## 5 Results and Discussion
### Results of Outlier Handling and Sample Size Determination Using Coefficient of Variation (CV)
#### 5.1.2 Outlier Handling and Sample Size Calculation for CHF3 Tier 3 DRE Data  
For CHF3 gas, 39 Tier 3 DREs were used, and the sample size was determined after handling outliers in each case (Table 8). The value corresponding to Q3 of the CHF3 gas DRE values was found to be 0.999, while the value corresponding to Q1 was 0.987. IQR for Q3 minus Q1 was found to be 0.013, while the figure considering 1.5 times the IQR was found to be 0.019. Considering these values, the DRE values for CHF3 gas were judged to be outliers if they were higher than 1.019 or lower than 0.967. \begin{table}
\begin{tabular}{c c} \hline \hline
**Classification** & **Value** \\ \hline Q3(75 th Percentile) & 0.938 \\ Q1(25 th Percentile) & 0.775 \\ IQR & 0.163 \\ IQR \(\times\) 1.5 & 0.244 \\ Maximum(Q3 \(+\) 1.5 \(\times\) IQR) & 1.182 \\ Minimum(Q1 \(-\) 1.5 \(\times\) IQR) & 0.531 \\ \hline \hline \end{tabular}
\end{table} 
Table 6: Requirements for handling outliers in the Burn scrubber Tier 3 DRE during CF4. \begin{table}
\begin{tabular}{c c c c} \hline \hline
**Classification** & **Case 1** & **Case 2** & **Case 3** \\ \hline CV & 0.10 & 0.02 & 0.05 \\ Z score & 1.96 & 1.96 & 1.96 \\ (95\% confidence interval) & 1\% & 1\% & 1\% \\ Error level & 337 & 17 & 85 \\ Estimated number of sample & 337 & 17 & 85 \\ \hline \hline \end{tabular}
\end{table} 
Table 7: Sample size for CF4 DRE development considering outlier cases and CVs. \begin{table}
\begin{tabular}{c c c} \hline \hline
**Classification** & **Case 1** & **Case 2** & **Case 3** \\ \hline Sample & 44 & 36 & 44 \\ Mean & 0.921 & 0.961 & 0.94 \\ SD & 0.092 & 0.02 & 0.04 \\ \hline \hline \end{tabular}
\end{table} 
Table 5: DRE values for CF4 gas based on outlier cases. Results of the Tier 3 DRE values for CHF3 gas based on the case with outlier handling are shown in Table 9. Case 1, which used existing data, had the lowest mean of 0.985 and the largest standard deviation. Case 2, which removed the outliers, had five fewer samples than before; here, the obtained mean was the highest among all three cases (0.995), and the standard deviation was the lowest (0.008). Case 3, which adjusted outliers to extreme values, had mean (0.993) and standard deviation (0.012) values that are in between those obtained for Case 1 and Case 2. For CHF3, we also checked the characteristics of the handled outliers for validation purposes. The characteristic information of the current data is scrubber, and in the case of CHF3, all five of the handled outliers had burn-type attributes. Therefore, we checked the difference between outliers in the CHF3 Tier 3 DRE values by only including burn-type scrubbers. Of the CHF3 gas DRE values, Q3 was found to be 0.99, and Q1 was found to be 0.954 when only the burn-type scrubber was considered. IQR for Q3 minus Q1 was found to be 0.046, while the figure considering 1.5 times the IQR was found to be 0.069. Considering these values, for CHF3 gases, the burn-type DRE values above 1.068 or below 0.089 were judged as outliers. When reviewing the DRE values for the burn type using the outlier criteria, two values were found to be outliers, which were lower than the four outliers obtained for CHF3 (Table 10). This is because the mean of the burn-type scrubber for CHF3 was 0.967, and the standard deviation was 0.051, which is relatively not much larger than the standard deviation of the burn type for CF4, so the DRE values for CHF3 were found to include some outliers as well. However, even in this case, the criteria for handling outliers can vary depending on whether the scrubber has information or not, indicating that much attention is needed to handle outliers. Thus, we believe that relatively more information is needed to handle outliers in F-gas. \begin{table}
\begin{tabular}{c c} \hline \hline
**Classification** & **Value** \\ \hline Q3(75 th Percentile) & 0.999 \\ Q1(25 th Percentile) & 0.954 \\ IQR & 0.046 \\ IQR \(\times\) 1.5 & 0.069 \\ Maximum(Q3 + 1.5 \(\times\) IQR) & 1.068 \\ Minimum(Q1 \(-\) 1.5 \(\times\) IQR) & 0.089 \\ \hline \hline \end{tabular}
\end{table}