## 3 Part I: Localization of Real and Virtual Sources in the Absence of Visual Cues
### Results  
Figure 5 shows response vs. target azimuths and elevations for TestReal (Real Source) and TestVR (V11, V13, V2, V23, HTK). Each circle represents an individual response of a subject. If a pair of target and response azimuths were on different sides of the interaural axis, a front-back reversal was suspected. Responses classified as front-back reversals are indicated with \(\times\) in the upper row of Figure 5, for which target and response pairs within \(\pm\)7.5\({}^{\circ}\) off the interaural axis were not checked for reversals. For one subject, some target and response azimuths were swapped in the front-back and left-right directions. These cases, indicated with \(\diamondsuit\) in Figure 5, were suspected to be caused either by wearing the headphones inversely (left and right ears switched) or not resetting the head tracker, and were therefore classified as invalid and discarded from further analysis. **Azimuth:** The azimuth error was calculated as the absolute difference between target and response azimuths. Front-back reversals were excluded from the error calculation. Figure 6a shows the azimuth error averaged over 14 subjects and 15 target positions. With real sources in TestReal, the average azimuth error was 8\({}^{\circ}\). In TestVR, a comparable average azimuth error as that of real sources was achieved with V11 (8.3\({}^{\circ}\)). The largest average azimuth errors occurred with HTK (9.9\({}^{\circ}\)) and with V21 (10.1\({}^{\circ}\)), followed by V23 (11.7\({}^{\circ}\)) and V13 (13.3\({}^{\circ}\)). VAH syntheses including horizontal and non-horizontal directions in the calculation of the spectral weights (V13 and V23) led to larger average azimuth errors  
Figure 5: **(Top)** Response azimuth (ordinate) vs. target azimuth (abscissa) and (**Bottom**) response elevation (ordinate) vs. target elevation (abscissa), when listening to real sources in TestReal (Real Source) or to virtual sources in TestVR (generated with V11, V13, V21, V23 and HTK). The circles represent the responses of the 14 subjects. Responses marked with \(\diamondsuit\) indicate invalid localizations. Responses classified as front-back reversals are marked with \(\times\) in the top row. Dashed lines represent possible subject responses in cases of perfect front-back confusion. compared to real sources and VAH syntheses including only horizontal directions (V11 and V21). According to the Shapiro-Wilk test of normality, the azimuth error could be assumed to be normally distributed. Accordingly, a one-way repeated-measures ANOVA was performed, which revealed a significant difference in the azimuth error when localizing real or different virtual sources (F(5, 65) = 10.1, \(p\) < 0.001). The post-hoc multiple comparison with Bonferroni correction (_p_ < 0.05) indicated significantly higher average azimuth errors for V13 compared to V11 and real sources. In Figure 6b, the average azimuth error over 14 subjects is shown separately for target positions grouped into front and behind. Remember that virtual sources in TestVR were rendered for horizontal head orientations restricted to the frontal range (\(-90^{\circ}\leq\theta_{h}\leq+90^{\circ}\)), and in TestReal, subjects were asked not to move their heads beyond this range. With the exception of V23, the average azimuth errors were lower for sources in front than sources behind. For target sources in the frontal hemisphere, the subject could rotate his head towards the target source to a region where the interaural differences and the minimum audible angle were the smallest. When facing the sound source directly, subjects could give more accurate azimuth responses than they could to target sources behind. **Elevation:** The elevation error was calculated as the absolute difference between target and response elevations, separately for negative (\(<\)0\({}^{\circ}\), **N**), zero (=0\({}^{\circ}\), **Z**) and positive (\(>\)0\({}^{\circ}\), **P**) target elevations. The lower part of Figure 7 shows the elevation error averaged over 14 subjects.