## 4 Discussion  
Considering the various prediction solutions obtained in the \"Results\" section, new opportunities have arisen for exploring underlying relationships. A quick visual way to recap the dataset similarities is to employ the \"stripes\" design for an informative plot summary. Its standardizing facility, in terms of furnishing a concentrated and robust description of the combined dataset propensities, is shown in Figure 6. Likewise, the 50% boxplot area is narrower for the average permeate flux and the COD rejection rate; it is distinctively larger for the cumulative flux decline, which might imply that it is susceptible to greater variability. It is surprising that in all three datasets, it is the 25% of the data below the median that is confined to a thinner (not-symmetrical) stripe. However, it is only the distribution curve of the cumulative flux decline that exposes a skewness, in view of the fact that the data mode is situated in the vicinity that favors lower measurements. To affirm the potentiality of such visual artifacts, tests of normality were carried out according to the Kolmogorov-Smirnov and Shapiro-Wilk procedures. The combined replications for each quality characteristic response are compared in Table 9. Both tests confirm the symmetry of the measurements, as shown in Table 9 (IBM SPSS v.29). To assess the shape statistics for the three characteristic responses, the skewness and kurtosis estimations are provided in Table 10 (IBM SPSS v.29). The low skewness statistic values, along with their mediocre standard errors, may attest to the symmetry for each of the three datasets. On the other hand, the kurtosis estimations may not be so discerning between mesokurtic or platykurtic tendencies. To further support the above arguments, it is beneficial to have a robust view of the contrasting trends in the combined datasets, for each of the three characteristic responses, on QQ-plot displays. Figure 7 shows that in all three graphs, datapoints above the trendline consistently outnumber those below it. However, all datapoints, in all three cases, are fairly well behaved, since they are all well contained within their 95% confidence bands. Figure 6: “Stripes” design plot summary for the combined dataset of (**A**) average permeate flux (\(\mathrm{J_{p}}\)), (**B**) COD rejection rate (COD), and (**C**) cumulative flux decline (SFD). \begin{table}
\begin{tabular}{l c c c c c c} \hline \hline  & \multicolumn{2}{c}{**Kolmogorov–Smirnov Test a**} & \multicolumn{3}{c}{**Shapiro–Wilk Test**} \\ \cline{2-7}  & **Statistic** & **Df** & **Sig.** & **Statistic** & **Df** & **Sig.** \\ \hline \(\mathrm{J_{p}}\) & 0.096 & 27 & 0.200 * & 0.980 & 27 & 0.860 \\ \hline
**COD** & 0.082 & 27 & 0.200 * & 0.968 & 27 & 0.549 \\ \hline
**SFD** & 0.124 & 27 & 0.200 * & 0.947 & 27 & 0.182 \\ \hline \hline \end{tabular}
\end{table} 
Table 9: Tests of normality for the combined dataset of (A) average permeate flux (\(\mathrm{J_{p}}\)), (B) COD rejection rate (COD), and (C) cumulative flux decline (SFD) (IBM SPSS v.29). Figure 7: QQ-plot depictions of the combined dataset of (**A**) average permeate flux (\(\rm{J_{P}}\)), (**B**) COD rejection rate (COD), and (**C**) cumulative flux decline (SFD). \begin{table}
\begin{tabular}{l c c c c} \hline \hline  & \multicolumn{2}{c}{**Skewness**} & \multicolumn{2}{c}{**Kurtosis**} \\  & **Statistic** & **Std. Error** & **Statistic** & **Std. Error** \\ \hline \(\rm{J_{P}}\) & 0.174 & 0.448 & \(-\)0.447 & 0.872 \\ COD & \(-\)0.007 & 0.448 & \(-\)0.844 & 0.872 \\ SFD & 0.293 & 0.448 & \(-\)1.043 & 0.872 \\ \hline \hline \end{tabular}
\end{table} 
Table 10: Skewness and kurtosis estimations for the combined replicated datasets: (A) average permeate flux (\(\rm{J_{P}}\)), (B) COD rejection rate (COD), and (C) cumulative flux decline (SFD) (IBM SPSS v.29). The next step is to inspect for any instabilities within each factor setting and delineate possible sources of discrepancies in the resulting predictions.