## 3 Results
### Machine Learning Decoding  
Table 1 provides an overview of the number of sensors and shows the mean, standard deviation (std), minimum, and maximum cross-validation accuracy for each sensor subset over all participants. The sensor locations of each subset correspond to those detailed in Figure 3.  
After performing an independent sample \(t\)-test between decoding accuracies obtained with the full sensor set and those obtained when using the different subsets, the results show that none of the observed differences in mean accuracy are statistically significant. The resulting \(p\)-values of 0.90 (half), 0.91 (BCI Comp), 0.74 (OpenBCI 16), 0.18 (OpenBCI 8), 0.52 (Motor cortex), and 0.25 (MC Reduced) do not allow rejection of the null hypothesis, meaning decoding accuracies are the same. The trends in Table 1 indicate that there is great variability in the cross-validation results when using the full set of 64 channels, with a standard deviation of 0.15. This is also the case for other sensor subsets with observed standard deviations that are equal or larger. For the full set of electrodes, the lowest accuracy was below random chance at 0.31, while the highest achieved accuracy was 1.00. On average, the accuracy for the full set of sensors is 0.67. To visualize trends in the decoding results, Figure 5 visualizes the cross-validation results for each sensor subset in a box-plot format. \begin{table}
\begin{tabular}{l r r r r r} \hline \hline
**Sensor Subset** & **\# Sensors** & **Mean Acc.** & **Std. Acc.** & **Min. Acc.** & **Max. Acc.** \\ \hline Full & 64 & 0.67 & 0.15 & 0.31 & 1.00 \\ Half & 32 & 0.67 & 0.16 & 0.31 & 1.00 \\ BCI Comp & 21 & 0.67 & 0.15 & 0.34 & 1.00 \\ OpenBCI 16 & 16 & 0.66 & 0.15 & 0.23 & 0.98 \\ OpenBCI 8 & 8 & 0.65 & 0.15 & 0.34 & 0.93 \\ Motor cortex & 24 & 0.66 & 0.16 & 0.27 & 1.00 \\ MC reduced & 9 & 0.65 & 0.15 & 0.35 & 0.94 \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Overview of mean cross-validation accuracy results for each considered sensor subset. Figure 5: Cross-validation accuracies for different sensor subsets. From this figure, we can observe that the maximum accuracy is slightly lower for both OpenBCI sensor subsets and the MC reduced subset. For the other subsets, the maximum accuracy of 1.0 is retained. We can also observe that the minimum accuracy seems to increase for some sensor subsets, while it appears to decrease for others. For median accuracy, the observed difference between groups appears slightly larger, with the OpenBCI 8 subset being the lowest. These results indicate that it should be feasible to downscale the number of sensors used for MI decoding. To investigate how performance is distributed at the level of individual participants, Figure 6 shows the average decoding accuracies on the full set of sensors for each participant separately. The figure shows that decoding accuracies for individual participants still have a large variability in most cases. Intra-subject variability is reduced compared to the overall performance. When comparing the decoding accuracy between the participant with the highest average performance (P12) and the one with the lowest average performance (P02), a statistical difference is observed (\(p<0.01\)). To determine whether the absence of a significant difference between sensor subsets persists at the individual participant level, the decoding accuracies of the participants with the highest (P12) and lowest (P02) median decoding accuracy are compared. The individual decoding accuracies for each sensor subset can be found in Figure 7a and Figure 7b, respectively. The largest difference in median accuracy can be observed in Figure 7a with a difference of 0.1 for the OpenBCI 8 subset. There are also no significant differences in mean accuracy for these individual participants, with p-values ranging between 0.55 and 0.84, and between 0.48 and 0.95, respectively. However, we can notice a reduced variance and an apparent increase in minimum accuracy for specific sensor subsets.