# Adaptive Jamming Mitigation for Clustered Energy-Efficient LoRa-BLE Hybrid Wireless Sensor Networks
## 3 Materials and Methods
### Statistical Analysis  
The statistical validation results provide an analysis of data before and after the implementation of a mitigation strategy in three different network configurations: BLE, LoRa, and BLE-LoRa Hybrid. The results are based on three key statistical tests: the normality test (Anderson-Darling Test), [PERSON]'s test for variance homogeneity, and a statistical significance test (either \(T\)-test or Mann-Whitney U test, depending on normality conditions). The null hypothesis \((H_{0})\) assumed that there was no significant difference between the mitigation strategy and the baseline network performance, while the alternative hypothesis \((H_{1})\) stated that the proposed mitigation technique leads to a statistically significant reduction in energy consumption and retransmissions. The results demonstrated a \(p\)-value \(<\) 0.05, confirming that the observed improvements were statistically significant. Additionally, confidence intervals (95%) were computed to quantify the variability of the measurements, ensuring that the reported reductions were not due to random fluctuations. The dataset from real-world deployments was subjected to normality tests (Shapiro-Wilk) and variance homogeneity tests ([PERSON]'s test) to verify the assumptions of parametric testing. The statistical validation confirms that the proposed approach effectively enhances network efficiency and resilience against jamming attacks while ensuring that the observed improvements are not incidental but rather a consistent outcome of the adaptive mitigation strategy. We made a MATLAB R2024b script that performs a statistical validation of energy consumption reductions before and after the implementation of a mitigation strategy across three different network configurations: BLE, LoRa, and BLE-LoRa hybrid. We applied three key statistical tests: the Anderson-Darling normality test, [PERSON]'s test for variance homogeneity, and a statistical significance test using either the Wilcoxon Rank-Sum Test or a \(t\)-test, depending on data normality. Regarding energy, the normality test results indicate that none of the datasets follow a normal distribution, as all cases returned a value of 1. This finding necessitated the use of non-parametric statistical methods, specifically the Wilcoxon Rank-Sum Test, to ensure the reliability of the analysis. [PERSON]'s test for variance homogeneity showed significant differences in variance before and after mitigation, with all networks yielding a \(p\)-value of 0.00000. This confirms that the mitigation strategy altered the behavior of energy consumption across the networks, further reinforcing the need for non-parametric statistical methods. The statistical significance test demonstrated highly significant differences in energy consumption, as evidenced by the \(p\)-values of 0.00000 across all network configurations. This confirms that the mitigation strategy substantially improves network efficiency and resilience against jamming attacks. The findings provide strong evidence that the proposed mitigation approach significantly reduces energy consumption. The changes in variance confirm that energy behavior is altered post-mitigation, and the statistical validation ensures the robustness of the reported improvements. These results strengthen the credibility of the study and confirm that the proposed strategy effectively enhances network performance. Regarding retransmissions, the normality test evaluates whether the retransmission data follow a normal distribution, where a result of 0 indicates normality and 1 indicates non-normality. In the BLE network, the results show that retransmission data before and after mitigation do not follow a normal distribution, suggesting that the retransmission values are likely skewed or have non-Gaussian characteristics. In contrast, for the LoRa network, the retransmissions were normally distributed before mitigation but deviated from normality after mitigation, indicating a shift in data distribution.