13 Statistical Techniques for the Interpretation of Analytical Data 697
Ma98Ma98Ma99
Ma99Ai97Ai97Ai98Ai98Tr97
Tr97Tr98Tr98Mo97Mo97Mo98Mo98–2.0 –1.5 –1.0 –0.5 0.0 0.5 1.0 1.5 2.0
PC1 (49.3%)–2.5–2.0–1.5–1.0–0.50.00.51.01.52.0PC2 (20.8%)Fig. 13.4Plot of the 16 varietal wines in the plane defined by the first two principal components
octanoic acid (–0.861), and explains 49.3% of the totalvariance, while decanoic
acid (–0.793) and isoamylic alcohols (0.720) contribute more to the second princi-
pal component, which explains 20.8% of the total variance; the scores for the 16
samples of wine in the first two principal components (Table 13.15). In Fig. 13.4,
the 16 wines are plotted on the plane defined by the first two principal components.
From the figure, wines of the red varieties (Trepat and Monastrell) appear on the
left side of the plane, grouped by year of harvest, with lower values for PC1, while
wines of white varieties (Malvar and Air ́en) are found on the right side of the plane,
that is to say, they have greater values for PC1 and are grouped by year of harvest
(the red varieties essentially have lower concentrations of 1-propanol and higher
concentrations ofcis-3-hexen-1-ol, 1-hexanol and octanoic acid than the white vari-
eties). The second principal component mainly differentiates between wines from
the two harvests. It can be observed that the greatest cause of variation among the
samples is due to the factor variety, followed by harvest.
13.3.2.3 Cluster Analysis (CA)
Theobjective of this technique is to look for natural clusters among the n obser-
vations(sometimes between thepvariables) of the data matrixX(n,p). Considering
these observations as points of space for the variables (X 1 ,X 2 ,...,Xp), there are
two techniques to search for groups:hierarchical onesthat reveal similarities among