# Auralization of High-Order Directional Sources from First-Order RIR Measurements
## 3 Listening Experiment--Comparative Study
### Results and Discussion
Data points, outliers, and standard deviation and 95% confidence region ellipses are indicated as dots, crosses, and not-filled and filled ellipses, respectively. The two-dimensional source position indications yield a clear bivariate distribution, cf. Figure 7, and with a mean angular offset between the main axis of the standard deviation ellipse and the mean perceived direction \(\varphi_{p}\) (defined by listener and mean position of the perceived sound) of only \(3.52^{\circ}\), we may assume the variations to be independent along the perceptual axis of distance and direction. As this visual evaluation may be difficult, we use a Wilcoxon signed-rank test [53] with a Bonferroni-Holm correction [54] to determine \(p\)-values of pairwise comparisons between test conditions and define \(p<0.05\) as significantly different throughout this article. We employ nonparametric statistics as we do not assume a normal distribution of ratings and due to the correction ([PERSON], 2020, Bonferroni-Holm Correction for Multiple Comparisons, [[https://www.mathworks.com/matlabcentral/fileexchange/28303-bonferroni-holm-correction-for-multiple-comparisons](https://www.mathworks.com/matlabcentral/fileexchange/28303-bonferroni-holm-correction-for-multiple-comparisons)]([https://www.mathworks.com/matlabcentral/fileexchange/28303-bonferroni-holm-correction-for-multiple-comparisons](https://www.mathworks.com/matlabcentral/fileexchange/28303-bonferroni-holm-correction-for-multiple-comparisons))) \(p\)-values can exceed the expected range and thus \(p>1\) is valid. The _Matlab_ script of the statistical analysis and the raw listener ratings are available online in the accompanying project ([[https://phaidra.kug.ac.at/o:104416](https://phaidra.kug.ac.at/o:104416)]([https://phaidra.kug.ac.at/o:104416](https://phaidra.kug.ac.at/o:104416))). A detailed discussion of the results in terms of localizability, direction, and distance is given below. LocalizabilityThe median values and 95% confidence interval of the area under the standard deviation ellipse pooled for all beam directions \(\varphi_{S}\) are depicted per auralization technique in Figure 8. While the median values indicate highest and lowest localizability for the \(Dy\) and \(Em\) techniques, respectively, the differences among all techniques is not significant (\(p>1.7\)). DirectionAll ratings are transformed into a polar coordinate system with the listener at the center and are analyzed for azimuth and radius, i.e., direction and distance, separately. Due to the findings in [22] we assume that the \(Dy\) auralization can be used as the reference condition. Thus, the \(p\)-values are given for testing the significance levels between \(Dy\) and all other conditions. The median values and 95% confidence intervals for all beam directions and auralization techniques are shown in Figure 9 and the in \(p\)-values between the reference condition (\(Dy\)) and the other techniques are presented in Table 1.  
Figure 8: Median value and 95% confidence interval of the area under the standard deviation ellipse pooled for all beam directions \(\varphi_{S}\). Despite an almost symmetrical set-up (cf. Figure 5) and only a slight change in beam direction, the direction results for the beams steered towards \(\varphi_{S}=-82^{\circ}\) and \(\varphi_{S}=90^{\circ}\) show some deviation. Ratings for \(\varphi_{S}=90^{\circ}\) are less consistent (larger confidence interval) and the auditory event is localized more closely to the IKO for all techniques, when compared to \(\varphi_{S}=-82^{\circ}\). This can be explained when taking a closer look at the (ideal) 3 rd-order max-\(r_{\text{E}}\) weighted beam pattern as depicted in Figure 5. While for \(\varphi_{S}=90^{\circ}\) a side lobe is pointing towards the listener, this side lobe is almost avoided (\(-5\) dB lower) for \(\varphi_{S}=-82^{\circ}\). Overall, there is no significant difference between the directional mapping of the \(Dy\) and \(Sr\) techniques. For all other techniques we found significant differences for some beam directions.