Comparison of two or more sensory data sets

When many data sets for the same set of products (objects) are available it is of interest to look for the common information and to analyze the individual deviations. When the panellists in a sensory panel test a set of food products one might be interested in the answer to many questions. How are the products positioned, on the average, in sensory space Are there regions which are not well 

A powerful technique which allows to answer such questions is Generalized Procrustes Analysis (GPA). This is a generalization of the Procrustes rotation method to the case of more than two data sets. As explained in Chapter 36 Procrustes analysis applies three basic operations to each data set with the objective to optimize their similarity, i.e. to reduce their distance. Each data set can be seen as defining a configuration of its rows (objects, food samples, products) in a space defined by the columns (sensory attributes) of that data set. In geometrical terms the (squared) distance between two data sets equals the sum over the squared distances between the two positions (one for data set and one for Xg) for each object. 

It is not strictly required to use the same attributes in each data set. This allows the comparison of independent QDA results obtained by different laboratories or development departments in collaborative studies. Also within a single panel, individual panellists may work with personal lists of attributes. When the sensory attributes are chosen freely by the individual panellist one speaks of Free Choice Profiling. When each panellist uses such a personal list of attributes, it is likely that 

So far, the nature of the variables was the same for all data sets, viz. sensory attributes. This is not strictly required. One may also analyze sets of data referring to different types of data (processing conditions, composition, instrumental measurements, sensory variables). However, regression-type methods are better suited for linking such diverse data sets, as explained in the next section. 

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