Statistical thinking in empirical enquiry

Advancing technology is inexorably shifting the demand for statisticians from being operators of mechanical procedures to being thinkers. Coupled with this is a perceived lack of development of statistical thinking in students. This chapter discusses the thought processes involved in statistical problem solving in the broad sense from problem formulation to conclusions. It draws on the literature and in-depth interviews, with statistics students and practising statisticians, which aimed at uncovering their statistical reasoning processes. From these interviews from all four exploratory studies, a four dimensional statistical thinking framework for empirical enquiry has been identified. It includes an investigative cycle, an interrogative cycle, types of thinking and dispositions. There are a number of associated elements such as techniques for thinking and constraints on thinking. The characterisation of these processes through models, that can be used as a basis for thinking tools or frameworks for the enhancement of problem-solving, is begun in this chapter. Tools of this form would complement the mathematical models used in analysis. The tools would also address areas of the process of statistical investigation that the mathematical models do not, particularly in areas requiring the synthesis of problem-contextual and statistical understanding. The central element of published definitions of statistical thinking is<br>"variation." The role of variation in the statistical conception of real-world problems, including the search for causes, is further discussed.