## 7 Results and Performance Evaluation
### Performance Evaluation  
Performance evaluation of any model that detects a jamming attack is a difficult proposition because there is no known theoretical or practical model that can be taken as a bench-mark for comparison. It is perhaps because of this that all of the authors related with jamming detection quoted so far, except [PERSON] _et al._[3], have chosen not to evaluate their methods. Even the performance evaluation method described by [PERSON] _et al._, is ambiguous because they have neither defined the 'jammed nodes ratio' (ratio of the number of nodes successfully jammed by the jammer to the number of nodes covered by the jammer?) nor have they described the method to calculate it; but have used it to study the performance parameters, 'detection rate' and 'false positive rate', as a function of the 'jammed nodes ratio'. We, therefore first define some terms which we use in our performance evaluation and then describe how these are calculated or obtained, where necessary. We then compare our results with those of [PERSON] _et al._[  
system (simulation) and the experts were compared using statistical software, SPSS 11.5. We used the chi-square test for grouped comparison of data with degree of freedom (df) being 3 (as the number of groups are 4: NORMAL, LOW, MEDIUM, and HIGH), and level of significance (p) being 0.05 with the corresponding table value to be 7.815 giving a confidence interval of 95%. The test results for one of the simulations, as described in Figure 6 and Figure 8, are given in Table 7.  
We mention here that 712 simulations (238 out of 240 for 25-node, 237 out of 240 for 50-node, and 237 out of 240 for100-node configurations) out of 720 simulations passed the chi-square test. The mean TDR and FDR from these 712 simulations were collated for different jammed node ratios (jnr) under different configurations (total number of nodes in the simulation, n) for different types of jammers. The values of TDR and FDR for 100 nodes configuration for different types of jammers for different types of jamming indices are given in Table 8 and Table 9, respectively. \begin{table}
\begin{tabular}{|p{42.7 pt}|p{42.7 pt}|p{42.7 pt}|p{42.7 pt}|p{42.7 pt}|p{42.7 pt}|p{42.7 pt}|p{42.7 pt}|p{42.7 pt}|p{42.7 pt}|} \hline \multirow{3}{*}{**Group of**} & **No. of nodes placed placed by system** & **No. of nodes placed by system** & **No. of nodes placed by system (T)** & **TDR = placed by system (T)** & **FDR = placed by system (T)** & **FDR = (T)** & **Jnr = 100.E/** \\ \cline{2-10}  & **N. of nodes placed** & **No. of nodes placed by system (O)** & **(E)** & **system (T)** & **system (T)** & **SFD (F)** & **100.T/E** & **25** \\ \hline Normal & 4 & 4 & 0 & 4 & 0 & 100\% & 0\% & 16\% \\ Low & 5 & 5 & 0 & 5 & 0 & 100\% & 0\% & 20\% \\ Medium & 4 & 4 & 0 & 4 & 0 & 100\% & 0\% & 16\% \\ High & 12 & 12 & 0 & 12 & 0 & 100\% & 0\% & 48\% \\ Total & 25 & 25 & 0 & 25 & 0 & - & - & - \\ \hline \end{tabular}
\end{table} 
Table 7: Test results for one of the simulations, as described in Figure 6 and Figure 8. The results pass the chi-square test as the total under (O-E)\({}^{2}\)/E, 0 is less than the table value of 7.815.