## 4 Results Evaluation
### Model Validation
#### 4.2.2 Empirical Macro Validation
So, using R statistical programming language, a Shapiro-Wilk test [90] was performed for deciding the normality of all real data (i.e., 2G, 3G and 4G) and simulation data. As it is presented in Table 10, since each of model's outputs had 1500 experiments (i.e., runs), each of them was divided into fifteen 100-run blocks. Every block shows a probability distribution resulting from the average of 100 different experiments of each telecoms technology in each network structure type (i.e., each telecoms technology's average simulated data in 100 runs in each of network structures). \begin{table}
\begin{tabular}{c c c c} \hline \hline  & \multicolumn{3}{c}{**MTTs**} \\ \cline{2-4}  & **2G** & **3G** & **4G** \\ \cline{2-4}  & Block 1 (average of 1 – 100 & Block 1 (average of 1 – 100 & Block 1 (average of 1 – 100 & 1 – 100 \\  & experiments) & Experiments) & Block 2 (average of 101 – 200 & 101 – 200 \\
**PAN** & Block 2 (average of 1 – 200 & Block 2 (average of 1 – 100 & Block 2 (average of 1 – 100 & 1 – 100 \\  & experiments) & experiments) & experiments) \\
**Network Structure** &. &. &. \\  & Block 15 (average 101 - 1500 & Block 15 (average 101 - 1500 & Block 1401 – 1500 \\  & experiments) & experiments) & experiments) \\  & Block 1 (average of 1 – 100 & Block 1 (average of 1 – 100 & 1 – 100 \\  & experiments) & experiments) & experiments) \\
**WSN** & Block 2 (average of 101 – 200 & Block 2 (average of 101 – 200 & Block 2 (average of 101 – 200 \\  & experiments) & experiments) & experiments) \\
**-** &. &. &. \\  & Block 15 (average 101 - 1500 & Block 2 (average 101 – 1500 & Block 2 (average 101 – 1500 \\  & experiments) & experiments) \\ \hline \hline \end{tabular}
\end{table} 
Table 10: Division of model’s outputs experiments into 15 blocks. \begin{table}
\begin{tabular}{c c c c} \hline \hline  & \multicolumn{3}{c}{**MTTs**} \\ \cline{2-4}  & **2G** & **3G** & **4G** \\ \cline{2-4}  & Experiment 1 & Experiment 1 & Experiment 1 \\  &. &. &. \\
**PAN** & Experiment 750 & Experiment 750 & Experiment 750 \\  &. &. &. \\
**Network Structures** & Experiment 1500 & Experiment 1500 & Experiment 1500 \\  & Experiment 1 & Experiment 1 & Experiment 1 \\  &. &. &. \\
**WSN** & Experiment 750 & Experiment 750 & Experiment 750 \\  &. &. &. \\  & Experiment 1500 & Experiment 1500 & Experiment 1500 \\ \hline \hline \end{tabular}
\end{table} 
Table 9: Model’s outputs experiments. H\({}_{0}\) Hypothesis signifies that the correlation of two samples (i.e., simulation data vs. real-world) is less than or equal to zero. As seen in column 3 of Table 12, all H\({}_{0}\) hypotheses are rejected (the p-value is far less than 0.05), meaning that the model has shown an acceptable predictive accuracy in both network structures. Therefore, the model's outputs are empirically validated. To pinpoint which social network has the highest performance and can serve as the best explanation for the social structure of the case study, the correlation coefficient of all blocks has been measured and presented in Table 13.  
In terms of 2G simulation, as it can be seen in Figure 11, the performance of WSN (i.e., P\({}_{\text{WSN}}\)) is better than that of PAN (i.e., P\({}_{\text{PAN}}\)). The correlation performance of these two social networks in simulating the diffusion of 2G has been numerically presented in column 2 of Table 13.