Several of Chicago’s largest charter schools chains are cramming more than a year’s worth of learning into a single school year, according to a new study by well-respected researchers at Stanford University.

CREDO analysts — using data from 2011-12 through 2014-15 school years for 5,700 schools in 26 states — examined how different charter management structures affect student learning growth. It found generally that although quality varies across the country, chains of three or more schools generally fare better than stand-alone schools, and owner-operated charters fared better than schools that hired out their day-to-day management.

In Chicago, the bulk of the privately managed but publicly funded charter schools are operated by the same folks who hold the charter. Ten local operators, including three of the city’s largest chains, were included in the study by the Center for Research on Education Outcomes who have for years compared charter school performance across the nation.

Lead analyst James L. Woodworth translated the academic growth of year-over-year test scores into additional days of learning based on a 180-day school year. And he found that students at the Noble Network of Charter Schools received the equivalent of nearly two years’ worth of math instruction in a single year and UNO Charter School Network students got about 28 extra days of learning in math and 22 in reading.

“It does look like there’s some advantage to being in a [charter management organization] when opening and operating new schools,” Woodworth said. But he warned, “highly replicated is not a guarantee of quality.”

But contrary to national trends for the tiny segment of charters operating as hybrids, Chicago International Charter School showed significant losses, where students apparently learned less than a year’s worth of core academics in a single school year — about 62 days of math and 39 days of reading, according to the study. Nationally, on average, students in hybrid schools enjoyed the equivalent of 51 extra days in math and 46 in reading.

Officials from CICS and UCSN declined to comment, saying they had not reviewed the study. Noble wouldn’t make anyone available for an interview.