# To what extent does AFQT correlate with IQ?

Wikipedia has a pretty non-informative page as to the nature of the (US) Armed Forces Qualification Test (AFQT) as it mostly talks of results ranges etc. What I could descipher from there is it that it has three (or maybe four, depending on how one counts) [sub]parts,

• Arithmetic Reasoning (AR) – 30 questions in 36 minutes
• Mathematics Knowledge (MK) – 25 questions in 24 minutes
• Verbal Expression (VE)= (WK)+(PC)
• Word Knowledge (WK) – 35 questions in 11 minutes
• Paragraph Comprehension (PC) – 11 questions in 22 minutes

and

The formula for computing an AFQT score is: AR + MK + (2 x VE).

That sounds a bit like SAT... and a quick search found one paper that talks of "cognitive skills as measured by the AFQT". (SAT is pretty well correlated with IQ.) So, to what extent does AFQT correlate to more traditional IQ [sub-]scores?

## 1 Answer

An answer is found in an official memo, albeit from 1980, where

• the correlation of AFQT with WAIS (no version specified) was stated as 0.8 based on a Army "fact sheet" from 1965; the details of the comparative test could not be found
• an Air Force comparison found (in 1974) that the correlation (again with WAIS, no version specified) for white enlistees was (again) 0.8 but 0.77 for black enlistees.

(This ~0.8 is actually about the same as the correlation of IQ tests with SAT.) I don't know if the AFQT is still the same as back then.

A official-looking 2006 concordance/translation table of AFQT score with SAT scores can also be found, although it's rather summary; it doesn't mention a correlation coefficient.

• It is worth noting that the most commonly used IQ tests don't even correlate perfectly with themselves. Or said in another way, of course there is always some measurement error. A good IQ test may have test-retest correlation of $r = 0.9$, and hence the correlation of $0.8$ is actually an underestimation of the strength of the relation between IQ tests and the AFQT, because some of that remaining $1-0.8 = 0.2$ is simply measurement noise. – Eff Jul 16 '18 at 7:59