New York State’s charter schools are in a majority of cases outperforming their districts on state tests, even amid the sky-high gains shown throughout the state this year, an analysis by the New York Charter School Association of the scores released yesterday shows.

When compared to the overall scores for the school districts in which they are located, some charter schools — such as Bronx Preparatory in the South Bronx and the KIPP Infinity school in Harlem — had as much as double the portion of students scoring proficient in math and reading.

Also outperforming district schools are two charter schools opened by the city teachers union.

The United Federation of Teachers opened the elementary and secondary schools to disprove people who said charter schools succeed because their teachers are not represented by labor unions. The case was sullied earlier this year when reports of parental concern and teacher turnover emerged from the elementary charter school.

Now, union leaders are saying their score results show the schools are indeed a model; at the elementary school, where students were tested for the first time this year, 98% of third-graders scored proficient on math, compared to 81% at other district public schools, and 82% scored proficient at reading, compared to 51% at district schools.

The high school, opened last year, also saw higher proficiency rates than district schools.

A smaller group of charter schools performed worse than their districts. The Ross Global Academy Charter School, which is housed inside the Department of Education’s headquarters at Tweed Courthouse and has suffered high teacher and principal turnover, underperformed its district’s average by about five percentage points on the state reading test, though its students performed above the city average on the test.

New York State’s education commissioner, Richard Mills, released the test scores yesterday afternoon amid swirling concern that they were too high to reflect true educational improvements.

The scores, which shot up at many schools by double-digit proportions, were first reported in The New York Sun.

Yesterday Mr. Mills defended the test scores’ reliability, saying the tests had been rigorously reviewed by the federal Department of Education and by a technical advisory group of scholars and psychometricians who gave their stamps of approval. “They challenge every aspect of what we are doing, and they are a tough market I can assure you,” Mr. Mills said of the advisory group. “This process has passed muster with them.”

State officials provided a document from the federal education department from this spring saying New York’s state standards and tests have been fully approved, with just one recommendation related to assessments given to students with severe disabilities.

Several psychometricians and education experts told the Sun that score inflation — in which rising test scores do not reflect real rises in academic knowledge — is rampant across the country, and present in New York, too.

Mayor Bloomberg dismissed that notion. “You can’t get better at doing math problems unless you know more math,” he said.

Several possible mayoral candidates expressed doubt about the test scores.

“I don’t believe in any of the state tests,” Rep. Anthony Weiner, a Democrat who is a likely candidate for mayor in 2009, told the Sun.

The city’s public advocate, Betsy Gotbaum, said the scores raise questions. “If New York City is making such a big jump on our performance on state tests, why do our scores on the NAEP test — this nation’s gold standard test — remain flat?” she asked. “And why did so many other cities in the state, including traditionally low-performing ones like Buffalo and Rochester, see similar dramatic increases?”