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Theg factor^[a] is a construct developed inpsychometric investigations ofcognitive abilities and humanintelligence. It is a variable that summarizes positivecorrelations among different cognitive tasks, reflecting the assertion 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.^{[citation needed]} Theg factor typically accounts for 40 to 50 percent of the between-individual performance differences on a givencognitive test, and composite scores ("IQ scores") based on many tests are frequently regarded as estimates of individuals' standing on theg factor.^[1] The termsIQ, general intelligence, general cognitive ability, general mental ability, and simplyintelligence are often used interchangeably to refer to this common core shared by cognitive tests.^[2] However, theg factor itself is a mathematical construct indicating the level of observed correlation between cognitive tasks.^[3] The measured value of this construct depends on the cognitive tasks that are used, and little is known about the underlying causes of the observed correlations.

The existence of theg factor was originally proposed by the English psychologistCharles Spearman in the early years of the 20th century. He observed that children's performance ratings, across seemingly unrelated school subjects, were positivelycorrelated, 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 labeledg, and many narrow task-specific ability factors. Soon after Spearman proposed the existence ofg, it was challenged byGodfrey Thomson, who presented evidence that such intercorrelations among test results could arise even if nog-factor existed.^[4]

Traditionally, research ong has concentrated on psychometric investigations of test data, with a special emphasis onfactor analytic approaches. However, empirical research on the nature ofg has also drawn upon experimentalcognitive psychology andmental chronometry, brain anatomy and physiology,quantitative andmolecular genetics, andprimate evolution.^[5]: 545 Research in the field ofbehavioral genetics has shown that the construct ofg isheritable in measured populations. It has a number of other biological correlates, includingbrain size. It is also a significant predictor of individual differences in many social outcomes, particularly in education and employment.

Critics have contended that an emphasis ong is misplaced and entails a devaluation of other important abilities. Some scientists, includingStephen J. Gould, have argued that the concept ofg is a merelyreified construct rather than avalid measure of human intelligence.

n a famous research paper published in 1904,^[8] English psychologistCharles Spearman observed that children's performance measures across seemingly unrelated school subjects were positively correlated. The consistent finding of universally positivecorrelation 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".^[9]

Usingfactor analysis or related statistical methods, it is possible to identify a single common factor that can be regarded as a summary variable characterizing the correlations between all the different tests in a test battery. Spearman referred to this common factor as thegeneral factor, or simplyg. (By convention,g is always printed as a lower case italic.) Mathematically, theg factor isa source of variance among individuals, which means that one cannot meaningfully speak of any one individual's mental abilities consisting ofg or other factors to any specified degree. One can only speak of an individual's standing ong (or other factors) compared to other individuals in a relevant population.^[10][11][12]

Different tests in a test battery may correlate with (or "load onto") theg factor of the battery to different degrees. These correlations are known asg loadings. An individual test taker'sg factor score, representing their relative standing on theg factor in the total group of individuals, can be estimated using theg loadings. Full-scale IQ scores from a test battery will usually be highly correlated withg factor scores, and they are often regarded as estimates ofg. For example, the correlations betweeng factor scores and full-scale IQ scores fromDavid Wechsler's tests have been found to be greater than .95.^[1][10][13] The terms IQ, general intelligence, general cognitive ability, general mental ability, or simply intelligence are frequently used interchangeably to refer to the common core shared by cognitive tests.^[2]

Theg loadings of mental tests are always positive and usually range between .10 and .90, with a mean of about .60 and a standard deviation of about .15.Raven's Progressive Matrices is among the tests with the highestg loadings, around .80. Tests of vocabulary and general information are also typically found to have highg loadings.^[14][15] However, theg loading of the same test may vary somewhat depending on the composition of the test battery.^[16]

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 higherg loading. Similarly, theg loadings of arithmetic computation, spelling, and word reading tests are lower than those of arithmetic problem solving, text composition, and reading comprehension tests, respectively.^[10][17]

Test difficulty andg 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 ofg loadings. For example, tests ofrote memory have been shown to have the same level of difficulty but considerably lowerg loadings than many tests that involve reasoning.^[17][18]

Spearman's research on intelligence originated from his research on measurement. He studied Francis Galton's theories of intelligence and was intriuged by why Galton failed to find associations between different performance metrics and common indicators of intelligence.^[5]: 22 Spearman posited that the tests Galton used contained substantialmeasurement error and were unreliable–the same person obtained a different score upon being tested again.^[5]: 22 Spearman developed procedures to correct correlation coefficients for various influences to estimate the "true relationship", including a procedure to disattenuate correlations.^{[19]: 3–4} These ideas regarding true scores, measurement error and procedures for correcting correlations form the basis for what is now known asclassical test theory.^{[19]: 3–4} When he applied these procedures to the data he had gathered for measures of intelligence and what he called sensory discrimination ability, he obtained correlations approaching 1.^{[19]: 3 [20]: 186-187}

