Comment on Open thread, 7-14 July 2014

Sun, 13 Jul 2014 17:11:52 GMT

It might, but there are subtleties you have to take into account. For example, ceiling effects will hide the claimed effect, and if there's not enough floor, can even produce a lower mean.

Imagine you have a test of 10 4-multiple-choice questions, male mean = female mean but males have higher variance, and the average student's score on the test would be 8, so lots of students score a perfect 10 but you would have to be retarded to score <=2. What will the mean by gender look like under this scenario? Since the male variance is higher, there will be several times more near-retarded boys than girls scoring in the lower ranks like 3-4; there will nearly as many normal boys as normal girls with normal scores like 7-9; and the rest will score 10 - but the many more boys than girls who are far out on the tail (are genius at maths) will also score 10 and look like fairly ordinary types. So the dim boys drag down the mean of all boys, the ordinary boys by definition match their girl counterparts, while the geniuses can't show their stuff and might as well have not been tested at all; and so on net, it looks like the boys perform worse than the girls even though they actually are the same on average and have a higher variance. This is because I invented a test which is able to pick up on the differences among the low-performers (by devoting 7 questions to them) but not among the high-performers (just 2 questions), and this favors the group with the least representation among both tails (females).

And most real-world exams are uninterested in making very fine gradations among the top 1% of students like you need to if you want to answer questions about 'how many female Fields Medalists - top mathematician in the entire world - should there be?' because with non-adaptive tests you would have to force the 99% of ordinary people to slog through endless reams of questions they have no idea about. (American schools have no incentive to look because they are not evaluated under No Child Left Behind based on how many world-class students pass through their halls, they're evaluated on the average student and especially the minorities.)

Other issues include to what extent those exams are based on class grades (the usual situation is boys do worse on grades, better on exams, because grades measure how much you can ingratiate yourself to your teacher by things like sitting still and doing even the most tedious moronic homework each and every time) and whether the exam are being administered after puberty where the increased variance is expected to manifest itself.

Discuss