IQ has nothing at all to do with education. In fact for IQ to be accurately measured the test can’t rely on information that can be learned.
IQ is a measurement of the ability to understand. IF one has a higher IQ they would be able to achieve a higher education level, but the IQ was there before the education.
A rather stupid person can attain an advanced education if they work hard enough, or they are ‘helped’ along.
Early life exposure to an educational environment can actually increase IQ. But I was making no claim that having a higher education increases IQ. It does, however, fairly strongly correlate with it—which was my point.
Sure, there are lots of dull PhDs in education, but not too many stupid PhDs in physics—and the overall average correlation is still fairly strong.