<p>@smdur1970: Thanks for the thought-provoking post. I tried to think of implications for the naviance data I can access. The scattergrams are not divided by sex, but I speculated that perhaps the boys you identified who are not applying have lower GPAs but not necessarily lower SATs. That is, they may be as bright on average but not as dedicated. Alas, when I looked at the data from one school, the UVa admits had a higher average GPA by .06 but W&M had a higher average SAT (1600) by 20 points. (The sample sizes are around 80 but I do not have the stomach to estimate standard deviations.) Obviously, this is the data for admits not applicants, it is just one school, and there are many other factors that are not being controlled. But, as of now, I was not able to come up with supporting evidence. </p>
<p>The one thing that gives me pause is the general character of the scattegrams. I have posted before that the UVa scattergram seems very regular but W&M does not. (For those who have not seen the scattergrams, they plot SAT on the horizontal axis and GPA on the vertical. Admits show up as green squares while non-admits show up as a red X.) If you fit a curve to the UVa data in an attempt to separate the admits from the non-admits, there would be very few observations on the wrong side of the curve (i.e., admits below or non-admits above). At W&M, there would be. My previous hypothesis was that W&M just puts a lot of weight on other dimensions (essays, letters of recommendation, etc.) But there is another hypothesis that is consistent: There could be lots of female non-admits above the curve and male admits below.</p>