Wednesday, March 07, 2007

g: A precis   posted by Alex B. @ 3/07/2007 08:35:00 PM


The study of intelligence goes back many millennia, but, as such, it was usually defined as a nebulous construct and it fell more under the domain of philosophy than, say, science. Enter Francis Galton. With his Darwinian ancestry and precocious nature, Galton became fascinated by human variability and spent most of his life pursuing various distributaries from this river (e.g., dactylography, anthropology). Most important to the field of individual differences, was his study of the nature of human cognitive abilities. That is, he was one the first (if not the first) to make a systematic study of human variation in cognitive abilities. In doing so, he developed a cadre of "brass instruments" to measure various aspects of basic human abilities, which, to him, were all related to this underlying, general cognitive ability.

People lay too much stress on apparent specialities, thinking over-rashly that, because a man is devoted to some particular pursuit, he could not possibly have succeeded in anything else. They might as well say that, because a youth had fallen desperately in love with a brunette, he could not possibly have fallen in love with a blonde. He may or may not have more natural liking for the former type of beauty than the latter, but it is more probable a not the affair was mainly or wholly due to a general amorousness of disposition (Galton, 1869, p. 6)

While in his time, his elementary task/sensory discrimination data did not support his hypothesis that they were related to other "common sense" criteria such as education and occupation, later, when Fisherian analysis were applied, Galton was proved to be correct--that is, there were group differences in average scores (Johnson, McClearn, Yuen, Nagoshi, Ahern, & Cole, 1985).

In addition to his interest in elementary tasks, Galton was also interested in more traditional psychometrics. In fact, he convinced the British Association for the Advancement of Science to conduct a survey of mental capacities throughout British schools. William McDougal was appointed to head this up and his student, Sir Cyril Burt, got his initial taste of the field of applied psychometrics from this project (Burt, 1972).


As important as Galton was in developing the underpinnings to modern intelligence research, he was not able to conceive of a way to measure general cognitive ability. Instead, this task was accomplished by engineer-turned-psychologist Charles Spearman (1904). Spearman was able to accomplish this based on two of his mathematical "inventions:" Classical Test Theory (CTT) and Factor Analysis (FA). Neither one of these is particularly easy to explicate via BLOG form, but the bottom line is: (a) CTT allowed for one to find the correlation between two variables, disattenuated by (random) measurement error; and (b) FA allowed for one to extract commonalities in groups of correlations. That is: If variable A, variable B, and variable C are all highly correlated with each other, then they likely have something in common. FA allows one to "get at" the thing (loosely speaking) that they have in common.

For example, if we have the following correlations for A, B, and C, then the last row has the correlations between the variable and the common factor (i.e., factor loadings)


B 0.7

C 0.8 0.75

g loadings

0.864 0.810 0.926

Spearman called that underlying factor general intelligence, and that is still what is meant today when the moniker Spearman's g is used, even though the factor analytic techniques have greatly advanced since Spearman's day.

After Spearman's developments, there was a period of controversy as to (a) whether g existed, (b) if it existed, was it the only factor that could be extracted, and (c) if other factors could be extracted, could g be extracted at the same time? The details of this (needless?) argumentation need not concern this post (for a succinct summary, see Carroll, 1993), with the eventual conclusion being that, given a sufficient diversity of tests, g could be extracted, but other, more primary factors (e.g., Working memory, Long-term memory, Quantitative knowledge) could also be extracted. A picture is given below:

Spearman's g is at the apex, the more primary ability are the circles below, and the tests from which the factors were extracted are represented by the boxes [the circles are used as that is the common way of representing latent variables; likewise, boxes are common way of representing manifest variables]


Around the same time Spearman and his London School contemporaries were doing their work in g theory, the field of intelligence testing was arising--due in large part to Binet and Simon's work in France, Goddard and Terman's work in the US, and Burt's work in the UK. Today, intelligence is often used synonymously with IQ scores, which, outside of differential psychology and psychometrics, is also used synonymously with Spearman's g. They are similar concepts, undoubtedly, but they need distinction.