The concept of "general intelligence" first arose from Spearman's 1904 paper "'General Intelligence', Objectively Determined and Measured",^[21] where he applied his new statistical methods for correcting correlations to tests of ability to propose a two-factor theory of intelligence.^{[19]: 2–3} Based on the observation that tests of ability typically positively correlate with each other, he proposed that these tests all measure the same thing—general intelligence—and that individual tests measure a combination of two factors: 'general intelligence' (g), common to all tests, and a 'specific ability' (s), specific to one test.^{[5]: 30 [19]: 3 [22]: 372–373} This concept of "general intelligence" was supposed to provide an undisputed definition of intelligence which could be described as "objectively determined and measured".^[23]: 194 There were several corollaries of his theory, such as the claim that it is "possible torank order the measures in terms of their g-to-s ratio"^[19]. The most important was Spearman's law of tetrad differences, demonstrated by Spearman in 1924. It states that the pairwise products of two sets of correlations are equal–that is, their difference is zero. For four traits labeled 1, 2, 3, 4, this isr₁₃⋅r₂₄-r₂₃r₁₄=0.^{[19]: 4 [24]: 288} This is equivalent to the prediction that for a correlation matrix statistically removing the common factor "g" would yield a matrix of partial correlations that are all 0.^{[23]: 194 [25]: 209–210}

The first psychologist to raise problems with Spearman's work wasCyril Burt, who noted that mental effort was not factored into his analysis.^[26] Burt marshalled a larger set of data and showed that more factors than a single general factor were required to explain the correlations: the law of tetrad differences was not satisfied by the data.^{[5]: 31 [25]: 213–214}It was shown that correlations between certain pairs of tests were much higher than expected on Spearman's theory that their only common factor was general intelligence.^[19]: 13 Spearman knew about these problems as early as 1906, but attempted to dismiss the criticism by proposing that these higher than expected correlations were because the tests weren't meaningfully distinct.^{[5]: 31 [19]: 13} In subsequent years, many other psychologists showed a wider array of factors was needed to explain various sets of data: Spearman's two-factory theory didn't explain the correlations.^{[5]: 18 : 32 [25]: 213–214}

Other psychologists like Thomson provided alternative explanations for the same phenomena that he used to support the concept with what is now known as sampling theory.^[4][27] Thomson accepted Spearman's data and methodology of factor analysis, but interpreted the results differently.^{[28]: 3–4} He proposed that the mind was composed of innumerable independent bonds or units and any test sampled some subset of these bonds.^[19]: 10Simultaneous to Spearman's development of his theory ofg was an alternative theory fromGodfrey Thomson andEdward Thorndike who proposed that the positive intercorrelation of tests (positive manifold) was compatible with a theory of many common factors. Thorndike argued that performance on cognitive tests drew from numerous cognitive processes and that different cognitive tests draw from these different processes and can produce positive correlations as observed in test batteries.^{[25]: 219–220}

Despite these issues, Spearman's theory garnered early support.Lewis Terman, Stanford professor of psychology, drew upon Spearman's "general intelligence factor" when he revised Alfred Binet's intelligence scales to develop the Stanford-Binet Scales for American children.^[28]: 3

Spearman's 1927 bookThe Abilities of Man attempted to provide a comprehensive account of human intelligence, responding to his critics and compiling evidence in favor of his theory. He now argued that general intelligence was a reflection of "mental energy" that flowed throughout the brain, but different neural systems served as "mental engines" that explain the specific factors.^{[25]: 214–215} He also refined his concept of "g", not as equivalent to as concrete entity or synonym for intelligence, but as a magnitude that is identified as the common factor that underlies all mental abilities, and could be identified with tests of the tetrad equation.^{[25]: 215–216} By now, he reluctantly accepted the existence of group factors in addition to his general factor and specific factors.^[5]: 32 Following recognition that the arguments in his book did not sufficiently respond to critics evidence that not all data satisfied the tetrad condition, he put forth a different theory: that g was reflected in every ability measure and that this was proven by the positive correlations between tests of abilities, known as the "indifference of the indicator".^[25]: 218 This shift between theories has been noted as transforming "g" from a falsifiable hypothesis to an unfalsifiable result of mathematical necessity.^{[23]: 198-199 [29]: 10}

Another early criticism raised of the g theory wasfactor indeterminacy.^{[30][31]: 275–276, 376} In a review of Spearman's Ability of Man,Edwin Wilson pointed out that Spearman's theory did not defineg uniquely because it proposed more independent factors than observed psychological tests.^{[23]: 194–195} and it was possible to generate a different set of factor scores for a set of students that reproduces the same correlation matrix.^{[22]: 382–383 [20]: 237}

In response to these criticisms, some psychologists tried to rescue Spearman's theory by producing batteries of tests that would reflectg without introducing specific factor overlap that produces common factors other thang. Invariably these attempts failed and psychologists acknowledged that many common factors were needed to explain correlations between tests, as many as one third as many factors as tests in a battery.^{[23]: 195 [25]: 220–221}

