Colleges and universities have also taken a tougher stance, at least outwardly, after being battered by reports about sexual assault and binge drinking. Universities have shut down hundreds of offending fraternity chapters, and some have prohibited freshman-year pledging or imposed restrictions on alcohol. A smaller number have withdrawn formal recognition of all Greek-letter groups, forcing them to operate only off campus and without any official ties.

What is less clear is how much of a difference their actions make.

“This is a huge challenge because we don’t own the houses, we don’t own the property, we aren’t the national” organization governing fraternities, Penn State’s president, Eric Barron, said Monday in an interview.

Fraternities and their national umbrella groups dispute studies, which Dr. Barron cited, showing that fraternity members are disproportionately connected to binge drinking and sexual assault. They note that other organizations, like sports teams, also engage in hazing; at Florida A&M University, ritual abuse in the marching band killed a student in 2011, and several band members were prosecuted. Some of the deadly episodes that have been labeled fraternity hazing — at the University at Albany and Virginia State University — involved loosely organized groups with no national affiliation or school recognition.

There are no figures kept by the government or higher education groups of hazing incidents, student deaths, excessive drinking or fraternity discipline; individual schools and fraternities generally resist sharing internal data. But in 2013, Bloomberg News documented more than 60 deaths over eight years in fraternity activities, many of them involving initiation rituals for would-be members and heavy drinking.

Dr. Barron said university presidents around the country had been expanding educational programs to discourage drinking, creating stronger rules and, when all else failed, revoking fraternity charters. But fraternities have found creative ways to avoid new restrictions, he said; some whose charters have been revoked have simply “created underground organizations and just changed their names.”