Nonparametric methods for stratified C-sample designs: a case study

The analysis of C-sample designs in the presence of stratification is a problem frequently faced by practitioners. In the industrial field a variety of stratified analysis scenarios present themselves. Take, for example, a company that wishes to assess the performance of three different formulas for a new dishwasher detergent. Multiple dishwashers are used and multiple washes are carried out. At the end of each wash, an expert provides an evaluation of the cleaning performance of the formula. When analyzing the resulting data, the effect of using one dishwasher instead of another cannot be ignored, so each dishwasher is considered to be a separate stratum. Likewise, in the healthcare field it is quite common for multiple drugs to be tested on patients of different age groups. Each age group is again considered to be a stratum. In this paper we focus on a scenario from the field of education. We are interested in assessing how the performance of students from different degree programs at the University of Padova changes, in terms of university credits and grades, when compared with their entrance exam results. In other words, we want to assess whether people who achieved the best results in this exam perform best during their academic career. We propose a further extension of the NPC technique to address stochastic ordering problems in the presence of stratification. Indeed, the impact of the student’s choice of degree program cannot be ignored, therefore stratification must be considered in the testing procedure.