Statistical treatment of free sorting data

As mentioned above, a free sorting test yields a family of partitions of the same set of products, each partition being associated with a particular subject. For the statistical treatment of free sorting data, several strategies of analysis have been proposed. We refer to the book by Coxon (1999) for a comprehensive review of these strategies. We also refer to a French paper by Faye et al. (2011) for a comparison of several methods of analysis on the basis of a case study. 

Broadly speaking, the statistical strategies of analysis can be classified into two families of methods, namely (i) factor analytical methods including, in particular, multidimensional scaling (MDS) and multiple correspondence analysis (MCA) and (ii) methods pertaining to cluster analysis and additive trees. As is usually the case, the choice of one method over another depends on several factors (i) the domain of application (i.e. traditionally, some methods are more popular than others in each particular domain of application) (ii) the individual preferences and background of each practitioner and (iii) the availability of appropriate (and user-friendly) software. 

As an illustration, let us mention that the use of additive trees for analyzing free sorting data is relatively popular in psychology (Dubois, 1991), whereas in psychoacoustics, MDS methods are more often used (Gygi et al., 2007 MacAdams et al., 1995). In the field of sensory analysis that particularly interests us here, the mainstream is to use MDS methods (Faye et al., 2004 King et al., 1998 Lawless et al., 1995 Parr et al, 2007). However, alternative methods of analysis, such as multiple correspondences and allied methods, have also been proposed in this framework (Cadoret et al, 2009 Qannari et al., 2009 Takane, 1981,1982). 

Raw data of a fictitious subject who sorted n = 5 products in K = 2 clusters 

With no claims to exhaustiveness, we present in the Table 7.1 some of the most important strategies of analysis that have been proposed to analyze free sorting data. 

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As pointed out in the section devoted to the statistical treatment of free sorting data, the determination of a consensus partition is based on the maximization of a criterion that reflects the extent to which the subjects agree with this consensus partition. Figure 7.8 shows the evolution of the optimization criterion according to the number of groups of the consensus partition. The maximum value is obtained with seven groups of car body styles. 

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