Educators have long studied the achievement gap, in which black and Hispanic pupils and low-income students of all races perform at much lower levels than their white, Asian and better-off peers. A new study released on Tuesday by a group that supported efforts to attain more money for city schools looked at the educational opportunities available to poor and minority students and found the choices lacking.

The report by the Schott Foundation for Public Education found that poor and minority students have fewer opportunities to attend the city’s best public schools largely because of where they live.

The study’s authors looked at state math and English scores at 500 middle schools in the 2009-2010 school year. The schools were sorted into four groups from highest to lowest test scores, with an equal number of schools in each. The authors then looked at how many students in each of the city’s 32 community school districts are able to attend local middle schools that scored in the 75th percentile, or top quarter.

The study did not include charter schools. Most of the charters are in low-income and minority communities, and some of them have impressive test scores.

The study found that wealthier neighborhoods have more access to better schools. For example, all of the students in District 26 in Queens — which includes Douglaston and Little Neck — have an opportunity to attend a high-performing middle school. Most students can also attend high-scoring schools in Manhattan’s District 2 and 3.

But in five districts, which include Harlem, the Bronx and Bedford-Stuyvesant, no students can attend a middle school that performs in the top quarter. The local middle schools just don’t have the test scores. The report also found that, within the 32 districts, whites and Asians are more likely to attend high-scoring schools than blacks and Hispanics.

The Schott Foundation helped finance the now defunct Campaign for Fiscal Equity, which won a lawsuit finding New York City’s public schools were shortchanged by the state. It also gives grants to the Alliance for Quality Education and the New York State Conference of the N.A.A.C.P.

The report’s main author, researcher Michael Holzman, called the findings evidence of educational “redlining,” because of the disparities, and said they were “an embarrassment to the city,”

“What we have is a situation where children who are most in need of what New York City public education can offer them are the least-likely to be able to have access to it,” he said.

The report challenges the Bloomberg administration’s argument that it is providing more high quality choices for families by opening about 500 schools in the past decade, including more than a hundred privately managed charter schools.

But by not including the charters, the study failed to take into account the full range of options available to students, especially in the city’s poorest neighborhoods.

Mr. Holzman said charters were not included because they only served only 2 percent of all city students in the 2009-2010 school year, though the percentile is higher in low-income areas.

The study also did not provide any comparison data to previous years to show whether things have gotten better or worse. And it did not say how many students from each district had the opportunity to attend a school in the top 50th to 74th percentile, meaning their scores aren’t in the very top but are still better than average.

Department of Education spokesman Frank Thomas said the city is making progress in closing achievement gaps.

“Over the last ten years, our reforms have focused almost entirely on creating better schools for students who were failed by the system for decades,” he said. “While there is much more work to do, the reality is that black and Hispanic students in New York City are graduating at their highest rates ever, and continue to narrow the achievement gap year after year. A report that fails to acknowledge this progress is shortsighted and overlooks the gains made by thousands of students during that time.”

The Schott study, however, also found evidence of disparity in teacher quality. It found that districts with high poverty rates have fewer experienced and highly educated teachers (those with a masters degree plus 30 additional credits) than wealthier districts, where teachers tend to stay for a long time. The report says the city winds up spending 19 percent more educating students in the wealthier districts because their teachers make more money.

Meanwhile, the same districts that have the lowest performing middle schools also send few children to gifted and talented programs and specialized high schools. This was confirmed in data released last week by the Department of Education finding that so many more children from Manhattan and brownstone Brooklyn qualify for gifted and talented programs than students in low-income neighborhoods such as District 7 of the South Bronx, where fewer than 100 prekindergarten children took the test and only six were eligible.

The Schott Foundation is calling on the city to expand tutoring and test-preparation services so that more students can take the admissions test for specialized high schools. It also wants the city to test all incoming kindergarten students for gifted and talented programs, because so many families in poor communities don’t even have their children tested.

It also proposes a cap on the percentage of new teachers who are allowed to work in high-poverty districts, and for the state to restore and increase aid to New York City.

The Department of Education says testing all pre-K students would result in a significant loss of instructional time because it takes about an hour to test each of these children one-on-one. It has also questioned the logistics of capping the percentage of new teachers working in low-performing districts, which tend to have the most vacancies.

“We are always working to attract the highest quality teachers to our lower performing schools,” said the spokesman, Mr. Thomas, adding that this is the city’s plan for the 26 schools it plans to close and reopen this fall.