## 4 Discussion
### Manipulating the S/N Ratio  
The original definition of the signal-to-noise ratio (S/N), originally proposed by [PERSON] in optimization analysis [15], integrates the practical expectation value and standard deviation in many alternative equations to satisfy various users' criteria [21; 22; 23]. However, the S/N definition should satisfy [PERSON]'s optimization principle, i.e., (1) to minimize the random error first, and then, the systematic error; (2) the systematic error can be effectively suppressed by identifying the adjustment factor, which can change the average of practical data without influencing the random error in measurements. However, a simplified S/N can be given for rapid calculation as adopted by some researchers [14]:  
\[\frac{S}{N}(\eta_{i})=-10\text{log}\Big{[}(\textit{Avg}(difference)_{i})^{2} \Big{]} \tag{7}\]  
Notably, Equation (7) involves only the difference between the practical measurement and the theoretical value of the derived area from the sonography scanned image by the \"low-the-better\" principle. In contrast, the proposed Equation (6) emphasizes either a small difference or a low statistical deviation among three independent trials. Accordingly, the derived simplified S/N values of each group were 43.28, 46.48, 56.43, 48.74, 50.33, 49.94, 43.12, 51.97, 45.19, 48.81, 45.34, 46.29, 49.58, 46.78, 43.17, 49.73, 46.24, and 47.36, respectively. The fish-bone plot of the simplified S/N is depicted in Figure 3. As clearly illustrated, the predominant factors became the (D) amplitude gain or (E) imaging compression ratio while the original S/N definition via Equation (6) implied that the dominant factor was the (C) frame rate. However, the frame rate is the most dominant factor from the ANOVA  
\begin{table}
\begin{tabular}{c c c c} \hline \hline \multirow{2}{*}{**Factor**} & **Conventional** & **Combined with** & **Optimal Setting** \\  & **(The 1 st Group)** & **The Highest S/N** & **(The 4 th Group)** \\ \hline (A) angle of probe (degree) & 0 & 0 & 0 \\ (B) water depth (cm) & 5 & 6 & 6 \\ (C) frame rate (/s) & 45 & 45 & 45 \\ (D) amplitude gain (\%) & 50 & 60 & 50 \\ (E) compress ratio (\%) & 45 & 55 & 50 \\
**S/N (dB)** & **19.39** & **16.63** & **19.72** \\ \hline \hline \end{tabular}
\end{table}
Table 5: The S/N ratio derived for the conventional (1 st group), combined with the highest S/N of each factor, and the optimal setting (4 th group) by sonography scanning.  
test (SS\({}_{\text{c}}\) = 56.6%, refer to Table 4). However, neither the amplitude nor the compression ratio passed the ANOVA inspection (i.e., they were insignificant in the F test). Thus, it is appropriate to emphasize the deviation among repeat trials in each preset group (cf. Equation (6)). In contrast, emphasizing only the difference between the practical survey and theoretical preset to obtain a high S/N ratio (cf. Equation (7)) is not a good option for robust designation, although it provides rapid results for reference. A comprehensive definition of S/N should always integrate a low random error (i.e., _stdev_ in this study) and high expectation value (i.e., _Avg(difference)_ in this study) altogether in the practical survey.