NYT published a brain-dead article filled with statistical fallacies (link).

Since the Times has people on staff who know statistics, the real explanation for such an article is "story-first thinking". Data mined to support a story line.

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The headline of the article provokes its least convincing statistic - that only seven black students were offered spots at Stuyvesant, one of the nation's top public high schools famous for STEM, out of 762 offers.

The position of the author is that the above statistic reveals systematic "racial and ethnic disparities". In statistics of education, "disparity" is a descriptive statistic describing a gap, which is different from "discrimination," which suggests foul play. The former is correlation while the latter is causation. This author mischievously used the term disparity while avoiding discrimination, even though the entire article presumes the disparity is unfair.

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In fact, Stuyvesant (plus seven other similar schools in New York) only considers one factor in admissions, the student's score in the Specialized High Schools Admissions Test (SHSAT), and so the admission decision is not tainted by any judgmental criteria. All test-takers are ranked in order of test score, and then, each student is allocated a spot in their most preferred school - if all slots in the school have been filled, then the next preferred school is considered, and so on.

This allocation method guarantees "fairness" in the sense that if a student isn't allocated to a school higher on his/her preference list, it's because every offer for that school went to students who have scored higher on the SHSAT.

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If we are interested in the question of whether the allocation of offers is fair across ethnic groups, the right question is: among students of similar ability (for example, score bands), do black or Latino students have a lower offer rate than whites and Asians?

This question of fairness pops in everywhere in education. In Chapter 3 of **Numbers Rule Your World** (link), I examined it in the context of designing fair SAT questions.

Surprise, surprise. Such data have not been released. Since there are no data, I'll explain conceptually how the numbers work.

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Let's assume 30% of test-takers are Asians, and 20% each are blacks, latinos, and whites, and 10% others. Assume 50% of offers are given to Asians, 30% to whites, 5% each to blacks and latinos, and 10% to others. Overall, 15% of the test-takers receive an offer.

Given those assumptions, the offer rate for Asians is 25%, for whites it's 23%, for blacks and Latinos, it's 4%. Asians and whites are 1.5-1.7x more likely than the average to get an offer, while the offer rates of blacks and Latinos are a quarter of the average.

The NYT claims this proves that the process unfairly favors Asian and white students at the detriment of blacks and Latinos.

Not so fast. Remember all offers are completely determined by test scores, without any judgmental factors. So the proportion of students who receive offers is the same as the proportion who score above the cutoff score. Think of the cutoff score as the score of the last student taken up by a school. This cutoff score is an outcome of the offer process, not an input.

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We can now split each subgroup into those who score above the cutoff and those below. Among Asians, the split is 25%-75%; whites, 23%-77%; blacks, 4%-96%; Latinos, 4%-96%; others, 15%-85%.

The reason why Asians and whites have more offers is because they have higher SHSAT scores.

Let's now insist that the offer rate for every ethnic group must equal the overall rate of 15%. For Asians and whites with a higher score distribution, this necessarily means that we cannot accept everyone above the cutoff score. It turns out that we can only accept about 60-67% of those who score above the cutoff score, and 0% of those who score below, in order to get to a weighted average of 15%.

For blacks and Latinos, we'd take 100% of those who score above the cutoff, but that isn't enough to get to 15%. We also must take 12% of those who score below the cutoff.

This is the unspoken math behind the NYT article. They are proposing: rejecting 40% of high-scoring Asians and whites while accepting 100% of high-scoring blacks and Latinos; and accepting 12% of low-scoring blacks and Latinos while rejecting 100% of low-scoring Asians and whites.

Shame.

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