# Varietal Authentication of Extra Virgin Olive Oils by Triacylglycerlycerols and Volatiles Analysis
## Results and Discussion
### Discriminant Analysis  
Previous papers have shown that TAG stereospecific analysis coupled with multivariate statistical data analysis was successfully used to characterize vegetable [22; 23; 37] and animal [38; 39; 40] foods. Generally, LDA is the best known and more widely used method to highlight differences between groups and to classify them. Moreover, it is known that LDA is an important parametric method useful to discriminate samples when the sample allocation is just known [41]. In this study, in order to classify and discriminate EVOO samples of different cultivars (Dolce Agogia, Frantoio, Lecino, and Moraiolo), multivariate parametric LDA technique was used. To better evaluate the influence of FA (total and intrapositional) compositions and volatile fraction in the classification of the oils, the results of the analytical determinations were elaborated by LDA. The statistical elaborations were performed considering the total and intrapositional FA percent compositions in TAG positions (_sn_-1, _sn_-2, and _sn_-3) of monovarietal EVOO samples, reported in Tables 1 and 2, respectively. Afterwards, the statistical elaborations were performed considering the volatile percent compositions of monovarietal EVOO samples, reported in Table 3.  
The statistical elaboration of the results of the stereospecific analysis of the TAG provided interesting results for the characterization of oil samples obtained from different varieties of _O. europea_; the theory that the intrapositional TAG compositions represent a fingerprint of the most represented fraction of the oils is confirmed. In fact, these compositions depend on the specificity of the acyltransferase involved in the process of biosynthesis of the TAG, and are therefore species-specific [42]. The selection of the most significant variables was performed by stepwise analysis. Table 4 shows the canonical Fisher's linear discriminant characteristics (eigenvalue, percentage of variance, and significance test) of the testing data (FA compositions and volatiles) from monovarietal EVOO samples. It can be emphasized that LDA performed on volatile data showed higher percentage of the variance explained (97.8 vs 54.8) and canonical correlation (1.000 vs 0.965) for the first discriminant function in respect to FA compositional data. The statistical significance of each discriminant function was also evaluated on the basis of the Wilks' lambda factor; it showed that the first two functions for volatile data were significant (_p_ < 0.05). In fact, [PERSON] lambda values of the first two discriminant functions (0.000) showed an optimal discriminant power of the model, with a better discriminant power of volatiles in respect to FA data. The significance values (0.000 for the first two functions) indicated that there was a highly significant difference between the group centroids for volatile data. \begin{table}
\begin{tabular}{c c c c c c c} \hline \hline \multirow{2}{*}{**Function**} & \multicolumn{3}{c}{**FA**} & \multicolumn{3}{c}{**Volatiles**} \\ \cline{2-7}  & **1** & **2** & **3** & **1** & **2** & **3** \\ \hline Eigenvalue & 13.773 & 9.214 & 2.120 & 22302.442 & 435.448 & 59.557 \\ \% of variance & 54.8 & 36.7 & 8.4 & 97.8 & 1.9 & 0.3 \\ Cumulative (\%) & 54.8 & 91.5 & 100 & 97.8 & 99.7 & 100.0 \\ Canonical correlation & 0.965 & 0.950 & 0.824 & 1.000 & 0.999 & 0.992 \\ Test of function & 1–3 & 2-3 & 3 & 1–3 & 2-3 & 3 \\ Wilk’s lambda & 0.002 & 0.031 & 0.0320 & 0.000 & 0.000 & 0.017 \\ Chi–square & 46.159 & 25.963 & 8.535 & 80.779 & 40.729 & 16.414 \\ df & 33 & 20 & 9 & 18 & 10 & 4 \\ Signif. & 0.064 & 0.167 & 0.481 & 0.000 & 0.000 & 0.003 \\ \hline \hline \end{tabular}
\end{table} 
Table 4: [PERSON]’s linear discriminant functions and functions at group centroids obtained from LDA analysis using FA or volatiles percent compositions of monovarietal EVOO samples. Table 5 shows the standardized canonical discriminant function coefficients.