CHC Theory, Cognitive Assessment

Is g an ability?

Here is an excerpt from an early draft of the forthcoming chapter I wrote with Kevin McGrew. Almost of all of this section was removed because the chapter was starting to look like it was going to be over 200 pages. Editing the chapter down to 100 pages was painful and many parts we liked were removed:
Is g an ability?

The controversy about the theoretical status of g may have less fire and venom if some misunderstandings are cleared up. First, Spearman did not believe that performance on tests was affected by g and only g. In a review of a book by his rival Godfrey Thomson, Spearman (1940, p. 306) clarified his position.

“For I myself, no less than Thomson, accept the hypothesis that the observed test-scores, and therefore their correlations, derive originally from a great number of small causes; as genes, neurones, etc. Indeed this much seems to be accepted universally. We only disagree as to the way in which this derivation is to be explained.”

Second, Spearman (1927, p. 92) always maintained, even in his first paper about g (Spearman, 1904, p. 284), that g might consist of more than one general factor. Cattell (1943) noted that this was an anticipation of Gf-Gc Theory. Third, Spearman did not consider g to be an ability, or even a thing. Yes, you read that sentence correctly. Surprisingly, neither does Arthur Jensen, perhaps the most (in)famous living proponent of Spearman’s theory. Wait! The paper describing the discovery of g was called “‘General Intelligence’: Objectively Determined and Measured.” Surely this means that Spearman believed that g was general intelligence. Yes, but not really. Spearman thought it unproductive to equate g with intelligence, the latter being a complex amalgamation of many abilities (Jensen, 2000). Spearman believed that “intelligence” is a folk concept and thus no one can say anything scientific about it because everyone can define it whichever way they wish. Contemplating the contradictory definitions of intelligence moved Spearman (1927, p. 14) to erupt,

“Chaos itself can go no farther! The disagreement between different testers—indeed, even between the doctrine and the practice of the selfsame tester—has reached its apogee. […] In truth, ‘intelligence’ has become a mere vocal sound, a word with so many meanings that finally it has none.”

Spearman had a much more subtle conceptualization of g than many critics give him credit for. In discussing the difficulty of equating g with intelligence, or variations of that word with more precise meanings such as abstraction or adaptation, Spearman (1927, p.88) explained,

“Even the best of these renderings of intelligence, however, always presents one serious general difficulty. This is that such terms as adaptation, abstraction, and so forth denote entire mental operations; whereas our g, as we have seen, measures only a factor in any operation, not the whole of it.”

At a conference in which the proceedings were published in an edited volume (Bock, Goode, & Webb, 2000), Maynard Smith argued that there isn’t a thing called athletic ability but rather it is a performance category. That is, athletic ability would have various components such as heart volume, muscle size, etc. Smith went on to argue that g, like athletic ability, is simply a correlate that is statistically good at predicting performance. Jensen, in reply, said, “No one who has worked in this field has ever thought of g as an entity or thing. Spearman, who discovered g, actually said the very same thing that you’re saying now, and Cyril Burt and Hans Eysenck said that also: just about everyone who has worked in this field has not been confused on that point.” (Bock, Goode, & Webb, 2000, p. 29). In a later discussion at the same conference, Jensen clarified his point by saying that g is not a thing but is instead the total action of many things. He then listed a number of candidates that might explain why disparate regions and functions of the brain tend to function at a similar level within the same person such as the amount of myelination of axons, the efficiency of neural signaling, and the total number of neurons in the brain (Bock, Goode, & Webb, 2000, p. 52). Note that none of these hypotheses suggest that g is an ability. Rather, g is what makes abilities similar to each other within a particular person’s brain.

In Jensen’s remarks, all of the influences on g were parameters of brain functioning. We can extend Jensen’s reasoning to environmental influences with a thought experiment. Suspend disbelief for a moment and suppose that there is only one general influence on brain functioning: lead exposure. Because of individual differences in degree of lead exposure, all brain functions are positively correlated and thus a factor analysis would find a psychometric g-factor. Undoubtedly, it would be a smaller g-factor than is actually observed but it would exist.

