Girls are much more likely than boys to be bullied at school, with almost twice as many on the receiving end of cyberbullying and social exclusion by other pupils, according to a government study.

The figures from a survey of 10,000 pupils at schools in England in year 11 – children aged 15 or 16 – revealed a decline in reports of bullying overall and particularly in incidents of violent bullying, which mainly affects boys.

But girls reported a rise in bullying, with more than one in three telling researchers they had been affected in the previous year, while only about one in four boys said they had been victims of bullying in any form.

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The report published by the Department for Education said the overall trends around bulling in schools were “broadly positive”, with the rate of bullying reported falling from 37% of pupils in year 10 to 30% for the same cohort 12 months later in year 11.

Incidents of bullying were slightly lower compared with a similar study in 2006, forms of violent bullying were lower than a decade before – with threats of violence reported by pupils down from 14% to 10%, and actual violence down from 10% to 6%.

“While violent forms of bullying have declined significantly, name calling and social exclusion have increased since 2006. The success in reducing violent bullying shows what can be achieved; the challenge is to replicate this success across all forms of bullying,” the report concluded.

Tom Bennett, an adviser to the DfE on behaviour policies and teacher training, said the overall reduction was to be welcomed but warned that bullying was “an evergreen problem” when students were competing for attention and status.

“It’s perhaps unsurprising to see boys as more likely to experience violence, and girls to be the victims of social exclusion,” he said. “The latter is less visible, and the bruises it leaves can be intangible.

“The problem this causes is that it means such bullying can fall below the radar, and schools need to be proactive in both creating cultures where students feel safe and valued, and also respond accurately and quickly to allegations.

“The complexity of who is the bully and who is the bullied also often makes policing this sphere unbelievably difficult, and the inexorable move of such activities online presents huge challenges to even the most concerned teacher.”

The data comes from the third wave of a longitudinal study of young people in England managed by the DfE, with the surveys conducted in 2015 and 2014. The longer-term comparison was with a similar survey taken in 2006.

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Cyberbullying did not feature in the 2006 version, but 10% of the 15- and 16-year-olds reported being affected in the most recent study.

For girls the most common form of bullying was name calling and social exclusion, with both types having increased significantly since 2006. But the rise occurred entirely for girls, with boys reporting no increase in either types of bullying. While one in five girls reported being a victim of social exclusion, fewer than one in 10 boys did.

Disabled children and children with special needs also reported much higher incidents of bullying than other pupils.

The survey results also showed that pupils who were victims of bullying received lower GCSE results than their peers who hadn’t been bullied, by the equivalent of two grades in one GCSE exam.

But the authors of the research said it was “important to note that this simple correlation does not demonstrate causation between bullying and lower GCSE performance; there are likely to be many other factors involved”.