What is the “right” age to get your child a smartphone? It’s a question that vexes many parents — torn between their pleading tweens and researchers who warn about the potential harms of constant connectivity. But new study findings strengthen the case for holding off.

The study, published in the journal Pediatrics on Monday, found that children who had a smartphone by age 12 were at higher risk of depression, obesity and insufficient sleep than those who did not yet have one. Researchers had analyzed data from more than 10,500 children who participated in the Adolescent Brain Cognitive Development Study — the largest long-term look at children’s brain development in the United States to date.

The younger that children under 12 were when they got their first smartphones, the study found,

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