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Students cross Harvard Yard at Harvard University in Cambridge, Mass., in January.Credit Brian Snyder/Reuters

In four years of college, more than one-fourth of undergraduate women at a large group of leading universities said they had been sexually assaulted by force or when they were incapacitated, according to one of the largest studies of its kind, released Monday.

Responding to a survey commissioned by the Association of American Universities, 27.2 percent of female college seniors reported that, since entering college, they had experienced some kind of unwanted sexual contact — anything from touching to rape — carried out by incapacitation, usually due to alcohol or drugs, or by force. Nearly half of those, 13.5 percent, had experienced penetration, attempted penetration or oral sex.

The survey bolstered findings from previous studies but stands out for its sheer size — 150,000 students at 27 colleges and universities took part last spring — and for the prominence of the institutions involved, which include many of the nation’s elite campuses, including all of the Ivy League except Princeton.

Last year, President Obama convened the first White House task force on college sexual assault, part of a growing demand for colleges to acknowledge, measure and address the problem. That task force, like members of Congress and victim advocates, called on colleges to conduct rigorous “campus climate” surveys, including detailed information on the frequency of assault and harassment.

Previous studies have estimated that about one in five women are sexually assaulted while at college, though comparisons are difficult because the studies use varying definitions of sexual assault.

The new study cautioned that only 19 percent of students responded to the survey, far below the rates of some previous studies.

The A.A.U. survey found that even in the most serious assaults, those involving penetration, almost three-fourths of victims did not report the episode to anyone in authority, let alone law enforcement. The reason victims gave most often for not reporting episodes was that they did not think the episodes were serious enough to report; others said they felt ashamed, or did not think they would be taken seriously.

“This survey is significant confirmation of a major problem, and it confirms what we’ve been saying about the mind-set on campus and the reception survivors expect to encounter,” said Zoe Ridolfi-Starr, deputy director of Know Your IX, an advocacy group that fights sexual assault.

Most of the institutions in the study released their own figures from the survey, and several of the most respected ones had some of the highest rates of sexual assault by force or incapacitation for undergraduate women — 34.6 percent at Yale, 34.3 percent at the University of Michigan, and 29.2 percent at Harvard.

The findings were “profoundly troubling,” said Yale’s president, Peter Salovey. Yale’s handling of sexual assault has come under particular scrutiny in recent years, and the university has taken a number of steps to address it. Thomas Conroy, a university spokesman, said Monday that because the A.A.U. report was the first of its kind for Yale it was impossible to know whether those measures had paid off.

Senator Kirsten Gillibrand, Democrat of New York, praised the study but expressed impatience that Congress had not acted to force colleges to improve their handling of sexual assault. “How many surveys will it take before we act with the urgency these crimes demand?” she asked.

Some previous studies have focused more narrowly on rape and attempted rape, but the A.A.U. survey included much broader categories. It found that, when including acts carried out without force or incapacitation but with coercion or a lack of consent — which some colleges now define as sexual assault — one-third of senior women had experienced unwanted sexual contact during college.

John D. Foubert, a professor of higher education at Oklahoma State University who studies campus sexual assault, said he was troubled by the low response rate and by the A.A.U. study’s use of slightly different definitions from previous studies.

“This is pretty consistent with what we’ve seen before,” he said.

Across the 27 universities, men experienced much lower — but still significant — rates of sexual assault than women; 8.6 percent of male seniors said they had experienced some kind of unwanted sexual contact, including 2.9 percent who said they had experienced penetration, attempted penetration or oral sex, carried out by force or incapacitation.

Transgender students and others who do not identify as either male or female had higher rates of assault than women. Experts said this was the first large-scale study they knew of to measure the extent of the problem for transgender students.