Analyzing assessors and products in sorting tasks: DISTATIS, theory and applications

In this paper we present a new method called distatis that can be applied to the analysis of sorting data. Distatis is a generalization of classical multidimensional scaling which allows one to analyze 3-ways distance tables. When used for analyzing sorting tasks, distatis takes into account individual sorting data. Specifically, when distatis is used to analyze the results of an experiment in which several assessors sort a set of products, we obtain two types of maps: One for the assessors and one for the products. In these maps, the proximity between two points reflects their similarity, and therefore these maps can be read using the same rules as standard metric multidimensional scaling methods or principal component analysis. Technically, distatis starts by transforming the individual sorting data into cross-product matrices as in classical mds and evaluating the similarity between these matrices (using Escoufier’s RV coefficient). Then it computes a compromise matrix which is the best aggregate (in the least square sense, as statis does) of the individual cross-product matrices and analyzes it with pca. The individual matrices are then projected onto the compromise space. In this paper, we present a short tutorial, and we illustrate how to use distatis with a sorting task in which ten assessors evaluated eight beers. We also provide some insights into how distatis evaluates the similarity between assessors.