Statistical Thinking in Empirical Enquiry

TLDR: In this paper, a four-dimensional framework has been identified for statistical thinking in empirical enquiry, including an investigative cycle, an interrogative cycle, types of thinking and dispositions.

Abstract: Summary This paper 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 aimed at uncovering their statistical reasoning processes. From these interviews, a four-dimensional framework has been identified for statistical thinking in empirical enquiry. It includes an investigative cycle, an interrogative cycle, types of thinking and dispositions. We have begun to characterise these processes through models that can be used as a basis for thinking tools or frameworks for the enhancement of problem-solving. Tools of this form would complement the mathematical models used in analysis and address areas of the process of statistical investigation that the mathematical models do not, particularly areas requiring the synthesis of problem-contextual and statistical understanding. The central element of published definitions of statistical thinking is "variation". We further discuss the role of variation in the statistical conception of real-world problems, including the search for causes.