The construction of the SAT distribution curves, broken down by race, are explained in steps [A] & [B]:
[A] Where do the data come from?
Whites; 49.1%
Asian Americans: 22.2%
Blacks: 14.6%
Hispanics or Latino 11.6%
Native Americans or Pacific Islanders 2.5%
Whites; 1576
Asian Americans: 1654
Blacks: 1277
Hispanics or Latino 1354
So far as the Math SAT scores are concerned, the blacks and Hispanics are low-score-heavy when compared with the so called normal distribution (i.e. real Gaussian) while Asians are high-score-heavier and white students show a fairly good normal distribution. I conjecture that the same characteristics apply to "writing" and "critical reading" SAT performances, but much LESS pronounced than the math situation.
[B] The racial characteristic of the
total
SAT score distributions, described in
words
:
The following is simulated, based on data described in section [A]. But DOJ may soon have the real admissions data to construct the REAL curves. Note: Unfortunately, the maximum SAT score in 2015 is 2400 points, not the 1600 points when Espenshade did his study.
Whites
will have a fairly regular Gaussian curve centered on 1576 with a one standard deviation width of about 130, with a height that is arbitrarily set at 100 counts in arbitrary units.
Blacks
will have a Gaussian curve centered on 1277 with a one standard deviation width of about
120, with a height that is roughly 13 that of the white or 31counts (The height difference is owing to the fact that the number of
black applicants to Harvard is only
1/3* that of whites.)
Hispanics
will have a low-score-heavy Gaussian curve centered on 1354 with a one standard deviation width of about 130, with a height hat is roughly 1/4 that of the white or 24 counts (The height difference is owing to the fact that the number of Hispanic applicants is about1/4* that of whites.)
Asian Americans
will have a high-score-heavy distribution curve centered on 1654 with a one standard deviation width of about 170, and with a height that is roughly 39% that of the whites (The one standard deviation of the Asian curve is wider which requires its height to decrease so that the area ratio of White/Asia remains at 49.1/22.2. It is not so important that a reader doesn't understand the above technical statement.
)
Special notes:
(1) U
nfortunately, the highest SAT score in 2015 is 2400 points, not the 1600 points when Espenshade did his study. Hence,
while Espenshade reported that 140 SAT points were deducted from Asians, on this 2400 maximum SAT scale, the 140 points become (140 x 2400/1600) = 210 SAT pts.
(2) The area below each curve is proportional to the number of applicants of each race.
I arbitrarily set the max count of applicants to 100. That shouldn't affect the illustrative nature of the following diagram.
(3) There are 2 known defect ins the above diagram. (i) Only students with high SAT score apply to Harvard. Hence the peaks of all 4 curves should be shifted more to the right. However, the high score end of the tails will NOT shift. (ii) The
formula used for drawingt the Gaussian curves is:
µ
and
are respectively mean value and one standard deviation.
However, in the real world few distributions are perfect Gaussians.