The use of univariate, bivariate, and multivariate statistical techniques, such as analysis of variance, multiple comparisons of means, and linear correlations, has spread widely in the area of Food Science and Technology. However, the use of supervised and unsupervised statistical techniques (chemometrics) in order to analyze and model experimental data from physicochemical, sensory, metabolomics, quality control, nutritional, microbiological, and chemical assays in food research has gained more space. Therefore, we present here a manuscript with theoretical details, a critical analysis of published work, and a guideline for the reader to check and propose mathematical models of experimental results using the most promising supervised and unsupervised multivariate statistical techniques, namely: principal component analysis, hierarchical cluster analysis, linear discriminant analysis, partial least square regression, k-nearest neighbors, and soft independent modeling of class analogy. In addition, the overall features, advantages, and limitations of such statistical methods are presented and discussed. Published examples are focused on sensory, chemical, and antioxidant activity of a wide range of fruit juices consumed worldwide.

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The main goal of this work was to propose an authentication model based on the phenolic composition and antioxidant and metal chelating capacities of purple grape juices produced in Brazil and Europe in order to assess their typicality. For this purpose, organic, conventional, and biodynamic grape juices produced in Brazil (n = 65) and in Europe (n = 31) were analyzed and different multivariate class-modeling and classification statistical techniques were employed to differentiate juices based on the geographical origin and crop system. Overall, Brazilian juices, regardless of the crop system adopted, presented higher contents of total phenolic compounds and flavonoids, total monomeric anthocyanins, proanthocyanidins, flavonols, flavanols, cyanidin-3-glucoside, delphinidin-3-glucoside, and malvidin-3,5-glucoside. No differences were observed for trans-resveratrol, malvidin-3-glucoside, and pelargonidin-3-glucoside between countries and among crop systems. A total of 91% of Brazilian and 97% of European juices were adroitly classified using partial least squares discriminant analysis when the producing region was considered (92% efficiency), in which the free-radical scavenging activity toward 2,2-diphenyl-1-picrylhydrazyl, content of total phenolic compounds, gallic acid, and malvidin-3-glucoside were the variables responsible for the classification. Intraregional models based on soft independent modeling of class analogy were able to differentiate organic from conventional Brazilian juices as well as conventional and organic/biodynamic European juices.

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