The assumption sits at the heart of a raging debate about elite high schools in Boston and New York City: that schools like Stuyvesant and Boston Latin offer the very best preparation for college that the public school system can provide.

“Why isn’t every public school in New York City a Brooklyn Tech-caliber school?” Congresswoman Alexandria Ocasio-Cortez said recently, referring to one of New York City’s test-in high schools. “Every one should be.”

“Admission to Stuyvesant has been a ticket out of poverty for hundreds of thousands of brilliant, non-wealthy New York kids,” tweeted New York Times columnist Bret Stephens.

But studies looking at the test-in schools in those cities and in Chicago have found that students receive little if any measurable benefit from attending them. Students with similar qualifications who attend high school elsewhere end up with comparable SAT scores and college admissions offers, they find.

“There is perhaps too much attention on these test schools as if they’re lifesavers, and we have evidence that maybe they’re not,” said Tomas Monarrez, who studies segregation at the Urban Institute.

That doesn’t mean the push to change admissions rules is misguided. In New York City, just 11 percent of admissions offers to specialized school this year went to black and Hispanic students, though they make up the vast majority of the public school system. In Boston, there’s a 30-point gap between the share of black and Hispanic students at exam schools and the district as a whole.

“There’s benefit to having diversity beyond a test score,” said Parag Pathak, an MIT researcher who has studied Boston and New York’s exam schools. Students may gain access to harder-to-measure benefits like advanced courses, a more challenging school environment, and an influential alumni network.

“A lot of these social networks that you create in these types of schools are probably really valuable — if you get to meet the right kid and then the dad of that kid ends up giving you a Wall Street job,” said Monarrez.

But the findings do underscore a key misconception about why students who attend those schools do well. It’s not because the schools are offering something entirely unique; it’s at least partially because the process selects students who are primed for academic success.

Studies in Boston, Chicago, and New York City show little gain from attending most elite schools

In a 2014 study titled “The Elite Illusion,” Pathak and other researchers compared students who just made the cut to attend a test-in school in Boston or New York City and similar students who fell just short. (Notably, the Boston schools, unlike New York City’s, don’t rely exclusively on test scores for admissions decisions.)

The difference in test scores, including on the SAT and Advanced Placement exams, between the two groups was largely nonexistent.

Perhaps more important to parents and students is whether attending one of those household-name schools helps kids get into a better college. The answer, according to a separate study focusing on New York City’s specialized high school graduates between 1994 and 2013, is not really.

There was no evidence that those students were more likely to enroll in college, complete college, or attend an especially elite institution than comparable students who went to high school elsewhere. There was also little difference between students who just missed the cutoff for Stuyvesant but got into another of the test-in schools, like Bronx Science.

The Boston study came to similar conclusions.

In some cases, there were even negative effects: Students who just made it into Brooklyn Tech were actually 2 percentage points less likely to graduate from a four-year college as a result.

“An exam school education produces only scattered gains for applicants,” wrote one set of researchers. “While the exam school students in our samples typically have good outcomes, most of these students would likely have done well without the benefit of an exam school education.”

These studies, including one in Chicago, come with an important caveat: they only include students who narrowly made it into the test-in schools. It’s possible that those students don’t benefit, but others do.

Researchers were able to look at a broader cross section of students in a separate Chicago study. They compared students at Chicago’s selective high schools, which admit students based on their test scores, grades, and neighborhood, to other students who looked similar in eighth grade but went elsewhere for high school.

Students at the selective schools saw no clear academic gains, including on ACT and AP exams. Students actually had slightly lower GPAs if they attend a selective school, though that may have been because the courses were more difficult.

The Chicago study does find some benefits to the selective schools, though. Students there reported feeling safer, having better behaved classmates, and facing higher academic expectations. In turn, students were slightly less likely to be suspended and be absent — all valuable outcomes for parents and students.

“The major advantage of selective schools is that they provide a more desirable school environment,” the paper explains. “Students are more likely to feel positive about their high school experiences at selective schools.”

Still, that didn’t translate into higher high school graduation, college attendance, or college completion rates. Students from low-income neighborhoods actually ended up at less-selective colleges, on average, as a result of going to a top high school.

“Schools can look like they have a large effect on student outcomes, while these apparent successes should actually be attributed to the students themselves,” the Chicago researchers say.

We can’t say for sure whether the results would look the same today, though, or if the schools’ selection criteria were changed.

High schools do matter, but perhaps more so for students at lower-achieving schools

One potential conclusion from this line of research is that high schools just don’t matter that much. Perhaps, by that point, students’ trajectories are just difficult to budge.

But this research and other studies don’t back up that conclusion, either. The Chicago study found students benefited a lot from going to a non-selective school with high test scores and graduation rates rather than a school with very poor results. Other research has shown that Chicago’s and Boston’s charter high schools substantially boost students’ test scores and four-year college enrollment rates, too.

High schools matter, in other words, but research shows they may matter more for students not at the top of the academic heap. It’s also possible high schools matter a lot for all types of students, but those who fall just short of an elite school end up at equally good schools.

Navigating this is all made more complicated by the fact that it can be difficult for students and parents to find reliable metrics of high school quality. A New York City study by some of the same researchers found that families often choose schools based on the types of students who attend, not the quality of the school itself.

It’s also true that those two things were positively correlated to some degree. In other words, families aren’t wrong to perceive a relationship between school and student performance, even if that relationship doesn’t seem to apply to the most elite schools.

Where do the results leave the debate about admissions policies of elite high schools?

The specialized school findings don’t change anything for Tahseen Chowdhury, who graduated last year from Stuyvesant, where he was student body president. Attending Stuyvesant meant achieving a goal that was very important to his family. “I first heard about Stuyvesant when I was in kindergarten, maybe,” he said.

Chowdhury says the education and experience he was offered at Stuyvesant was excellent, even if the benefits aren’t easy to quantify. “I value the student experience in the school more than I value the numbers that come out of it,” he said, describing the extra funding the specialized schools get and the numerous student-run clubs Stuyvesant offered.

Some of the researchers make a similar point. “The many clubs and activities found at some exam schools may expose students to ideas and concepts not easily captured by achievement tests or our post-secondary outcomes,” wrote the Boston and New York City researchers.

That idea strengthens the case for adjusting the selection process to admit more black and Hispanic students who otherwise wouldn’t have access to those resources.

“It is still important to try to open the door of these schools,” The Urban Institute’s Monarrez said. “But perhaps [we should] just not think of these schools as the best and only answer to these problems.”