# Automating Stimulation Frequency Selection for SSVEP-Based Brain-Computer Interfaces
## 5 Experimental Evaluation
### Pre-Processing and Descriptive Statistics
The result of the calculation of the \(K_{fa}\) coefficient at the second harmonic in the case of the photostimulus frequency of 22 Hz (44 Hz in Table 6) can also be considered acceptable. These results suggest an extremely low ability  
Figure 5: Frequency applicability coefficient values for subject 3. The values of the \(K_{fa}\) coefficient calculated for the fundamental and second harmonics can be averaged to obtain an even more strict value of the \(K_{fa}\) coefficient, since it equally accounts for the results achieved at the fundamental and multiple harmonics of a particular photostimulus frequency. The results of calculating the mean value of the \(K_{fa}\) coefficients for the fundamental and second harmonics are shown in Figure 6 for subject 3. According to the values of this coefficient, we can assess which photostimuli frequencies are capable of producing the fastest and most stable SSVEP potentials on both the fundamental and second harmonics simultaneously. Thus, for subject 3, these are photostimuli with frequencies of 13 (O2 and Oz leads), 15-16 (O1 lead), and 17 (O2 and Oz leads) Hz. The results of calculating this coefficient for the remaining subjects are presented in Table 7.  
Based on Table 7, the most optimal (exactly equal to one) frequencies for subject 7, who demonstrates the best results among all participants in terms of the \(K_{sp}\) and \(K_{o}\) coefficients, are the photostimuli frequencies of 7-10 Hz and 12 Hz. At the same time, the subject still has enough numbers of the averaged coefficient \(K_{fa}\), as close to one as possible, namely, for \begin{table}
\begin{tabular}{c c c c c c c c} \hline \hline
**Frequency (Hz)** & **Subj 1** & **Subj 2** & **Subj 3** & **Subj 4** & **Subj 5** & **Subj 6** & **Subj 7** & **Subj 8** \\ \hline  
\hline \hline \end{tabular}
\end{table} 
Table 7: Mean \(K_{fa}\) coefficients at photostimuli frequencies, lead Oz. Figure 6: Mean frequency applicability coefficient values for subject 3.  
the photostimuli frequencies 11, 13, 15, and 21 Hz. Subject 3, on the other hand, did not show any photostimulus frequency that could be recognized as optimal in terms of this coefficient because the maximum values of the coefficients \(K_{fa}\) for the fundamental and second harmonics did not overlap with each other in the frequency range (Tables 5 and 6). Additionally, as mentioned above, for each of the participants involved in the experiment, and for each stimulation frequency, we calculated the theta-beta ratio. This ratio is considered in the context of this study as an indicator of subjective stress or discomfort experienced during prolonged stimulation at a specific frequency. Individual values of these calculated ratios are presented in Table 8.  
The analysis of the obtained data revealed that the mean value of the index for the entire sample was 6.09 (SD = 3.54) during stimulation session and 5.47 (SD = 4.14) during the resting state with eyes closed. These data, among other things, indicate high values of inter-subject variability of the measured index. When examining the plot of the index values for individual frequencies, a noticeable decline in theta-beta ratio scores is observed for males at frequencies of 20-21 Hz, with a tendency to return to average values with further increases in stimulation frequency (Figure 7). The overall downward trend of the obtained values may indicate a decrease in discomfort when transitioning from a low- to high-frequency stimulation, which is consistent with existing literature data [21]. Conducting a more detailed statistical analysis across groups that differ in terms of gender or stimulation frequency is challenging due to the small sample size within this pilot study. The resulting theta-beta ratios are then normalized to a range of 0 to 1 according to Equation (8) to obtain a discomfort coefficient \(K_{d}\).