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.

The lottery process enabled the researchers to compare what happened to two groups of students that started out statistically identical: those who were admitted to the small schools and those who lost the lotteries and wound up in older, larger schools. That type of comparison is considered the “gold standard” in education research.

The original study, released in 2010, found that the small high schools had positive effects on their students — but it looked only at the schools’ very first enrollees. Last year, MDRC’s report looked at those students in the fifth year after they enrolled and also at the second set of students who enrolled at the schools, finding similar gains. The newest edition adds a third cohort of students and also starts to dig into what differentiated small high schools with high graduation rates through interviews with staff.

The report finds that the higher graduation rate — 74.6 percent, compared to 65.1 percent for students who were not admitted — continued for the third group of students who enrolled and cut across all groups of students, regardless of their race, gender, family income, or academic skills upon enrollment.

For the first time, the researchers were also able to examine small schools’ effects on students with disabilities and English language learners, finding graduation gains for them as well. Those subgroups had been omitted from previous reports because the schools had enrolled few students in them in their first two years, a fact that critics of MDRC’s research said last year undermined the firm’s conclusions.

Also for the first time, MDRC hired the Research Alliance for New York City’s Schools, a nonprofit that a former MDRC official founded in 2008, to interview principals and teachers from the 25 highest-performing small schools in the study. They were told that high expectations, strong relationships between adults and students, and high-quality teachers were seen as key to the schools’ success. Principals cited their teachers first more than half of the time, while nearly two thirds of teachers cited their relationships with students first.

The principals and teachers told the researchers that they worried that space, finances, and staffing issues would impede their schools’ ability to succeed in the future.

The next installment of the longitudinal research study will try to turn the anecdotes into hard data through a statistical analysis of what differentiates the small schools. MDRC also plans to look at teacher turnover at the schools, the relative cost of operating them, and their graduates’ performance after high school.

So far, MDRC has found that students at the small schools were more likely to meet the state’s college readiness standards in English, but not in math.

MDRC’s complete report is below.