## 3 Results and Discussion
### Fingerprinting for Saffron Authenticity
#### 3.1.2 Statistical Analysis to Reveal Adulterated Saffron Aqueous Extracts Univariate Analysis  
The binned 1D \({}^{1}\)H NOESY NMR spectra data constituted 58 (samples) by 227 (spectra bins) data matrix. Upon normalization to constant sum and auto-scaling, the obtained data were subjected to a univariate analysis method providing a preliminary overview of features that are potentially significant in discriminating the samples under study (see Figure S3 in Supplementary Materials for a visual inspection of 1D \({}^{1}\)H NOESY NMR spectra of authentic saffron aqueous extracts and adulterated ones). The unpaired two-sample Wilcoxon test (also known as the Wilcoxon rank-sum test or Mann-Whitney test) as a non-parametric alternative to the unpaired two-samples \(t\)-test was used to compare two independent groups of samples [50]. As a result, 72 significant features selected by \(t\)-tests with a \(p\)-value threshold of 0.05 were detected (see Table S2 in Supplementary Materials for the full list of the top 50 features identified by the Wilcoxon rank-sum test). Among these, the most important variables were related to the spectral regions containing signals ascribed to crocin at 1.79, 6.15, 6.47, and 5.63 ppm, glucose at 3.67 ppm, and formic acid at 8.43 ppm (Figure 1). While variables related to crocin and formic acid were positively correlated to the pure saffron samples (see Supplementary Materials, Figure S4a-e), the variable related to glucose was positively related to the adulterated samples (see Supplementary Materials, Figure S4f). Figure 1: Results of the Wilcoxon rank-sum test. Important features selected by \(t\)-tests with threshold \(p\) = 0.05. The red circles represent features above the threshold. The \(p\) values were transformed by \(-\)log10 so that the more significant features (with smaller \(p\) values) are plotted higher on the graph. An agglomerative hierarchical cluster analysis was performed using the _hclust_ function in package _stat_, to detect similarities among the samples under investigation. Selecting the opportune similarity measure and clustering algorithm, each sample begins as a separate cluster and the algorithm proceeds to combine them until all samples belong to one cluster. Specifically, using _Pearson_ as distance measure and _average_ as a clustering algorithm (clustering uses the centroids of the observations), it was possible to obtain useful information on the metabolites that most characterized the authentic saffron samples compared to the adulterated ones, and vice versa. As a result, the investigated samples clustered into two main groups as observed in the obtained dendrogram (see Figure S5 in Supplementary Materials for further details). The first cluster was composed of pure saffron samples, while the second group contained adulterated samples. Interestingly, the samples which were adulterated with safflower (indicated with S) clustered separately from the samples adulterated with turmeric (indicated with T). Moreover, within each group of adulterated samples, a clear similarity according to the level of adulteration (5, 10, and 20 wt%) was noticeable. When the results of the hierarchical analysis were analyzed through a heatmap, further information could be extrapolated (Figure 2). In agreement with the results provided by the univariate analysis, the adulterated samples were characterized by higher levels of saccharides, like sucrose (3.59 ppm), fructose (buckets at 3.99 and 4.03 ppm, respectively), and glucose (buckets at 3.67 and 5.39 ppm, respectively, containing also the overlapping signals related to the gentiobiose bound to crocetin). In particular, the samples of saffron previously adulterated with turmeric presented a higher content of these saccharides. On the other hand, the samples adulterated with safflower were characterized by a higher level of succinic acid (bucket at 2.55 ppm).