An analysis of primary school test results in England suggests that successful schools are not likely to improve when they become academies.


But the study, by education data firm SchoolDash, says there can be gains for disadvantaged pupils in struggling primary schools that convert.


Most secondary schools are academies, but only about one in six primary schools has changed status.


The study comes as the government wants all state schools to become academies.


Research into the achievement of academies has tended to focus on secondary schools, whose numbers have risen over more than a decade.


But if all schools are forced to become academies, the greatest impact will be among primary schools, where more than 13,000 schools will need to change.


This SchoolDash analysis compared the performance in test results of academies with local authority primaries in similar circumstances, such as levels of deprivation.


Most primary academies are "converter" academies, which tended to be high-achieving before becoming academies.


The research found "no evidence" that academy status brought improvements to these schools or that such schools were any better than their local authority counterparts.


But the smaller number of "sponsored" academies, more likely to have been previously under-achieving, made more progress when they became academies.


These improvements were "especially noticeable for disadvantaged pupils", said SchoolDash founder Timo Hannay.


"The challenge for those who support compulsory academisation is to explain why a good school should be forced to convert against its wishes if there are unlikely to be any tangible academic gains," said Dr Hannay.


"And the challenge for those who oppose it is to explain how else they would reduce the disparity between the best and the worst schools in the country, a gap that is still far too wide."


The study also shows the wide regional variations in the spread of academies.


There are some authorities where more than half of primary schools are already academies, including Bournemouth, Darlington and Middlesbrough.