Lognormality of data is killing for the methods of social scientists. If I were to hypothesize the underlying mechanism then it would be that raw skill is lognormally distributed for those taking tests at all (at least participating in these test usually entails an implicit lower bound on IQ, but also from the long tail of high performance in say sports), tests try to measure performance but with a reduction to normality (or 4 categories) and then people estimate their own skills based on their task and grading experiences which are also reduction to a normal or constant distribution. (“I was always a B- in math in high school and expect that to have distribution X and this test to follow that distribution“).

It’s three places where reductions in dimensionality take place both implicitly and explicitly. I don’t envy researchers trying to unpeel this onion. I do like the unraveling of all these problems that pop up in pretty accessible designed experiments. It makes for better understanding.