This paper proposes a QoS-based trust evaluation model for black box data services. Under the black-box model, data services neither export (meta)-data about conditions in which they are deployed and collect and process data nor the quality of data they deliver. Therefore, the black-box model creates blind spots about the extent to which data providers can be trusted to be used to build target applications. The trust evaluation model for black box data services introduced in this paper originally combines QoS indicators, like service performance and data quality, to determine services trustworthiness. The paper also introduces DETECT: a Data sErvice as a black box Trust Evaluation arChitecTure, that validates our model. The trust model and its associated monitoring strategies have been assessed in experiments with representative case studies. The results demonstrate the feasibility and effectiveness of our solution.