## 4 Data Processing and Sample Size Determination Methods
### Sample Size Determination Methods  
Here, sample size determination methods used for developing the national greenhouse gas emission factors were evaluated, including the Neyman allocation method, which is a stratified sampling method, and sample size determination method, which is based on the coefficient of variation (CV) used by the International Organization for Standardization (ISO) and Korean national organizations.  
\[n=\frac{\left(\sum_{i=1}^{L}N_{i}S_{h}\right)^{2}}{N^{2}D+\sum_{i=1}^{L}N_{i}S _{h}^{2}} \tag{1}\]  
Here,  
\(n\): Total number of sample business sites  
\(N\): Number of population business sites  
\(S\): Standard deviation per stratum  
\(h\): Subscript for strata (energy sources and facilities)  
\(D\): \((\frac{B}{N_{Z_{i/2}}})^{2}\)  
\(B\): Margin of error  
\(z_{a/2}\):The value of a standard normal distribution with a confidence level of \((1-\alpha)\) (with a 95% confidence level, this would be approximately 1.96).  
In the method of determining the sample size using the CV, the sample size is first calculated based on the CV of the existing measured data, and the method is based on the assumption that the CV of the existing measured data is known. This method suggests that a figure of 0.5 can be utilized when there is no prior information about the target. However, in this method, having information on the existing population helps to determine the sample size of the population more accurately. The method for determining the sample size using the CV is shown in Equation (2).  
\[n_{0}=\frac{Z_{a/2}^{2}\times CV^{2}}{e^{2}} \tag{2}\]  
Here,  
\(n_{0}\): Initial sample size  
\(CV\): Coefficient of variation  
\(e\): Precision  
\(z_{a/2}\): \((1-\alpha)\) Confidence coefficient below 100% confidence level  
If \(N/n<20\), correct according to Equation (3).  
\[n=\frac{n_{0}\times N}{n_{0}+N} \tag{3}\]  
Here,  
\(n\): Sample size  
\(N\): Total population size  
In this study, we approached the sample size determination from two perspectives. Concerning the CV method, the CV information available on the existing measurement data was sufficient to calculate the sample size; hence, we chose this method, assuming that the relevant information is unknown. Additionally, in this method, we considered details about outlier handling. This method requires careful examination, especially when there is no prior information; therefore, we handled outliers under the assumption that there was no prior information and then reviewed the suitability of outlier handling based on prior information for validation.  
For stratified sampling, there must be information about the data to be stratified so that the relevant data must be identifiable. In the case of stratified sampling, stratification was performed using the data related to scrubber types that can be obtained further in this study. For this study, technical information on scrubbers was obtained by surveying companies that use the gas and requesting data from relevant organizations. Because there was some prior information in this case and the number of data reduced considerably when divided into scrubber types, it is suggested that there would be difficulties in interpreting the results to apply the outlier handling method. Hence, the relevant part was not considered.