Identification of significant factors by an extension of ANOVA–PCA based on multi-block analysis

A modification of the ANOVA–PCA method, proposed by Harrington et al. to identify significant factors and interactions in an experimental design, is presented in this article. The modified method uses the idea of multiple table analysis, and looks for the common dimensions underlying the different data tables, or data blocks, generated by the “ANOVA-step” of the ANOVA–PCA method, in order to identify the significant factors. In this paper, the “Common Component and Specific Weights Analysis” method is used to analyse the calculated multi-block data set. This new method, called AComDim, was compared to the standard ANOVA–PCA method, by analysing four real data sets. Parameters computed during the AComDim procedure enable the computation of F-values to check whether the variability of each original data block is significantly greater than that of the noise.