I'd like to correct something I said earlier. Admission rates were higher for blacks and hispanics than tehy were for Whites and Asians. I had the numbers reversed.
But looking over these data, I found some interesting things.
In 2007, there were a total of 19,345 applicants, and of those, 12,219 were admitted. (See footnote on page 6 of study for these data)
Of those 12,219, 84.9% were white, 7.8% were Asian, 4.4% were Hispanic, and 2.9% were black according to the table found on page 6.
Translated into actual numbers of students would mean that 10,373.931 were white, 953.082 were Asian, 537.636 were Hispanic, and 354.351 were black. When you look at that, you can see how they rounded things so the actual numbers were 10,374 white, 953 Asian, 538 Hispanic, and 354 black.
Now, this is interesting because it means that 2,500 or so white students of the white students who were admitted to UW-Madison fell into 25th percentile.
What I find disconcerting about this "study" is that it discusses means and percentiles, but fails to show any standard deviations. Thankfully, they did give percentiles and ranges for those percentiles so for the ranges that show a normal distribution (the whites and Asians) standard deviations can be calculated. (Blacks and hispanics appear to have skewed distributions which means that I'd need more data than what is offered to determine SD)
The distribution they showed for whites indicated that the median was 1330, the score for the 25th percentile was 1260 and the score for the 75th percentile was 1400. As you can see, there are 90 points between 25th percentile and 50th percentile (which is what a median is) and there are 90 points between the 50th percentile and the 75th percentile. this strongly indicates that the distribution was a bell curve. thus, we know that Z-score (which is a percentage of the SD) for the 25th percentile is -0.6745. If we have 90 points at 67.45% of the SD, this means that the SD is actually about 133 points. This makes sense if you are aware that the score that is a full standard deviation below the mean is approximately the 16th percentile.
Now, what these data allow us to do is calculate the raw number of white students that were admitted to UW-Madison who had scores at or below the median score for black students.
To do this, we first have to calculate the z-score that the median score for blacks would be on the white scale. As we know from the "study", the median score for blacks was 170 points below the median for whites. This represents a z-score of -1.278.
This z-score is representative of about the 10th percentile in a standard distribution (meaning 10% of white students who were admitted were at or below this score).
Thus, we can take 10% of 10,374 and that will be the raw number of white students who were admitted with scores at or below the median score for blacks. Since this is the median for blacks, we know that 50% of the total 354 were admitted with scores at or below this number.
In more simple terms, about 1,037 white students got into UW-Madison with a score of 1190 or lower on the SAT compared to about 177 black students who were admitted with scores at or below 1190.
If we take it out to two SD's below the mean, it represents about 2% of the total whites who were admitted compared to the bottom 25% of blacks admitted (2 SD's below the mean for whites is 1094, while the bottom quartile for blacks was 1090).
this means that 207 white students were accepted with scores lower than 1094 while around 89 black students were accepted with scores below 1090.
One potential confound that exists is student athletes, who are often accepted with lower scores. It'd be interesting to see how many of these in the lower levels are admitted in part due to athletics.
