Post Number:#82
June 19th, 2012, 7:00 pm
One aspect of the question has not been discussed here at any length—the construction of the general intelligence factor or g factor through factor analysis. Since it bears on the definition of intelligence itself, it may be worth the time. It's technical, but interesting.
In everyday life intelligence is not a quality observed directly like height or weight, instead it is a quality inferred from success in school, work, and problem solving. People who excel at lots of different mental activities are deemed intelligent.
Since a direct controlled measurement is desirable for scientific studies and practical uses, intelligence testing was developed over the last century. A good intelligence test should be independent of cultural factors and education—conditions not easily met. Intelligence scores from different tests are positively correlated among themselves and positively correlated with success in school and work, that is, they all generally vary in the same direction. They are not perfectly correlated, just as height and weight are not perfectly correlated. Tall people overall weigh more than short people, but there are tall and skinny people and short heavy people.
How are scores from different intelligence tests to be compared and evaluated? If they are all measuring the same ability, they ought to be highly correlated with each other and over time for the same individual. If not, are they actually measuring intelligence? This is the kind of question that factor analysis is designed to help resolve. You might think that simply averaging the scores of all the different intelligence tests would be a good way to find a better measure of intelligence than any one of them could offer. That is not always a bad idea, but mathematically there is a better one—factor analysis.
The mathematics of factor analysis is linear algebra, not the most advanced mathematics by any means, but too much to explain here. To keep it simple, suppose you have two intelligence tests that generally agree, T1 and T2. That is, they do not exactly agree, but they correlate. The idea is to find out what it is they measure in common and use that constructed measure or factor to serve as a better proxy for intelligence than either would be by itself. If that factor is called F, then the result of the analysis would be to find F along with λ1, λ2, ε1,ε2
so that we have
T1 = λ1F + ε1 and T2 = λ2F + ε2.
In other words at the end of the analysis you can see what the unobserved factor F contributes to T1 and T2 and in effect the two original variables are determined by one constructed variable. The general solution to this problem is not unique. The idea goes back to Charles Spearman in a paper published in 1904 and it was developed specifically to deal with the question of intelligence. The mathematical technique has since been used in many areas, but especially in the social and psychological sciences where concepts are hard to measure directly.
Those who use this technique in the analysis of intelligence testing call the constructed factor g for general intelligence factor. It cannot be measured directly and its distribution over the population cannot be known, but might be expected to be a normal distribution. The real question then that underlies the discussion here is whether g—however defined— in any sense measures something real, a latent and unobserved variable that is an accurate numerical reflection of what we mean by intelligence or whether it is simply an artificial construct with little meaning.
A major controversy over this question arose with the publication of Stephen Jay Gould's book The Mismeasure of Man in which he discussed the use of factor analysis in estimating intelligence and argued against it. Gould's book was popular and won awards, but it also drew vehement criticism from those in the field who were using factor analysis. A similar controversy erupted again after publication of The Bell Curve in 1994, but not specifically over the use of factor analysis.
The g factor remains the essential item in arguments that intelligence is hereditary and varies among ethnic groups.
Everywhere I have sought peace and never found it except in a corner with a book. —Thomas à Kempis