Analysis of variance of designed chromatographic data sets: The analysis of variance-target projection approach

Direct application of popular approaches, e.g., Principal Component Analysis (PCA) or Partial Least Squares (PLS) to chromatographic data originating from a well-designed experimental study including more than one factor is not recommended. In the case of a well-designed experiment involving two or more factors (crossed or nested), data are usually decomposed into the contributions associated with the studied factors (and with their interactions), and the individual effect matrices are then analyzed using, e.g., PCA, as in the case of ASCA (analysis of variance combined with simultaneous component analysis). As an alternative to the ASCA method, we propose the application of PLS followed by target projection (TP), which allows a one-factor representation of the model for each column in the design dummy matrix. PLS application follows after proper deflation of the experimental matrix, i.e., to what are called the residuals under the reduced ANOVA model. The proposed approach (ANOVA-TP) is well suited for the study of designed chromatographic data of complex samples. It allows testing of statistical significance of the studied effects, 'biomarker' identification, and enables straightforward visualization and accurate estimation of between- and within-class variance. The proposed approach has been successfully applied to a case study aimed at evaluating the effect of pasteurization on the concentrations of various phenolic constituents of rooibos tea of different quality grades and its outcomes have been compared to those of ASCA.