In 1938,Louis Thurstone developed a theory of intelligence contrary to both Spearman and Thomson.^{[19]: 14 [32]: 14} He, like Thomson, proposed that there were separate factors that were unrelated to each other,^[19] but he proposed a smaller set of just seven primary mental abilities.^[32]: 14 Thurstone developed the method ofmultiple factor analysis to identify the number of factors needed to explain a matrix of observed correlations.^[19]: 14 His early results using orthogonal factors identified as many as 13 factors, which he believed conclusively refuted Spearman's theory, though a reanalysis of his results showed that Spearman's g theory could explain the data as well.^{[19]: 15–16} Later Thurstone abandoned the idea of completely independent factors and posited correlated factors, analyzing test data using oblique factor analysis but left him without a strong criticism of Spearman's theory.^{[19]: 16–17} After the 1940s, studies using Thurstone's methods proliferated, identifying increasing numbers of mental abilities.^[25]: 232 One example wasJoy Paul Guilford's "Structure-of-Intellectual" model which proposed 3 facets of ability - contents, products, operations - that can be composed in different ways to obtain 150 different abilities.^{[5]: 115 [33]: 10} Lloyd Humphries argued that following Thurstone's publications, "psychometrists and factor analysts have tended to lose sight of the general factor in intelligence".^[34]

By 1941, Raymond Cattell, who had worked with Spearman, proposed a two common factor theory of intelligence.^[25]: 228 Cattell's theory proposed two high level factors: Gc (crystallized intelligence) that reflected learned knowledge and general information and Gf (fluid intelligence) that closely resembled Spearman's conceptualization of g.^{[25]: 228–229} Since proposing these factors, Cattell and his student John Horn proposed a number of other 'general factors' or 'broad factors' like Gs (visual inspection speed), Ga (auditory thinking), Gv (visual-spatial reasoning), Gq (quantitative reasoning), Gr (fluency in recall).^[5]: 124 Their theory is what Arthur Jensen calls a "truncated hierarchy", as it extracts many factors but not one unitary "general" factor on top of the hierarchy.^[5]: 124

Jensen mounted defenses of the g-factor from its many critics over the course of his career. His first major workHow Much Can We Boost IQ and Scholastic Achievement? described Spearman's development of the concept of "general intelligence" in support of what Urbach calls the "hard core of the hereditarian program".^{[35]: 9 [36]: 65 [37]} In the dispute among psychometricians over general intelligence, Jensen fiercely argued for its existence,^[38]: 397 presenting it as a fact that self-respecting psychometrician could deny.^[38]: 398 In that article, Jensen presented a hierarchical model of intelligence, where abilities operate two levels: Level I and Level II.^{[35]: 110 [39]: 65} In his later workThe g Factor: The Science of Mental Ability, Jensen offered an extensive synthesis of a large body of research to argue that g is a legitimate scientific construct based in human biology with far-reaching effects on human life.^[40][41]

In some ways,Arthur Jensen resuscitated Spearman'sg theory,^{[28]: 50 [42]: 7} but his arguments reflect a marked shift from Spearman's theory of factors to its replacement with principal components.^{[23]: 199 [42]}

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 theg factor, and it typically accounts for 40 to 50 percent of the variance in IQ test batteries.^[43] The presence of correlations between many widely varying cognitive tests has often been taken as evidence for the existence ofg, but mathematically the correlations do not provide any more or less support for the existence ofg than for the existence of multiple factors of intelligence.^[44]

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 (denoteds); and second, ag 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 thatg alone could not account for all correlations between tests. Specifically, it was found that even after controlling forg, some tests were still correlated with each other. This led to the postulation ofgroup factors that represent variance that groups of tests with similar task demands (e.g., verbal, spatial, or numerical) have in common in addition to the sharedg variance.^[45]

Throughfactor rotation, it is, in principle, possible to produce an infinite number of different factor solutions that are mathematically equivalent in their ability to account for the intercorrelations among cognitive tests. These include solutions that do not contain ag factor. Thus factor analysis alone cannot establish what the underlying structure of intelligence is. In choosing between different factor solutions, researchers have to examine the results of factor analysis together with other information about the structure of cognitive abilities.^[46]

There are many psychologically relevant reasons for preferring factor solutions that contain ag factor. These include the existence of the positive manifold, the fact that certain kinds of tests (generally the more complex ones) have consistently largerg loadings, the substantial invariance ofg factors across different test batteries, the impossibility of constructing test batteries that do not yield ag factor, and the widespread practical validity ofg as a predictor of individual outcomes. Theg factor, together with group factors, best represents the empirically established fact that, on average, overall ability differencesbetween individuals are greater than differences among abilitieswithin individuals, while a factor solution with orthogonal factors withoutg obscures this fact. Moreover,g appears to be the most heritable component of intelligence.^[47] Research utilizing the techniques ofconfirmatory factor analysis has also provided support for the existence ofg.^[46]

Ag 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 ofg on test scores.^[16][48]

While the existence ofg 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.^[49]

