Big data and big data analytics have been the subject of a great deal of positive discussion, not only in traditionally upbeat popular management magazines but also in nominally scientific and therefore professionally sceptical academic journals. Research was undertaken to assess the impact on the quality of inferences drawn from big data of the quality of the underlying data and the quality of the processes applied to it. Empirical study is difficult, however, because big data is emergent, and hence the phenomena are unstable, and likely to vary considerably across different settings. A research technique was accordingly sought that enabled theoretical treatment to be complemented by consideration of real-world data. The paper introduces Quasi-Empirical Scenario Analysis, which involves plausible story-lines, each commencing with a real-world situation and postulating lines of plot-development. This enables interactions among factors to be analysed, potential outcomes to be identified, and hypotheses to be generated. The set of seven scenarios that was developed investigated the nature and impacts of shortfalls in data and decision quality in a range of settings. In all cases, doubts arise about the reliability of inferences that arise from big data analytics. This in turn causes concern about the impacts of big data analysis on return on investment and on public policy outcomes. The research method was found to offer promise in the challenging contexts of technologies in the process of rapid change.