A graphical tool to compare groups of subjects on categorical variables

This paper proposes a graphical statistical tool easy to interpret that can be used to compare the behaviour of different groups of subjects (individuals or organizations) with respect to categorical variables. The construction of the proposed graph is based on the combination of (i) an unusual application of the Nonlinear Principal Components Analysis, oriented to quantify categorical variables and focused on the so-called Projected Centroid Plot, (ii) the Inferential Confidence Intervals, and (iii) a nonparametric bootstrap study. An application investigates the quality of work in social cooperatives by exploring the relations between quality of work and characteristics of workers (gender, age, education, membership) and cooperatives (area, type – A or B, dimension – in terms of number of workers). Results easily show how the groups of workers behave on the categorical variables of quality of work.