## 4 Experimental Setup and Results
### Wilcoxon Test  
Finally, the Wilcoxon signed-rank test [52] was implemented to compare the performance of different SNN models trained using the SNNtrainer3D application. The Wilcoxon signed-rank test is a non-parametric statistical test used to compare two paired samples to assess whether their population mean ranks differ. It is particularly suitable for situations where the normality assumption cannot be met for the paired differences. The assumptions are that (a) the data pairs are dependent, (b) the data are measured on at least an ordinal scale, allowing them to be ranked, and (c) the distribution of differences between pairs is symmetric about the median. Regarding the test procedure, it computes the differences \(D_{i}=x_{i}-y_{i}\) for each pair of observations \((x_{i},y_{i})\). Then, it ranks the absolute values of these differences \(|D_{i}|\), excluding any pairs where \(D_{i}=0\). Next, it assigns the original signs of the \(D_{i}\) values to their corresponding ranks. Finally, it sums up the signed ranks. The test statistic \(W\) is taken as the smaller of the sum of positive ranks (\(W^{+}\)) and the sum of negative ranks (\(W^{-}\)). More exactly, the Wilcoxon signed-rank test is calculated as seen in Equation (13) [52]:  
\[W=\min(W^{+},W^{-}) \tag{13}\] \begin{table}
\begin{tabular}{c c c} \hline \hline
**SNN Architecture** & **Neurons** & **FLOPs** \\ \hline  & 100 & 158,800 \\  & 80 & 127,040 \\  & 50 & 79,400 \\ Alpha, LIF, Lapicque, Synaptic & 30 & 47,640 \\  & 25 & 39,700 \\  & 20 & 31,760 \\  & 15 & 23,820 \\  & 10 & 15,880 \\ \hline \hline \end{tabular}
\end{table} 
Table 3: Comparison regarding the total FLOPs for each SNN architecture. where \(W^{+}\) is the sum of ranks for positive differences and \(W^{-}\) is the sum of ranks for negative differences. The decision rule is that under the null hypothesis \(H_{0}\) that the median of the differences between the pairs is zero, compare \(W\) against a critical value from Wilcoxon signed-rank tables or use a \(p\)-value to decide whether to reject \(H_{0}\). The Wilcoxon signed-rank test results are calculated in Table 4, a comprehensive table comparing different SNN neuron architectures. As can be seen in Table 4, the key findings from the Wilcoxon signed-rank test results are that (a) the 80-neuron Alpha model achieves the highest accuracy at 98.64% but is not significantly different from the 100-neuron Alpha, 100-neuron LIF, 80-neuron Synaptic, 100-neuron Synaptic, 25-neuron LIF, 25-neuron Synaptic, or 50-neuron Synaptic models (\(p>0.05\)); (b) LIF and Alpha consistently outperform Lapicque at all neuron counts, with most \(p\)-values \(<0.05\), indicating statistically significant differences; (c) the 25-neuron Synaptic model reaches an accuracy of 97.97%, comparable to the best-performing models with more neurons, suggesting that the Synaptic neuron type can achieve high accuracy with fewer neurons; (d) the 25-neuron Lapicque model achieves an accuracy of 90.16%, higher than the 10-neuron and 15-neuron Lapicque models but still significantly lower than the other neuron types at the same neuron count; (e) increasing neurons generally improves accuracy, but with diminishing returns past 25 neurons, as seen by the increasing \(p\)-values in the rightmost columns. More exactly, the data reveals that the 80+ neuron LIF and Alpha models, along with the 25-neuron Synaptic model, achieve the best performance. Lapicque performs significantly worse at all neuron counts, but the 25-neuron Lapicque model shows improvement over its 10-neuron and 15-neuron counterparts. The accuracy gains from adding neurons diminish past 25 neurons, with the 25-neuron Synaptic model providing a good balance between accuracy and computational efficiency.