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RALEIGH (AP) — An unpublished study by Duke University researchers that says black students are more likely to switch to less difficult majors has upset some students, who say the research is emblematic of more entrenched racial problems.

The study, which opponents of affirmative action are using in a case they want the U.S. Supreme Court to consider, concludes black students match the GPA of whites over time partially because they switch to majors that require less study time and have less stringent grading standards. Opponents of affirmative action cite the study in a case they want the U.S. Supreme Court to consider.

About three dozen students held a silent protest Sunday outside a speech by black political strategist Donna Brazile that was part of the school's annual Martin Luther King Jr. observance. And members of the Black Student Alliance have met with the provost to express their unhappiness with the study and other issues on campus.

"I don't know what needs to happen to make Duke wake up," said Nana Asante, a senior psychology major and president of the Black Student Alliance.

The reaction from black students has surprised one of the researchers, who said he wanted to show the need to find ways to keep minorities in difficult majors such as the natural sciences, economics and engineering.

Peter Arcidiacono, an economics professor at Duke, wrote the paper in May 2011 along with a graduate student and Ken Spenner, a sociology professor. Spenner and Arcidiacono are white. It's been under review since June at the Journal of Public Economics.

The statistics would likely reflect trends at other schools, Arcidiacono said. The study notes that national science organizations have spent millions to increase the ranks of black science students.

"It's not just a Duke issue. It's a national issue," he said.

The researchers analyzed data from surveys of more than 1,500 Duke students before college and during the first, second and fourth college years. Blacks and whites initially expressed a similar interest in tougher fields of study such as science and engineering, but 68 percent of blacks ultimately choose humanities and social science majors, compared with less than 55 percent of whites. The research found similar trends for legacy students — those whose parents are alumni.

The study's claim that majors such as natural sciences required more study time was based on students' responses to survey questions about how many hours they spent each week on studying and homework. The study found that those fields required 50 percent more study time than social sciences and humanities courses.

"I view the lack of (minority) representation in the sciences to be a problem, and I include my own field of economics," Arcidiacono said. "I'd like to see programs that are successful in increasing that representation."

Black students at Duke haven't taken that impression from the study, which came to light when the Chronicle of Higher Education wrote about it earlier this month. Affirmative action opponents cite the study in briefs involving a challenge of the undergraduate admissions policy at the University of Texas at Austin.

"What kind of image does this present not only of the academic undertakings of black students at Duke, but also of the merit and legitimacy of our degrees?" Asante asked. "And then, of course, it's calling into question ... the legitimacy of how we even got to Duke in the first place."

Duke, a private university, has about 6,500 undergraduate students, about 47 percent of them white and 10 percent black. The largest group of minorities is Asian-American at 21 percent. Duke has no set formula for admitting students, school spokesman Mike Schoenfeld said. Instead, the admissions process takes into account many factors, including race, ethnicity and legacy status. The school selects about 1,700 students each year from more than 31,000 applicants.

"The experience of black students, and indeed of all students, at Duke is of deep and ongoing interest to the university, and we take very seriously the issues that have been raised," Schoenfeld said.

The study is the latest issue to trouble black students at Duke, Asante said. She said administrators have not responded to questions about plans to renovate the Mary Lou Williams Center for Black Culture and have not given support for the black student group's recruitment weekend.

Schoenfeld said the Williams Center is a gem and officials are working with students to find a new, visible location for it. And he said the recruitment weekend is more important than ever because Duke received a record number of black student applications this year.

But a letter to the editor of the student newspaper, signed by the provost and other administrators, failed to address concerns about those issues and the racial climate, Asante said.

"In failing to do that, it reaffirmed its own ignorance in terms of the necessity of acknowledging, accepting and working to change that climate," Asante said.