## 3 Part I: Localization of Real and Virtual Sources in the Absence of Visual Cues
### Results
According to the Shapiro-Wilk test of normality, the elevation errors could not be assumed to be normally distributed. Therefore, the Friedman test was applied, according to which there were significant differences in the average elevation error when localizing real or different virtual sources for negative (_p_ < 10\({}^{-4}\)) and zero (_p_ = 0.01) target elevations. The multiple comparison after the Friedman test (function friendanmc in R [21]) revealed significantly different average elevation errors between real sources and V11, between real sources and V21 (for negative target elevations) and between real sources and V23 (for zero target elevations). Figure 6: **(a)** Azimuth error, averaged over 14 subjects and all target sources, when localizing real sources in TestReal (Real Source) and virtual sources in TestVR (generated with V11, V13, V21, V23 and HTK). Horizontal bars indicate significant differences (post-hoc multiple comparisons with Bonferroni correction, \(p\) < 0.05). **(b)** Azimuth error, averaged over 14 subjects for target sources grouped into front and back. All error bars indicate 95% confidence intervals. To offer some information about the signs of the response elevations, the upper part of Figure 7 shows, for each average elevation error split into N, Z and P, the percentages of response elevations which were positive, zero or negative. To calculate these percentages, response elevations were classified as positive or negative, if they were above \(+5^{\circ}\) or below \(-5^{\circ}\), respectively; and they were classified as zero if they were between \(-5^{\circ}\) and \(+5^{\circ}\). With real sources, the signs of response elevations were in good agreement with the signs of target elevations, i.e., the majority of negative, zero and positive real target sources were perceived correctly as negative, zero and positive, respectively. Nevertheless, it should be noted that, as shown in the lower part of Figure 5, the response elevations for TestReal extended from below \(-50^{\circ}\) to above \(+70^{\circ}\), although the target elevations varied between \(-20^{\circ}\) and \(+25^{\circ}\) only. Indeed, subjects tended to underestimate negative elevations and overestimate positive elevations. This was presumably caused by response mapping to the GUI, which included the additional step of translating the perceived elevation in the vertical angle to the horizontal plane, which apparently could not be performed correctly by the subjects. With virtual sources, on the other hand, accordance of the signs between target and response elevations could be observed only in a weak form for V23 and HTK; for V11, V13 and V21, target elevations were perceived as zero or positive most of the time, regardless of the sign of the target elevation. Additionally, with HTK, a large percentage of zero target elevations were perceived as positive. **Externalization rate:** Externalization rate was defined as the percentage of the time a target source was perceived as outside the head. The responses given for the source distance were converted into an externalization rate by dividing them into two groups: \"not externalized\" (scores 0 and 1) and \"externalized\" (scores 2, 3 and 4), and then calculating the percentage of responses classified as externalized. Figure 8 shows the externalization rate over target azimuths. Figure 7: Average elevation error, when localizing real sources in TestReal (Real Source) and virtual sources in TestVR (generated with V11,V13, V21, V23 and HTK). (**Bottom**) Absolute error, averaged over 14 subjects for negative (N), zero (Z) and positive (P) target elevations. Error bars indicate 95% confidence intervals. (**Top**) Percentages of response elevations, which were perceived as negative (below \(-5^{\circ}\)), zero (between \(-5^{\circ}\) and \(+5^{\circ}\)) or positive (above \(+5^{\circ}\)). As the polar diagrams in Figure 8 show, real sources were almost always externalized, which was an expected result.