## 3 Results
### Nonparametric Characteristic Correlation Estimation and Characteristic Selection on Efficiency
#### 3.2.2 The Nanofiltration Process  
As shown in Table 4, the [PERSON]'s \(\rho\) correlation coefficient values for the pairs (1) j-EC, (2) EC-TN, (3) EC-TP, (4) EC-NO\({}_{3}\) and (5) TN-NO\({}_{3}\) suggested that there might be a noticeable relationship between some pairs of characteristics. However, the two pairs EC-TN and EC-TP appeared to include a correlation coefficient of zero. Thus, they were removed from the five-pair group. Moreover, the pairs TN-NO\({}_{3}\) and j-EC included very weak (lower-bound) correlation coefficient values of \(-0.139\) and \(-0.049\), respectively. This \begin{table}
\begin{tabular}{l c c c c} \hline \hline  & \multicolumn{1}{c}{**Spearman’s**} & \multicolumn{1}{c}{**Significance**} & \multicolumn{2}{c}{**95\% Confidence Intervals**} \\  & **Rho** & **(Two-Tailed)** & \multicolumn{2}{c}{**(Two-Tailed)**\({}^{\text{a,b}}\)**} \\ \cline{2-5}  & \(-\)EC & \(-\)0.017 & 0.966 & \(-\)0.686 & 0.668 \\ j—SAR & \(-\)0.621 & 0.074 & \(-\)0.914 & 0.096 \\ j—Turb & \(-\)0.134 & 0.731 & \(-\)0.744 & 0.597 \\ j—TN & 0.343 & 0.366 & \(-\)0.435 & 0.828 \\ j—TP & 0.294 & 0.442 & \(-\)0.478 & 0.810 \\ j—NO\({}_{3}\) & \(-\)0.322 & 0.398 & \(-\)0.820 & 0.454 \\ EC—SAR & \(-\)0.179 & 0.645 & \(-\)0.763 & 0.567 \\ EC—Turb & 0.201 & 0.604 & \(-\)0.551 & 0.773 \\ EC—TN & \(-\)0.561 & 0.116 & \(-\)0.897 & 0.188 \\ EC—TP & 0.689 & 0.040 & 0.022 & 0.932 \\ EC—NO\({}_{3}\) & 0.252 & 0.512 & \(-\)0.512 & 0.794 \\ SAR—Turb & \(-\)0.180 & 0.644 & \(-\)0.764 & 0.566 \\ SAR—TN & \(-\)0.419 & 0.262 & \(-\)0.854 & 0.361 \\ SAR—TP & \(-\)0.262 & 0.496 & \(-\)0.798 & 0.505 \\ SAR—NO\({}_{3}\) & \(-\)0.022 & 0.955 & \(-\)0.689 & 0.665 \\ Turb—TN & \(-\)0.055 & 0.889 & \(-\)0.706 & 0.646 \\ Turb—TP & 0.308 & 0.420 & \(-\)0.466 & 0.815 \\ Turb—NO\({}_{3}\) & \(-\)0.127 & 0.745 & \(-\)0.740 & 0.602 \\ TN—TP & \(-\)0.371 & 0.325 & \(-\)0.838 & 0.409 \\ TN—NO\({}_{3}\) & \(-\)0.131 & 0.737 & \(-\)0.742 & 0.599 \\ TP—NO\({}_{3}\) & 0.202 & 0.602 & \(-\)0.551 & 0.773 \\ \hline \hline \end{tabular} \({}^{\text{a}}\) Estimation is based on [PERSON]’s r-to-z transformation. \({}^{\text{b}}\) Estimation of standard error is based on the formula proposed by [PERSON], [PERSON] and [PERSON].  
\end{table} 
Table 2: Confidence intervals for [PERSON]’s \(\rho\) correlation coefficients of the seven ultrafiltration process characteristics. \begin{table}
\begin{tabular}{l c c c c} \hline \hline \multicolumn{1}{c}{**Characteristics**} & \multicolumn{1}{c}{**QCD**} & \multicolumn{1}{c}{**Efficiency**} & \multicolumn{1}{c}{**Relative**} & \multicolumn{1}{c}{**Cumulative**} \\ \cline{2-5} \multicolumn{1}{c}{**(Ultrafiltration Process)**} & & & & **Relative** & **Relative Efficiency** \\ \hline \hline \multicolumn{1}{c}{**Turbidity**} & 0.35 & 0.123 & 0.664 & 0.664 \\ \hline \hline \multicolumn{1}{c}{**TN**} & 0.16 & 0.0256 & 0.139 & 0.803 \\ \hline \hline \multicolumn{1}{c}{**NO\({}_{3}\)**} & 0.14 & 0.0196 & 0.106 & 0.909 \\ \hline \hline \multicolumn{1}{c}{**J**} & 0.097 & 0.00941 & 0.051 & 0.960 \\ \hline \hline \multicolumn{1}{c}{**TP**} & 0.082 & 0.00672 & 0.036 & 0.997 \\ \hline \hline \multicolumn{1}{c}{**SAR**} & 0.019 & 0.000361 & 0.002 & 0.999 \\ \hline \hline \multicolumn{1}{c}{**EC**} & 0.016 & 0.000256 & 0.001 & 1 \\ \hline \multicolumn{1}{c}{Total} & 0.18445 & 1 & & \\ \hline \hline \end{tabular}
\end{table} 
Table 3: Relative importance of the seven ultrafiltration process characteristics based on the efficiency (QCD\({}^{\text{2}}\)). made their selection doubtful, and they were removed from the initial pair screening list. It was only the Spearman's \(\rho\) correlation coefficient value of the EC-NO\({}_{3}\) pair that appeared to be convincingly significant (\(p\) < 0.01). Even though the upper bound of its correlation coefficient estimate indicates a very strong negative correlation (\(-\)0.976), the lower bound of the confidence interval did not uphold the strong pairing, but it allowed the possibility for a moderate relationship (correlation coefficient value of \(-\)0.507).