“We found that there’s no age at which you can give a child a phone that’s better or worse for reading comprehension, so it’s just having a phone at all,” said lead author and UCLA psychology professor Patricia Greenfield. “That’s true in third grade, and it’s true in sixth grade.”

This seems overly broad to claim based on an observational study. Or rather, they did an experiment, but what they tested in their experiment is different than what they're claiming here. The groups weren't 'kids who aren't allowed to have a phone' and 'kids who are allowed to have a phone', it was 'kids that had their phone with them at school that day' and 'kids who didn't have their phone with them at school that day', and they further broke it up by taking some of the kids with phones and taking their phone away from them for the duration of the experiment.

That is not what your press release is selling me, UCLA!