Dr. Green asked Mr. LaCour for the raw data after the study came under fire. Mr. LaCour said in the letter to Dr. McNutt that he erased the raw data months ago, “to protect those who answered the survey,” Dr. McNutt said.

She said that it was possible some voters had responded to some surveys, but that it was most likely that too few had done so to provide enough data to reach persuasive conclusions.

Survey data comes in many forms, and the form that journal peer-reviewers see and that appears with the published paper is the “cleaned” and analyzed data. These are the charts, tables, and graphs that extract meaning from the raw material — piles of questionnaires, transcripts of conversations, “screen grabs” of online forms. Many study co-authors never see the raw material.

Mr. Kalla, trying to find out why he and Dr. Broockman were getting such a low response rate, called the survey company that had been working with Mr. LaCour. The company, which he declined to name, denied any knowledge of the project, he said.

“We were over at Dave’s place, and he was listening to my side of the conversation, and when I hung up,” we just looked at each other, he said. “Then we went right back into the data, because we’re nerdy data guys and that’s what we do.”

On Saturday, they quickly found several other anomalies in Mr. LaCour’s analysis and called their former instructor, Dr. Green. Over the weekend, the three of them, with the help of an assistant professor at Yale, Peter Aronow, discovered that statistical manipulations could easily have accounted for the findings. Dr. Green called Mr. LaCour’s academic adviser, Lynn Vavreck, a professor, who confronted Mr. LaCour.

Dr. McNutt of Science said editors there were still grappling with a decision on retracting.

“This has just hit us,” she said. “There will be a lot of time for lessons learned. We’re definitely going to be thinking a lot about this and what could have been done to prevent this from happening.”