Researchers from the Universite de Montreal have been looking into the links between lack of sleep and hyperactivity in small children. 2,057 mothers answered yearly questionnaires about how well their children slept and their hyperactivity. The study found that children who didn't sleep long were generally hyperactive boys who lived under adverse family conditions. The link between lack of sleep and hyperactivity was weaker than the link between hyperactivity and lack of sleep but the children who slept persistently for at least 11 hours had low hyperactivity scores. Boys whose mothers were less well-educated, came from a poor family, who were comforted outside the bed or who got into bed with Mum and Dad after waking up in the night were more at risk of having a bad night's sleep and becoming hyperactive.
You can find out more about this research at