# Quantifying Auditory Presence Using Electroencephalography
## 3 Results  
### Experiment 1  
In Experiment 1, 16 sets of valid data were collected. Data from two participants were ruled out due to their poor condition during the experiment. One participant in Group I reported that he was sleepy and could not concentrate on the experiment, and one participant in Group II reported that he got distracted by his phone. The presence scores calculated from the questionnaires are displayed in Figure 3, in which Participant 1-8 belonged to Group I, and Participant 9-16 belonged to Group II. It demonstrates a dramatic difference in the presence score between Programs A and B. Presence score rated for Program A was higher than B for almost all participants except Participant 10. The presence score was normally distributed according to the Kolmogorov-Smirnov method (for Program A, \(p\) = 0.104; for Program B, \(p\) = 0.466). Given that each participant rated the presence score for Programs A and B successively, the presence score for Programs A and B should be treated as pairs when evaluating the difference between them. The paired \(t\)-test showed that the difference in presence score was significant at a significance level of 0.05 (\(p\) = 1.28 \(\times 10^{-4}\)). Besides, paired \(t\)-tests were also carried out on the difference in the ratings of each question between the two programs. The results showed that there was significant difference between the two programs for all four questions. (For Question 1, \(p\) = 2.85 \(\times 10^{-4}\); for Question 2, \(p\) = 1.25 \(\times 10^{-4}\); for Question 3, \(p\) = 3.195 \(\times 10^{-3}\); for Question 4, \(p\) = 8.2 \(\times 10^{-5}\).) Calculated EEG indices in Experiment 1 are shown in Table 1. The absolute powers of theta, alpha and beta and a series of power ratios are presented. The power ratios used were T/A (theta/alpha), T/AB (theta/alpha+beta), T/B (theta/beta) and A/B (alpha/beta). It can be seen that the distribution of these EEG indices fluctuated greatly. For different participants, the fluctuation was large, and even for the same participant in different stages, the indices still varied vastly. The values of all EEG indices for both Programs A and B (each column of Table 1) did not meet the normal distribution (\(p\) < 0.05) according to the Kolmogorov-Smirnov method, indicating the paired t-test was no longer suitable. Thus, the Wilcoxon signed rank test [46] was used instead, which does not require the data to be normally distributed. \begin{table}
\begin{tabular}{c c c c c c c c c c c c c c c} \hline \hline \multirow{2}{*}{Participant} & \multicolumn{2}{c}{**Theta (\(\mu\) V\({}^{2}\)/Hz)**} & \multicolumn{2}{c}{**Alpha (\(\mu\) V\({}^{2}\)/Hz)**} & \multicolumn{2}{c}{**Beta (\(\mu\) V\({}^{2}\)/Hz)**} & \multicolumn{2}{c}{**T/A**} & \multicolumn{2}{c}{**T/AB**} & \multicolumn{2}{c}{**T/B**} & \multicolumn{2}{c}{**A/B**} \\ \cline{2-13}  & **A** & **B** & **A** & **B** & **A** & **B** & **A** & **B** & **A** & **B** & **A** & **B** & **A** & **B** \\ \hline
1 & 6.445 & 5.354 & 141.570 & 95. Results of the Wilcoxon signed rank test for each EEG index pair (for example, theta power for Programs A and B) are shown in Table 2. It can be seen that only the difference in beta power between Programs A and B was significant at a significance level of 0.05. The differences in alpha power, T/AB and T/B were close to significant. Because of the significant difference in both presence score and specific EEG indices between Programs A and B, it is worth analyzing the correlation between them. To this end, we used the chi-squared test, a non-parametric statistic. Data were first transformed into the dichotomous format for further processing, as shown in Table 3. If the presence score for Program A is higher than B, it would be marked as 1, and 0 if otherwise. Meanwhile, if the EEG index, for example, T/B for Program A is higher than B, it would be marked as 1 as well.