The nursery rhyme study was unable to "evaluate the severity of the episodes of violence", the authors say.
"For instance, 'Here comes the chopper to chop off your head' (Oranges and Lemons), or a blackbird pecking off someone's nose (Sing a Song of Sixpence) probably has a different impact level to someone falling out of a bed (Six in a Bed)," they note.
The study measured episodes of violence, recorded as accidental, aggressive or intentional. Jack and Jill has three incidents, they write, two accidental and one aggressive.
The two tumbling down the hill are the accidental episodes and the aggressive is being bound with vinegar and brown paper, as seen in the rhyme below:
Jack and Jill went up the hill to fetch a pail of water
Jack fell down and broke his crown
And Jill came tumbling after.
Up got Jack, and home did trot
As fast as he could caper
He went to bed and bound his head
With vinegar and brown paper.
The poem is thought to refer to genuine episodes of violence. Jack is said to be King Louis XVI who came a cropper during the French Revolution. Jack lost his crown as a result of beheading followed by his Queen Marie Antoinette (Jill), who came tumbling after.