## 3 Results
### Localization Accuracy Results  
The statistical analysis is based on repeated measures of analysis of variance (ANOVA) [32] and was performed according to [33]. Since there were 25 independent participants with multiple measured data points, their results with the same parameters (HRTF, vertical or horizontal plane, starting or ending angle) were averaged as independent data points. In total, each participant contributed 12 data points for the analysis. For each of the three HRTFs, there were horizontal or vertical starting and ending perceived sound source directions represented by their azimuth or elevation angles, respectively. The obtained data that was statistically analyzed were the absolute (non-negative) values of the deviation from the correct azimuth (or elevation) starting and ending directions of the virtual sound source. If the occasional missing data arose from the participant's unsureness about the starting or ending angle of the virtual sound source, the average absolute deviation for the corresponding data point was computed without the missing value by utilizing other available deviation data from the same data point. There was always at least one selected angle for each data point for each participant, resulting in no missing data from the independent data points for all the participants, which was an important factor regarding the proper usage of repeated measures in ANOVA. Since there were a small number of outliers (less than two outliers for every 25-point data set), the mean/median imputation technique was employed to adapt outlier values for ANOVA. Normality testing using [PERSON]'s test was performed on all data sets, demonstrating that the data are normally distributed. Finally, [PERSON]'s test of sphericity was used to verify that the null hypothesis of equivalent variances of differences was fulfilled. Box and whisker plots were generated for the absolute deviation from true horizontal and vertical starting and ending points, as presented in Figure 4.  
ANOVA results were calculated as follows:  
* For the horizontal starting angle: F(48,2) = 7.052, \(p\) = 0.002;
* For the horizontal ending angle: F(48,2) = 3.223, \(p\) = 0.049;
* For the vertical starting angle: F(48,2) = 10.113, \(p\) = 0.000216;
* For the vertical ending angle: F(48,2) = 4.542, \(p\) = 0.016. The data obtained from the experiment indicates the existence of statistically significant differences for all four investigated parameters regarding the HRTF that was used. To further assess the performance of individual HRTFs compared to other HRTFs, a pairwise comparison was performed, and the results are presented in Table 1. \begin{table}
\begin{tabular}{c c c c c c c} \hline \hline  & \multicolumn{2}{c}{**Gen\&Oth Pair 1**} & \multicolumn{2}{c}{**Ind\&Gen Pair 2**} & \multicolumn{2}{c}{**Ind\&Oth Pair 3**} \\ \hline  & \(p\)**-Value** & **adj. \(p\)-Value 4** & \(p\)**-Value 4** & \(p\)**-Value 4** & \(p\)**-Value 4** & \(p\)**-Value 4** \\ \hline Horizontal starting angle & 0.002 & 0.006 & 0.005 & 0.015 & 0.894 & 1.000 \\ Horizontal ending angle & 0.031 & 0.094 & 0.086 & 0.256 & 0.623 & 1.000 \\ Vertical starting angle & 0.214 & 0.642 & 0.002 & 0.007 & 0.0006 & 0.002 \\ Vertical ending angle & 0.674 & 1.000 & 0.007 & 0.022 & 0.016 & 0.050 \\ \hline \hline \end{tabular}  
* Comparison between generic HRTF and the individual HRTF of another person. 2 Comparison between the participant’s own individual HRTF and generic HRTF. 3 Comparison between the participant’s own individual HRTF and the individual HRTF of another person. 4 \(p\)-value adjusted with the Bonferroni correction.  
\end{table} 
Table 1: Pairwise comparison of differences between HRTF sets. Figure 4: Box and whisker plots for the absolute deviation from a true angle as the measure of localization accuracy, depending on the used HRTF, for: (**a**) the horizontal starting angle; (**b**) the horizontal ending angle; (**c**) the vertical starting angle; and (**d**) the vertical ending angle of the virtual sound source.