The study, which Dr. Fuller wrote with John R. Novak, director of research for the Long Beach Unified School District, identified two Oakland schools whose students, on average, performed at statistically equal levels on standardized tests.

One, Manzanita Elementary, serves a diverse population that includes black, Latino, Asian, low–income and limited–English students. The other, Golden Gate Elementary, serves primarily black students, with some also falling into the low–income category, giving the school just two groups under the federal law's accountability system, the study said.

As a result of its diverse population, Manzanita had to meet test–participation and achievement–growth targets in 18 categories.

Manzanita dramatically raised student proficiency levels, hitting 17 of the 18 necessary targets, the study said. But black students at the school narrowly missed their proficiency target in math. Golden Gate, because of its more homogeneous student body, needed to meet targets in only six categories, and succeeded.

Manzanita was labeled as needing improvement and Golden Gate was not, the study said.

Eugene W. Hickok, the acting deputy secretary of the United States Department of Education, said he was not surprised by the study's results but disagreed with the authors' interpretation.

"There's a certain logic that the more subgroups you have — the more boxes you have to check off — the more difficult it will be to make adequate yearly progress," Dr. Hickok said. "But to conclude that N.C.L.B. punishes diversity is a non sequitur. As a public school, you have an obligation to all your kids. If special ed kids are not doing well, then you have an obligation to take care of that."