g factor (psychometrics)

The g factor (short for "general factor") is a construct developed in psychometric investigations of cognitive abilities. It is a summary measure that characterizes the all-positive correlations that empirical research has consistently found to exist between mental tests, regardless of the tests' contents. The g factor typically accounts for 40 to 50 percent of the variance in IQ test performance, and IQ test scores are often regarded as estimates of the individual's standing on the g factor.

The existence of the g factor was originally proposed by the English psychologist Charles Spearman in the early years of the 20th century. He observed that schoolchildren's grades across seemingly unrelated 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, the g factor, the one source of variance common to all tests.

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. While the existence of g as a statistical regularity is well-established and uncontroversial, there is no consensus as to what causes the positive correlations between tests.

Behavioral genetic research has established that the construct of g is highly heritable. 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 the world of work. The most widely accepted contemporary theories of intelligence incorporate the g factor. However, critics of g have contended that an emphasis on g is misleading and entails a devaluation of other important cognitive abilities.

Mental testing and g

Spearman's correlation matrix for six measures of school performance. All the correlations are positive, a phenomenon referred as the positive manifold.

	Classics	French	English	Math	Pitch	Music
Classics	-
French	.83	-
English	.78	.67	-
Math	.70	.67	.64	-
Pitch	.66	.65	.54	.45	-
Music	.63	.57	.51	.51	.40	-

Mental tests may be designed to measure different aspects of cognition. 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. The English psychologist Charles Spearman was the first to describe this phenomenon.^{[citation needed]} He observed that schoolchildren's grades across seemingly unrelated subjects were positively correlated. This finding has since been replicated numerous times. The consistent finding of universally positive correlation matrices of mental test results (or the "positive manifold"), despite large differences in tests' contents, has been described as "arguably the most replicated result in all psychology."

It is possible to construct a single common factor that can be regarded as a primary summary variable characterizing the correlations between different tests in a test battery. Spearman referred to this common factor as the general factor, or simply g.

Different tests in a test battery may correlate with (or "load onto") the g factor of the battery to different degrees. These correlations are known as g loadings. An individual test taker's g factor score can be estimated using the loadings. Full-scale IQ scores from a test battery will usually be highly correlated with g factor scores. For example, the correlations between g factor scores and full-scale IQ scores from Wechsler's tests have been found to be greater than .95. The g loadings of mental tests are always positive and range from slightly greater than zero to slightly less than unity. Raven's Progressive Matrices is among the tests with the highest g loadings, around .80. Tests of vocabulary and general information are also typically found to have high g loadings.

The complexity of tests and the demands they place on mental manipulation are related to the tests' 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. In contrast, test difficulty and g loadings are distinct concepts that may or may not be empirically related in any specific situation. 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.

Theories of g

While the existence of g as a statistical regularity is well-established and uncontroversial among experts, there is no consensus as to what causes the positive intercorrelations. Several explanations have been proposed.

Charles Spearman reasoned that correlations between tests reflected the influence of a common causal factor, a general mental ability that enters into performance on all kinds of mental tasks. He hypothesized that g was equivalent with "mental energy". However, this was more of a metaphorical explanation, and Spearman remained agnostic about the physical basis of this energy, expecting that future research would uncover the exact physiological nature of g.

Similarly to Spearman, Arthur Jensen has maintained that all mental tasks tap into g to some degree. Jensen has argued that g cannot be described in terms of the item characteristics or information content of tests, pointing out that very dissimilar mental tasks may have nearly equal g loadings. He has hypothesized that g corresponds to individual differences in the speed or efficiency of the neural processes associated with mental abilities.

Another theory holds that g is identical or nearly identical to working memory capacity. Among other evidence for this view, some studies have found factors representing g and working memory to be perfectly correlated. However, in a meta-analysis the correlation was found to be considerable lower.

The so-called sampling theory of g, originally developed by E.L. Thorndike and Godfrey Thomson, proposes that the existence of the positive manifold can be explained without reference to a unitary underlying capacity. According to the 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. Thus, the positive manifold arises due to a measurement problem, that is, an inability to measure more fine-grained, presumably uncorrelated mental processes.

The mutualist theory of g proposes that cognitive processes are initially uncorrelated, but that the positive manifold arises during individual development due to mutual beneficial relations between cognitive processes. 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.

