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This article by LaPorta basically states that cell phones can be an addiction. She later goes on to relate the addiction to gambling or cigarette addiction.
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This article by Jenaro is some of the earliest research describing how many people in a survey are addicted. It also states that anxiety and depression are effects of addiction
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This research by Roberts looks at the differences in cell phone activities between male and female college students
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Pavia's findings in this research make it easier to test whether people are addicted to their smartphones or not.
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The effects of cell phone addiction are studied by Elhai here. He finds new effects of addiction.
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Sapacz, Rockman, and Clark find what circumstances lead to the most anxiety in cell phone addicts.