It is a variable that summarizes positive correlations among different cognitive tasks, reflecting the fact that an individual's performance on one type of cognitive task tends to be comparable to that person's performance on other kinds of cognitive tasks. The g factor typically accounts for 4. He observed that children's performance ratings, across seemingly unrelated school subjects, were positively correlated, and reasoned that these correlations reflected the influence of an underlying general mental ability that entered into performance on all kinds of mental tests. Spearman suggested that all mental performance could be conceptualized in terms of a single general ability factor, which he labeled g, and a large number of narrow task- specific ability factors.

Today's factor models of intelligence typically represent cognitive abilities as a three- level hierarchy, where there are a large number of narrow factors at the bottom of the hierarchy, a handful of broad, more general factors at the intermediate level, and at the apex a single factor, referred to as the g factor, which represents the variance common to all cognitive tasks. Traditionally, research on g has concentrated on psychometric investigations of test data, with a special emphasis on factor analytic approaches.

However, empirical research on the nature of g has also drawn upon experimental cognitive psychology and mental chronometry, brain anatomy and physiology, quantitative and molecular genetics, and primate evolution. It has a number of other biological correlates, including brain size. It is also a significant predictor of individual differences in many social outcomes, particularly in education and employment.

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The most widely accepted contemporary theories of intelligence incorporate the g factor. All the correlations are positive, a phenomenon referred as the positive manifold.

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The bottom row shows the g loadings of each performance measure. The subtests are Vocabulary, Similarities, Information, Comprehension, Picture arrangement, Block design, Arithmetic, Picture completion, Digit span, Object assembly, and Digit symbol.

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The bottom row shows the g loadings of each subtest. Specific domains assessed by tests include mathematical skill, verbal fluency, spatial visualization, and memory, among others. However, individuals who excel at one type of test tend to excel at other kinds of tests, too, while those who do poorly on one test tend to do so on all tests, regardless of the tests' contents. This finding has since been replicated numerous times.

The consistent finding of universally positive correlation matrices of mental test results (or the . Spearman referred to this common factor as the general factor, or simply g.

One can only speak of an individual's standing on g (or other factors) compared to other individuals in a relevant population. These correlations are known as g loadings. An individual test taker's g factor score, representing his or her relative standing on the g factor in the total group of individuals, can be estimated using the g loadings. Full- scale IQ scores from a test battery will usually be highly correlated with g factor scores, and they are often regarded as estimates of g.

For example, the correlations between g factor scores and full- scale IQ scores from David Wechsler's tests have been found to be greater than . Raven's Progressive Matrices is among the tests with the highest g loadings, around .

Tests of vocabulary and general information are also typically found to have high g loadings. For example, in the forward digit span test the subject is asked to repeat a sequence of digits in the order of their presentation after hearing them once at a rate of one digit per second. The backward digit span test is otherwise the same except that the subject is asked to repeat the digits in the reverse order to that in which they were presented. The backward digit span test is more complex than the forward digit span test, and it has a significantly higher g loading.

Similarly, the g loadings of arithmetic computation, spelling, and word reading tests are lower than those of arithmetic problem solving, text composition, and reading comprehension tests, respectively. Tests that have the same difficulty level, as indexed by the proportion of test items that are failed by test takers, may exhibit a wide range of g loadings. For example, tests of rote memory have been shown to have the same level of difficulty but considerably lower g loadings than many tests that involve reasoning.

Several explanations have been proposed. However, he thought that the best indicators of g were those tests that reflected what he called the eduction of relations and correlates, which included abilities such as deduction, induction, problem solving, grasping relationships, inferring rules, and spotting differences and similarities.

Spearman hypothesized that g was equivalent with . However, this was more of a metaphorical explanation, and he remained agnostic about the physical basis of this energy, expecting that future research would uncover the exact physiological nature of g. According to Jensen, the g factor represents a . Wechsler similarly contended that g is not an ability at all but rather some general property of the brain. Jensen hypothesized that g corresponds to individual differences in the speed or efficiency of the neural processes associated with mental abilities.

Thorndike and Godfrey Thomson, proposes that the existence of the positive manifold can be explained without reference to a unitary underlying capacity. According to this theory, there are a number of uncorrelated mental processes, and all tests draw upon different samples of these processes. The intercorrelations between tests are caused by an overlap between processes tapped by the tests. Similarly, high correlations between different batteries could be due to them measuring the same set of abilities rather than the same ability. Based on the sampling theory, one might expect that related cognitive tests share many elements and thus be highly correlated. However, some closely related tests, such as forward and backward digit span, are only modestly correlated, while some seemingly completely dissimilar tests, such as vocabulary tests and Raven's matrices, are consistently highly correlated.

Another problematic finding is that brain damage frequently leads to specific cognitive impairments rather than a general impairment one might expect based on the sampling theory. Thus there is no single process or capacity underlying the positive correlations between tests. During the course of development, the theory holds, any one particularly efficient process will benefit other processes, with the result that the processes will end up being correlated with one another. Thus similarly high IQs in different persons may stem from quite different initial advantages that they had.

Each small oval is a hypothetical mental test. The blue areas correspond to test- specific variance (s), while the purple areas represent the variance attributed to g. Factor analysis is a family of mathematical techniques that can be used to represent correlations between intelligence tests in terms of a smaller number of variables known as factors. The purpose is to simplify the correlation matrix by using hypothetical underlying factors to explain the patterns in it. When all correlations in a matrix are positive, as they are in the case of IQ, factor analysis will yield a general factor common to all tests.

The general factor of IQ tests is referred to as the g factor, and it typically accounts for 4. IQ test batteries. Initially, he developed a model of intelligence in which variations in all intelligence test scores are explained by only two kinds of variables: first, factors that are specific to each test (denoted s); and second, a g factor that accounts for the positive correlations across tests. This is known as Spearman's two- factor theory.