# Practical Methodology for a Three-Dimensional-Printed Hybrid Desalination System
## Appendix A  
This appendix presents a detailed analysis of variance (ANOVA) to assess the statistical significance of variations observed across different experimental groups within the hybrid RED/ED system, comparing continuous (Co) and batch (Ba) modes. Each experimental group contains seven data points, which are averages from at least three repetitions of each experiment. This consistent sample size across all groups establishes a solid foundation for subsequent comparisons. The results of the ANOVA analysis are presented in Table 11, providing a comprehensive view of the statistical metrics calculated for each group.  
The degrees of freedom (_DF_) for error within each group were calculated based on the model structure, considering the total number of observations and the parameters estimated. Specifically, the degrees of freedom in this analysis follow Equation (A1):  
\[DF_{ERROR}=N-DF_{model}-1\] (A1)  
where \(N\) represents the total observations (7 points per group), and the _DF_ model is the number of estimated parameters, excluding the intercept. This standardized approach enables a consistent and reliable estimation of error across all models, facilitating robust comparisons between the batch and continuous modes.  
Pearson's correlation coefficients (\(r\)) provide insight into the linear relationships between the studied variables. The Pearson correlation coefficients (\(r\)) reveal strong linear relationships between the studied variables in both the brine and desalinated water streams. Positive correlations in the brine stream indicate a direct relationship between operational time and conductivity, where conductivity increases as time progresses. This trend is consistent in both batch and continuous modes, as shown by the upward slope in the graph. In contrast, the desalinated water stream exhibits negative correlations, reflecting an inverse relationship between time and conductivity, where conductivity decreases over time as the desalination process advances. This inverse trend highlights the system's effectiveness in reducing salinity in the desalinated stream over time. The opposing behaviors observed--where conductivity rises in the brine stream due to salt concentration and falls in the desalinated stream as ions are removed--underscore the system's efficiency in achieving ion separation, with the Pearson correlation coefficients capturing these linear relationships robustly.  
The F-values reported in the ANOVA table, which represent the ratio of the variance explained by the model to the unexplained variance, underscore the robustness of the models. High F-values, paired with \(p\)-values well below the 0.05 threshold, indicate that the observed variance is largely attributed to the experimental factors rather than random variability. This statistical significance implies that the effects captured by the models are the result of genuine relationships between the variables rather than random fluctuations within the data, applicable to both batch and continuous modes. The R-squared (R\({}^{2}\)) values further corroborate this interpretation, showing that a significant portion of the data variability is explained by the models, with values close to 1 indicating a strong fit. This robustness in model fit, combined with the consistency in sample size and degrees of freedom, reinforces the reliability of the statistical findings. The high R-squared values suggest that the models effectively capture the dynamics of the system, providing a reliable basis for understanding the interplay between operational parameters and desalination outcomes in the RED/ED hybrid system.