## 6 Statistical Analysis
### Multivariate Analysis
#### 6.2.1 Descriptive, Exploratory or Discriminating Models  
These models are tools that analyze a data matrix and evaluate the repeatability of measures by sample grouping according to the shared degree of similarity. This implies that the values or groups with significant differences are notably separated, allowing the easy and quick identification of atypical values in this manner. From these techniques, self-organizing maps, principal component analysis (PCA), and hierarchical clustering analysis are among the most recognized methods [213; 214]. PCA is a mathematical tool that aims to symbolize the present variations on a data set by using a reduced number of factors [214], i.e., PCA contracts the number of original variables to fewer ones denominated as principal components, which are linear combinations of initial factors [213; 215]. The results of PCA can be inspected visually by means of scatterplots in 2D or 3D that make it easy to verify the individual data groupings or discriminations, although the results can also be evaluated by using factor loading tables that describe the results in numerical terms [214]. PCA is one of the most popular descriptive models because it is often employed in plant VOC profiling, for example, in volatiles emitted by flowers and nectar [69], the leaf interface [63], fresh fruit [109], coffee [108],essential oils [99], and more. This method has also helped in the investigation of changes in VOC emission patterns in plants directly affected by herbivory, as in the case of _Dittrichia viscosa_ attacked by _Myopites stylatus_[73], in profiles comparing healthy and mechanically damaged California nuts (_Juglans reggia_ L.) [70], in broccoli infested with the _Delia radicum_ fly larvae [79], and in the analysis of herbivore response changes to a plant under particular conditions, such as in the presence of endophytes [43] or during induced chemical defense [24]. Non-metric multi-dimensional scaling (NMDS) is an ordination technique suitable for analyzing a wide variety of data. NMDS involves few underlying assumptions and any distance measurement can be used. Unlike most ordination methods, a small number of axis in NMDS are selected by the user before analyzing the data; while in most other methods a big number of axes are calculated, few are visualized and the others remain as hidden axes of variation. Additionally, although most ordination methods obtain a unique solution, the NMDS is a numerical procedure searching for an iteratively-convergent solution, so the algorithm stops if an acceptable solution is reached. Owing to the multiple solutions that are produced, somewhat different ordinations can be obtained [216]. Despite the fact that this technique is slower than others, and in some cases fails to find the best solution due to being stuck in local minima, the increase of computing power has widely overcome these problems. This technique has been used to visualize and analyze plant-insect interactions such as the change in the emission of VOCs by _Phaseolus lunatus_ in response to herbivory [217], the effects of volatile emissions of asparagus on its associated early season pest species (e.g., asparagus miner) [218], the differential attraction of pollinators by monkey flowers [219] and asclepiads [220], and the differential attraction of _Spodoptera litteralis_ to five host plant species [221]. On the other hand, the HCA is a method that explores the sample distribution in groups by representing a hierarchy, which is shown in a dendrogram that consists of a tree-shaped scheme that displays the samples and exhibits their respective relationships and organization [214]. In contrast to the PCA, the individual data are not explicitly shown in the dendrogram because the hierarchy is calculated from the sample dataset. HCA has been used for assessing VOCs from cultured plants, such as loquat (_Eriobotrya japonica_ [PERSON].)