Statistics as a catalyst to learning by scientific method part II - A discussion

Industrial success requires efficient experimentation both for the improvem ent of existing products and processes and for development of new ones. Bec ause results are usually known quickly, the natural way to experiment is to use information from each group of runs to plan the next. Such investigati on employs a scientific paradigm in which data drives an alternation of ind uction and deduction. This process can suggest at each stage how questions that are still at issue can be resolved. Response surface methods are a gro up of statistical techniques specifically designed to catalyze scientific l earning of this kind. In this paper, the scientific paradigm for discovery and sequential learning is contrasted with the mathematical paradigm for th e proof of theorems. It is argued that, because statistical training unduly emphasizes mathematics at the expense of science, confusion between the tw o paradigms occurs. This has resulted in emphasis on the development and us e of "one-shot" statistical procedures which mimic the mathematical paradig m-examples are hypothesis testing and the use of alphabetically optimal des igns. Such one-shot procedures, where the model is assumed known a priori a nd fixed, are appropriate for some practical problems and are attractive be cause they allow rigorous development of theories of statistics based on ma thematics alone. By contrast, discovery of new knowledge requires the use o f the scientific paradigm in which the model is continually changing. Scien tific method is thus mathematically incoherent. The importance of robustnes s is discussed both for analysis and design, and the relationship between t hese two kinds of robustness is clarified. Implications for teaching are di scussed.