# Auralization of High-Order Directional Sources from First-Order RIR Measurements
## 3 Listening Experiment--Comparative Study
### Results and Discussion  
The positions of the perceived sound objects are given in the Cartesian coordinate system with the listener at the origin. As results show little to no variation in height (\(z\) coordinate), we focus on an evaluation of the \(x,y\) coordinates. Overall inspection in two dimensionsIn a first processing step, outliers are defined as responses lying outside a Mahalanobis distance (in estimated standard deviations) of three within a preliminary, non-robust analysis. After removal of the outliers, we use bivariate statistical analysis to estimate the means and their standard deviation and 95% confidence region according to [PERSON]'s T2 distribution (see [51] Ch. 3). The result of this analysis are depicted in Figure 7, where data points, outliers, and standard deviation and confidence region ellipses are indicated as dots, crosses, and not-filled and filled ellipses, respectively. In case of similar sizes of the statistical spreads, statistically significant differences may be inspected by observing whether the mean value of one condition lies outside the 95% (\(p<0.05\)) confidence ellipses of the other conditions. While each row of Figure 7 depicts the results for all auralization techniques and a certain beam direction \(\varphi_{S}\), each column shows the perceived position of the auditory events per technique and for all beam directions \(\varphi_{S}=[0^{\circ},-36^{\circ},-82^{\circ},180^{\circ},90^{\circ}]\). Thus, comparison within the rows is used to identify differences across auralization techniques, and comparison within each column gives indication if each auralization technique is able to reproduce the well-described perceptual effects of the IKO [7], or similar devices. These effects are explained by exciting pronounced propagation paths and dimming the direct path, which is known to evoke auditory events whose position needs not coincide with the physical source. Moreover, [PERSON] et al. [5] showed that the IKO's directivity allows for altering the DRR and thus, for controlling the perceived distance, e.g., by steering the beam towards or away from the listener. Overall, we observe that all techniques are qualitatively able reproduce the perceptual effects known from studies involving the physical IKO [5,7], cf. columns in Figure 7. The ratings show a clear consensus with the expected positions of the auditory events, i.e., by steering a beam towards a reflector \(\varphi_{S}=[-36^{\circ},-82^{\circ},90^{\circ}]\) the auditory event is located near the respective reflector baffle. Moreover, steering the beam towards \(\varphi_{S}=0^{\circ}\) away from the listener and \(\varphi_{S}=-180^{\circ}\) towards the listener either evokes an auditory event behind the physical IKO or a very close one, respectively. We found that the ratings per beam direction \(\varphi_{S}\) are significantly different for all auralization techniques. A detailed analysis of the differences related to the auralization techniques, cf. rows in Figure 7, is done for independent univariate attributes. These univariate attributes were not asked separately in the listening experiment, but they are obtained for the subsequent analysis by mapping of the responses to the following independent attributes (i) localizability, (ii) the direction, and (iii) distance. This analysis is based on the following considerations. As defined by [PERSON] et al. [52], localizability is related to the ability to asses the spatial extent and location of a sound source. If this task is difficult, the localizability is low and if localizability is high, a sound source is clearly delimited. Moreover, localizability is often associated with the perceived extent of as sound source and thus we assume that the area of the standard deviation ellipse can be used as an indication of the localizability. Figure 7: Bivariate statistical analysis of the perceived position of the auditory event per beam direction \(\varphi_{S}\) (columns) and per auralization technique (rows).