A Qualitative Study of Engineering Students' Reasoning About Statistical Variability

Every aircraft you have ever flown on has been designed using probabilistically-flawed, potentially dangerous criteria (del Rosario et al. 2021, AIAA-J). That these criteria have been in use for over a half-century---but were only recently identified as dangerous---speaks to the difficulty of teaching such concepts to engineering students. Clearly, improvements to teaching probability and statistics to engineers are needed. Key to statistical thinking is an understanding of and facility with variability (Wild and Pfannkuch, 1999). This work lays foundations for improved statistical literacy among engineers, enabling a multi-disciplinary approach to engineering statistics. We present a novel theoretical framework for both teaching statistical variability and studying engineers' reasoning under variability. While past frameworks for variability focus on a statistician's perspective (e.g. Peters 2011), our framework centralizes the engineering perspective by explicitly considering physical modeling, and makes use of established insights in manufacturing variability (Shewhart 1931). Using this framework, we have developed an interview protocol and deductive coding scheme, and deployed these qualitative tools in interviews with engineering students. Results from these interviews support the validity of the coding scheme, agree with documented trends in current aerospace practice, and suggest possible teaching interventions for innovative engineering pedagogy. Implications for future multi-disciplinary teaching of engineering statistics will be discussed. del Rosario, Fenrich, and Iaccarino, "When are Allowables Conservative?" (2021) AIAA Journal Wild and Pfannkuch, "Statistical Thinking in Empirical Enquiry" (1999) International Statistical Review Peters "Robust Understanding of Statistical Variation" (2011) Statistics Education Research Journal Shewhart, Economic control of quality of manufactured product (1931) Macmillan And Co. Ltd, London