose that you had some theoretical reason to believe that the data from the original K tests had been generated by two or more underlying mental factors that were statistically related to each other. Returning to the athletic example, you might want to argue that decathlon scores were determined by the strength and speed of the athletes, and that there is a statistical relationship between strength and speed. Reasoning such as this is called specifying a factor structure for the underlying abilities. Gould claimed that psychometricians could not distinguish between alternative factor structures. Today they can.
During the 1970s the Swedish psychometrician Karl Jreskog developed a statistical technique for evaluating the fit of a multivariate data to an arbitrary, a priori specified factor structure. This made it possible to compare two proposals about the structure of intelligence to data, to see which theory best fit the facts. The new methods have been applied to a number of new data sets (notably Gustafsson 1984) and have become standard in evaluating models of intelligence. In a related, highly technical but very important volume, John Carroll (1993) used somewhat different methods to reanalyze a great many important data sets that have been collected over the past 60 years. The results of these independent analyses were quite consistent. Skipping over some details, human intellectual competence appears to divide along three dimensions. Following Raymond Cattell (1971) and John
Horn (1985), I shall refer to these dimensions as fluid intelligence (Gf), crystallized intelligence (Gc), and visual-spatial reasoning (Gv).
Cattell and Horn describe them as follows:
Fluid intelligence is the ability to develop techniques for solving problems that are new and unusual, from the perspective of the problem solver.
Crystallized intelligence is the ability to bring previously acquired, often culturally defined, problem-solving methods to bear on the current problem. Note that this implies both that the problem solver knows the methods
and recognizes that they are relevant in the current situation.
Visual-spatial reasoning is a somewhat specialized ability to use visual images and visual relationships in problem solving?for instance, to construct in your mind a picture of the sort of mental space that I described above in discussing factor-analytic studies. Interestingly, visual-spatial reasoning appears to be an important part of understanding mathematics.
Crystallized- and fluid-intelligence measures are substantially correlated. For instance, Horn reported a study in which Gf and Gc measures
were extracted from an analysis of the WAIS. The correlation between factors was 0.61. Such findings have led believers in just one intelligence to argue that Gf and Gc are simply different flavors of a general intelligence (IQ) factor. This argument cannot be answered one way or the other solely by looking at correlations between tests. However, it can be attacked by
stepping outside of factor analysis and looking at how Gf and Gc measures respond to manipulations that might change mental competence. It
turns out that they respond differently.
The most striking example is aging. Measures of Gf generally decrease from early adulthood onward, whereas Gc measures remain constant or even increase throughout most of the working years (Horn 1985; Horn and
Noll 1994). This is not surprising. Experience counts; most of the key leadership positions in our society are held by people over 40. On the other hand, middle-aged and older people do take longer than younger people to understand
new problem-solving methods and to deal with unfamiliar tasks. Age is not the only variable that can be shown to have different influences on fluid and crystallized intelligence. Alcoholism shows similar effects.
Since variables such as age, which is not itself a cognitive operation, have different influences on different types of tests, it follows that there cannot be just one ability underlying test performance. This argument moves
away from the psychometric tradition, which focuses only on test scores, and towards the cognitive-psychology approach to intelligence. As the name suggests, it is derived from a more general theory about what human thought is, so a word about the general theory is in order.
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