A new study by a Harvard economist that shows New York City charter schools pushing ahead of traditional public schools on standardized tests could have educators across the country looking to the city for lessons.

The study paints a detailed picture of the city’s charter schools, finding wide policy differences compared to traditional public schools — uniforms are almost universal and Saturday school is popular — as well as a test score gap of 3.8 points on math tests and 1.6 points on reading tests.

Charter schools are privately operated public schools that enjoy freedom in exchange for a promise to meet certain achievement goals or be shut down.

Entering a scholarly debate that has so far reached no consensus, the report is the first comprehensive study of charter schools to use random assignment, a methodology that is considered the gold standard in education research.

Researchers took advantage of New York City charter schools’ popularity — applications outnumber available seats, on average, 3 to 1 — comparing students who applied and were accepted through a random lottery to students who were rejected. They found charter school students scoring higher in the years studied, grades three through eight.

The rises in scores each year are modest, with math gains representing 12% of a performance level — city schools have four performance levels delineating achievement — and 3.5% for reading.

But researchers said the difference was still significant. “That’s a small effect, but it’s only one year,” a professor of education at the University of Arkansas, Patrick Wolf, said. “If these gains build consistently over time, they would start to move more of these disadvantages students to a level of proficiency.

A researcher at Columbia University’s Teachers College, Jack Buckley, said the study adds to a consensus that charter schools are having positive impacts, raising a new question: “Why? What is it about the schools that’s driving this?” he said.

The researchers, led by an economist, Caroline Hoxby, who is reportedly moving to Stanford University from Harvard University, said they could not give a definitive answer to Mr. Buckley’s question, but noted that a longer school day was the only policy statistically related to the higher test scores. They also cited policy differences common to charter schools, including school uniforms and merit-based bonuses for teachers.

The president of the National Alliance for Public Charter Schools, Nelson Smith, said a reason for the results could be the support of the New York City Department of Education. “Successful charter schools don’t happen by accident,” he said.

Mayor Bloomberg and his schools chancellor, Joel Klein, are strong supporters of city charter schools. They have provided public buildings for charter schools and lobbied for the lift in the number of charter schools allowed by state law that was signed by Governor Spitzer in the spring. In September, the city will have 60 charter schools, and more applications for charters are being processed. Charter schools are sometimes criticized for “skimming” the best students from public schools. The report’s data show charter schools were enrolling slightly fewer special education students than public schools (11% vs. 13%, respectively) and found charter schools had far fewer English-language learners (4% vs. 14% for public schools). It also found charter students were more likely to be poor and far more likely to be black. In 2005–06, 68% of charter school students were black, compared to 32% of students citywide.