Kees Jan can't
Kees-Jan Kan, a young Dutchman, has recently rediscovered one of the most basic facts in IQ testing: That it's easiest to detect IQ differences if the people you are studying (Ss) have a common background. So if the Ss are all in the same class at school, for instance, a vocabulary test (finding out how many hard words they know) will give you a quick and easy way to sort them out. And you will find that the guys who know lots of words are also good at a whole range of puzzles, even mathematical ones.
So a common background optimizes your chances of assessing IQ accurately. And to be a bit technical, vocab loads highly on 'g' (the general factor in intelligence), meaning that, where it can be used, it is a powerful predictor of other abilities. Vocab is however convenient rather than essential in IQ measurement. Tests designed for use among people who do not have a common background (such as the Raven PMs) don't use it but still work perfectly well.
On those basic facts, KJK has erected an elaborate theory, which comes to the conclusions that IQ is mostly cultural, with a genetic component much smaller that is generally thought. And it is the cultural part which is hereditary.
To arrive at that, KJK goes via the concept of the "cultural load" of each IQ question -- which he assesses by looking at how often a question has to be altered when you are adminstering it to a new and different population. And he finds that by removing (statistically) the influence of cultural load, all other correlations are much reduced.
When we look more closely at his data, however (e.g. Table 3.1 in KJK's doctoral dissertation) we find that only two out of 11 question types have a high cultural load: Vocab and general knowledge. And the cultural dependency of those two question types has been obvious to everyone since the year dot.
What is interesting however is that the remaining 9 question types have low to negligible cultural load. In other words, we could remove the vocab and knowledge subtests from the overall test and still have a robust test. So my conclusion is that what KJK should have done from the beginning is to remove those two flawed item types from his calculations altogether. Once you do that all his exciting findings melt away. His findings rely on items that he himself knows to be flawed.
There is a summary of KJK's dissertation at The Unscientific American -- JR