It was found that 2.54 per cent of the tweets containing the username of male public figures contained abuse, compared to only 0.95 per cent of the tweets received by prominent women.
Of the 94,528 messages for Morgan 8,258 were abusive while 1,190 of the 45,815 messages received by Ricky Gervais were abusive.
Jessie J had to put up with 263 abusive messages among the 322,433 she received, while 183 tweets to Rita Ora out of 110,089 were offensive - but as performers who seek to entertain rather than provoke a reaction the study found that it was celebrities who faced the lowest levels of abuse.
Journalism was the only category where women received more abuse than men, with female journalists and TV news presenters receiving roughly three times as much abuse as their male counterparts.
The results mark the launch of a Demos report - Vox Digitas - investigating how the wealth of data on social media can increasingly be used to monitor trends in public attitudes.
Report co-author Carl Miller said: "Receiving criticism has long been part and parcel of being in the public eye. But Twitter is providing newer, more direct ways, for the public to hurl abuse at celebrities and prominent personalities.
"We found that not only are men more often the target of this abuse, but are also more likely to be the ones behind the attacks.
"Social media is now an important part of social life and researching it is vital to understand the world that we now live in. It allows us to gather more evidence about society and politics than ever before, spot emerging problems, and, above all help us know what to do about them."
- AAP