Cluster Analysis

Cluster analysis (CA) is another data-reduction method. It, too, can be used to examine the responses of panelists to learn whether panel members are responding alike. CA can take several different forms. Whereas PCA depends on examination of variance, CA is basically a measure of proximity. It can be calculated on the basis of distance, correlation, or the effect they have on variance by lumping together or separating other individual elements or tentative clusters. There are several forms of depicting proximity. There are single linkage, centroid linkage, average linkage, density linkage, and minimum variance. One of the most useful is the agglomerative hierarchical clustering technique, of which Ward's minimum variance method is one. Ward's method uses the square of the Euclidean distance as the proximity measure. Some publications refer to the representation as a tree; others call it an icicle. Whether distance, correlation, or variance, the basic purpose of CA is the same. Things having characteristics in common form a cluster; things dissimilar to the first have to go into a second cluster, etc. Having characteristics in common does not necessarily mean that the objects in a cluster are related. Sensory leaders hope that their panelists will form a single cluster; but just being grouped together does not mean the panelists are related. They merely happen to be together because they respond alike; only rarely are panel members kin. Table 1 shows cluster analysis applied to the 20 panelists who examined the five kinds of Finnish sour rye bread for 12 attributes (13). Ta bles 2 and 3 show the kinds of output obtained by different clustering processes. There are some differences because hierarchial clustering was used for the icicle formation (Table 2) and the VARCLUS routine of the SAS package (14) was used for Table 3. Either one of the clustering processes serves the purpose of the sensory analyst, who is generally interested in only the major groups formed. Here there are a few differences in the assignment of panelists, but they reveal essentially the same information. Both processes said that panelists 7 and 12 responded least like any of the others. From other information (15) every one of the 20 panelists was an accomplished sensory judge who could reproduce his or her assignment of scores. The only flaw was that the panel did not operate as one unit. The panelists of each of the clusters arrived at the same decision, three of the kinds of bread were sensorially different, but they didn't reach the same conclusion by the same pathway.

Sometimes CA is used to learn if resolution of product differences can be stepped up. By applying CA to a group

Table 1. Ward's Minimum Variance Cluster Analysis Applied to the Scale Values of 20 Panelists Evaluating 12 Attributes of Finnish Wholemeal Sour Rye Bread

Panelists i—Partial R2

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