In this thought experiment, g is not an ability. It is not lead exposure itself, but the effect of lead exposure. There is no g to be found in any person’s brain. Instead, g is a property of the group of people tested. Analogously, a statistical mean is not a property of individuals but a group property (Bartholomew, 2004). This hypothetical g emerges because lead exposure influences all of the brain at the same time and because some people are exposed to more lead than are others.

In the thought experiment above, the assumptions were unrealistically simple and restrictive. It is certain that individual differences in brain functioning is influenced in part by genetic differences among individuals and that some genetic differences affect almost all cognitive abilities (Exhibit A: Down Syndrome). Some genetic differences affect some abilities more than others (e.g., William’s Syndrome, caused by a deletion of about 26 genes on chromosome 7, is associated with impaired spatial processing but relatively intact verbal ability). Thus, there are general genetic influences on brain functioning and there are genetic differences that affect only a subset of brain functions.

The fact that there are some genetic differences with general effects on cognitive ability (and there are probably many) is enough to produce at least a small g-factor, and possibly a large one. However, there are many environmental effects that affect most aspects of cognitive functioning. Lead exposure is just one of many toxins that likely operate this way (e.g., mercury & arsenic). There are viruses and other pathogens that infect the brain more or less indiscriminately and thus have an effect on all cognitive abilities. Many head injuries are relatively focal (e.g., microstrokes and bullet wounds) but others are more global (e.g., large strokes and blunt force trauma) and thus increase the size of psychometric g. Poor nutrition probably hampers the functioning of individual neurons indiscriminately but the systems that govern the most vital brain functions have more robust mechanisms and greater redundancy so that temporary periods of extreme malnourishment affect some brain functions more than others. Even when you are a little hungry, the first abilities to suffer are highly g-loaded and evolutionarily new abilities such as working memory and controlled attention.

Societal forces probably also increase the size of psychometric g. Economic inequality ensures that some people will have more of everything that enhances cognitive abilities and more protection from everything that diminishes them. This means that influences on cognitive abilities that are not intrinsically connected (e.g., living in highly polluted environments, being exposed to water-borne parasites, poor medical care, poor schools, cultural practices that fail to encourage excellence in cognitively demanding domains, reduced access to knowledgeable mentors among many many others) are correlated. Correlated influences on abilities cause otherwise independent cognitive abilities to be correlated, increasing the size of psychometric g. How much any of these factors increase the size of psychometric g (if at all) is not yet known. The point is that just because abilities are influenced by a common cause, does not mean that the common cause is an ability.

There are two false dichotomies we should be careful to avoid. The first is the distinction between nature and nurture. There are many reasons that genetic and environmental effects on cognitive abilities might be correlated, including the possibility that genes affect the environment and the possibility that the environment alters the effect of genes. The second false choice is the notion that either psychometric g is an ability or it is not. Note that if we allow that some of psychometric g is determined by things that are not abilities, it does not mean that there are no truly general abilities (e.g., working memory, processing speed, fluid intelligence, and so forth). Both types of general influences on abilities can be present.

In this section, we have argued that not even the inventor of g considered it to be an ability. Why do so many scholars write as if Spearman believed otherwise? In truth, he (and Jensen as well) often wrote in a sort of mental shorthand as if g were an ability or a thing that a person could have more of or less of. Cattell (1943) gives this elegantly persuasive justification:

Obviously “g” is no more resident in the individual than the horsepower of a car is resident in the engine. It is a concept derived from the relations between the individual and his environment. But what trait that we normally project into and assign to the individual is not? The important further condition is that the factor is not determinable by the individual and his environment but only in relation to a group and its environment. A test factor loading or an individual’s factor endowment has meaning only in relation to a population and an environment. But it is difficult to see why there should be any objection to the concept of intelligence being given so abstract a habitation when economists, for example, are quite prepared to assign to such a simple, concrete notion as “price” an equally relational existence. (p. 19)


7 thoughts on “Is g an ability?

