The g factor is a construct developed in psychometric investigations of cognitive abilities and human intelligence that summarizes positive correlations among different cognitive tasks. The g factor typically accounts for 40 to 50 percent of the between-individual performance differences on a given cognitive test, and composite scores ("IQ scores") based on many tests are frequently regarded as estimates of individuals' standing on the g factor.Kamphaus et al. 2005 The terms IQ, general intelligence, general cognitive ability, general mental ability, and simply intelligence are often used interchangeably to refer to this common core shared by cognitive tests. However, the g factor itself is a statistical construct driven by the level of observed correlation between cognitive tasks. 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 the g factor was originally proposed by the English psychologist Charles Spearman in the early years of the 20th century. 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 many narrow task-specific ability factors. Soon after Spearman proposed the existence of g, it was challenged by Godfrey Thomson, who presented evidence that such intercorrelations among test results could arise even if no g-factor existed.
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. Research in the field of behavioral genetics has shown that the construct of g is heritable in measured populations. 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.
Critics have contended that an emphasis on g is misplaced and entails a devaluation of other important abilities. Some scientists, including Stephen J. Gould, have said that the concept of g is a merely reified construct rather than a valid measure of human intelligence.
Concept
Spearman's correlation matrix for six measures of school performance. All the correlations are positive, the positive manifold phenomenon. The bottom row shows the g loadings of each performance measure.Adapted from Jensen 1998, 24. The correlation matrix was originally published in Spearman 1904, and it is based on the school performance of a sample of English children. While this analysis is historically important and has been highly influential, it does not meet modern technical standards. See Mackintosh 2011, 44ff. and Horn & McArdle 2007 for discussion of Spearman's methods. Classics French English Math Pitch Music Classics – French .83 – English .78 .67 – Math .70 .67 .64 – Pitch discrimination .66 .65 .54 .45 – Music .63 .57 .51 .51 .40 – g loadings .958 .882 .803 .750 .673 .646
Subtest intercorrelations in a sample of Scottish subjects who completed the WAIS-R battery. The subtests are Vocabulary, Similarities, Information, Comprehension, Picture arrangement, Block design, Arithmetic, Picture completion, Digit span, Object assembly, and Digit symbol. The bottom row shows the g loadings of each subtest. Adapted from Chabris 2007, Table 19.1. V S I C PA BD A PC DSp OA DS V – S .67- I .72 .59- C .70 .58 .59 - PA .51 .53 .50 .42 - BD .45 .46 .45 .39 .43 - A .48 .43 .55 .45 .41 .44 – PC .49 .52 .52 .46 .48 .45 .30 - DSp .46 .40 .36 .36 .31 .32 .47 .23 - OA .32 .40 .32 .29 .36 .58 .33 .41 .14- DS .32 .33 .26 .30 .28 .36 .28 .26 .27 .25- g loadings .83 .80 .80 .75 .70 .70 .68 .68 .56 .56 .48
In a famous research paper published in 1904,Spearman 1904 English psychologist Charles Spearman observed that children's performance measures across seemingly unrelated school subjects were positively correlated. 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".Deary 2000, 6
Using factor 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 the general factor, or simply g. (By convention, g is always printed as a lower case italic.) Mathematically, the g factor is a source of variance among individuals, which means that one cannot meaningfully speak of any one individual's mental abilities consisting of g or other factors to any specified degree. One can only speak of an individual's standing on g (or other factors) compared to other individuals in a relevant population.Jensen 1992Jensen 1998, 28van deer Maas et al. 2006
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, representing their 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 .95.Jensen 1998, 26, 36–39 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.
The g 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 highest g loadings, around .80. Tests of vocabulary and general information are also typically found to have high g loadings.Jensen 1998, 26, 36–39, 89–90Jensen 2002 However, the g loading of the same test may vary somewhat depending on the composition of the test battery.Floyd et al. 2009
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. 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.Jensen 1980, 213
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.Jensen 1998, 94
History Spearman's early research
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. Spearman posited that the tests Galton used contained substantial measurement error and were unreliable–the same person obtained a different score upon being tested again. Spearman developed procedures to correct correlation coefficients for various influences to estimate the "true relationship", including a procedure to disattenuate correlations. These ideas regarding true scores, measurement error and procedures for correcting correlations form the basis for what is now known as classical test theory. 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.
The concept of "general intelligence" first arose from Spearman's 1904 paper "'General Intelligence', Objectively Determined and Measured", where he applied his new statistical methods for correcting correlations to tests of ability to propose a two-factor theory of intelligence. 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. This concept of "general intelligence" was supposed to provide an undisputed definition of intelligence which could be described as "objectively determined and measured". There were several corollaries of his theory, such as the claim that it is "possible to rank order the measures in terms of their g-to-s ratio". 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 is . 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.
Early critics The first psychologist to raise problems with Spearman's work was Cyril Burt, who noted that mental effort was not factored into his analysis. 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.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. 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. 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.