## 4 Part II: The Impact of Head Tracking on the Localization Performance
### Results  
Figure 10 shows response vs. target azimuths and elevations reported by 14 subjects in TestDynamic and TestStatic. Responses marked with a \(\times\) indicate front-back reversals and the response marked with a \(\diamondsuit\) for HTK indicates an invalid localization (for the same subject as in Part I) and was excluded from further analysis. **Azimuth:** Figure 11a shows the azimuth error averaged over 14 subjects and 15 target source positions for different BRIRs in TestDynamic and TestStatic. Front-back reversals were excluded from the error calculation. According to the Shapiro-Wilk test of normality, the azimuth error could be assumed to be normally distributed. Therefore, a paired \(t\)-test was applied which revealed that for all BRIRs, the average azimuth error was significantly higher in TestStatic compared to TestDynamic (\(t\)-values shown in Figure 11a). In Figure 11b, the average azimuth error is shown for the 14 subjects separately for target positions grouped into front and back. For target sources both in front and behind, the average azimuth error was higher in TestStatic compared to TestDynamic. Since front-back reversals were excluded from the azimuth error calculation, the results indicate that for cases where no front-back reversals occurred, the azimuth error was smaller with head movement, though limited to the frontal hemisphere, than without head movement. **Elevation:** The lower part of Figure 12 shows the elevation error averaged over 14 subjects in both tests, separately for negative, zero and positive target elevations. The upper part of Figure 12 shows the percentages of response elevations which were positive, zero or negative, calculated in a similar way as in Section 3.2. According to the Shapiro-Wilk test of normality, the average elevation errors could not be assumed to be normally distributed. Therefore, the Wilcoxon signed-rank test was applied separately to the negative, zero and positive target elevations, which revealed no significant differences in the average elevation error in TestDynamic compared to TestStatic for any of the groups of positive, zero and negative target elevations and for any of the BRIRs. This means that there was apparently no effect of head movement on the vertical localization accuracy. The accordance of  
Figure 10: Response azimuth or elevation (ordinate) vs. target azimuth or elevation (abscissa). (**Left**) Results when listening to virtual sources generated with V11, V21, V23 and HTK in TestDynamic. (**Right**) Results when listening to virtual sources generated with V11\({}_{s}\), V21\({}_{s}\), V23\({}_{s}\) and HTKs in TestStatic. Responses marked with a \(\times\) indicate front–back reversals and the response marked with a \(\diamondsuit\) indicates an invalid localization. Dashed lines represent possible subject responses in case of a perfect front–back confusion. the signs between target and response elevations could be observed, though in a weak form, only for HTK and HTK\({}_{\text{s}}\) and for V23 and V23\({}_{\text{s}}\). **Externalization rate:** To calculate the externalization rate as defined in Part I, the responses given for the source distance were divided into two groups: \"not externalized\" (scores 0 and 1) and \"externalized\" (scores 2 and 3). Figure 13 shows the externalization rate over the target azimuths. Figure 11: (**a**) Azimuth error, averaged over 14 subjects and all target sources when localizing virtual sources generated with V11, V21, V23 and HTK in TestDynamic and with V11\({}_{\text{s}}\), V21\({}_{\text{s}}\), V23\({}_{\text{s}}\) and HTK\({}_{\text{s}}\) in TestStatic. Horizontal bars indicate significant differences (according to paired \(t\)-test). (**b**) Azimuth error in TestDynamic and TestStatic, averaged over 14 subjects for target sources grouped into front and back. All error bars indicate 95% confidence intervals.