Cohen took full advantage of the Freedom of Information Act to collect an amazingly revealing data set. TJ begins the admissions process by ranking students from #1 to around #800 using test scores and GPA. They then have a fuzzier process to decide the 400 best students to admit out of the finalists.
The estimated admissions probabilities for students ranked #300 or better are always above 90%, regardless of race and gender. But wide disparities open up for students with lower rankings:
Cohen interprets this as clear evidence of massive discrimination in favor of black students, and in terms of statistical significance, he's right. However, the magnitude of this effect is small: Only ten black students were admitted, and four of these were in the top half of the distribution. Thus, AA at TJ displaced roughly six non-black students out of 400.
What Cohen strangely does not emphasize is that gender discrimination probably had a larger effect. Yes, it is less statistically significant. But since 43% of the finalists were female, moderate gender-based AA matters. Consider: Women ranked around #400-500 were about 7 percentage-points more likely to be accepted than men. Evening out the conditional acceptance rates for these centiles alone would give males roughly another 6 slots.