Investigating control-centred results after uncentred principal component analysis

In sensory evaluation, principal component analysis (PCA) is often used to explore differences between products. In some studies, there is one control product (e.g. a reference or benchmark) and many test products, where test-control paired differences are of primary interest. We discovered two equivalent ways to investigate these results using PCA. The first is a centred PCA of column-centred test-control paired comparisons, which includes both test-control paired differences and control-test paired differences. The second is an uncentred PCA of a control-centred matrix. We show why these two approaches are equivalent. We also show the truncated total bootstrap method, which is used to investigate uncertainty, yields equivalent results in both solutions. The uncentred PCA of a control-centred matrix is more computationally efficient and facilitates interpretations by situating the control product at the origin of score plots. The proposed methods are illustrated using a data set from a trained sensory panel for a control product and nine test product formulations.