# Investigating the Potential Use of EEG for the Objective Measurement of Auditory Presence
## 3 Results  
### Experiment 1  
First, data for 2 of the 18 participants were excluded since they reported being distracted during the experiment. Then, data for another 3 participants were excluded by the algorithm due to the strict criteria for estimating the PAF. The algorithm requires the following conditions to be met to produce a valid estimate of PAF: (1) the peak frequency must appear within the alpha band's frequency range; (2) the peak power must exceed the minimum amount of normalized power estimated by the algorithm to qualify as a potential PAF candidate; (3) the peak's height must exceed all other competitors by at least 20% ; (4) at least three channels should yield valid PAF estimates, in order to calculate cross-channel averages [47]. Thus, 13 sets of valid data were collected, as shown in Table 1.  
It can be observed that the presence scores for Program A were generally greater than those for Program B. A paired \(t\)-test was carried out, which showed that the difference in presence scores was significant at a significance level of 0.05 (\(p\) = 1.98 \(\times\) 10\({}^{-4}\)). In contrast, the PAF estimates for Program A were generally lower than those for Program B. The results of the paired \(t\)-test also demonstrated that the PAF estimates for Programs A and B were significantly different (\(p\) = 0.040). That is, when participants subjectively experienced higher levels of presence, they tended to show a lower PAF.  
To further investigate the correlation between the change in presence score and PAF, a McNemar test was conducted. This is a non-parametric statistical test for paired data within the scope of chi-squared tests [48]. The data were first transformed into a dichotomous format, as shown in Table 2. The transformation rule was that if the presence score for  
\begin{table}
\begin{tabular}{c c c c c c} \hline \hline \multirow{2}{*}{**Participant**} & \multirow{2}{*}{**Group**} & **Presence Score (A)** & **Presence Score (B)** & **PAF (A)/Hz** & **PAF (B)/Hz** \\ \hline
1 & I & 26 & 10 & 9.733 & 9.935 \\
2 & I & 34 & 21 & 9.250 & 9.776 \\
3 & I & 28 & 33 & 11.506 & 10.666 \\
4 & I & 34 & 16 & 9.511 & 9.743 \\
5 & I & 32 & 20 & 10.012 & 11.629 \\  
Program A was greater than that for Program B, it would be marked as 1, and otherwise it would be marked as 0. Likewise, if the PAF for Program A was lower than that for Program B, it would be marked as 1. Please note that the transformation rules for presence score and PAF were different to account for their opposite change direction.  
In this way, the McNemar test was conducted and revealed no significant differences (\(p=1.000\)). Furthermore, the Pearson correlation coefficient was 0.677 (\(p=0.011\)). Both these results indicated that if the presence score for Program A was higher than that for Program B, it was highly likely that the PAF for Program A was lower than that for Program B. That is, using the presence score and the PAF to determine the level of presence yielded nearly the same results. Another statistical metric, Cohen's kappa, could also be used. In general, this is used to determine whether different observers would reach the same conclusion. Kappa is standardized to a scale of \(-1\) to 1. Kappa values of 1 indicate perfect agreement, kappa values of 0 indicate agreement equivalent to chance, and negative values indicate agreement less than chance [49]. The results showed kappa = 0.629 (\(p=0.015\)), which indicated that there was an agreement between these two criteria (presence score and PAF) for determining the level of presence.