g Factor (psychometrics) - Mental Testing and g

Mental Testing and g

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. In a famous research paper published in 1904, he observed that children's performance measures across seemingly unrelated school 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." Zero or negative correlations between tests suggest the presence of sampling error or restriction of the range of ability in the sample studied.

Using factor analysis or related statistical methods, it is possible to compute 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 entails that one cannot meaningfully speak of any one individual's mental abilities consisting of g or other factors to any specified degrees. One can only speak of an individual's standing on g (or other factors) compared to other individuals in a relevant population.

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 his or her relative standing on the g factor in the total group of individuals, can be estimated using the g loadings. Full-scale IQ scores from a test battery will usually be highly correlated with g factor scores, and they are often regarded as estimates of g. For example, the correlations between g factor scores and full-scale IQ scores from Wechsler's tests have been found to be greater than .95. 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. However, the g loading of the same test may vary somewhat depending on the composition of the test battery.

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.

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.