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. However, he thought that the best indicators ofg were those tests that reflected what he calledthe eduction of relations and correlates, which included abilities such asdeduction,induction, problem solving, grasping relationships, inferring rules, and spotting differences and similarities. Spearman hypothesized thatg was equivalent with "mental energy". 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 ofg.^[50]

Following Spearman,Arthur Jensen maintained that all mental tasks tap intog to some degree. According to Jensen, theg factor represents a "distillate" of scores on different tests rather than a summation or an average of such scores, with factor analysis acting as thedistillation procedure.^[15] He argued thatg cannot be described in terms of the item characteristics or information content of tests, pointing out that very dissimilar mental tasks may have nearly equalg loadings. Wechsler similarly contended thatg is not an ability at all but rather some general property of the brain. Jensen hypothesized thatg corresponds to individual differences in the speed or efficiency of the neural processes associated with mental abilities.^[51] He also suggested that given the associations betweeng andelementary cognitive tasks, it should be possible to construct aratio scale test ofg that usestime as the unit of measurement.^[52]

The so-called sampling theory ofg, originally developed byEdward Thorndike andGodfrey 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 inter correlations between tests are caused by an overlap between processes tapped by the tests.^[53][54] Thus, the positive manifold arises due to a measurement problem, an inability to measure more fine-grained, presumably uncorrelated mental processes.^[12]

It has been shown that it is not possible to distinguish statistically between Spearman's model ofg and the sampling model; both are equally able to account for inter correlations among tests.^[55] The sampling theory is also consistent with the observation that more complex mental tasks have higherg loading, because more complex tasks are expected to involve a larger sampling of neural elements and therefore have more of them in common with other tasks.^[56]

Some researchers have argued that the sampling model invalidatesg as a psychological concept, because the model suggests thatg factors derived from different test batteries simply reflect the shared elements of the particular tests contained in each battery rather than ag that is common to all tests. Similarly, high correlations between different batteries could be due to them measuring the same set of abilities rather thanthe same ability.^[57]

Critics have argued that the sampling theory is incongruent with certain empirical findings. 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.^[12][58]

The "mutualism" model ofg 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.^[12][59] Critics have argued that the observed correlations between theg loadings and the heritability coefficients of subtests are problematic for the mutualism theory.^[60]

Raymond Cattell, a student of Charles Spearman's, modified the unitaryg factor model and dividedg into two broad, relatively independent domains: fluid intelligence (Gf) and crystallized intelligence (Gc). Gf is conceptualized as a capacity to figure out novel problems, and it is best assessed with tests with little cultural or scholastic content, such as Raven's matrices. Gc can be thought of as consolidated knowledge, reflecting the skills and information that an individual acquires and retains throughout his or her life. Gc is dependent on education and other forms of acculturation, and it is best assessed with tests that emphasize scholastic and cultural knowledge.^[2][61][62] Gf can be thought to primarily consist ofcurrent reasoning and problem solving capabilities, while Gc reflects the outcome ofpreviously executed cognitive processes.^[63]

The rationale for the separation of Gf and Gc was to explain individuals' cognitive development over time. While Gf and Gc have been found to be highly correlated, they differ in the way they change over a lifetime. Gf tends to peak at around age 20, slowly declining thereafter. In contrast, Gc is stable or increases across adulthood. A single general factor has been criticized as obscuring this bifurcated pattern of development. Cattell argued that Gf reflected individual differences in the efficiency of thecentral nervous system. Gc was, in Cattell's thinking, the result of a person "investing" his or her Gf in learning experiences throughout life.^{[2][57][61][64]}

Cattell, together withJohn Horn, later expanded theGf-Gc model to include a number of other broad abilities, such as Gq (quantitative reasoning) and Gv (visual-spatial reasoning). While all the broad ability factors in the extended Gf-Gc model are positively correlated and thus would enable the extraction of a higher orderg factor, Cattell and Horn maintained that it would be erroneous to posit that a general factor underlies these broad abilities. They argued thatg factors computed from different test batteries are not invariant and would give different values ofg, and that the correlations among tests arise because it is difficult to test just one ability at a time.^[2][65][66]

However, several researchers have suggested that the Gf-Gc model is compatible with ag-centered understanding of cognitive abilities. For example,John B. Carroll'sthree-stratum model of intelligence includes both Gf and Gc together with a higher-orderg factor. Based on factor analyses of many data sets, some researchers have also argued that Gf andg are one and the same factor and thatg factors from different test batteries are substantially invariant provided that the batteries are large and diverse.^[61][67][68]

Several theorists have proposed that there are intellectual abilities that are uncorrelated with each other. Among the earliest wasL.L. Thurstone who created a model ofprimary mental abilities representing supposedly independent domains of intelligence. However, Thurstone's tests of these abilities were found to produce a strong general factor. He argued that the lack of independence among his tests reflected the difficulty of constructing "factorially pure" tests that measured just one ability. Similarly,J.P. Guilford proposed a model of intelligence that comprised up to 180 distinct, uncorrelated abilities, and claimed to be able to test all of them. Later analyses have shown that the factorial procedures Guilford presented as evidence for his theory did not provide support for it, and that the test data that he claimed provided evidence againstg did in fact exhibit the usual pattern of intercorrelations after correction for statistical artifacts.^[69][70]

More recently,Howard Gardner has developed thetheory of multiple intelligences. He posits the existence of nine different and independent domains of intelligence, such as mathematical, linguistic, spatial, musical, bodily-kinesthetic, meta-cognitive, and existential intelligences, and contends that individuals who fail in some of them may excel in others. According to Gardner, tests and schools traditionally emphasize only linguistic and logical abilities while neglecting other forms of intelligence.

