Children’s advocates called the administrators’ convictions a victory for accountability. “We can no longer put institutional loyalty above protecting kids,” said Cathleen Palm, the founder of the Center for Children’s Justice, a nonprofit that pushed for changes to Pennsylvania’s child abuse policies in the wake of the scandal.

Supporters of Mr. Spanier and Mr. Paterno held up the acquittal on the conspiracy charge as vindication. “The story should be that there was no conspiracy to cover up child abuse at Penn State,” said Maribeth Roman Schmidt, the executive director of Penn Staters for Responsible Stewardship, an alumni group opposed to the sudden ouster of Mr. Paterno and the administrators.

Mr. Spanier has long maintained that he was unaware of the seriousness of the accusations against Mr. Sandusky, who prosecutors said met his victims through his charity work, drawing them in with trips to football games and other gifts. The trial, which began with jury selection on Monday after years of legal delays, offered victims and their families the possibility of new information about what the university’s highest-ranking officials knew about Mr. Sandusky. Supporters of Mr. Spanier and the administration hoped it would absolve the university of some wrongdoing.

“In the view of the jury, with respect to Spanier, and by their own admission, as to Curley and Schultz, these former leaders fell short,” Penn State said in a statement released after the verdict. “And while we cannot undo the past, we have rededicated ourselves and our university to act always with the highest integrity, in affirming the shared values of our community.”

Mr. Spanier sued the university, accusing it of violating their separation agreement. The university countersued, seeking to recoup more than $5 million it has paid him.

Prosecutors contended that Mr. Spanier, along with Mr. Curley and Mr. Schultz, was aware of a 2001 report that Mr. Sandusky had showered with a young boy at the university, but that they failed to tell the authorities, acting instead to keep the matter quiet. That choice, prosecutors said, allowed Mr. Sandusky to keep abusing boys for years.

They have often pointed to an email written by Mr. Spanier about the episode, after the decision was made to go to Mr. Sandusky directly and tell him to get counseling, rather than alerting the authorities.