## 3 Results and Discussion
### Standard Uncertainty of the Assigned Values
#### 3.2.2 Uncertainty Components of the Assigned Values  
The results corresponding to the estimation of the various uncertainty components are shown in Table 2.  
Figure 1: Combined standard uncertainty obtained for milk freezing point in the PT rounds conducted between 2017 and 2021. The standard uncertainty on the CRM certificate of the reference saline solution, \(\text{Lactrol}^{\text{\textregistered}}\) 530, supplied by Advance Instruments, has remained invariable over the different rounds of PT in this program, even if from different manufacturing batches. For this research, an uncertainty value has been estimated based on the data provided by the saline solution supplier, as explained in Section 2.2.4. As can be seen in Table 2, the components that contribute most to the estimation of the uncertainty of the assigned value are the standard uncertainty from the CRM certificate, \(u_{CRM}\), and the standard uncertainty of the PT item assay, \(u_{\pi_{PTI}}\), with the latter resulting in 100% of the PT rounds with a value greater than that estimated in the design (0.48 m\({}^{\circ}\)C) [17]. By incorporating the uncertainty of the CRM certificate, this becomes one of the most important sources to contribute to the estimation of the uncertainty of the assigned value. With respect to the uncertainty resulting from the CRM analysis, \(u_{\pi_{CRM}}\), a value lower than the one estimated in the design (0.72 m\({}^{\circ}\)C) [17] was obtained in 100% of the PT rounds. The estimated standard uncertainty of the assigned value would not allow the ISO 13528:2022 [13] criterion to be met in any of the PT rounds where the thermistor method was used (as noted in Section 3.2.1); therefore, the performance of the participants would have to be evaluated by incorporating the uncertainty using the z\({}^{\prime}\)-score. However, in an article published by [PERSON] and [PERSON] [11], it is noted that higher ratios between the uncertainty of the assigned value and the standard deviation for proficiency assessment may be appropriate in some scenarios, and ratios of up to 0.5\(\sigma\) might be acceptable. However, this article referred specifically to PTs where the assigned value (and its uncertainty) were based on the results obtained by the participants (consensus values). It is worth mentioning that, in the present investigation, the uncertainty of the assigned value in none of the rounds was greater than 0.5\(\sigma\). On the other hand, ISO 13528:2022 [13] states that the absolute value of z\({}^{\prime}\)-score will always be lower than that of z-score by a factor that can be estimated by Equation (6) as follows:  
\[\frac{z^{\prime}-score}{z-score}=\frac{\hat{\sigma}}{\sqrt{\left(\hat{\sigma} ^{2}+u_{\hat{x}}^{2}\right)}} \tag{6}\]  
By applying Equation (6), when the uncertainty of the assigned value is less than 0.3\(\sigma\), the z\({}^{\prime}\)-score value would be lower than the z-score by a factor ranging from 0.96 to 1, thus being almost identical, and therefore, the uncertainty is considered to be negligible [13]. When applying the same formula with an uncertainty equal to 0.4\(\hat{\sigma}\), the factor would