The Globe reviewed seventh-, eighth-, and 10th-grade MCAS proficiency rates in English and math from 20 charter schools in cities and towns across Greater Boston. Most charter schools did better overall than the community in which they are based.

In Lawrence, the Community Day Charter Public School easily bested the city’s troubled public school system.

On the South Shore, charter schools mostly did well on the English tests, but had some struggles in math, with Foxborough Regional Charter a prime example. The well-respected school had some of the top 10th-grade scores in the state, but its seventh- and eighth-grade students fell short of the state median in math, and as a result showed mixed results compared with Foxborough’s public schools.

And west of Boston, the Advanced Math and Science Academy Charter School in Marlborough outpaced not just many schools in the region, but also statewide.

When compared with their performance on the 2011 MCAS tests, the charter schools had varied success. Focusing on the percentage of students who scored either advanced or proficient, about a third of the 20 charter schools surveyed by the Globe did about the same as a year ago, a third did somewhat better, and a third somewhat worse.

Glenn Koocher, executive director of the Massachusetts Association of School Committees, said a comparison of charter schools with traditional schools is unfair, since charter schools can gain an advantage by weeding out underachieving students.

“It’s the quality of the cherry-picked students that gives charter schools the advantage in many cases,” he said. “They don’t have special-education kids in the same complexity and number as the general-sending districts. . . . They send their troubled students back to the sending districts or counsel them out, or they don’t recruit them in the first place. It’s absolutely a function of skillfully recruiting the students who are higher achievers.”

Charter school advocates insist they aren’t keeping only the best students, and they say other factors are at work.

“Generally charters offer longer school days and school years, so there’s more time in the classroom for children,” said Dominic Slowey, spokesman for the Massachusetts Charter Public School Association.

He called Koocher’s arguments “tired.”

“Our enrollment is determined by random lottery and so we can’t control our enrollment,” said Slowey. “We also can’t push kids out. That would be illegal.”

Charter schools are public schools authorized by the Education Reform Act of 1993. They have flexibility that public districts don’t have, such as the ability to hire nonunion teachers, but they also have tougher accountability standards and must demonstrate success within five years or risk losing their state charter.

Bruce Bean, data manager for the Community Partners Initiative of Lawrence, which is affiliated with Community Day, analyzes data for the charter school association and other clients.

He crunched the numbers for grades 7, 8, and 10, using percentages of students scoring proficient or better in English and math. He found, as in 2011, that most charter school students statewide did better than counterparts in their sending districts by a healthy margin, on average.

Bean said part of that can be attributed to the strict accountability of charter schools required by the state. The state closes charter schools that aren’t doing well, he said.

Asked whether charter schools are selecting more motivated families whose children often are better students, he responded that the demographics he has analyzed show the same patterns in charter schools and traditional public schools.

“It is a lottery,” said Bean. “I guess somewhere in the kids’ life somebody had to say ‘I want to fill out a form, an application form,’ but other than that you’re getting pretty much the same demographics that you get in other schools.”

In Marlborough, the Advanced Math and Science Academy outperformed the city’s public schools, and it also outperforms most schools in the state. It was one of only 15 schools statewide that saw 100 percent of 10th-graders pass both English and math this year.