**1.2 Chemometric methods and quality control**

The chemometric methods consist of a number of statistical, mathematical and graphic techniques that analyze many variables simultaneously (Lonni, 2005). The method used in this study is as follows:

Principal components analysis (PCA).

This method is based on the transformation of a group of original quatitative variables into another group of unrelated independent variables, known as principal components. The components have to be interpreted independently of one another, as they contain part of the variance that is not expressed in any other principal component (Pla, 1986; López & Hidalgo, 1994).

The criterion of Cliff in 1987 was adopted for selecting the number of components that should be used for the analysis, which states that the eigenvalues of acceptable components should explain 70% of the total variance (López & Hidalgo, 1994).

Proportion of variance explained: in general statistical programs provide information of the eigenvectors and, in some cases, the correlation between the original variables and the principal components. However, these correlations can be calculated from the eigenvectors in the following formula (Pla, 1986):

$$r(jk) = l(jk) \propto (\lambda(\mathbf{x})) \ 1/2/s(ij) \tag{1}$$

where,

*r*(*jk*)= correlation between the original variable *x(j)* and the *k*-esim component.

*l*(*jk*) = *j*-esim element of the *k*-esim eigenvector.

λ(κ)= *k*-esim eigenvalue.

*s*(*ij*) = variances of the correlation matrix.

In most studies it is important to determine the degree of discrimination of the variables so that those with the most and least variation can be identified.

Using PCA it is possible to determine the degree of discrimination, quantifying the proportion of variance explained by each original variable of the selected components; to do this it is necessary to add the squares of the correlation formed by each original variable with the selected components. This is possible as the components are not correlated (Pla, 1986). In the case of a variable in series: *rx1*2 + *rx2*2 + *rx3*2 = proportion of the variance explained, having selected three components. It should to be taken into account that the variables that explain a larger proportion of variance are the most discrimatory and therefore they are more important.

The UV/Visible spectra of populations of two species, *Baccharis articulata* (Lam.) Pers. and *B. trimera* can be seen in Figure 2. In this figure it is difficult to distinguish which spectrum corresponds to which species, but the resolution is greater when PCA is applied (Figure 3) and different coordinates can be seen for the corresponding populations of one species or another.

The chemometric methods consist of a number of statistical, mathematical and graphic techniques that analyze many variables simultaneously (Lonni, 2005). The method used in

This method is based on the transformation of a group of original quatitative variables into another group of unrelated independent variables, known as principal components. The components have to be interpreted independently of one another, as they contain part of the variance that is not expressed in any other principal component (Pla, 1986; López &

The criterion of Cliff in 1987 was adopted for selecting the number of components that should be used for the analysis, which states that the eigenvalues of acceptable components

Proportion of variance explained: in general statistical programs provide information of the eigenvectors and, in some cases, the correlation between the original variables and the principal components. However, these correlations can be calculated from the eigenvectors

 *r*(*jk*) = *l*(*jk*) x (λ(κ)) *1/2/s*(*ij*) (1)

In most studies it is important to determine the degree of discrimination of the variables so

Using PCA it is possible to determine the degree of discrimination, quantifying the proportion of variance explained by each original variable of the selected components; to do this it is necessary to add the squares of the correlation formed by each original variable with the selected components. This is possible as the components are not correlated (Pla, 1986). In the case of a variable in series: *rx1*2 + *rx2*2 + *rx3*2 = proportion of the variance explained, having selected three components. It should to be taken into account that the variables that explain a larger proportion of variance are the most discrimatory and

The UV/Visible spectra of populations of two species, *Baccharis articulata* (Lam.) Pers. and *B. trimera* can be seen in Figure 2. In this figure it is difficult to distinguish which spectrum corresponds to which species, but the resolution is greater when PCA is applied (Figure 3) and different coordinates can be seen for the corresponding populations of one species or

*r*(*jk*)= correlation between the original variable *x(j)* and the *k*-esim component.

should explain 70% of the total variance (López & Hidalgo, 1994).

**1.2 Chemometric methods and quality control** 

this study is as follows:

Hidalgo, 1994).

where,

another.

Principal components analysis (PCA).

in the following formula (Pla, 1986):

λ(κ)= *k*-esim eigenvalue.

*l*(*jk*) = *j*-esim element of the *k*-esim eigenvector.

that those with the most and least variation can be identified.

*s*(*ij*) = variances of the correlation matrix.

therefore they are more important.

Fig. 2. Absorption UV/Visible spectra. **A**, *Baccharis articulata* (Ba); **B**, *Baccharis trimera* (Bt) populations. BA, Buenos Aires; COR, Corrientes; ER, Entre Ríos; SF, Santa Fe. Numbers indicate when there is more than one population of the same species