While popular amongeducationalists, Gardner's theory has been much criticized by psychologists and psychometricians. One criticism is that the theory contradicts both scientific and everyday usages of the wordintelligence. Several researchers have argued that not all of Gardner'sintelligences fall within the cognitive sphere. For example, Gardner contends that a successful career in professional sports or popular music reflects bodily-kinestheticintelligence and musicalintelligence, respectively, even though one might usually talk of athletic and musicalskills,talents, orabilities instead.

Another criticism of Gardner's theory is that many of his purportedly independent domains of intelligence are in fact correlated with each other. Responding to empirical analyses showing correlations between the domains, Gardner has argued that the correlations exist because of thecommon format of tests and because all tests require linguistic and logical skills. His critics have in turn pointed out that not all IQ tests are administered in the paper-and-pencil format, that aside from linguistic and logical abilities, IQ test batteries contain also measures of, for example, spatial abilities, and that elementary cognitive tasks (for example, inspection time and reaction time) that do not involve linguistic or logical reasoning correlate with conventional IQ batteries, too.^{[71][72][73][74]}

Robert Sternberg, working with various colleagues, has also suggested that intelligence has dimensions independent ofg. He argues that there are three classes of intelligence: analytic, practical, and creative. According to Sternberg, traditional psychometric tests measure only analytic intelligence, and should be augmented to test creative and practical intelligence as well. He has devised several tests to this effect. Sternberg equates analytic intelligence with academic intelligence, and contrasts it with practical intelligence, defined as an ability to deal with ill-defined real-life problems. Tacit intelligence is an important component of practical intelligence, consisting of knowledge that is not explicitly taught but is required in many real-life situations. Assessing creativity independent of intelligence tests has traditionally proved difficult, but Sternberg and colleagues have claimed to have created valid tests of creativity, too.

The validation of Sternberg's theory requires that the three abilities tested are substantially uncorrelated and have independent predictive validity. Sternberg has conducted many experiments which he claims confirm the validity of his theory, but several researchers have disputed this conclusion. For example, in his reanalysis of a validation study of Sternberg's STAT test,Nathan Brody showed that the predictive validity of the STAT, a test of three allegedly independent abilities, was almost solely due to a single general factor underlying the tests, which Brody equated with theg factor.^[75][76]

James Flynn has argued that intelligence should be conceptualized at three different levels: brain physiology, cognitive differences between individuals, and social trends in intelligence over time. According to this model, theg factor is a useful concept with respect to individual differences but its explanatory power is limited when the focus of investigation is either brain physiology, or, especially, the effect of social trends on intelligence. Flynn has criticized the notion that cognitive gains over time, or the Flynn effect, are "hollow" if they cannot be shown to be increases ing. He argues that the Flynn effect reflects shifting social priorities and individuals' adaptation to them. To apply the individual differences concept ofg to the Flynn effect is to confuse different levels of analysis. On the other hand, according to Flynn, it is also fallacious to deny, by referring to trends in intelligence over time, that some individuals have "better brains and minds" to cope with the cognitive demands of their particular time. At the level of brain physiology, Flynn has emphasized both that localized neural clusters can be affected differently by cognitive exercise, and that there are important factors that affect all neural clusters.^[77]

Spearman proposed the principle of theindifference of the indicator, according to which the precise content of intelligence tests is unimportant for the purposes of identifyingg, becauseg enters into performance on all kinds of tests. Any test can therefore be used as an indicator ofg.^[78] Following Spearman, Arthur Jensen more recently argued that ag 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.^[79] According to this view, every mental test, no matter how distinctive, calls ong to some extent. Thus a composite score of a number of different tests will load ontog more strongly than any of the individual test scores, because theg 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 ofg.^[80]

In contrast,L. L. Thurstone argued that ag factor extracted from a test battery reflects the average of all the abilities called for by the particular battery, and thatg therefore varies from one battery to another and "has no fundamental psychological significance."^[81] Along similar lines,John Horn argued thatg 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.^[65][82]

