# Assessing Ambisonics Sound Source Localization by Means of Virtual Reality and Gamification Tools
## 4 Results
### Sound Localization Second Round: Horizontal and Vertical Planes  
In the second round, sound localization in the horizontal and vertical planes was assessed, generating responses with both azimuth and elevation information. Consequently, the results of this second round are treated as spherical data. First, it was necessary to evaluate the normality of the data to determine whether to use parametric or non-parametric statistics. The Rayleigh test was employed to assess the normality of the data [31]. The Rayleigh test statistic (Z) was 115.04 (\(p<0.001\)), indicating that the sound localizations were significantly different from a uniform distribution (\(\alpha=0.05\)). This suggests that the data are clustered or concentrated in specific directions. Therefore, the next step was to analyze whether these groupings differed from the actual positions where the stimuli were played. Given that the data do not conform to normality, a non-parametric statistical analysis was necessary to assess whether the perceived locations matched the actual locations where the stimuli were played. The Hodges-Ajne test provides a non-parametric measure to compare a fixed angular position, which, in this case, is the actual location where the audio was played, against the population mean of participants' responses [32; 33]. The results of the Hodges-Ajne test are shown in Figure 7. Significant differences were observed for the angles 0\({}^{\circ}\), 45\({}^{\circ}\), 90\({}^{\circ}\), 135\({}^{\circ}\), 225\({}^{\circ}\), 270\({}^{\circ}\), and 315\({}^{\circ}\) at both elevations (\(p<0.05\)), indicating that the sound localizations were significantly different from a uniform distribution but aligned with the actual location where the stimuli were played. In contrast, for the angles 180\({}^{\circ}\) at both elevations (0\({}^{\circ}\) and 35\({}^{\circ}\)), the \(p\)-values (\(p=0.121\)) suggest that the responses were not significantly different from a uniform distribution around the reproduced angle. It is also interesting to analyze whether the participants' responses were different in perception of elevation. That case only occurs at four angles where the sound was reproduced at 0\({}^{\circ}\) and 35\({}^{\circ}\) elevation. These cases are at 0\({}^{\circ}\), 90\({}^{\circ}\), 180\({}^{\circ}\), and 270\({}^{\circ}\). In this case, we want to compare two population samples--responses for elevation at 0\({}^{\circ}\) and at 35\({}^{\circ}\)--at the four angles evaluated (0\({}^{\circ}\), 90\({}^{\circ}\), 180\({}^{\circ}\), and 270\({}^{\circ}\)). The Mardia-Watson-Wheeler (MWW) test is a nonparametric statistical method used to compare the distributions of two or more angular populations [30]. Therefore, the MWW test was performed for the angles 0\({}^{\circ}\), 90\({}^{\circ}\), 180\({}^{\circ}\), and 270\({}^{\circ}\) at two different elevations (0\({}^{\circ}\) and 35\({}^{\circ}\)). The results indicate a significant main effect of elevation on the sound localization data across the angles 0\({}^{\circ}\), 90\({}^{\circ}\), 180\({}^{\circ}\), and 270\({}^{\circ}\) (\(\chi^{2}=26.9877\), \(p<0.0001\)), suggesting that the distributions of responses differ significantly between the two elevations.