Psychometric theories have generally sought to understand the structure of intelligence: What form does it take, and what are its parts, if any? Such theories have generally been based on and established by data obtained from tests of mental abilities, including analogies (e.g., lawyer is to client as doctor is to __), classifications (e.g., Which word does not belong with the others? robin, sparrow, chicken, blue jay), and series completions (e.g., What number comes next in the following series? 3, 6, 10, 15, 21,_).

Psychometric theories are based on a model that portrays intelligence as a composite of abilities measured by mental tests. This model can be quantified. For example, performance on a number-series test might represent a weighted composite of number, reasoning, and memory abilities for a complex series. Mathematical models allow for weakness in one area to be offset by strong ability in another area of test performance. In this way, superior ability in reasoning can compensate for a deficiency in number ability.

One of the earliest of the psychometric theories came from the British psychologist Charles E. Spearman (1863–1945), who published his first major article on intelligence in 1904. He noticed what may seem obvious now—that people who did well on one mental-ability test tended to do well on others, while people who performed poorly on one of them also tended to perform poorly on others. To identify the underlying sources of these performance differences, Spearman devised factor analysis, a statistical technique that examines patterns of individual differences in test scores. He concluded that just two kinds of factors underlie all individual differences in test scores. The first and more important factor, which he labeled the “general factor,” or g, pervades performance on all tasks requiring intelligence. In other words, regardless of the task, if it requires intelligence, it requires g. The second factor is specifically related to each particular test. For example, when someone takes a test of arithmetical reasoning, his performance on the test requires a general factor that is common to all tests (g) and a specific factor that is related to whatever mental operations are required for mathematical reasoning as distinct from other kinds of thinking. But what, exactly, is g? After all, giving something a name is not the same as understanding what it is. Spearman did not know exactly what the general factor was, but he proposed in 1927 that it might be something like “mental energy.”

The American psychologist L.L. Thurstone disagreed with Spearman’s theory, arguing instead that there were seven factors, which he identified as the “primary mental abilities.” These seven abilities, according to Thurstone, were verbal comprehension (as involved in the knowledge of vocabulary and in reading), verbal fluency (as involved in writing and in producing words), number (as involved in solving fairly simple numerical computation and arithmetical reasoning problems), spatial visualization (as involved in visualizing and manipulating objects, such as fitting a set of suitcases into an automobile trunk), inductive reasoning (as involved in completing a number series or in predicting the future on the basis of past experience), memory (as involved in recalling people’s names or faces, and perceptual speed (as involved in rapid proofreading to discover typographical errors in a text).

Although the debate between Spearman and Thurstone has remained unresolved, other psychologists—such as Canadian Philip E. Vernon and American Raymond B. Cattell—have suggested that both were right in some respects. Vernon and Cattell viewed intellectual abilities as hierarchical, with g, or general ability, located at the top of the hierarchy. But below g are levels of gradually narrowing abilities, ending with the specific abilities identified by Spearman. Cattell, for example, suggested in Abilities: Their Structure, Growth, and Action (1971) that general ability can be subdivided into two further kinds, “fluid” and “crystallized.” Fluid abilities are the reasoning and problem-solving abilities measured by tests such as analogies, classifications, and series completions. Crystallized abilities, which are thought to derive from fluid abilities, include vocabulary, general information, and knowledge about specific fields. The American psychologist John L. Horn suggested that crystallized abilities more or less increase over a person’s life span, whereas fluid abilities increase in earlier years and decrease in later ones.

Most psychologists agreed that Spearman’s subdivision of abilities was too narrow, but not all agreed that the subdivision should be hierarchical. The American psychologist Joy Paul Guilford proposed a structure-of-intellect theory, which in its earlier versions postulated 120 abilities. In The Nature of Human Intelligence (1967), Guilford argued that abilities can be divided into five kinds of operation, four kinds of content, and six kinds of product. These facets can be variously combined to form 120 separate abilities. An example of such an ability would be cognition (operation) of semantic (content) relations (product), which would be involved in recognizing the relation between lawyer and client in the analogy problem above (lawyer is to client as doctor is to __). Guilford later increased the number of abilities proposed by his theory to 150.

Eventually it became apparent that there were serious problems with the basic approach to psychometric theory. A movement that had started by postulating one important ability had come, in one of its major manifestations, to recognize 150. Moreover, the psychometricians (as practitioners of factor analysis were called) lacked a scientific means of resolving their differences. Any method that could support so many theories seemed somewhat suspect. Most important, however, the psychometric theories failed to say anything substantive about the processes underlying intelligence. It is one thing to discuss “general ability” or “fluid ability” but quite another to describe just what is happening in people’s minds when they are exercising the ability in question. The solution to these problems, as proposed by cognitive psychologists, was to study directly the mental processes underlying intelligence and, perhaps, to relate them to the facets of intelligence posited by psychometricians.

The American psychologist John B. Carroll, in Human Cognitive Abilities (1993), proposed a “three-stratum” psychometric model of intelligence that expanded upon existing theories of intelligence. Many psychologists regard Carroll’s model as definitive, because it is based upon reanalyses of hundreds of data sets. In the first stratum, Carroll identified narrow abilities (roughly 50 in number) that included the seven primary abilities identified by Thurstone. According to Carroll, the middle stratum encompassed broad abilities (approximately 10) such as learning, retrieval ability, speediness, visual perception, fluid intelligence, and the production of ideas. The third stratum consisted solely of the general factor, g, as identified by Spearman. It might seem self-evident that the factor at the top would be the general factor, but it is not, since there is no guarantee that there is any general factor at all.

Both traditional and modern psychometric theories face certain problems. First, it has not been proved that a truly general ability encompassing all mental abilities actually exists. In The General Factor of Intelligence: How General Is It? (2002), edited by the psychologists Robert Sternberg (author of this article) and Elena Grigorenko, contributors to the edited volume provided competing views of the g factor, with many suggesting that specialized abilities are more important than a general ability, especially because they more readily explain individual variations in intellectual functioning. Second, psychometric theories cannot precisely characterize all that goes on in the mind. Third, it is not clear whether the tests on which psychometric theories are based are equally appropriate in all cultures. In fact, there is an assumption that successful performance on a test of intelligence or cognitive ability will depend on one’s familiarity with the cultural framework of those who wrote the test. In her 1997 paper “You Can’t Take It with You: Why Ability Assessments Don’t Cross Cultures,” the American psychologist Patricia M. Greenfield concluded that a single test may measure different abilities in different cultures. Her findings emphasized the importance of taking issues of cultural generality into account when creating abilities tests.