A number of people have been talking about the gender gap in math in the US recently. The debate was most likely initiated by Larry Summer’s comments on the small number of female researchers in hard sciences in the top US schools. So much so that there might also be some policy initiative to address the problem.
There, of course, has been some careful analysis of the gender gap phenomenon. Steve Levitt’s this paper is an example. However, there are some people who just tinker with the distribution of the test scores to infer something about differences in abilities between male and female students.
So the important question is can we use the distribution of test scores for male and female students to infer something about the difference in their abilities? My answer is a straight no. Technically there would arise what we call an endogeneity problem. Existence of social bias and the ever pervasive gender stereotyping has a great influence in shaping the preferences and development of certain abilities among male and female students. If this is the case, the resulting distribution would reflect these cultivated differences and hence any inference based on it about the gender gap is going to be obvious. It is like we planted one avocado and one mango tree a while back and then after some time infer that they give completely different fruits. How stupid would that be?