For the third time, an independent research group has found that the Bloomberg administration’s small high schools gave students who attended them a better chance of graduating.

Being randomly selected to attend small high schools opened by Bloomberg made students significantly more likely to graduate, even for students who entered in the schools’ third year, according to the report, conducted by researchers at the nonprofit firm MDRC. Students who entered in the schools’ first three years graduated in four years 70.4 percent of the time, compared to 60.9 percent of the time for similar students in other schools, according to the report.

The research was paid for by the Gates Foundation, which originally funded the small schools. The foundation put $150 million into the city’s small schools before ending its small-schools giving in 2008, citing lackluster college readiness rates.

The new report is the third installment in a series that examines “small schools of choice” that opened between 2002 and 2008 and did not select students based on their academic performance. Of the 123 schools that fit that bill, 105 had so many applicants that the schools selected among them randomly, through a lottery....

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