## 2 Materials and Methods
### Statistical Analysis  
Color data were analyzed using SAS Software [16] according to the following linear model:  
\[y_{\rm jil}=\upmu+\rm RT_{i}+\epsilon_{\rm jil} \tag{1}\]  
where y is the investigated variable; \(\upmu\) the overall mean; RT the fixed effect of processing stage; \(\epsilon\) the random residual error. [PERSON]'s test with a \(p\)-value threshold lower than 0.05 was used to compare means. Fat, moisture, fatty acids, and VOCs data were analyzed using SAS Software [16] according to the following linear model:  
\[y_{\rm jil}=\upmu+\rm RT_{i}+H_{j}+\epsilon_{\rm jil} \tag{2}\]where y is the investigated variable; u the overall mean; RT the fixed effect of processing stage (2 levels for fat, moisture, and fatty acids; 8 levels for VOCs); H the random effect of ham (with repeated measures in time); \(\varepsilon\) the random residual error. [PERSON]'s test with a \(p\)-value threshold lower than 0.05 was used to compare means. VOCs trend during ripening and seasoning was also analyzed by SAS software (SAS Institute, Inc., Charlotte, NC, USA) applying 3 multivariate statistical techniques: stepwise discriminant analysis (SDA), CDA, and DA. The aim of multivariate analysis was to assess if there were groups of VOCs able to characterize the different ripening and seasoning times studied. Furthermore, multivariate approach was also used to outline the contribution of the identified VOCs in properly classifying hams according to their seasoning time only. Groups separation was tested by [PERSON]'s T-square test [17]. However, this test can be developed only if the pooled (co)variance matrix of data is not singular. In our research, the number of hams (rows in the matrix of data) is lower than the number of volatile compounds (columns). In this condition, any multivariate technique becomes meaningless because the (co)variance matrix does not have a full rank [18]. Therefore, a reduction of the space-variables was required. For this reason, before CDA and DA, the SDA was applied to the data to select a restricted subset of linearly independent variables, the VOCs, able to discriminate groups [19]. The obtained compounds were used in the CDA and the DA. The CDA derives a set of new variables, called canonical functions (CAN), that are linear combination of the original compounds. For k-groups involved in the CDA, k-1 CANs are extracted. The structure of a CAN is:  
\[\text{CAN}=c_{1}X_{1}+c_{2}X_{2}+\ldots\ldots\ldots+c_{n}X_{n} \tag{3}\]  
where \(c_{n}\) are the canonical coefficients (CCs) and \(Xi\) are the scores of original variables. CCs indicate the partial contribution of each variable in composing the CAN. The greater the CC, the more the variable contributes to compose the CAN. The distance between groups was evaluated by using the Mahalanobis' distance, whereas the effective groups' separation was tested with the corresponding [PERSON]'s T-square test ([PERSON] et al., 2000). Finally, the DA was performed to classify ham samples into seasoning groups. The above-mentioned statistical approaches were successively applied to volatile compounds data according to the following two scenarios. In the first scenario, VOCs data were arranged in two major seasoning classes: the low maturing class (LMC) with samples belonging to 0, 1, 3, and 6 months; the high maturing class (HMC) with samples belonging to 12, 14, 16, and 18 months of seasoning. In the second scenario, only samples belonging to HMC were considered. The discriminant procedures were applied to detect the most discriminant compounds able to correctly separate groups involved in the two scenarios. To validate the results, considering the reduced number of involved hams, the leave-one-out cross-validation technique was adopted. In practice, in each scenario, SDA, CDA, and DA were applied 10 times (being 10 the hams involved in the study) by using, at each run, one ham as validation sample. At the end, ten datasets of variables were obtained. Since compounds selected at each round could be different, the ten groups of variables were joined.