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 are identified in standard settings under 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 false negatives as more costly than false positives, and that this leads less skilled radiologists to optimally choose lower diagnosis thresholds. Variation in accuracy can explain 55 percent of variation in diagnostic decisions, and policies that improve skills perform better than uniform decision guidelines. Misinterpreting skill variation as preference variation can lead to highly misleading results.