How they interact with their phones, tablets and computers is the best predictor of emotional or social problems connected with screen addiction, according to the study.
Researchers said the warning signs can include if screen time interferes with daily activities, causes conflict for the child or in the family or is the only activity that brings them joy.
Sarah Domoff, assistant professor of psychology at Central Michigan University who led the study, said: "Typically, researchers and clinicians quantify or consider the amount of screen time as of paramount importance in determining what is normal or not normal or healthy or unhealthy.
"Our study has demonstrated that there is more to it than number of hours. What matters most is whether screen use causes problems in other areas of life or has become an all-consuming activity."
Children who use media in unhealthy ways have problems with relationships, conduct and other emotional symptoms, Professor Domoff added.
Previous research has looked at adolescents and screen use.
But Professor Domoff said this is understood to be the first tool in the United States that measures screen media addiction in children ages 4-11.
She believes it will be a valuable tool for parents, clinicians and researchers.
However further work is needed to examine whether the emotional and behaviour problems or the media addiction came first, which the study did not address.
The research appeared in the Psychology of Popular Media Culture, a journal of the American Psychological Association.
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