This manuscript considers that the composition of Manzanilla and Hojiblanca fats are compositional data (CoDa). Thus, the work applies CoDa analysis (CoDA) to investigate the effect of processing and packaging on the fatty acid profiles of these cultivars. To this aim, the values of the fat components in percentages were successively subjected to exploratory CoDA tools and, later, transformed into ilr (isometric log-ratio) coordinates in the Euclidean space, where they were subjected to the standard multivariate techniques. The results from the first approach (bar plots of geometric means, tetrahedral plots, compositional biplots, and balance dendrograms) showed that the effect of processing was limited while most of the variability among the fatty acid (FA) profiles was due to cultivars. The application of the standard multivariate methods (i.e., Canonical variates, Linear Discriminant Analysis (LDA), ANOVA/MANOVA with bootstrapping and n = 1000, and nested General Linear Model (GLM)) to the ilr coordinates transformed data, following Ward's clustering or descending order of variances criteria, showed similar effects to the exploratory analysis but also showed that Hojiblanca was more sensitive to fat modifications than Manzanilla. On the contrary, associating GLM changes in ilr with fatty acids was not straightforward because of the complex deduction of some coordinates. Therefore, according to the CoDA, table olive fatty acid profiles are scarcely affected by Spanish-style processing compared with the differences between cultivars. This work has demonstrated that CoDA could be successfully applied to study the fatty acid profiles of olive fat and olive oils and may represent a model for the statistical analysis of other fats, with the advantage of applying appropriate statistical techniques and preventing misinterpretations.
Keywords: Hojiblanca cv; Manzanilla cv; Spanish-style green table olives; compositional data analysis; fatty acids; processing.