Once more, It's been shown that for a few cultures on a small norming sample on particular tests (IQ, SAT) that standard deviation on math related scores is gr

Once more, It's been shown that for a few cultures on a small norming sample on particular tests (IQ, SAT) that standard deviation on math related scores is greater than that for women. The bulk of the standard deviation is accounts for by people testing around the mean, because most of the scores are around the mean. Knowledge of the standard deviation does not, as our financial markets recently showed, correlate so well with extreme outliers, as those with Olympic level abilities are likely to have. And the sorts of thinking demanded by those taking an IQ test or the SAT are not so similar to those required by Olympiad level problem solving (correlated and similar though they are). And the sort of thinking required of Olympiad level problems is not so similar to that required for success in research mathematics (helpful and correlated though they are), as shown by the large numbers of people who attain great honors in such competitions and do not end up really producing much original work. And it's been shown and is frankly straightforward to see how cultural influences can effect both interest and resources available for bright young minds of any background or gender. We just don't know enough about one's aptitude and its interaction with the environment to make such blanket statements. Men have more variance in aptitude! It's like a difference of a standard deviation of 14.5 points for women and 15.5 points for men. Keep in mind also that a core component of most IQ tests and the SAT is time pressure. In the SAT it's raw time pressure, and in psychologist administered IQ tests you have several factor: one being an explicit time weighting, two being the the fact that the speed of one's response can give you a much higher score, three being that your answers are subjectively weighted by the psychologist (which could already introduce bias), and if you seem unsure you'll be docked points, and if you seem sure but speak vaguely you can often turn a yes into a no, and four whether or not they move forward in sections depends on how quickly you're answering. It's been shown by Benbow et. al. that, at least in America, girl's confidence with mathematics is astonishingly uncorrelated with their performance (unlike with boys, who, if they're good, tend to think they're even better.) It is completely reasonable that if you're more unsure about your own abilities you might hesitate for just a bit longer, sound a little less confident, hazard fewer guesses. This will, by itself, reduce variance in one's score. You'd need to account for only a 6% difference to explain the variance in score. (Also, from what I know, too, the selection processes of countries like Romania, Bulgaria, Russia, Ukraine, Hungary, China, and the USA are anything but a random pick. They can be quite grueling, actually.)