To show that different batteries reflect the sameg, one must administer several test batteries to the same individuals, extractg factors from each battery, and show that the factors are highly correlated. This can be done within a confirmatory factor analysis framework.^[49] Wendy Johnson and colleagues have published two such studies^[83][84] finding correlations between g factors extracted from different batteries between .95–1.00 for most batteries, while the correlations ranged from .79 to .96 for theCattell 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 thatg factors derived from different test batteries are the same provided that the batteries are diverse enough. This approach has been criticized by psychologistLazar Stankov in the Handbook of Understanding and Measuring Intelligence, who concluded "Correlations between the g factors from different test batteries are not unity."^[85]

A study authored byScott Barry Kaufman and colleagues showed that the general factor extracted from theWoodjock-Johnson cognitive abilities test, and the general factor extracted from the Achievement test batteries are highly correlated, but not isomorphic.^[86]

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

SLODR was originally proposed in 1927 byCharles Spearman,^[87] 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.^[88] They reported that for subtests of both theWAIS and theWISC, 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.^[89]

SLODR 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.^[90] However, as both Deary et al. (1996)^[90] and Tucker-Drob (2009)^[91] have pointed out, dividing the continuous distribution of intelligence into an arbitrary number of discrete ability groups is less than ideal for examining SLODR. Tucker-Drob (2009)^[91] extensively reviewed the literature on SLODR and the various methods by which it had been previously tested, and proposed that SLODR 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 SLODR. 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.

A recent meta-analytic study by Blum and Holling^[92] also provided support for the differentiation hypothesis. As opposed to most research on the topic, this work made it possible to study ability and age variables as continuous predictors of theg saturation, and not just to compare lower- vs. higher-skilled or younger vs. older groups of testees. Results demonstrate that the mean correlation andg loadings of cognitive ability tests decrease with increasing ability, yet increase with respondent age. SLODR, as described byCharles Spearman, could be confirmed by ag-saturation decrease as a function of IQ as well as ag-saturation increase from middle age to senescence. Specifically speaking, for samples with a mean intelligence that is two standard deviations (i.e., 30 IQ-points) higher, the mean correlation to be expected is decreased by approximately .15 points. The question remains whether a difference of this magnitude could result in a greater apparent factorial complexity when cognitive data are factored for the higher-ability sample, as opposed to the lower-ability sample. It seems likely that greater factor dimensionality should tend to be observed for the case of higher ability, but the magnitude of this effect (i.e., how much more likely and how many more factors) remains uncertain.

Evidence of a general factor of intelligence has also been observed in non-human animals. Studies have shown thatg is responsible for 47% of the variance at the species level inprimates^[93] and around 55% of the individual variance observed inmice.^[94][95] A review and meta-analysis of general intelligence, however, found that the average correlation among cognitive abilities was 0.18 and suggested that overall support forg is weak in non-human animals.^[96]

Although it is not assessable using the same intelligence measures used in humans, cognitive ability can be measured with a variety of interactive and observational tools focusing oninnovation,habit reversal,social learning, and responses tonovelty. Non-human models ofg such as mice are used to studygenetic influences on intelligence andneurological developmental research into the mechanisms behind and biological correlates ofg.^[97]

Similar tog for individuals, a new research path aims to extract a general collective intelligence factorc for groups displaying a group's general ability to perform a wide range of tasks.^[98] Definition, operationalization and statistical approach for thisc factor are derived from and similar tog. Causes, predictive validity as well as additional parallels tog are investigated.^[99]

g has a number of correlates in the brain. Studies usingmagnetic resonance imaging (MRI) have established thatg and total brain volume are moderately correlated (r~.3–.4). External head size has a correlation of ~.2 withg. MRI research on brain regions indicates that the volumes offrontal,parietal andtemporal cortices, and thehippocampus are also correlated withg, generally at .25 or more, while the correlations, averaged over many studies, with overallgrey matter and overallwhite matter have been found to be .31 and .27, respectively. Some but not all studies have also found positive correlations betweeng and cortical thickness. However, the underlying reasons for these associations between the quantity of brain tissue and differences in cognitive abilities remain largely unknown.^[2]

Most researchers believe that intelligence cannot be localized to a single brain region, such as the frontal lobe. Brainlesion studies have found small but consistent associations indicating that people with more white matter lesions tend to have lower cognitive ability. Research utilizingNMR spectroscopy has discovered somewhat inconsistent but generally positive correlations between intelligence and white matter integrity, supporting the notion that white matter is important for intelligence.^[2]

Some research suggests that aside from the integrity of white matter, also its organizational efficiency is related to intelligence. The hypothesis that brain efficiency has a role in intelligence is supported by functional MRI research showing that more intelligent people generally process information more efficiently, i.e., they use fewer brain resources for the same task than less intelligent people.^[2]

Small but relatively consistent associations with intelligence test scores include also brain activity, as measured byEEG records orevent-related potentials, andnerve conduction velocity.^[100][101]

Heritability is the proportion of phenotypic variance in a trait in a population that can be attributed to genetic factors. The heritability ofg has been estimated to fall between 40 and 80 percent using twin, adoption, and other family study designs as well as molecular genetic methods. Estimates based on the totality of evidence place the heritability ofg at about 50%.^[102] It has been found to increase linearly with age.

