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We’ve all seen them — the parents on the playground sitting hunched over their iPhones as their children teeter toward (or egg on) disaster. And chances are, we’ve also likely been them. But are the effects of our digital distraction really such a big deal? One father, a research fellow at Yale University, decided to find out, and the results of his study might make you cringe: Smartphones, Craig Palsson concludes, have caused an spike in the number of children getting injured, particularly for the 5-and-under set.

“I argue that smartphones have caused an increase in child injuries, and that at least part of this reason is that smartphones distract parents while they are supervising their children,” he writes in his 35-page report, “That Smarts! Smartphones and Child Injuries.” Palsson established causation between smartphones and child injuries by tracking two sets of data: the 10 percent increase of nonfatal, unintentional injuries to children between 2006 and 2012, according to the Centers for Disease Control and Prevention (CDC); and the 3G rollout data of corresponding cities as tracked by the National Electronic Injury Surveillance System.

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“When 3G comes to the area, injuries increase, and I can control for other changes by looking at hospitals that don’t have 3G yet,” Palsson explains in an email to Yahoo Parenting. “Furthermore, the patterns match what we expect if phones are distracting parents: Younger kids are affected more than older kids (who are under less supervision). And injuries increase in activities where parental supervision could make a difference — children are hurt on playgrounds, at pools, and falling down stairs.”

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Palsson was in fact his own case study: He began noticing that using his phone — not even a smartphone! — was distracting him during playtime with his kids. “If parents are distracted enough that their kids are injured,” he says, “I think it’s worth questioning how interactions are affected where the consequence is not immediate and salient.”

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Those are the types of questions Catherine Steiner-Adair, clinical psychologist and author of “The Big Disconnect: Protecting Childhood and Family Relationships in the Digital Age,” contends with often in her research. “There is no question that parents are now challenged by the lure of their iPhone and the desire to ‘just check.’ But that’s when we’ll miss our baby slipping in the bathtub or climbing out of a booster seat,” she tells Yahoo Parenting, noting that she’s heard many parents speak of the guilt they felt when their child wound up with stitches for an injury received while they were busy texting. “When you are, quote, watching your child at the playground, and they are up on a slide and you are ‘just checking’ your text or email, you are not watching them.”

But what if you’ve got really good, important reasons for using your smartphone when you’re with your kids? Writer Jennifer Hicks recently raised that question in her essay “Dear Mom on the iPhone: You’re Doing Fine,” pointing out that parents may be doing something worthwhile such as “responding to clients, sending a proposal,” or even posting on Facebook to “offer condolences for the loss of a loved one,” all while their child gets the benefit of playing in the fresh air. “Or maybe,” she writes, “you realize that watching your kid every second of every day isn’t necessary and that it’s totally acceptable and actually good for everyone involved — for you to have a few minutes to yourself. At the park. On your phone.”

But physical injuries may not be the only possible repercussions of such behavior, Steiner-Adair notes. In her 1,000-plus interviews with young children for her book, she’s heard heartbreaking comments along the lines of: “My mommy’s smartphone is the ‘stupid phone’ — she talks on it when she’s pushing me on the swing and I don’t like it.” Because we’ve developed a psychological dependence on our devices, she warns, “we are unintentionally giving kids the idea that they are boring — because with just the sound of a ‘ping,’ we will divert our attention from them, midsentence.”

She has a few suggestions to balance your attention between the kids and the device:

•Determine how extreme your diversion is. Use the app Checky to learn how often you check your phone. For many, Steiner-Adair notes, it’s up to 100 times a day.

•Be more mindful. Pay attention to how often you turn away from your kid and reach for the phone, and temper it by asking yourself, How important is every little email coming through? “This requires thoughtful self-discipline,” she says.

•Separate digital time. When you’re with your child, Steiner-Adair suggests, set aside several times a day to check your phone — and don’t look during the nonallotted times. “It will strengthen your relationship with your child,” she says.