Intelligence. A nebulous construct at best, it had eluded a century of definition, and, in Arthur Jensen's (1998) own words, "psychologists are incapable of reaching a consensus on its definition" (p. 48) As it cannot be defined, we will not use it any further.

Spearman's g. It is the primary factor extracted from the correlation matrix of a group of variables that all measure some aspect of cognitive ability. That is, it is the part of the covariance that all the variables have in common with each other.

Intelligence Quotient (IQ). An imperfect measure of Spearman's g. That is, in modern IQ tests, IQ scores are the weighted average of performance all the subtests involved. This is sometimes referred to as "intelligence in general" as opposed to "general intelligence" (i.e., Spearman's g), but for general purposes an IQ score can be thought of as rough measure of Spearman's' g, plus some (random) measurement error. Usually these scores are scaled such that most people will have a score between 90 and 110; mental retardation is a serious consideration for people with IQs below 70, as giftedness is a serious consideration for people with IQs greater that 120.

Why All the Fuss?

As presented, one may easily come to the conclusion of, so what? IQ/g sounds like it is another entry in the massive world of psychobabble, along with mental bonds, closure, and life coaching. The fuss is this:

No other variable in the history of psychology has (strongly) predicted such a wide variety of life outcomes.

  • Educational Outcomes (Deary, Strand, Smith, & Fernandes, 2007; Kuncel, Hezlett, & Ones, 2004)

  • Physical Health/Accidents (Gottfredson, 2004; Gottfredson & Deary, 2004).

  • Reaction Time to Cognitive Tasks (Jensen, 2006)

  • Occupation Status (Gottfredson, 1986; Herrnstein & Murray, 1994)

  • Job Success (Schmidt & Hunter, 1998, 2004)

  • Crime (Ellis & Walsh, 2003).

  • Race Differences (Lynn, 2005; Rushton & Jensen, 2005)

  • Sex Differences (Lynn & Irwing, 2004)

  • GDP (Lynn & Vanhanen, 2006)

And this is to just name a few.

If I were to stop here, one might be under the impression that g/IQ are important, but (a) there are other forms of "intelligence"; and (b) that IQ is just a product of the environment and can be raised (almost) at will.

Multiple Intelligences

The theory of Multiple Intelligences (MI) stems from Howard Gardner who (now) posits that g exists, but so do other forms of independent "intelligences" that (equally) predict life success. His other forms are things like interpersonal skills, intrapersonal knowledge, and kinesthetic ability. Since in the 25 years since MI has been around, Gardner has refused to test his hypotheses, it really is not even worth mentioning anymore. Thus, I won't (for some empirical work showing why Gardner is, well, wrong, see Visser, Ashton, & Verson, 2006, under review).

Triarchic Theory of Intelligence

This works stem from the work of Robert Sternberg, and his theory of cognitive ability that, similar to Gardner, posits that g exists, but that there are independent cognitive entities that are useful in life, such as practical intelligence; he even goes so far as to say that these independent entities are better predictors of life outcomes than g. Unfortunately, like Gardner, he doesn't readily submit his theories to much empiricism, and his claims, to date, are unsubstantiated (for an excellent critique, see Gottfredson, 2003).

Stability and Raising g/IQ

If one is under the impression that the environment can have massive influence on g, the logical product of that belief is that massive government programs should be able to raise cognitive abilities. In short, they do not. They produce short-term gains, but the gains do not last long (see, for example, Spitz, 1986, 1992). This is not to say that other things, such as nutritional supplementation, might not be able to increase cognitive performance, but massive environmental programs, at least as implemented in the past 50 years, have not. Moreover, IQ scores measured when one is 10ish are consistent, very consistent, with IQ scores measured almost 70 years later on the same individuals (Deary, Whalley, Lemmon, Crawford & Starr, 2000). That is, despite a life's worth of diversity of experience, your IQ when you are in Middle School is very predictive of your IQ when you retire.

Take Home Message

g is ubiquitous in cognitive tasks, it is stable across time in individuals, and no other variable in the history of psychology has been able to predict so many life outcomes, so well.


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