Nearly 40% of students who enter New York City public schools in the first grade are gone by the eighth grade, a new study by New York University researchers concludes. Those who leave tend to be academically weaker than those who stay.

The researchers looked at data on a single class of city students, the one that should have graduated high school last year, following from the first grade to the time they should have reached eighth grade, in 2003.

Only 35% of students moved steadily from one grade to the next and finally reached the eighth grade. Another large group, 37%, had left New York City public schools altogether.

The director of NYU’s Institute for Education and Social Policy, Amy Ellen Schwartz, said the findings challenge a prevailing image of how schooling works. “The kids we start out with and then the kids who we see later on — in fact, they’re substantially not the same kids,” she said.

The research also challenges a common idea about who leaves New York City public schools — the perception that middle-class, higher-performing students make up the bulk of those who exit. In fact, those students who stayed in the public schools scored above average on math tests, while those who left scored below. “The evidence does not support the hypothesis that the ‘best’ students leave,” the study concluded.

Ms. Schwartz said the study’s findings on retention also came as a surprise to her.

Mayor Bloomberg has touted his retention policies, moves that require students to pass tests in order to move from one grade to the next. Yet the study found that, for a cohort that went to school before Mr. Bloomberg took office, one in 10 children had been retained at least once.

The study ended at the eighth-grade level because no full data was available to track students’ high school years, Ms. Schwartz said.