Of a nationally representative sample of more than 40,000 public and private high school students responding to the survey, 59.4 percent admitted to having cheated on a test — including 55 percent of honors students — and one in three had done so twice or more in the previous year.

In addition, more than 80 percent of the respondents said they had copied homework, more than one-third had plagiarized an Internet document for a class assignment, and 61 percent reported having lied to a teacher about “something important” at least once in the past year. By contrast, only about 20 percent of students surveyed reported having cheated in sports.

In the first of the four experiments by the Harvard-Duke team, researchers asked 76 participants on the Massachusetts Institute of Technology campus to take a short test of “math IQ” and score their own sheets. Half the tests had an answer key at the bottom of the page. After completing the test, all participants were asked to predict how many questions they would answer correctly on a second, 100-question test without an answer key.

The other related experiments repeated the scenario with 345 students at the University of North Carolina, but required the participants to actually take the test after predicting how well they would do. In one variation, the participants were told they would receive money for the second test based on both the number correct and how close the participant’s predicted score came to the actual score.

Participants who had access to the test answers tended to use them. In the first rounds of testing in each scenario, mean scores were significantly higher among students who could sneak a peek at the answer key at the bottom. That fits with previous studies showing that, all else being equal, a majority of those who can cheat, do.

Yet the Harvard-Duke research also showed that cheaters lied to themselves.

In a preliminary experiment involving 36 Harvard students, participants were asked simply to imagine cheating on the first test and then taking the second without an opportunity to cheat. Those participants predicted that they would perform worse on the second test, without the opportunity to cheat.