## 3 Results
### Technical Measurement Uncertainty  
For the random effects, repeatability and run standard deviations were estimated (Table 8). The random variation between runs was negligible, i.e., total observed variation is explained by the factors and the repeatability component. For the factorial effects, the mean difference in log copies per droplet across the two factor levels was calculated (Table 8). For the two random components (run and repeatability), and for each factor both a constant and a proportional term were estimated.  
As shown in Table 8, for all factors except two (cartridge and time interval: droplet-PCR), at least one of the two terms (constant or proportional) is statistically significant. In particular, the two factors--Technician and Supermix--display a considerable effect. Due to the magnitude of the effect of the factor Supermix, the in-house reproducibility precision was estimated separately for the two Supermixes. As a result, it was no longer possible to obtain estimates for all seven factors on the basis of the two separate (smaller) data sets (corresponding to the two Supermixes). Accordingly, in each of the two evaluations, only three factorial effects were estimated: day, cartridge, and time interval: extraction-droplet.  
At all five contamination levels, very similar relative standard deviation (i.e., the ratio between standard deviation and the mean value, abbreviated as RSD) values were obtained for both random and factorial effects for both Supermixes. As illustrated in Tables 9 and 10, random variability shows a reverse pattern with the contamination level. Increasing the contamination level from 200 to 10,000 cells/mL was followed by a reduction in variability (78.5% to 23.3%) for the Supermix without dUTP. Similarly, for the Supermix with dUTP, the variability was reduced from 75.4% to 22.1%. The binomial (Poisson) component corresponds to the distributional uncertainty, and it is very large at low contamination levels (200 cells/mL: 58% for Supermix without dUTP and 55.1% for Supermix with dUTP). The recovery correction term corresponds to the statistical uncertainty of the estimation of the mean copy numbers at each contamination level. For further details regarding the statistical model and the meaning of the different components, the reader is referred to [PERSON] et al. ([42], preprint).  
\begin{table}
\begin{tabular}{c c c c} \hline \hline \multirow{2}{*}{**Type**} & \multirow{2}{*}{**Effect**} & \multicolumn{2}{c}{**Estimate**} \\ \cline{3-4}  & & **Constant Term** & **Proportional Term** \\ \hline \multirow{3}{*}{Random} & Repeatability & 1.039 \(\times\)\(10^{-1}\) & 5.699 \(\times\)\(10^{-2}\) \\ \cline{2-4}  & Run & 4.560 \(\times\)\(10^{-5}\) & 2.301 \(\times\)\(10^{-5}\) \\ \hline \multirow{5}{*}{Factorial} & Day & 0.005 & 0.113 \\ \cline{2-4}  & Technician & 0.237 & 0.054 \\ \cline{2-4}  & Supermix & 0.270 & 0.055 \\ \cline{2-4}  & Cartridge & 0.051 & 0.025 \\ \cline{2-4}  & Time interval: & 0.067 & 0.086 \\ \cline{2-4}  & extraction-droplet & & \\ \cline{2-4}  & Time interval: & 0.037 & 0.008 \\ \cline{2-4}  & droplet-PCR & & \\ \cline{2-4}  & Time interval: & 0.160 & 0.087 \\ \cline{2-4}  & PCR-reading & & \\ \hline \hline \end{tabular}
\end{table}
Table 8: Absolute value of parameter effects. Significant effects (5%) are highlighted.