A new study by Harvard University is raising questions about a recent federal report that said public school children perform as well or better that their private school peers on national reading and mathematics tests.

The Harvard study released yesterday called the earlier report’s analysis “flawed” and said that its findings were unreliable because it underreported the number of disadvantaged students in private schools.

The government report — which fanned the flames of the school voucher debate when it was released last month — compared the scores of fourth- and eighth-grade students from nearly 7,000 public schools and 530 private schools on the National Assessment of Educational Progress test. When factors such as race and wealth were taken into account, students in public schools scored the same or better than students at private schools, the government report said.

The study was conducted by the National Center for Education Statistics, a research arm of the U.S. Department of Education, using scores from 2003 tests.

“This new study does a good job of showing the defects of the U.S. Department of Education study,” a Manhattan Institute scholar, Jay Greene, a professor at the University of Arkansas, said.

Proponents of school vouchers quickly jumped on the report, questioning the research methodology. At the same time, public school advocates — including unions representing teachers — criticized the Bush administration for quietly releasing the report on a Friday afternoon in July, claiming it was given little attention because it did not show that private school students performed better.

Results favorable to private schools would likely give a boost to the administration’s efforts to promote school choice programs such as charter schools and money for school vouchers.

Just days after the report was published, a government professor at Harvard, Paul Peterson, who is also the editor of “Education Next,” a journal on education policy, raised questions about the methodology of the report.

While the earlier report counted the number of poor students based in part on how many received free lunch and other subsidized federal programs, Mr. Peterson, who wrote the study released yesterday, said that it was an inaccurate measure of poverty in part because it is more difficult for private school students to apply to those programs.

“You have an undercount of disadvantaged students in the private schools,” Mr. Peterson said about the federal study.

A spokesman for the U.S. Department of Education, Chad Colby, said that the National Center for Education Statistic’s report was not very useful because it did not help parents decide where to send their children to school.

“What we do at the department is try to make schools better,” Mr. Colby said. He referred questions about criticism of the report to the report’s author, Henry Braun, who could not be reached for comment.

Mr. Greene said that to accurately compare students at public and private schools researchers must randomly place students at those schools so that the backgrounds of the two groups are the same. He said that eight studies conducted over the past decade using similar random methods have all found that private school students perform better.

Mr. Peterson said that it was impossible for him to draw any conclusions about whether students at private or public schools performed better based on the available data.

Asked about the importance of the study, the author of a series of parent guides to the city’s public schools and director of insideschools.org, Clara Hemphill, said: “We obviously all want the best for all of our children and if somebody has the answer of how to provide that, we all want to know about it.”