Factor structure

An illustration of Spearman's two-factor intelligence theory. 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 mathematical technique that can be used to represent correlations between intelligence tests in terms of a smaller number of variables, or 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 40 to 50 percent of the variance in IQ test batteries.

Charles Spearman developed factor analysis in order to study correlations between tests. 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; and second, a g factor that accounts for the positive correlations across tests. This is known as Spearman's two-factor theory. Later research based on more diverse test batteries than those used by Spearman demonstrated that g alone could not account for all correlations between tests. Specifically, it was found that even after controlling for g, some tests were still correlated with each other. This led to the postulation of group factors that represent variance that groups of tests with similar task demands (e.g., verbal, spatial, numerical, or mechanical) have in common in addition to the shared g variance.

Today's theories of the factor structure of cognitive abilities usually incorporate a common factor labeled g, group factors, and narrow ability factors. There's a broad contemporary consensus that cognitive variance between people can be conceptualized at three hierarchical levels, distinguished by their degree of generality: at the lowest, least general level there are a large number of narrow first-order factors; at a higher level, there are a relatively small number – somewhere between five and ten – of broad (i.e., more general) second-order factors; and at the apex, there's a single third-order factor, g, the general factor common to all tests.

A g factor can be computed from a correlation matrix of test results using several different methods. These include exploratory factor analysis, principal components analysis (PCA), and confirmatory factor analysis. Different factor-extraction methods produce highly consistent results, although PCA has sometimes been found to produce inflated estimates of the influence of g on test scores.

"Indifference of the indicator"

Spearman proposed the principle of the indifference of the indicator, according to which the precise content of intelligence tests is unimportant for the purposes of identifying g, because g enters into performance on all kinds of tests. Following Spearman, Arthur Jensen has more recently argued that a g factor extracted from one test battery will always be the same, within the limits of measurement error, as that extracted from another battery, provided that the batteries are large and diverse. According to this view, every mental test, no matter how distinctive, contains some g. Thus a composite score of a number of different tests will have relatively more g than any of the individual test scores, because the g components cumulate into the composite score, while the uncorrelated non-g components will cancel each other out. Theoretically, the composite score of an infinitely large, diverse test battery would, then, be a perfect measure of g.

In contrast, L.L. Thurstone argued that a g factor extracted from a test battery reflects the average of all the abilities called for by the particular battery, and that g therefore varies from a battery to another and "has no fundamental psychological significance." Along similar lines, John Horn argued that g factors are meaningless because they are not invariant across test batteries, maintaining that correlations between different ability measures arise because it is difficult to define a human action that depends on just one ability.

To show that different batteries reflect the same g, one must administer several test batteries to the same individuals, extract g factors from each battery, and show that the factors are highly correlated. Wendy Johnson and colleagues have published two such studies. The first found that the correlations between g factors extracted from three different batteries correlated at .99, .99, and 1.00, supporting the hypothesis that g factors from different batteries are the same and that the identification of g is not dependent on the specific abilities assessed. The second study found that g factors derived from four of five test batteries correlated at between .95–1.00, while the correlations ranged from .79 to .96 for the fifth battery, the Cattell Culture Fair Intelligence Test (the CFIT). They attributed the somewhat lower correlations with the CFIT battery to its lack of content diversity for it contains only matrix-type items, and interpreted the findings as supporting the contention that g factors derived from different test batteries are the same provided that the batteries are diverse enough. The results suggest that the same g can be consistently identified from different test batteries.

Mental chronometry and g

Main article: Mental chronometry

Elementary cognitive tasks (ECTs) also correlate strongly with g. ECTs are, as the name suggests, simple tasks that apparently require very little intelligence, but still correlate strongly with more exhaustive intelligence tests. Determining whether a light is red or blue and determining whether there are four or five squares drawn on a computer screen are two examples of ECTs. The answers to such questions are usually provided by quickly pressing buttons. Often, in addition to buttons for the two options provided, a third button is held down from the start of the test. When the stimulus is given to the subject, he removes his hand from the starting button to the button of the correct answer. This allows the examiner to determine how much time was spent thinking about the answer to the question (reaction time, usually measured in small fractions of second), and how much time was spent on physical hand movement to the correct button (movement time). Reaction time correlates strongly with g, while movement time correlates less strongly. ECT testing has allowed quantitative examination of hypotheses concerning test bias, subject motivation, and group differences. By virtue of their simplicity, ECTs provide a link between classical IQ testing and biological inquiries such as fMRI studies.

