How to get someone’s g

“Intelligence”, “IQ”, “g“, are terms that are often bandied around.  The following may be helpful: the gist of how to get someone’s g score, which is often used as the measure of someone’s IQ (e.g. that’s the “IQ”/”intelligence” that’s referred to in the recentish BBC news article linking childhood intelligence and vegetarianism).

1. Give many people a load of tests of ability.
2. Zap everyone’s scores with PCA or factor analysis.
3. g is the first component and usually explains around 60% of the variance.  Here’s a picture of g with some other components.
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 has a mean of 100 and a s.d. of 15.

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