The distributed and global nature of data science creates challenges for evaluating the quality, import and potential impact of the data and knowledge claims being produced. This has significant consequences for the management and oversight of responsibilities and accountabilities in data science. In particular, it makes it difficult to determine who is responsible for what output, and how such responsibilities relate to each other; what ‘participation’ means and which accountabilities it involves, with regard to data ownership, donation and sharing as well as data analysis, re-use and authorship; and whether the trust placed on automated tools for data mining and interpretation is warranted (especially as data processing strategies and tools are often developed separately from the situations of data use where ethical concerns typically emerge). To address these challenges, this paper advocates a participative, reflexive management of data practices. Regulatory structures should encourage data scientists to examine the historical lineages and ethical implications of their work at regular intervals. They should also foster awareness of the multitude of skills and perspectives involved in data science, highlighting how each perspective is partial and in need of confrontation with others. This approach has the potential to improve not only the ethical oversight for data science initiatives, but also the quality and reliability of research outputs. This article is part of the themed issue ‘The ethical impact of data science’.