Sensory analysis, that is the description of food or beverages by a panel of judges, has become increasingly important in the development of commercial foodstuffs. In general terms, sensory analysis involves scoring, for intensity, the adjectives of a vocabulary which adequately describes every nuance of sensory property found in the sample. The data from a sensory analysis of a set of samples are matrices of scores, one for each judge, with rows corresponding to adjectives, and columns to samples. This can be interpreted as a set of configurations, one for each judge, where points correspond to samples, and dimensions to adjectives. The question of how to combine the scores by each judge to summarise the information on the samples, is of particular interest. This thesis concentrates on combining judge scores by generalized Procrustes analysis, the method of simultaneously matching a set of configurations by translation, rotation/reflection and scaling. This analysis has intrinsic appeal as it allows each judge to have his own interpretation of the adjectives. The only constraint is that the judges must place samples in the same relative positions within their own private scoring schemes. The asymptotic distribution of the residual sum of squares after a generalized Procrustes analysis is discussed, and the sum of squares before transformation is shown to partition into sums of squares for translation, rotation/reflection scaling and a residual. Therefore, the effects of the Procrustes transformations can be presented in an ANOVA format. The use of complementary pair-wise Procrustes rotation is shown to be made redundant by a modification to the generalized Procrustes analysis, which gives a Euclidean representation of the judges. A worked example illustrates the advantage, over the panel mean, of a generalized Procrustes analysis, and a summary of the sample information by the consensus configuration.
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