## 2 Processing of HS-SPME-GC-MS Data on Wine Volatiles by Multivariate Statistics
### Anova-Manova  
A great volume of data is usually obtained for wine volatile compounds by HS-SPME-GC-MS analysis, therefore, in order to understand if there are significant differences between the means of data referred to different groups of samples, analysis of variance (ANOVA) is generally the mostly adopted statistical method. ANOVA allows to check if the so called null-hypothesis, i.e., the one stating that samples in all groups are taken from populations with the same mean value, can be accepted or not. If the null hypothesis is rejected, post-hoc methods performing a multiple comparison between the mean values of the groups can be applied to verify which of them differ significantly. Commonly adopted approaches to make multiple comparisons between means under the assumption of Gaussian distribution of data are the Tukey's and the Tukey-Kramer's methods, which are appropriate when the within-group variances are comparable with each other and are used for groups including equal or different numbers of data, respectively.  
One Way ANOVA described so far is suitable if the effect of a single factor (independent variable) is to be determined; when the effect of more than one factor has to be evaluated, the multi-way ANOVA, also called N-way ANOVA can be used. This technique provides not only information about the effect of a single factor on the dependent variable (peak area or compound concentration), but also about the effects of the interactions among factors. Different contributes are reported in the literature on the application of multi-way ANOVA analysis to determine if there were statistically significant differences between wine varieties ([PERSON] et al., 2018) and wines aged in wood barrels ([PERSON] et al., 2018). [PERSON] et al. (2018) used a two-way ANOVA analysis to characterize the volatile profile of new white wine varieties made from _Monastrell_ grapes grown in southeastern Spain. The analysis considered different groups of aromatic compounds in wines as a function of variety and vintage, revealing a great variability for different samples in terms of the concentrations obtained in the different families of volatile compounds.  
The comparison of multivariate sample means can be obtained by Multivariate ANOVA (MANOVA), in which covariance between dependent variables is used to test the statistical significance of the differences. [PERSON] et al. (2018) used MANOVA to study the effects of oak origin, barrel volume, and barrel age on all the constituents measured in wines. [PERSON] et al. (2018) determined the effects of variety, clarification, temperature, and yeast type on all constituents of the acid fraction, higher alcohols, and conventional parameters of wines obtained from grape must of _Muscatel_ and _Malvasia_ varieties. MANOVA analysis was employed to compare the variations of volatile compounds in the white wine _Muscat Ottoned_ variety aged in the presence of untoasted oak chips, toasted oak chips, and  
Figure 2: Schematic diagram of different objectives and multivariate statistical analysis techniques used for HS-SPME/GC-MS data.  
untoasted barrel, considering three ageing periods [45]. ANOVA has also been recruited in descriptive sensory analysis, to check overall differences among the products for aroma, taste, and mouthfeel terms [46].