Statistical Thinking: One Statistician's Perspective

This paper discusses some characteristic ways of reasoning within the discipline of statistics from the perspective of someone who is both a practising statistician and teaching statistician. It is cOnjectured that recognition of variation and critically evaluating and distinguishing the types of variation are essential components in the statistical reasoning process. Statistical thinking appears to be the interaction between the real situation and the statistical model. The role of variation in statistical thinking and the implications for teaching are also discussed. Background The development of students' statistical thinking is considered by statIsticians (Bailar, 1988; Barabba, 1991; Snee, 1993; Wild, 1994)) to be crucial for the enhancement of student learning in statistics courses. This challenge to the current statistics teaching practice of teaching procedures raises questions as to what are the characteristics of statistical thinking and what approaches should be used in teaching for the development of statistical thinking? After interviewing some undergraduate students in two separate case studies (pfannkuch & Brown, 1996; Pfannkuch, 1996) on their solutions and reactions to statistically based information and problems some hypotheses were formed on the development of their statistical thinking. In order to broaden and understand the fmdings from these studies it was decided to investigate the nature of statistical thinking from a practitioner's or 'expert's' perspective. These statisticians would be in the position of commentating either from reflection on their own statistical thinking and/or on their clients' or students' statistical thinking. Through this interaction with 'experts' it was hoped that further insights would be gained into the characteristics of statistical thinking and that this would be informative for conjecturing the type of statistical thinking that should be developed in students. It would also confIrm or refute previous fmdings which had been solely derived from student data. Method Several statisticians were individually interviewed in depth for approximately ninety minutes. Broad questions were asked; the interview following a semi-structured protocol based on the statistical enquiry empirical cycle. The interviews were audio-taped and transcribed. Each statistician had his own perspective on statistics, dependent upon the type of statistical work he was involved in and his own beliefs and experiences. Each one focussed on different aspects in a statistical investigation to explain his perceptions. For the purposes of this paper one statistician's view is presented and analysed. Ray (not his real name) is a private consultant, working mainly in quality management and is also a supervisor and lecturer for Stage 3 (final year) undergraduate project students. In the Stage 3 course he has specifically developed a module on statistical thinking. Therefore Ray was considered to be in a position to comment on statistical thinking from a practitioner's and teacher's perspective. An analysis and discussion of his responses, including implications for teaching, is presented in this paper. The analysis and interpretation of Ray's comments were presented to him for corroboration.