## 4 Discussion
### Confirmatory Analysis  
For an empirical calibration to be acceptable, the regression equation for a specific analyte should have a correlation coefficient of r \(\geq\) 0.98 [28]. Eleven out of the 27 equations given in Tables 3-5 met this requirement. Additionally, the proxies obtained (Figure 3) for Cd, Ni, and Hg indicated that the predicted data were of high quality (definitive, R\({}^{2}\) > 0.9) while those for As, Cr, and Se can be considered to be screening-level data (R\({}^{2}\) > 0.5) according to the EPA criteria [28]. In Figures 2 and 3, it can be observed that the highest RD values were observed for the smallest concentrations of the target elements. For the reference samples, the EPA method [28] indicated that the measured value for each target analyte should be within \(\pm\)20% RD of the true value to be acceptable. This value (20%) is considered as the limit of adequate precision of the individual results.  
Discarding the data below the limits indicated in Figure 3 (As < 2.8 mg kg\({}^{-1}\), Cd < 0.21 mg kg\({}^{-1}\), Cr < 58 mg kg\({}^{-1}\), Se < 280 mg kg\({}^{-1}\)), the remaining predicted data reached the R\({}^{2}\) criteria of definitive (high-quality) data for all the elements. These cutoff limits have been selected approximately using visual observation of the plots in Figure 3. The limits could be considered as an approximation to the quantification limits (LOQ) of the adjustments used.  
For the elements As, Cd, Ni, and Cr, most of the organic fertilizer samples were found among the discarded samples. The sample with high RD values was the one with the lowest concentrations of all the elements considered (Figure 4). However, the predictions of Hg and Se values in organic fertilizers were satisfactory, despite the low number of samples of organic fertilizers used in the calibration and the low concentration of these elements in these samples. In the case of compost samples, in general, the predictions were good and only a higher magnitude RD was observed in Figure 4 for the two to three samples that presented the lowest concentrations of the target elements. In the sludge type, a significant RD (>50%) was found for the Ni and Hg predicted contents of several samples. The fit of the equations used for sludge (Table 4) can be improved and it may be necessary to have a larger number and more geographic diversity of samples for calibration such that additional terms may be included in the equations.  
The limits established by European legislation [35] for these contaminants in a growing medium are 1.5 mg Cd kg\({}^{-1}\), 1000 ug Hg kg\({}^{-1}\), 50 mg Ni kg\({}^{-1}\), and 40 mg inorganic As kg\({}^{-1}\). As can be seen in Figure 2, these limits are included (for Cd, Hg, Ni) or are higher (for As) than the ranges in which these elements have been determined. Furthermore, the precision of the predictions (Figure 4) above the indicated values was, in general, satisfactory. Only a few samples of sewage sludge, a type for which much higher statutory limits apply [36], exceeded the RD limit of 20%. This means that the pXRF technique with the indicated proxies could be valid to test the compliance of these types of products, at least for quality control purposes in the field or the factory applications. Even an analyte with more than 20% RD may be used, as long as its linearity is satisfactory, as it could allow for properly ranking samples and detecting outliers [37].