Ninety-one percent of the nation’s colleges have told the federal government there were no rapes reported on their campuses in 2014, a statistic that the American Association of University Women said “defies reality.”

The AAUW on Thursday assailed the federal Clery Act data, information that colleges are required to disclose about sexual violence on the nation’s campuses, including the number of sexual assaults and rapes. The AAUW said it appears colleges must be concealing such cases because there is ample research and recent polling and survey data that shows college sexual assaults are a frequent and widespread problem that touch campuses from coast to coast.

A Washington Post-Kaiser Family Foundation national poll in June 2015 found that about 20 percent of college-aged women and five percent of college-aged men reported being sexually assaulted across the country. A survey from the Association of American Universities — drawing responses from 150,000 students at 27 schools, one of the largest studies ever of college sexual violence — found that more than 20 percent of female undergraduates said they were victims of sexual assault and misconduct.

“While even one incident of sexual violence is too many, we know that it remains prevalent on college campuses and we should expect schools to have reported incidents to disclose annually,” Anne Hedgepeth, AAUW’s government relations manager, said Thursday at the National Press Club, noting that it makes little sense that there are schools reporting no incidents. “Zeroes are the red flag.”

Hedgepeth and Lisa Maatz, AAUW’s vice president of government relations, said the low numbers of incidents of rape and other forms of sexual harassment are not reason to celebrate, saying instead that they should raise concern about campus sexual assault policies and reporting practices.

The Clery Act, first implemented in 1990, was updated with new requirements in 2013 under the Violence Against Women Reauthorization Act. Campuses are now required to disclose data on dating violence, domestic violence and stalking, in addition to the number of reported rape cases.

Ten percent of campuses disclosed cases that fell under the new categories in the 2014 Clery report. Maatz said the new data reveals that many schools have not risen to the legal requirements of both the Clery Act and Title IX, the federal anti-discrimination law.

“If the data was accurate, I’d be up here doing a happy dance for you,” Maatz said. “We have actual documentation to show that it is not.”

Some, however, believe that the Clery data — and other federal crime data — should be the barometer for such criminal activity, arguing that the rates of sexual assault found in research, surveys and polling far overstate the problem.

KC Johnson, a Brooklyn College history professor, told The Post in September that he was skeptical of the statistic that 1 in 5 female college students are sexually assaulted.

“If you take this data literally, it would suggest a violent crime rate at most campuses higher than in any city in the country,” Johnson, who tracks college sexual assault and due-process issues, said in September. “Which I think is somewhat dubious.”

Author and journalist Stuart Taylor Jr. expressed similar concerns last fall, when the AAU data was released. Taylor said the commonly cited 1 in 5 statistic is misleading.

“The problem is no doubt serious, if shrinking,” Taylor wrote in The Post. “But it has been vastly exaggerated by the Obama administration, anti-rape activists, their media allies and universities pandering to them.”

Maatz said that while there is evidence to suggest the numbers colleges report are off, there is not a clear reason why schools are disclosing inaccurate numbers. Maatz said it could be because students don’t feel comfortable reporting incidents to their schools or because campuses don’t have proper procedures in place.

“The silver lining in our findings is that campuses that reported one type of sexual violence often disclosed other types as well,” Hedgepeth said. “To us, that suggests some schools have built the necessary systems to welcome reports of all types and support survivors and disclose those statistics to the Department of Education. Others, with across the board zeros, have not.”

Hedgepeth said it is important to note that Clery Act data reveal the number of reported incidents, not the number of actual incidents occurring on campuses.

In response to a question about how a debunked 2014 Rolling Stone article involving an alleged gang rape at the University of Virginia might hinder the work of sexual assault awareness advocates, Maatz said the number of false sexual assault reports are low.

“False reports are not common,” she said. “They are not what is fueling the survivor and the advocacy anger about this epidemic on campus, what is fueling it is how often it is happening and how poorly it is being handled.”

Young men on college campuses are more likely to be assaulted themselves than falsely accused of the same crime, Maatz said, citing federal data.

Maatz also said it is not valid for universities to say they don’t receive reports because survivors disclose to local law enforcement instead of university police, because campuses are supposed to work with the community to gather data.

“This issue is not new,” she said. “When campus environments are hostile because of sexual harassment and violence, students can’t learn. It’s that simple and it’s that devastating. Schools have an important and necessary role to play in addressing this epidemic.”