Here’s a snapshot of the study’s findings:

1. Private schools are whiter than the overall school-age population in most states, particularly in the South and the West.

This map shows the gap between the percentage of all school-aged children who are white vs. the percentage of private-school students who are white. The biggest gap is in Mississippi, where in 2012, white students comprised 51 percent of all school-aged students but 87 percent of private-school students — a gap of 36 percentage points. The average national gap that year was about 15 percentage points.

2. Black, Latino and Native American students are underrepresented in private schools, also particularly in the South and West.

3. Private schools are more likely than public schools to be virtually all-white, defined as a school where 90 percent or more of students are white. Forty-three percent of the nation’s private school students attended virtually all-white schools, compared to 27 percent of public-school students.

The author of the analysis also puts forth a provocative argument: Because of this historical pattern, private schools that take public money (via vouchers and voucher-like programs) should not be able to select the students they admit. Instead, those schools should have to admit anyone who applies, just like public schools do, said Steve Suitts, who wrote the study as a senior fellow at the Southern Education Foundation.

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“The public-school system is built on the bedrock notion that we want each child to have a chance for a good education,” said Suitts, now an adjunct professor at Emory University. “And if private schools do not wish to advance that national purpose, then they ought not receive public funding.”

That argument does not make much sense to people who believe that voucher programs are a way to help low-income and minority students attend private schools they otherwise could not afford.

Greg Forster, a senior fellow at the Friedman Foundation for Educational Choice, said it’s not surprising that white students are more likely to attend private schools because the nation’s white families have higher incomes than other families, on average.

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“Private schools generally want to serve as many students as possible, but they can only serve those who are able to pay,” Forster said. “School choice levels the playing field by helping those with lower incomes have access to the choices that others now have and even take for granted. It is not a scandal that those who are able to access better schools choose to do so; it is a scandal that because of the government school monopoly, only some are able to access better schools.”

Forster pointed to Milwaukee — which has had a voucher program since 1990 — as evidence that vouchers can help increase minorities’ enrollment in private schools. In 1994, when racial data were first tracked, 75 percent of the city’s private-school students were white, he said; by 2008, the white share of private-school students had dropped to 35 percent.

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Suitts said economics are part of the pattern, but not all or even most of it. The number of black, Latino and Native American students enrolled in private schools is far lower than the number of minority families that could afford it, he said. He said he didn’t know of instances in which private schools rejected qualified minority students — but the enrollment patterns signify a problem.

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“The fact is that, over the years, African American families and non-white families have come to understand that these private schools are not schools that are open to them, especially in light of their traditional role and history related to desegregation of public schools,” he said.

The report recalls how private-school enrollment grew a half-century ago as courts were ordering public schools to integrate. The pattern was particularly pronounced in the South, where massive resistance to integration led to rapid private-school enrollment growth. Even as private-school enrollment has fallen across much of the country in recent decades, it has continued to grow in the South.

Over time, private schools in the South have accounted for a growing proportion of private-school enrollment nationwide.

And private schools in the South have a greater over-representation of white students than other regions.

Liz King, director of education policy for the Leadership Conference on Civil and Human Rights, said that the historical context is important because it shows how “private education can play a role in undermining civil-rights efforts.”

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If taxpayers are going to support private schools, she said, then those private schools should be subject to additional scrutiny and to the same civil-rights oversight and enforcement as public schools.

Forster, of the Friedman Foundation, doesn’t see the need for additional oversight or for a new requirement that private schools accepting public dollars accept every child who applies.

“It prevents schools from matching the right student to the right school,” he said. “Just as parents should have the right to say to schools, ‘You’re not the right fit for my child, I’m going to find another school,’ schools should also have the right to say to parents, ‘We’re not the right fit for your child.'”

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He said that multiple studies have shown that choice programs result in students moving from more-segregated to less-segregated schools.

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Forster also challenged Suitts’s methods for analyzing segregation in private vs. public schools. It can be misleading to compare enrollment patterns on a state level because that misses important nuances between individual schools and between different parts of a state, he said.

And he said that Suitts did not attempt to capture the segregation of students of color within either school sector, leaving out an important part of the picture of race and enrollment patterns.