The lawsuit against the university came from a group hoping to overturn a long-standing Supreme Court precedent that allows race to be considered as one factor among many in admissions, but prohibits universities from using racial quotas.

The group argued that Harvard had favored black and Hispanic applicants at the expense of another minority group — a strategic reversal of past affirmative action lawsuits in which the plaintiff complained that white students had been treated unfairly.

The judge, Allison D. Burroughs, rejected the plaintiff’s argument, and said that the university met the strict constitutional standard for considering race in its admissions process.

In her decision, Burroughs defended the benefits of diversity, saying it was not yet time to look beyond race in college admissions. “Diversity,” she wrote, “will foster the tolerance, acceptance and understanding that will ultimately make race conscious admissions obsolete.”

The case drew widespread scrutiny, including from dozens of other top-ranked colleges that expressed their support in court filings, and from the Justice Department, which backed the plaintiff and is pursuing its own investigation. The decision will be appealed and is widely expected to reach the Supreme Court.

The plaintiff, Students for Fair Admissions, represents a group of Asian-American students rejected by Harvard. Led by Edward Blum, a conservative activist who waged previous battles against affirmative action, the students accused the college of violating federal civil rights law by holding Asian Americans, who as a group get better test scores and grades than other races, to a higher standard. Harvard did this, they said, in part by downgrading applications from Asian Americans based on a subjective rating system that was vulnerable to stereotyping.

Students for Fair Admissions made four interrelated claims: that Harvard intentionally discriminated against Asian Americans; that it used race as a predominant factor in admissions decisions; that it racially balanced its classes; and that it had considered applicants’ race without first exhausting race-neutral alternatives to create diversity. Burroughs cleared the university of all four claims.

Still, she said that Harvard’s admissions process was “not perfect.”

The judge suggested that Harvard could do more to guard against the unconscious biases of admissions officers, echoing an argument that the plaintiff made at trial. She noted more explicit guidelines on using race that were developed for the officers during the litigation, and said the officers could also be made aware of significant statistical disparities related to race.

These criticisms are likely to drive a review of admissions at schools across the country, to make sure they are not vulnerable to the same suggestions.

Despite the imperfections, she said, the court would not tear down “a very fine admissions program that passes constitutional muster, solely because it could do better.”

In an email, Larry Bacow, Harvard’s president, credited Harvard students who testified during the trial with vividly making the case for diversity through their own stories. “The power of American higher education stems from a devotion to learning from our differences,” he said. “Affirming that promise will make our colleges, and our society, stronger still.”

Other universities breathed sighs of relief when the decision came out. “We are gratified that this decision unambiguously respects more than four decades of U.S. Supreme Court precedent,” Ted Mitchell, president of the American Council on Education, a trade group, said in a statement on Tuesday.

But they also recognized that the federal court ruling, while important, is just a step along the way and is far from the final say in the case.

Blum has filed additional challenges to affirmative action against the University of North Carolina at Chapel Hill in federal court and the University of Texas at Austin in state court.

The Harvard case raised powerful issues of class, race and power in American society. Critics of the university admissions process said it showed how the white establishment was afraid of losing its dominance to another racial group. Defenders said that while it might be flawed, the Harvard system tried to forge a more perfect society.

Harvard admissions officers pointed out that they could fill the freshman class with students with perfect test scores if they wanted to, and that figuring out which apparently highly qualified students to reject was a delicate, difficult balance.

Burroughs noted in her ruling that Asian American applicants were accepted to Harvard at the same rate as other applicants and now made up more than 20% of the admitted class, even though Asian Americans made up about 6% of the U.S. population.

Some students on Harvard’s campus said they were pleased with the decision, although they said they were apprehensive about what would happen if the case made it to the Supreme Court.

“Honestly for me, the overwhelming feeling is fear or a little bit of anxiety,” said Andrew Ham, 19, a sophomore from South Korea. “What I’m afraid of is affirmative action or race-conscious admissions being struck down nationwide.”

Zeel Patel, a sophomore who is Indian-Canadian, said that he disagreed with the judge’s decision, and that he hoped the Supreme Court would ultimately put a check on Harvard’s use of race in admissions.

“We all agree that diversity is important, but it’s more so like the means by which we actually get to the diversity,” he said.

The trial unveiled many secrets of Harvard’s arcane admissions process. There was testimony about a “Dean’s List” of students who were earmarked for special consideration because of their wealth and connections; about lowering the SAT requirements for white students in “sparse country,” rural areas where few applicants applied to Harvard; about how recruited athletes and the children of alumni and faculty received large preferences, and about how admissions officers from Ivy League schools got together every year to compare notes on admissions by race.

The Harvard trial contributed to a populist backlash against elite colleges that snowballed in the spring, when federal prosecutors accused 50 people of participating in a scheme by wealthy families to bribe their children’s way into schools like Stanford and Yale.

The trial was steeped in statistical evidence and terminology that spectators often struggled to understand. In the end, the judge’s 130-page decision was not overly seduced by statistics. But she sided more often than not with Harvard’s expert, David Card, an economist at the University of California, Berkeley.

She rejected the argument that “tips,” or admissions advantages, received by some black and Hispanic students were unfair. While some racial groups did receive tips, she said, “most Harvard students from every racial group have a roughly similar level of academic potential” despite significant differences in their SAT scores and grades.

The plaintiff had failed, she said, to counter Harvard’s argument that race-neutral admissions schemes, like admitting students based on where they lived, would lead to a decline in qualified black and Hispanic students.

The trial was painful for many Asian Americans, a group that overwhelmingly supports affirmative action but includes many people who feel they have been stereotyped in admissions.

Lee C. Cheng, a founder and director of the Asian American Legal Foundation, said he was concerned and surprised by the extent of the judge’s support for Harvard’s policy, which he viewed as racist.

“I think the data showed Harvard racially stereotyped a group of Americans who are supposed to have the same rights to be free from the stigma of racial classification,” Cheng said.

Others disagreed, and denounced the plaintiff’s efforts. Bhargavi Garimella, 18, a freshman from California who applauded the judge’s decision, said she was upset by how Blum had involved Asian Americans in his quest to end affirmative action.

“I was really uncomfortable with the idea of Asian-Americans as a whole being used,” she said, adding, “Taking down affirmative action would be detrimental to all people of color.”

In her decision, Burroughs imagined a future in which race would no longer be needed in admissions. She quoted the novelist Toni Morrison, who died in August, saying that “race is the least reliable information you can have about someone.”

But Morrison’s words, the judge said, had to “become accepted and understood before we close the curtain on race conscious admissions policies.”

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