Principal component analysis in sensory analysis: covariance or correlation matrix?

Abstract

When principal component analysis (PCA) is applied to descriptive analysis, the input data is a sample (rows) by descriptor (columns) matrix, usually formed from the mean values over assessors. This data matrix is the input to the PCA procedure of statistical softwares, which presents the option of performing PCA on either the covariance matrix (cov-PCA) or the correlation matrix (corr-PCA), both derived from the data matrix. A non-comprehensive survey of papers where PCA was used to analyze sensory descriptive data, showed that out of a total of 52 papers, 22 used corr-PCA, seven used cov-PCA and 23 did not say which PCA method they used. PCA of three real sensory data sets, showed how the results may change by either using cov-PCA or corr-PCA. Cov-PCA should be used in most cases as the sensory scales are the same for all attributes. Corr-PCA should only be used when there is a very good reason for doing so, rather than the reverse.