## How to get someone’s g

“Intelligence”, “IQ”, “g” (due to Spearman), are terms that are bandied around.

The following may be helpful: the gist of how to calculate someone’s g score, which is often used as the measure of someone’s “intelligence”.

For example, that’s the “IQ”/”intelligence” referred to in the recentish BBC article on research linking childhood intelligence and adult vegetarianism (clever children grow into clever vegetarian adults).

1. Give hundreds or thousands of people a dozen tests of ability.
2. Zap everyone’s scores with PCA or factor analysis.
3. g is the first component and usually explains around half the variance.  Here’s an example genre of analysis of g with other facets to psychometric intelligence.
4. Use the component to calculate a score.  For factor analysis there are many ways to do this, e.g. Thompson’s scores, Bartlett’s weighted least-squares.  The gist is that for each person you compute a weighted sum of their scores, where the weights are a function of how loaded the particular test score was on g.
5. To get something resembling an IQ score, scale it so it has a mean of 100 and an SD of 15.
6. Talk about it as if it were a substantive psychological construct, rather than a statistical artefact 😉

What is this mysterious g thing?

## Ye olde Spearman

A good test of whether someone understands g is if they characterise it as a general factor in intelligence test scores and not as general intelligence (i.e., a substantive rather than statistical construct). But it’s interesting to see what Spearman originally said in his 1904 “General Intelligence,” Objectively Determined and Measured. On p. 272:

“… we reach the profoundly important conclusion that there really exists a something that we may provisionally term “General Sensory Discrimination” and similarly a “General Intelligence,” and further that the functional correspondence between these two is not appreciably less than absolute.”

He goes on to describe this as a “general theorem”, refining it to (p. 273):

Whenever branches of intellectual activity are at all dissimilar, then their correlations with one another appear wholly due to their being all variously saturated with some common fundamental Function (or group of Functions).”

(Enthusiastic emphasis in original.)

There’s a recent argument against this (though perhaps not quite, given Spearman’s parenthetical “group of Functions”), by van der Maas, et al. (2006). The abstract:

“Scores on cognitive tasks used in intelligence tests correlate positively with each other, i.e., they display a positive manifold of correlations. The positive manifold is often explained by positing a dominant latent variable, the g-factor, associated with a single quantitative cognitive or biological process or capacity. In this paper we propose a new explanation of the positive manifold based on a dynamical model, in which reciprocal causation or mutualism plays a central role. It is shown that the positive manifold emerges purely by positive beneficial interactions between cognitive processes during development. A single underlying g-factor plays no role in the model. The model offers explanations of important findings in intelligence research, such as the hierarchical factor structure of intelligence, the low predictability of intelligence from early childhood performance, the integration/differentiation effect, the increase in heritability of g, the Jensen effect, and is consistent with current explanations of the Flynn effect.”