## 3 Results and Discussion
### Data Processing Results Obtained with SSIR
These numerical distributions allow the significance attached to each selected variable to be evaluated (\(p\)-value). The probabilistic calculation of the \(p\)-value was performed using equations 6 and 7 of reference [31]. The key idea of the SSIR method is that each variable acts as an a priori random extractor and classifier of samples. The \(p\)-value is then used to determine how difficult it is to find a certain number of treated samples within the set selected by the variable. In this study, each time the \(p\)-value is equal  
Figure 3: PCA representation of the treated and non-treated samples from the selected variables by SSIR. See text for more details. \begin{table}
\begin{tabular}{c c c c c c} \hline  & \multicolumn{2}{c}{**High Level**} & \multicolumn{2}{c}{**Low Level**} & \multirow{2}{*}{\(p\)**-Value 1**} \\ \cline{2-2}
**Variable \#** & \multicolumn{1}{c}{**Non-Treated**} & \multicolumn{1}{c}{**Treated**} & \multicolumn{1}{c}{**Non-Treated**} & \multicolumn{1}{c}{**Treated**} & \\  & **Samples** & **Samples** & **Samples** & **Samples** & \\ \hline
1 & 2 & 27 & 26 & 1 & 1.4\(\cdot 10^{-12}\) \\
2 & 5 & 28 & 23 & 0 & 3.1\(\cdot 10^{-11}\) \\
3 & 0 & 23 & 28 & 5 & 3.1\(\cdot 10^{-11}\) \\
4 & 0 & 23 & 28 & 5 & 3.1\(\cdot 10^{-11}\) \\
5 & 4 & 25 & 24 & 3 & 9.3\(\cdot 10^{-9}\) \\
6 & 0 & 16 & 28 & 12 & 7.3\(\cdot 10^{-7}\) \\
7 & 15 & 28 & 13 & 0 & 2.0\(\cdot 10^{-5}\) \\
8 & 14 & 27 & 14 & 1 & 7.1\(\cdot 10^{-5}\) \\
9 & 0 & 11 & 28 & 17 & 1.4\(\cdot 10^{-4}\) \\
10 & 0 & 11 & 28 & 17 & 1.4\(\cdot 10^{-4}\) \\
11 & 0 & 10 & 28 & 18 & 3.7\(\cdot 10^{-4}\) \\
12 & 10 & 0 & 18 & 28 & 3.7\(\cdot 10^{-4}\) \\
13 & 12 & 1 & 16 & 27 & 4.7\(\cdot 10^{-4}\) \\ \hline \end{tabular}  
* According to the formulation given in the text. The total number of samples is 56 of which 28 are treated and 28 are non-treated.  
\end{table} 
Table 3: Reckoning of high or low levels for dichotomic selected variables of the treated and non-treated samples. to or less than the predefined threshold, the variable was selected for classification purposes, as it is expected to correlate with the dichotomic classification of the samples. It has been found by inspection that, for all but the last two variables, there is a correlation with the increase in the chromatographic mean intensities of the treated samples with respect to the non-treated ones. Hence, the related ions are to be attached to compounds that were generated after sample treatment. This was surprising, as the treatment (temperature and washing cycles) was conducted with the aim of removing compounds. With regards to the last two variables in Table 2, the mean cumulative areas among treated samples is about half the areas found among the non-treated ones. These ions can be attributed to the process of compound removal. The selected variables in Table 3 were considered for modelling purposes. The variables were entered as descriptors in a PCA calculation using the original sum of collected peak intensities found before the dichotomization as the descriptor value (see supplementary Table S3). The scores map generated is depicted in Figure 3. The first principal component retains 58.3% of the variance, and the second, 19.6%. This constitutes an important increase with respect to the values found in Figure 1. Furthermore, it is clearly seen that the first component alone acts as a discriminant function for the classification of both types of samples. The loadings of the two first components are given in the last column in Table 2. The loadings along the first principal component are similar, and almost all the variables contribute equally. The last two variables are associated with a negative contribution. This is not surprising because these variables are associated with a possible disappearance of a compound, as has been mentioned above. The behavior of variables 11 and 12 is worth noting: both are attached to the same mass of 51 units, but the first appears in treated samples while the last one seems to disappear after the washing treatment.