As with heritability in general, the heritability ofg can be understood in reference to a specific population at a specific place and time, and findings for one population do not apply to a different population that is exposed to different environmental factors.^[103] A population that is exposed to strong environmental factors can be expected to have a lower level of heritability than a population that is exposed to only weak environmental factors. For example, one twin study found that genotype differences almost completely explain the variance in IQ scores within affluent families, but make close to zero contribution towards explaining IQ score differences in impoverished families.^[104] Notably, heritability findings also only refer to total variation within a population and do not support a genetic explanation for differences between groups.^[105] It is theoretically possible for the differences between the averageg of two groups to be 100% due to environmental factors even if the variance within each group is 100% heritable.

Much research points tog being a highlypolygenic trait influenced by many common genetic variants, each having only small effects. Another possibility is that heritable differences ing are due to individuals having different"loads" of rare, deleterious mutations, with genetic variation among individuals persisting due tomutation–selection balance.^[106][107]

Cross-cultural studies indicate that theg factor can be observed whenever a battery of diverse, complex cognitive tests is administered to a human sample. In some studies, the factor structure of IQ tests has also been found to be consistent across sexes and ethnic groups in the U.S. and elsewhere.^[101]

Most studies suggest that there are negligible differences in the mean level ofg between the sexes, but that sex differences in cognitive abilities are to be found in more narrow domains. For example, males generally outperform females in spatial tasks, while females generally outperform males in verbal tasks.^[108] Another difference that has been found in many studies is thatmales show more variability in both general and specific abilities than females, with proportionately more males at both the low end and the high end of the test score distribution.^[109]

Differences ing between racial and ethnic groups have been found, particularly in the U.S. between black- and white-identifying test takers, though these differences appear to have diminished significantly over time,^[110] and to be attributable to environmental (rather than genetic) causes.^[110][111] Some researchers have suggested that the magnitude of the black-white gap in cognitive test results is dependent on the magnitude of the test'sg loading, with tests showing higherg loading producing larger gaps (seeSpearman's hypothesis),^[112] while others have criticized this view as methodologically unfounded.^[113][114] Still others have noted that despite the increasingg loading of IQ test batteries over time, the performance gap between racial groups continues to diminish.^[110] Comparative analysis has shown that while a gap of approximately 1.1 standard deviation in mean IQ (around 16 points) between white and black Americans existed in the late 1960s, between 1972 and 2002 black Americans gained between 4 and 7 IQ points relative to non-Hispanic Whites, and that "theg gap between Blacks and Whites declined virtually in tandem with the IQ gap."^[110] In contrast, Americans of East Asian descent generally slightly outscore white Americans.^[115] It has been claimed that racial and ethnic differences similar to those found in the U.S. can be observed globally,^[116] but the significance, methodological grounding, and truth of such claims have all been disputed.^{[117][118][119][120][121]}

Elementary cognitive tasks (ECTs) also correlate strongly withg. 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, they remove their 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 withg, while movement time correlates less strongly.^[122]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 asfMRI studies.

One theory holds thatg is identical or nearly identical toworking memory capacity. Among other evidence for this view, some studies have found factors representingg and working memory to be perfectly correlated. However, in a meta-analysis the correlation was found to be considerably lower.^[123] One criticism that has been made of studies that identifyg with working memory is that "we do not advance understanding by showing that one mysterious concept is linked to another."^[124]

Psychometric theories of intelligence aim at quantifying intellectual growth and identifying ability differences between individuals and groups. In contrast,Jean Piaget'stheory of cognitive development seeks to understand qualitative changes in children's intellectual development. Piaget designed a number of tasks to verify hypotheses arising from his theory. The tasks were not intended to measure individual differences, and they have no equivalent in psychometric intelligence tests.^[125][126] For example, in one of the best-known Piagetianconservation tasks a child is asked if the amount of water in two identical glasses is the same. After the child agrees that the amount is the same, the investigator pours the water from one of the glasses into a glass of different shape so that the amount appears different although it remains the same. The child is then asked if the amount of water in the two glasses is the same or different.

Notwithstanding the different research traditions in which psychometric tests and Piagetian tasks were developed, the correlations between the two types of measures have been found to be consistently positive and generally moderate in magnitude. A common general factor underlies them. It has been shown that it is possible to construct a battery consisting of Piagetian tasks that is as good a measure ofg as standard IQ tests.^[125][127]

The traditional view in psychology is that there is no meaningful relationship betweenpersonality and intelligence, and that the two should be studied separately. Intelligence can be understood in terms of what an individualcan do, or what his or hermaximal performance is, while personality can be thought of in terms of what an individualwill typically do, or what his or her general tendencies of behavior are. Large-scale meta-analyses have found that there are hundreds of connections >.20 in magnitude between cognitive abilities and personality traits across theBig Five. This is despite the fact that correlations with the global Big Five factors themselves being small, except for Openness (.26).^[128] More interesting relations emerge at other levels (e.g., .23 for the activity facet of extraversion with general mental ability, -.29 for the uneven-tempered facet of neuroticism, .32 for the industriousness aspect of conscientiousness, .26 for the compassion aspect of agreeableness).^[129]