Spearman's law of diminishing returns

A number of researchers have suggested that the proportion of variation accounted for by g may not be uniform across all individuals within a population. Spearman's law of diminishing returns (SLDR), also termed the ability differentiation hypothesis, predicts that the positive correlations among different cognitive abilities are weaker among more intelligent subgroups of individuals. More specifically, SLDR predicts that the g factor will account for a smaller proportion of individual differences in cognitive tests scores at higher scores on the g factor.

SLDR was originally proposed by Charles Spearman, who reported that the average correlation between 12 cognitive ability tests was .466 in 78 normal children, and .782 in 22 "defective" children. Detterman and Daniel rediscovered this phenomenon in 1989. They reported that for subtests of both the WAIS and the WISC, subtest intercorrelations decreased monotonically with ability group, ranging from approximately an average intercorrelation of .7 among individuals with IQs less than 78 to .4 among individuals with IQs greater than 122.

SLDR has been replicated in a variety of child and adult samples who have been measured using broad arrays of cognitive tests. The most common approach has been to divide individuals into multiple ability groups using an observable proxy for their general intellectual ability, and then to either compare the average interrelation among the subtests across the different groups, or to compare the proportion of variation accounted for by a single common factor, in the different groups. However, as both Deary et al. (1996) and Tucker-Drob (2009) have pointed out, dividing the continuous distribution of intelligence into an arbitrary number of discrete ability groups is less than ideal for examining SLDR. Tucker-Drob (2009) extensively reviewed the literature on SLDR and the various methods by which it had been previously tested, and proposed that SLDR could be most appropriately captured by fitting a common factor model that allows the relations between the factor and its indicators to be nonlinear in nature. He applied such a factor model to a nationally representative data of children and adults in the United States and found consistent evidence for SLDR. For example, Tucker-Drob (2009) found that a general factor accounted for approximately 75% of the variation in seven different cognitive abilities among very low IQ adults, but only accounted for approximately 30% of the variation in the abilities among very high IQ adults.

Biological and genetic correlates of g

Main article: Heritability of IQ

The g-load of a test correlates with its heritability which Jensen has seen as supporting a genetic g as opposed to it being a statistical artifact. The degree of heritability can be estimated by, for example, examining how much inbreeding depression from cousin marriages affect a test or how much siblings differ from one another on a test.

g has a large number of biological correlates. Strong correlates include mass of the prefrontal lobe, overall brain mass, and glucose metabolization rate within the brain, and cortical thickness. g correlates less strongly, but significantly, with overall body size. There is conflicting evidence regarding the correlation between g and peripheral nerve conduction velocity, with some reports of significant positive correlations, and others of no or even negative correlations.^{[citation needed]} Some research has found the g completely mediates the relation between IQ and cortical thickness. Current research suggests that the heritability of g is approximately 0.85 - even higher than that for IQ itself - so the heritability of most test performance is thus attributable to g.

Brain size has long been known to be correlated with g. In 2001, an MRI study on twins showed that frontal gray matter volume was highly significantly correlated with g and highly heritable. A related study has reported that the correlation between brain size (reported to have a heritability of 0.85) and g is 0.4, and that correlation is mediated entirely by genetic factors. g has been observed in mice as well as humans.

g is connected with multiple genetic and mental disorders. Patients suffering from schizophrenia usually score lower on intelligence tests than their peers, after controlling for confounding factors such as socioeconomic status. Their intelligence scores tend to be lower, compared to general population (by as much as 15 points or 1 standard deviation), even before the onset of the disease. Many chromosomal abnormalities, such as Down Syndrome, 1q21.1 deletion syndrome, Jacobsen syndrome, and others, result in decreased intellectual abilities. A 2010 study found a negative correlation between g and the total length of certain rare deletions in human genome, suggesting that a substantial share of the variance in intelligence (as much as 45% of variance in the Anglo/white sample) is explained by such deletions.

Lehrl and Fischer (1990) have claimed that g is limited by the channel capacity of short-term memory. Mental power, or the capacity C of short-term memory (measured in bits of information), is the product of the individual mental speed Ck of information processing (in bit/s), and the duration time D (in s) of information in short-term working memory, meaning the duration of memory span. Hence:

C (bit) = Ck(bit/s) × D (s).

This theory has been tested and found wanting by Roberts et al. (1992). There is much evidence that g is closely related to measures of the capacity of working memory, but this capacity can not be measured in bits of information.