  1. Jonathon says:

    I think your discussion would be improved a great deal by giving a clear definition for the notion of “ability”. The levels of generalization involved in factor analysis do not seem to be entirely in favor of a non-ability characterization of g, for then we wouldn’t say “fluid intelligence/ability” or “crystal intelligence/ability” but “fluid non-something” and “crystal non-something” which is seriously stilted, awkward, and counter-intuitive.

    As for thing-ness, mathematical entities tend towards reification more often than not, so on that grounds you could find suitable criticism by rejecting the reification itself. I.e., just as an equation describes the dimensions of a sphere that need not exist (no “perfect” sphere really exists), g describes (to a greater or lesser extent) the relationships among a set of variables that need not itself (“perfectly”) exist. That is, it’s a means to model certain phenomena, not to serve as a postulated entity.

    Otherwise, I think this should help others come to a better understanding of how g fits into the greater psychometric picture.

    Hope you had an explosive 4th. 🙂


    P.S.: 11th paragraph 2nd sentence, the second “effect” should be “affect” as in “influence”. (First thing I check for if it’s being used as a verb or not, which usually helps. Or just a pesky midnight typo.)

    • Hi Jonathon,

      Thanks for catching the typo. It is fixed.

      Yes, the definition of an ability is a more complex issue than I had previously appreciated. Maybe I’ll post some thoughts on it later.

      I am not sure why Gf and Gc must have the same theoretical status as g.

      • Jonathon says:

        Mr. Schneider,

        Glad I could help a little.

        I didn’t mean to imply that Gf and Gc must have the same theoretical status as g (because they don’t); if we follow CHC Theory, the former are obviously Stratum II broad “abilities”, whereas the latter is a Stratum III general construct or factor. I meant to imply that in common parlance, we hear such things as “general cognitive *ability*” or “general *intelligence*” that are at once apparently (wrongly or rightly) implied by, or associated, with the construct g. Thus, this discussion would be further improved by exploring these terms, their uses, and how it is they’ve come into vogue. Scientific terms and concepts are not constant over time, and Spearman today might be disinclined from his initial estimations of the nature of g proper, i.e., things have changed somewhat since his time. (Case in point, phlogiston theory was in power for many years before it was realized that oxygen is the principal cause of combustion, not the non-thing called phlogiston. And I don’t seriously think g is today’s phlogiston.) However, I’m not so sure it’s to our benefit to emphasize what noted people of the past have said about this explicitly, because that would be mere idolatry, while their reasons and (valid) justifications could reveal many things of value which count as the substance of our inquiry, to be sure.

        Be that what it may, thanks for sharing. I appreciate your posts as they are informative and helpful. I’m even considering developing my own toys for evaluative purposes, despite or because of my amateur interest in this subject.


      • If your point is “If the same methods and evidence that cause us to think about Gc and Gf as abilities also say the same thing about g, then we should call g an ability,” then I agree. There is no reason to discriminate against g.

        I hope that I was not interpreted as saying that Spearman gets to define g for all time by right of being the original theorist. Arguments by authority are not terribly convincing. However, I dislike it when Spearman is misinterpreted and authors congratulate themselves for giving Strawman Spearman a good thrashing. If we are to disagree with Spearman and his heirs, we should be careful to disagree with things that they actually believed.

      • Jonathon says:

        Dr. Schneider,

        Yes, I can see where you’re coming from. Forgive me not fully grasping your intent.

        That said, I kind of like the sound of “Strawman Spearman”. He seems to scare a lot of crows.

        Kind regards,

  2. Karis Post says:

    This is such a lucid explanation – would it be all right for me to share it with the intern whom I will be supervising this school year? If so, is there a way I could get a copy?

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