These effects are strongest for people who depend on their smartphones, such as those who affirm a statement like, “I would have trouble getting through a normal day without my cell phone.”

But few people also know they’re paying this cognitive smartphone tax as it plays out. Few participants in the study reported feeling distracted by their phone during the exam, even if the data suggested their attention was not at full capacity.

“We have limited attentional resources, and we use some of them to point the rest of those resources in the right direction. Usually different things are important in different contexts, but some things—like your name—have a really privileged status,” says Adrian Ward, an author of the study and a psychologist who researches consumer decision-making at the University of Texas at Austin.

“This idea with smartphones is that it’s similarly relevant all of the time, and it gets this privileged attentional space. That’s not the default for other things,” Ward told me. “In a situation where you’re doing something other than, say, using your name, there’s a pretty good chance that whatever your phone represents is more likely to be relevant to you than whatever else is going on.”

In other words: If you grow dependent on your smartphone, it becomes a magical device that silently shouts your name at your brain at all times. (Now remember that this magical shouting device is the most popular consumer product ever made. In the developed world, almost everyone owns one of these magical shouting devices and carries it around with them everywhere.)

In the study, Ward and his colleagues examined the performance of more than 500 undergraduates on two different common psychological tests of memory and attention. In the first experiment, some participants were told to set their phones to silent without vibration and either leave them in their bag or put them on their desk. Other participants were asked to leave all their possessions, including their cell phone, outside the testing room.

In the second experiment, students were asked to leave their phones on their desk, in their bag, or out in the hall, just as in the first experiment. But some students were also asked to power their phone off, regardless of location.

In both experiments, students who left their phones outside the room seemed to do best on the test. They also found the trials easier—though, in follow-up interviews, they did not attribute this to their smartphone’s absence or presence. Throughout the study, in fact, respondents rarely attributed their success or failure on a certain test to their smartphone, and they almost never reported thinking they were underperforming on the tests.

Daniel Oppenheimer, a professor of psychology at the University of California, Los Angeles, noted that this effect is well-documented for enticing objects that aren’t smartphones. He was not connected to this research, though his research has focused on other vagaries of digital life. Several years ago, he and his colleagues suggested that students remember far more of a lecture when they take notes by hand rather than with a laptop.