There’s a large number of papers about the relationship between national intelligence and national scholastic scores, and to which degree the latter indexes the former. Some typical papers:

Because of papers like this, of which there’s 100s, it is actually quite difficult to find studies that relate scholastic tests to intelligence at the individual level since there’s no simple way to remove the national-level results from the search results (as far as I can work out!). However, John Fuerst was able to find two:

The first reports several latent correlations, finding β = .70 or so. The second reports some correlations between Raven’s SPM and PISA, at r = .56 or so. So the first is already adjusted for measurement error because it’s SEM based. However, the intelligence tests were pretty short, so there is some construct invalidity (i.e., it’s not measuring a broad enough g). In the second case, one has to adjust for measurement error and construct invalidity. Probably in both cases, doing these adjustments would bring up the estimated true correlation to about .80 or so. This is the typical value seen for other achievement tests and intelligence batteries in SEM. E.g.:

These studies generally find r = .70 to .80, towards the latter when stronger methods are used to estimate the latent relationship instead of the observed.

As a die-hard Jensenist, I will of course note that Jensen wrote back in 1969:

The Stanford-Binet and similar intelligence tests predict various measures of scholastic achievement with an average validity coefficient of about .5 to .6, and in longitudinal data comprising intelligence test and achievement measures on the same children over a number of years, the multiple correlation between intelligence and scholastic achievement is almost as high as the reliability of the measures will permit.

For the reader who wants a lot more, there is a 100+ page book chapter on it from 1993:

  • Jensen, A. R. (1993). “Psychometric g and achievement“. In B. R. Gifford (Ed.), Policy perspectives on educational testing. Norwell, MA: Kluwer Academic Publishers. Pp. 117-227.

Honorable mentions

Longitudinal studies: