## 4 Data Processing and Sample Size Determination Methods  
### Data Processing Methods  
When determining the sample size, it is important to consider outliers, especially when calculating measurements or representative values. In particular, when it comes to the development of national GHG emission factors, outliers should be carefully examined as they can be underestimated or overestimated [29; 30]. Careful examination of outliers is imperative, especially in the absence of detailed information concerning them. This study reviews the data processing methods commonly used in previous studies on inventory development and applies various ways of outlier handling to determine the appropriate sample size. \begin{table}
\begin{tabular}{c c} \hline \hline
**Methods** & **Details** \\ \hline Determining the confidence level and error level & M\&V Guidelines recommend 90\% \(\pm\) 10\% \\  & For general polls and statistical surveys, 95\% confidence level \\  & If the population is uninformed, maximum variance is assumed \\  & (the CV is often used) \\  & Preliminary survey or past information is used \\  & Calculates the sample size with a formula for determining the sample \\  & size based on the error for a given confidence interval \\  & Corrects the sample size for finite populations \\  & \(\rightarrow\) when N/n\({}_{0}\) (=1/f) is less than 20 \\ \hline \hline \end{tabular}
\end{table} 
Table 2: Procedure for determining the sample size with CVs of variation and required materials. \begin{table}
\begin{tabular}{c c c} \hline \hline
**Target Gases** & **Sample** & **Sampling Period** \\ \hline CF\({}_{4}\) & 44 & \\ CHF\({}_{3}\) & 39 & 2020–2021 \\ \hline \hline \end{tabular}
\end{table} 
Table 3: Collected Tier 3 DRE data content. Extreme values should be identified before assuming the presence of outliers. Although several methods are available to identify extreme values, the interquartile range (IQR) method is the most popular one among them and has been used in related research. IQR identifies extreme values and finds outliers via a box-and-whisker plot, which is one of the summary methods that integrate multiple information into one figure using several measurements, such as the position of the center and degree of scatter [31; 32]. From the box-and-whisker plot, you can identify most outliers in the data values in addition to the symmetry of the distribution, center of the data, degree of dispersion, and concentration of the tail of the distribution. Box-and-whisker plots are primarily built around interquartile values. A square box is drawn around 50% of the data at the center of the size-ordered data set, and lines of appropriate length are drawn and connected to the left and right (or below and above) of the box to represent the ranges of 25% of the data with smaller values and 25% of the data with larger values, respectively. The process of IQR is as follows: First, determine the interquartile values (Q\({}_{1}\), Q\({}_{2}(=\) median\()\), Q\({}_{3}\)). Second, connect Q\({}_{1}\) and Q\({}_{3}\) to a square box and draw a vertical line at the position of the median (Q\({}_{2}\)). Third, compute IQR \(=\) Q\({}_{3}-\) Q\({}_{1}\). Fourth, bound the box with a size range 1.5 \(\times\) IQR at each end and connect the minimum and maximum values within this range with lines from Q\({}_{1}\) and Q\({}_{3}\), respectively. Finally, indicate the data values that fall outside the two boundaries and determine these points as extreme values. A graphical representation of the above process is shown in Figure 1.  
There are different ways to handle outliers. First, you can choose to eliminate outliers to remove their influence. However, it has the disadvantage of reducing the overall number of data. Another way is to winsorize outliers. This method adjusts all values above and below the threshold set with the extreme upper and lower limits. The winsorizing method is less sensitive to outlier values because it can replace them with less extreme values [33; 34].