## 3 Results and Discussion
### Significance Analysis of Comparative Models  
The significant difference between the means of all comparative models was tested using one-way analysis of variance (ANOVA) because it is a parametric test for more than two samples. However, the Kruskal-Wallis test was used to identify the significant difference between the medians of five comparative models since it is a non-parametric test for more than two samples. The verification of the statistically significant models comes  
\begin{table}
\begin{tabular}{c c c c c} \hline \hline
**Model** & **MSE** & **RMSE** & **MAE** & \(\mathbf{R^{2}}\) \\ \hline
1D-CNN & 0.007 & 0.083 & 0.060 & 0.837 \\ \hline GB & 0.023 & 0.153 & 0.086 & 0.578 \\ \hline KNN & 0.014 & 0.118 & 0.079 & 0.603 \\ \hline RF & 0.014 & 0.119 & 0.092 & 0.292 \\ \hline SVM & 0.026 & 0.162 & 0.122 & 0.570 \\ \hline \hline \end{tabular}
\end{table}
Table 16: Comparative model validation result of the sand pack test with SAND_PROD_PER_AREA as the output.  
\begin{table}
\begin{tabular}{c c c c c} \hline \hline
**Model** & **MSE** & **RMSE** & **MAE** & \(\mathbf{R^{2}}\) \\ \hline
1D-CNN & 18.240 & 4.271 & 2.411 & 0.993 \\ \hline GB & 288.692 & 16.990 & 13.900 & 0.845 \\ \hline KNN & 18.570 & 4.309 & 2.535 & 0.990 \\ \hline RF & 77.758 & 8.818 & 5.854 & 0.954 \\ \hline SVM & 83.300 & 9.126 & 8.335 & 0.904 \\ \hline \hline \end{tabular}
\end{table}
Table 14: Comparative model validation result of the slurry test with RETAINED_PRM as the output.  
\begin{table}
\begin{tabular}{c c c c c} \hline \hline
**Model** & **MSE** & **RMSE** & **MAE** & \(\mathbf{R^{2}}\) \\ \hline
1D-CNN & 18.240 & 4.271 & 2.411 & 0.972 \\ \hline GB & 288.692 & 16.990 & 13.900 & 0.548 \\ \hline KNN & 18.570 & 4.309 & 2.535 & 0.564 \\ \hline RF & 77.758 & 8.818 & 5.854 & 0.735 \\ \hline SVM & 83.300 & 9.126 & 8.335 & 0.624 \\ \hline \hline \end{tabular}
\end{table}
Table 15: Comparative model validation result of the slurry test with SAND_PROD_PER_AREA as the output.  
\begin{table}
\begin{tabular}{c c c c c} \hline \hline
**Model** & **MSE** & **RMSE** & **MAE** & \(\mathbf{R^{2}}\) \\ \hline
1D-CNN & 18.240 & 4.271 & 2.411 & 0.993 \\ \hline GB & 288.692 & 16.990 & 13.900 & 0.845 \\ \hline KNN & 18.570 & 4.309 & 2.535 & 0.564 \\ \hline RF & 77.758 & 8.818 & 5.854 & 0.735 \\ \hline SVM & 83.300 & 9.126 & 8.335 & 0.624 \\ \hline \hline \end{tabular}
\end{table}
Table 15: Comparative model validation result of the slurry test with SAND_PROD_PER_AREA as the output.  
with the condition where the null hypothesis is rejected. The null hypothesis refers to the situation where the mean or median difference between all five models is not statistically significant. Suppose the \(p\)-value is less than the significance level of 0.05, and the F statistic value is greater than the F critical value. In this case, the null hypothesis was rejected for the ANOVA test. Still, if the H statistic value is greater than the Chi-square critical value, then the null hypothesis is rejected for the Kruskal-Wallis test. The significance analysis using the ANOVA and Kruskal-Wallis tests are presented Table 17.  
The significance analysis using ANOVA and Kruskal-Wallis tests in Table 17 showed that the \(p\)-values are less than 0.05 and the test statistics are greater than the critical values. Thus, the null hypothesis is rejected, indicating that the differences between the mean or median of all five models in predicting the plugging sign, retained permeability, and sand production are statistically significant.