IQ tests are a form of convergent preferential bias and they don’t test for abstraction or creativity which is more than half the definition of intelligence.
They don't test for creativity (though seeing a correlation between IQ and creativity would be interesting) but they almost certainly test the ability to deal with abstractions. That's pretty much what an I test is! What reason do you have for thinking otherwise?
They test for puzzles that appear as visual shape complexities which require use of the visual cortex. That is something a person might refer to as a visual abstraction. That isn't a practical abstraction, such as requiring a person to form an answer from the absent of acceptable criteria (to abstract or form something new to solve a problem).
It's not readily apparent to my that those two abilities should be distinct. It seems plenty likely that they would be at least highly correlated. While you're point about the visual cortex may be relevant, I don't think that's the whole story.
My understanding is that different IQ tests will rely on different kinds of questions (i.e. not all involve visual shapes; some involve word/logic puzzles). The point the scores for all IQ tests correlate very highly (and thus suggest that there exists some common factor).
It means a bias of coming together toward a tester's preferences. Do people excel on the few narrow performance meausures you find most correlated with intelligence?
There are divergent aptitude tests measure quantity and diversity of answers to a given question opposed to the one desired answer. Divergent tests are rarely performed, but at a stronger measure of creativity and problem solving which is typically what people actually want when they say intelligence. The reason why convergent testing is preferred over divergent test is because it is easier to measure and those simplified measures are easier to compare.
Can you provide a link for divergent aptitude tests? I'm afraid my search results all have to do with some young-adult fiction novel (called Divergent).
How much do such tests correlate with things like (for example) creative achievement?