Even though statistical thinking and critical thinking appear to have strong links from a theoretical point of view, empirical research into the intersections and potential interrelatedness of these aspects of competence is scarce. Our research suggests that thinking skills in both areas may be interdependent. Given this interconnection, it should be possible to stimulate both forms of thinking through the one task. This paper explores the implications of an exploratory qualitative study into processes when working on tasks encompassing both these areas for the design of tasks that simultaneously stimulate critical thinking and domain-specific thinking.