13 Statistical Techniques for the Interpretation of Analytical Data 705
Table 13.22Results of applying CVA to the data of 10 volatile compounds in order to discriminate
the four groups of varietal wines. Factor structure matrix:
Root 1 Root 2 Root 3
Methanol 0.0265 0.0682 –0.3696
1-Propanol –0.1184 –0.0282 0.6616
Isobutanol 0.0175 –0.0707 –0.0332
Isoamylic alcohols 0.0061 0.0201 –0.2463
1-Hexanol 0.0579 0.0541 –0.0282
cis-3-Hexen-1-ol 0.0994 0.0792 0.1281
Hexanoic acid –0.0129 –0.0597 0.3269
Octanoic acid 0.1023 –0.0101 0.0959
Decanoic acid 0.0535 –0.0530 0.0800
Ethyl octanoate 0.0009 –0.2568 –0.3631applying LDA and CVA to the data of 10 volatile compounds in order to dis-
criminate the four groups of varietal wines (Pozo-Bay ́on et al. 2001), obtained
with the STATISTICA program (Discriminant Analysisprocedure inMultivariate
Exploratory Techniquesmodule). The results of LDA include: the classification
functions (one for each group) for assigningthe samples(Table 13.16), the poste-
rior probabilities for the classification of wines(Table 13.17), and the classification
matrix in Table 13.18(100% correct assignment of the wines was obtained). The
results from CVA include: standardized coefficients for canonical (roots) variables
(Table 13.19), unstandardized canonical scores (Table 13.20), means of canonical
variables in the four groups (Table 13.21), and in the Table 13.22 the factor struc-
ture matrix (correlations between original and canonical variables). In Fig. 13.6, the
wines are plotted on the plane defined by the first two canonical variables. The red
varieties essentially have lower concentrations of 1-propanol and higher concentra-
tions ofcis-3-hexen-1-ol and octanoic acid than the white varieties. Ethyl octanoate
differentiates the two red varieties and also the two white varieties. The wines of the
Malvar and Air ́en varieties are close together in the figure. The results of hypotheses
tests about the mean vectors for each pair of groups are shown in Table 13.23. The
value of F-statistic (19.450 with 30 and 9 df), corresponding to the approximation of
-Wilks (0.00001) revealed the existence of significant differences between the four
mean vectors (P<0.01), in other words, the variables did differentiate the groups.
The value of F-statistic with 10 and 3 df toestablish the differences between mean
vectors in each pair of groups reveals significant differences (P<0.01) for all pairs
except for the Malvar and Air ́en groups (Fcal= 4. 948 <F. 95 , 10 , 3 = 8 .79).
Table 13.23F values (df = 10,3) from results of hypotheses tests about the mean vectors for each
pair of groups
Malvar Air ́en Trepat Monastrell
Malvar 4.948 169.103∗ 43.679∗
Air ́en 4.948 142.207∗ 37.862∗
Trepat 169.103∗ 142.207∗ 51.082∗
Monastrell 43.679∗ 37.862∗ 51.082∗
∗Significant differences between mean vectors in each pairs of groups (P<0.01).