Fundamental Constant of Sociology and Stuyvesant Admissions Test

At iSteve, Sailer posted analysis from La Griffe du Lion showing the FDNY tests followed the Fundamental Constant of Sociology. Readers of this blog should note that 'OneSTDV' derives from the law:

On tests of reasoning ability, the observed mean difference between non-Hispanic whites and African Americans is 1.1 ± 0.2.

On La Griffe's website, he shows the approximately one standard deviation gap applies to the SAT, LSAT, Bar exam, MCAT, and ACT.

I decided to look into the most high-stakes, and highly contested, scholastic exam in the country, the Specialized High Schools Admissions Test (SHSAT). High scorers on this test are offered admission to the Harvard, Yale, Princeton of New York high schools: Stuyvesant, Bronx Science, and Brooklyn Tech. Unsurprisingly, the test has been attacked by diversity groups, including ACORN, for exhibiting the same old racial trends (source: NYT):

Parents of black and Hispanic students have long complained about the lack of diversity in the elite schools’ enrollment

Among the 21,490 public school students who last year took the exam, the single gateway to eight high schools, 6 percent of blacks and 7 percent of Hispanics were offered admission, compared with 35 percent of Asians and 31 percent of white students.

Using the numbers above with Excel's norminv function and assuming a normal distribution, I calculated the z-score of the "passing standard" for each race. I subtracted the black z-score from the white z-score to obtain the gap as a scalar of the assumed equal standard deviation value. This is La Griffe's method but I explained it without integrals.

For overall test takers, the black-white gap was 1.06.

To decrease the racial disparities in access to test prep materials, educational quality, and studying motivation, a test prep institute was formed specifically for the SHSAT.

The test-prep institute, which includes a full-time five-week summer session and twice-a-week workshops during the school year, was a core part of the city’s strategy to diversify the ranks of the elite schools.

The results:

While 90 percent of Asians and 85 percent of white students at the institute take the test, 65 percent of blacks and 70 percent of Hispanics do; last year, of the institute graduates taking the test, 58 percent of the Asians, 49 percent of whites, 21 percent of Hispanics and 19 percent of blacks were offered admission.

The black-white gap for the test-institute students was 0.85. Notice a significantly lower proportion of blacks from the institute took the test. We can presume these would have been the worst scorers as their poor performance probably discouraged them from taking the actual exam. The slightly lower than normal gap can likely be attributed to this.

So, yet again, the fundamental law of sociology holds.