The associations between intelligence and personality have generally been interpreted in two main ways. The first perspective is that personality traits influence performance on intelligencetests. For example, a person may fail to perform at a maximal level on an IQ test due to his or her anxiety and stress-proneness. The second perspective considers intelligence and personality to beconceptually related, with personality traits determining how people apply and invest their cognitive abilities, leading to knowledge expansion and greater cognitive differentiation.^[130][131] Other theories (e.g., Cybernetic Trait Complexes Theory) view personality and cognitive ability as intertwined parameters of individuals that co-evolved and are also co-influenced during development (e.g., by early life starvation).^[132]

Some researchers believe that there is a threshold level ofg below which socially significantcreativity is rare, but that otherwise there is no relationship between the two. It has been suggested that this threshold is at least one standard deviation above the population mean. Above the threshold, personality differences are believed to be important determinants of individual variation in creativity.^[133][134]

Others have challenged the threshold theory. While not disputing that opportunity and personal attributes other than intelligence, such as energy and commitment, are important for creativity, they argue thatg is positively associated with creativity even at the high end of the ability distribution. The longitudinalStudy of Mathematically Precocious Youth has provided evidence for this contention. It has shown that individuals identified by standardized tests as intellectually gifted in early adolescence accomplish creative achievements (for example, securing patents or publishing literary or scientific works) at several times the rate of the general population, and that even within the top 1 percent of cognitive ability, those with higher ability are more likely to make outstanding achievements. The study has also suggested that the level ofg acts as a predictor of thelevel of achievement, while specific cognitive ability patterns predict therealm of achievement.^[135][136]

Research on the G-factor, as well as other psychometric values, has been widely criticized for not properly taking into account theeugenicist background of its research practices.^[137] The reductionism of the G-factor has been attributed to having evolved frompseudoscientific theories about race and intelligence.^[138] Spearman'sg and the concept of inherited, immutable intelligence were a boon for eugenicists and pseudoscientists alike.^[139]

Joseph L. Graves Jr. and Amanda Johnson have argued thatg "...is to the psychometricians whatHuygens'ether was to early physicists: a nonentity taken as an article of faith instead of one in need of verification by real data."^[140]

Some scientists have described the g factor, and psychometrics, as forms of pseudoscience.^[141]

Paleontologist and biologistStephen Jay Gould presented a critique in his 1981 bookThe Mismeasure of Man. He argued that psychometricians fallaciouslyreified theg factor into an ineluctable "thing" that provided a convenient explanation for human intelligence, grounded only in mathematical theory rather than the rigorous application of mathematical theory to biological knowledge.^[24] An example is provided in the work of Cyril Burt, published posthumously in 1972: "The two main conclusions we have reached seem clear and beyond all question. The hypothesis of a general factor entering into every type of cognitive process, tentatively suggested by speculations derived from neurology and biology, is fully borne out by the statistical evidence; and the contention that differences in this general factor depend largely on the individual's genetic constitution appears incontestable.The concept of an innate, general cognitive ability, which follows from these two assumptions, though admittedly sheerly an abstraction, is thus wholly consistent with the empirical facts."^[142]

Several researchers have criticized Gould's arguments. For example, they have rejected the accusation of reification, maintaining that the use of extracted factors such asg as potential causal variables whose reality can be supported or rejected by further investigations constitutes a normal scientific practice that in no way distinguishes psychometrics from other sciences. Critics have also suggested that Gould did not understand the purpose of factor analysis, and that he was ignorant of relevant methodological advances in the field. While different factor solutions may be mathematically equivalent in their ability to account for intercorrelations among tests, solutions that yield ag factor are psychologically preferable for several reasons extrinsic to factor analysis, including the phenomenon of the positive manifold, the fact that the sameg can emerge from quite different test batteries, the widespread practical validity ofg, and the linkage ofg to many biological variables.^{[46][47][page needed]}

John Horn andJohn McArdle have argued that the moderng theory, as espoused by, for example, Arthur Jensen, isunfalsifiable, because the existence of a common factor likeg followstautologically from positive correlations among tests. They contrasted the modern hierarchical theory ofg with Spearman's original two-factor theory which was readily falsifiable (and indeed was falsified).^[57]

• Charles Spearman – English psychologist (1863–1945)
• Factor analysis in psychometrics – Statistical method
• Fluid and crystallized intelligence – Factors of general intelligence
• Flynn effect – 20th-century rise in intelligence test scores
• Intelligence – Ability to perceive, infer, retain or apply information
• Intelligence quotient – Score from a test designed to assess intelligence
• Malleability of intelligence – Processes by which intelligence can change over time
• Spearman's hypothesis – Hypothesis in intelligence research
• Eugenics – Effort to improve purported human genetic quality

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