I have received a few questions on g, John Carroll’s Theory (technically the Cattell-Horn-Carroll (CHC) Theory, named after Raymond Cattell, John Horn and John Carroll), and intelligence.
While the field is far from in total agreement, I think these points are safe to say.
1. Intelligence is too broad and nebulous a term to use, except for common parlance. Moreover, it often evokes visceral reaction, which often hinders more than helps. Consequently, most use the term g, which stands for general intelligence (named by Charles Spearman). Spearman, like Galton and others before him, noticed that when he administered tests to kids that required cognitive ability (e.g., pitch discrimination, math facts), the zero-order correlations were all positive. Because of his rigorous math background (he was en engineer) he was able to use his correlation matrix to invent the technique of principal factor analysis (well, an early version of it anyway), which, basically, just took the first eigenroot and used the first set of eigenvectors. This gave him 2 things: a principal factor (which he called general intelligence, or g) and test-specific variance. There was lots of "controversy" over whether g was embedded in every cognitive task, and two of the main opponents were Raymond Cattell and John Horn. While over simplified, they said there were two general factors, Gf and Gc, which stand for fluid and crystallized general abilities, respectively, and not one common g. Gf was meant to denote the skills it takes to do tasks that require minimal previous knowledge (repeat numbers backwards, solve matrix analogies), and Gc was meant to denote the skills it takes to do tasks that do require specific content knowledge (vocabulary, math). While there was a debate on the specific hierarchy (i.e., whether g alone stood on top, or whether it was Gf and Gc), they all agreed that tasks could be broken down into specific (i.e., stuff that was unique to it alone) and general (i.e., stuff it shared with similar tests) parts. Well, this debate went on for a while until John Carroll came along with his 1993 classic, Human Cognitive Abilities, it which he re-factor analyzed hundreds of published cognitive test data sets (akin to a meta-analysis), using a factor analysis procedure that allows one to factor analyze correlated factors. The details are a little too complex to go into here (although he Carroll outlines it well in his book), but what he found was that when there were enough tests to analyze, g existed by itself as the higher order factor, but that there were 8 sub-factors (Gf and Gc being two of them) and under each subfactors were about 60 narrower abilities. See here for pictorial model. Because he had three different strata of abilities, ranging from specific to general, it is sometimes called the three-strata theory of cognitive abilities. Hands down, this is the most data-based and supported theory of cognitive ability currently viable.
2. Some researchers are more interested in g (e.g., Arthur Jensen), as it permeates all tests of cognitive ability, while others are more interested in some of the specific second order abilities (especially when working with those with learning difficulties) (e.g., the folks at IAP). Consequently, both study "intelligence", but with different goals for their research (i.e., differential psychology vs. clinical/practice-oriented psychology).
3. g, a subset of CHC theory, is probably the most researched aspect of the theory. After decades of research (about 100 years), these "facts" seem to have ample support, although new data is always being published:
a. g permeates every test that involves cognitive ability. Test is broadly defined and can mean regular daily activities (see Robert Gordon’s work), health and occupational outcomes (see Linda Gottfredson’s work—who, IMHO, ranks right up there with Arthur Jensen, Cyril Burt, and Charles Spearman for prolific research on g), reaction time (Mental Chronometric) tasks (see Arthur Jensen and Ian Deary’s work) or regular scholastic tasks.
b. g’s heritability is about .5, with it increasing as tasks get harder, and decreasing as tasks get easier. When you extract g from any body of tests, the heritability of performance goes to almost zero, which tends to show that it is the g component of a given task that is heritable, not the specific tasks themselves. Tony Vernon has done a lot here, as has Robert Plomin.
c. Race differences on cognitive ability tests tend to be primarily on the g factor. Phil Rushton has done oodles of work here. (some also say there is a sex difference, with men slightly higher, but I have not seen enough evidence to think it viable….at least at this time).
d. There appears to be a biological and neurological basis for g. The reason for this is that g correlates (and substantially so!) with a ton of biological variables. The best, although now a little dated, piece in this area was: Jensen, A. R., & Sinha, S. N. (1993). Physical correlates of human intelligence. In P.A. Vernon (Ed.) Biological approaches to the study of human intelligence (pp. 139-242). Norwood, NJ: Ablex. Although, also see Jensen’s Psycoloquy posts, and the second section of the new Jensen festschrift.
I am not a biologist by training, so I cannot critique the literature here as well as most of the folks who will read this post. From my readings though, the purponderance of evidence seems indicate that g does have a biological basis.