In the current data-rich environment, valorizing of data has become a common task in data science and requires the design of a statistical model to transform input data into a desirable output. The literature in data science regarding the design of new models is abundant, while in parallel, other streams of literature such as epistemology of science, has shown the relevance of anomalies in model design processes. Anomalies are to be understood as unexpected observations in data, an historical example being the discovery of Mercury based on its famous anomalous precession perihelion. Therefore, this paper addresses the various design processes in data science and their relationships to anomalies. To do so, we conceptualize what designing a data science model means, and we derive three design processes based on the latest theories in engineering design. This allows us to formulate assumptions regarding the relationships between each design process and anomalies, which we test with several case studies. Notably, three processes for the design of models in data science are identified and, for each of them, the following information is provided: (1) the various knowledge leveraged and generated and (2) the specific relations with anomalies. From a theoretical standpoint, this work is one of the first applications of design methods in data science. This work paves the way for more research at the intersection of engineering design and data science, which could enrich both fields.