Analysis of Categorical Response in Small Sample Experiments

Statistical design of experiments (DOE) is widely used today for process and product characterization and optimization. Owing to cost and time considerations, sometimes only a minimum number of experimental runs can be conducted, with added challenges in analysis when the experimental outcomes cannot be measured on a continuous scale and are expressed only in qualitative terms such as ‘excellent’, ‘satisfactory’ and ‘poor’: such outcomes are variously described as ‘categorical’, ‘attribute’, ‘qualitative’, ‘discrete’ or ‘counted’ in nature. This paper offers practical techniques of handling small experiments with such non‐standard DOE response data which are otherwise impossible to analyze by standard statistical software. The suggested procedures, built upon what is called a Likelihood Transfer Function (LTF), do not require complex data analysis but would yield results consistent with the constraints of experimental conditions as well as the objectives of stakeholders.