A student asked us: "Wouldn't the answer be a moderating variable because the health insurance influences the amount of pills the patient gets and therefore the "strength" ?"
This is an understandable mistake, since moderating variables do in fact affect the strength of a relationship. However, in this question stem, we are told that the discrepancy in the amount of pain pills prescribed is due to differences in insurance coverage. Since the relationship is caused by the variable of insurance, insurance must be a mediating variable. A moderating variable affects strength, but doesn't establish a relationship: the relationship must already be present for a moderating variable to exist.
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