I wonder whether there's any effect in the opposite direction: if members of a minority believe that their group performs better than average in some subject, are their scores higher than those of people who don't believe the same?

The kids at ds's school -- Asian and non-Asian alike -- joke about the 'Asian invasion' they see at competitions. I don't know whether this reflects a belief in some innate Asian superiority in math; I'm guessing the adults at these events (and maybe their kids, too) are all aware that the Chinese and Indian parents whose children excel there mostly come from the upper tier of their home countries' populations in terms of education.