However, initial studies attempting to find regions in the genome relating to intelligence have had little success. In 2001, a study used several hundred people in two groups, one with a very high IQ, average 160, and a control group with an average IQ of 102. The study used 1,842 DNA markers and put them through a five step inspection process to eliminate false positives. By the fifth step the study could not find a single gene that was related to intelligence. Critics of these studies say the failure to find a specific gene associated with intelligence is indicative of the complex nature of intelligence. They contend that intelligence is probably under the influence of several genes. Some estimate that as much as 40% of the genome may contribute to intelligence. A 2008 study found 6 SNPs which were significantly correlated with g, though the strongest one (corresponding to the gene DNAJC13 in chromosome 3) only explained 0.4% of the variance in g. As of 2011, Beijing Genomics Institute is in process of collecting volunteers with the objective of conducting a similar study.

A research group from Japan has recently claimed to have found evidence which supports the view that g is a highly genetically driven causal aspect of the brain:

Accordingly, our findings could furnish an argument against the typical criticisms offered by those who are opposed to the concept of g; in other words, g is an “artifact” (Simon, 1969) of the statistical methods that psychologists apply to the data. Gould (1981) argued that g, as a factor extracted from the factor analysis, is neither a “thing with physical reality” nor a “causal entity”, but is a “mathematical abstraction”, maintaining that “we cannot reify g as a ‘thing’ unless we have convincing, independent information beyond the fact of correlation itself.” Although the present study also draws information from correlations, we were able to depict the structure of human intelligence beyond the fact of phenotypic and genetic correlations with an explicit comparison between the independent pathway and the common pathway model; and as a “causal entity”, as a highly genetically driven entity.

Social correlates of g

Most measures of g positively correlate with conventional measures of success (income, academic achievement, job performance, career prestige) and negatively correlate with what are generally seen as undesirable life outcomes (school dropout, unplanned childbearing, poverty). Many studies suggest that specific cognitive abilities tapped by IQ tests do not predict job performance better than g alone. Research on differences in g between ethnic groups (see race and intelligence) has often sparked public controversy.

Challenges to g

In 1981, paleontologist and biologist Stephen Jay Gould voiced his objections to the concept of g, as well as intelligence testing in general, in his The Mismeasure of Man. Peter Schönemann has also argued for the non-existence of g.

Several researchers have argued that even if g was replaced by a model with several intelligences this would change the situation less than some may expect. All tests of cognitive ability would continue to be highly correlated with one another and there would still be group differences on cognitive tests as a group. It may however have implications for some arguments regarding whether such group differences are genetic such as Spearman's hypothesis.^{[citation needed]}

Bringsjord (2000) argued that the science of mental ability can be thought of as "computationalism" and is "either silly or pointless," and argued that "Mental ability tests measure differences in tasks that will soon be performed for all of us by computational agents."

Howard Gardner contends that the rare condition of savant syndrome argues against a single generalized intelligence. People with savant syndrome may have general IQs in the mentally retarded range but may possess certain mental abilities that are remarkable compared to the average person. These abilities include superior memory, extremely fast arithmetic calculation, advanced musical ability, rapid language learning and exceptional artistic ability. However, g does not prohibit the existence of more narrow abilities and there are a number of theories explaining savant syndrome that are not incompatible with g.

An alternative interpretation was recently advanced by van der Maas and colleagues in 2006. Their mutualism model assumes that intelligence depends on several independent mechanisms, none of which influences performance on all cognitive tests. These mechanisms support each other so that efficient operation of one of them makes efficient operation of the others more likely, thereby creating the positive correlations between intelligence tests. Rushton and Jensen argue that evidence for a genetic g, such as correlations between g-loadings and heritability of subtests, is problematic for the mutualism theory.

See also

• Charles Spearman
• Factor analysis in psychometrics
• Fluid and crystallized intelligence
• Flynn effect
• Intelligence
• Intelligence quotient
• Malleable intelligence
• Spearman's hypothesis

References

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Further reading

• Sternberg, Robert J.; Grigorenko, Elena L., eds. (2002). The General Factor of Intelligence: How General Is It?. Mahwah (NJ): Lawrence Erlbaum. ISBN 978-0-8058-3675-2. Lay summary (23 October 2010). 

External links

• A Genomewide Scan for Genes Underlying General Cognitive Ability
• Carroll model
• The General Intelligence Factor by Linda S. Gottfredson