Physicians, judges, teachers, and agents in many other settings differ systematically in the decisions they make when faced with similar cases. Standard approaches to interpreting and exploiting such differences assume they arise solely from variation in preferences. We develop an alternative framework that allows variation in both preferences and diagnostic skill, and show that both dimensions may be partially identified in standard settings under quasi-random assignment. We apply this framework to study pneumonia diagnoses by radiologists. Diagnosis rates vary widely among radiologists, and descriptive evidence suggests that a large component of this variation is due to differences in diagnostic skill. Our estimated model suggests that radiologists view failing to diagnose a patient with pneumonia as more costly than incorrectly diagnosing one without, and that this leads less-skilled radiologists to optimally choose lower diagnostic thresholds. Variation in skill can explain 39 percent of the variation in diagnostic decisions, and policies that improve skill perform better than uniform decision guidelines. Failing to account for skill variation can lead to highly misleading results in research designs that use agent assignments as instruments.