Mr. Hancock’s analysis of about 226 studies on the well-being of phone users concluded that “when you look at all these different kinds of well-being, the net effect size is essentially zero.”

The debate about screen time and mental health goes back to the early days of the iPhone. In 2011, the American Academy of Pediatrics published a widely cited paper that warned doctors about “Facebook depression.”

But by 2016, as more research came out, the academy revised that statement, deleting any mention of Facebook depression and emphasizing the conflicting evidence and the potential positive benefits of using social media.

Megan Moreno, one of the lead authors of the revised statement, said the original statement had been a problem “because it created panic without a strong basis of evidence.”

Dr. Moreno, a professor of pediatrics at the University of Wisconsin, said that in her own medical practice, she tends to be struck by the number of children with mental health problems who are helped by social media because of the resources and connections it provides.

Concern about the connection between smartphones and mental health has also been fed by high-profile works like a 2017 article in The Atlantic — and a related book — by the psychologist Jean Twenge, who argued that a recent rise in suicide and depression among teenagers was linked to the arrival of smartphones.

In her article, “Have Smartphones Ruined a Generation?,” Ms. Twenge attributed the sudden rise in reports of anxiety, depression and suicide from teens after 2012 to the spread of smartphones and social media.