Models used for Model-Based Diagnosis usually assume that observations, and predictions based on the system description are accurate. In some domains, however, this assumption is invalid. Observations may not be accurate or the behavior model of the system does not allow for accurate predictions. Therefore, the accuracy of predictions, which is a function of the accuracy of the observed system inputs and the behavior model of the system, may differ from the accuracy of the observed system outputs. This paper investigates the consequences of using inaccurate values.(1) The paper will show that traditional notions of preferred diagnoses such as abductive diagnosis and minimum consistency-based diagnosis are no longer suited if the available data has different accuracies. A new notion of preferred diagnoses, called maximal-confirmation diagnoses, is introduced.