## 3 Results and Discussion
### Assessment of Uncertainty  
3.8.1. Calculation \(\mathrm{u_{bias,N}}\)  
For this calculation, the data from the recovery tests were used. Over a period of one year, 23 recovery measurements were made on a spiked Ouzo sample; the recovery results are shown in Table 9. \begin{table}
\begin{tabular}{c c c c c c c c c} \hline \hline \multirow{2}{*}{**Experiment**} & \multicolumn{8}{c}{**Factors**} & \multirow{2}{*}{**mg/L DEHP**} \\ \cline{2-2} \cline{4-9}  & **A** & **B** & **C** & **D** & **E** & **F** & **G** \\ \hline
**1** & 1 & 1 & 1 & 1 & 1 & 1 & 1 & 1.07 & 1.03 \\ \hline
**2** & 1 & 1 & 1 & 2 & 2 & 2 & 2 & 1.00 & 1.02 \\ \hline
**3** & 1 & 2 & 2 & 1 & 1 & 2 & 2 & 1.03 & 1.03 \\ \hline
**4** & 1 & 2 & 2 & 2 & 2 & 1 & 1 & 1.00 & 1.05 \\ \hline
**5** & 2 & 1 & 2 & 1 & 2 & 1 & 2 & 1.07 & 1.04 \\ \hline
**6** & 2 & 1 & 2 & 2 & 1 & 2 & 1 & 1.04 & 1.06 \\ \hline
**7** & 2 & 2 & 1 & 1 & 2 & 2 & 1 & 1.05 & 1.07 \\ \hline
**8** & 2 & 2 & 1 & 2 & 1 & 1 & 2 & 1.09 & 1.03 \\ \hline \hline \end{tabular}
\end{table} 
Table 7: Experimental design of five-parameter two-level factors, to evaluate the ruggedness of method (according to [PERSON] experimental design, seven-parameter two-level factors). \begin{table}
\begin{tabular}{l c c c c} \hline \hline \multicolumn{4}{l}{**Analysis of Variance**} \\ \hline Source & DF & Adj SS & Adj MS & F-Value & \(p\)**-Value** \\ \(\mathbf{\Delta}\) & 1 & 0.003025 & 0.003025 & 5.48 & **0.041** \\ B & 1 & 0.000025 & 0.000025 & 0.05 & **0.836** \\ C & 1 & 0.000100 & 0.000100 & 0.18 & **0.680** \\ D & 1 & 0.000625 & 0.000625 & 1.13 & **0.313** \\ E & 1 & 0.000400 & 0.000400 & 0.72 & **0.415** \\ Error & 10 & 0.005525 & 0.000553 & & \\ Lack-of-Fit & 2 & 0.000625 & 0.000313 & 0.51 & 0.619 \\ Pure Error & 8 & 0.004900 & 0.000613 & & \\ Total & 15 & 0.009700 & & & \\ \hline \hline \end{tabular}
\end{table} 
Table 8: Analysis of variance table for the ruggedness of the method. According to Equation (4), the uncertainty of the accuracy was factored into the uncertainty of the spike concentration, i.e., the uncertainty of the volume of the flask that prepared the spiked sample, the uncertainty of the pipette that transferred the concentrated DEHP standard, and the uncertainty from the purity of the concentrated standard. Therefore, the relative standard uncertainty of systematic errors (from recovery) by NORDTEST, \(\mathrm{u_{bias,N}}\), is calculated from Equation (4) [14]:  
\[\mathrm{u_{bias,N}}=\sqrt{\mathrm{u_{conc}}^{2}+\mathrm{u_{vol}}^{2}+\left( \frac{\sum_{i=1}^{n}(R_{i}-100)^{2}}{n}\right)} \tag{4}\]  
\(\mathrm{u_{conc}}\): A certified DEHP reference standard was used for spike, for which the certificate gave purity = 99.90%, and uncertainty a = \(\pm\)0.05% for a significance level of 95%. In these cases, assuming a normal distribution, the standard uncertainty is given by Equation (5):  
\[\mathrm{u(purity)}=\frac{a}{k} \tag{5}\]  
where k is the coverage coefficient, which for a 95% significance level is k = 1.96 (more commonly k = 2). According to Equation (5) the standard uncertainty from standard purity is:  
\[\mathrm{u(purity)}=0.00025\]  
and the corresponding relative standard uncertainty is:  
\[\mathrm{u_{conc}}=\frac{\mathrm{u(purity)}}{\mathrm{purity}}100=0.025025\%\]  
\(\mathrm{u_{vol}}\): A volumetric flask (class A) Vbottle = 100 mL was used for the spike of the sample, which according to the manufacturer has a tolerance of a = \(\pm\)0.08 mL. The standard uncertainty due to the tolerance, assuming a quadratic distribution, is:  
\[\frac{0.08}{\sqrt{3}}=0.04618802\ \mathrm{mL}\]  
However, according to the manufacturer, the bottle is calibrated at 20 \({}^{\circ}\)C, while the laboratory temperature is 20 \(\pm\) 4 \({}^{\circ}\)C. The uncertainty from this source can be calculated from the estimate of the temperature range and the volume expansion coefficient. The volume expansion of the liquid is significantly greater than that of the flask, so only the volume expansion needs to be considered [13].