## 4 Experimental Investigations
### Subjective Experiment for Auditory Localization
#### 4.3.3 Results and Analysis  
Figure 13 shows the localization results of all the eight subjects by using the presented individualized HRTFs and the non-individualized ones of KEMAR dummy head. X-axis and Y-axis stand for the real azimuth and the perceived azimuth, respectively. Perfect correlation between target azimuth and response judgment corresponds points on line A on these graphs. That means the subjects' judgments were exactly the same as the real directions. On the other hand, points out of line B and line C correspond to localization errors larger than 45\({}^{\circ}\). Besides, points on the coordinate line of 180\({}^{\circ}\) correspond to front-back confusions. It can be observed that the individualized HRTFs achieve slightly better localization performance, both in accurate localization and smaller localization error. \begin{table}
\begin{tabular}{c c c c} \hline \(\mathbf{p}\) & \(\mathbf{H_{0}}\) & Mean\_ind & Mean\_non \\ \hline
0 & Rejected & 2.5521 & 2.0625 \\ \hline \end{tabular}
\end{table} 
Table 6: Post-hoc for ANOVA. Mean\_ind and mean\_non denote the mean classes of the individualized HRTFs and the non-individualized ones, respectively. Figure 13: Results of the subjective localization experiments, (**a1–a3**) denote the results of the three repetitions for the presented individualized HRTFs, (**b1–b3**) denote the results of the three repetitions for non-individual HRTFs. Different markers denote the results of different subjects, points on line A denote the correct perception results, points between line B and line C denote the results with minor localization errors. As a supplementary to the data shown in Figure 13, the localization accuracy rate, the average error angle and mean of the standard deviation of the error were calculated, and the results are listed in Table 7.  
It can be found from Table 7 that the localization accuracy rates of the individualized HRTFs were larger than those of non-individual ones, except subject 7. The average localization errors of the individualized HRTFs were smaller than the non-individualized ones for all the participants, even though the difference was not obvious for subject 8. Moreover, the standard deviations of the individualized HRTFs were smaller than the non-individualized ones for participants, except subject 8. The individualized HRTFs seemed to be preferable in auditory localization. To determine whether the experimental results were valid, two-way repeated variance analysis (ANOVA) was made for the localization errors of each subject under the significant level of \(\alpha=0.05\). The two factors were HRTF species and testing azimuth. It was hypothesized that both the HRTF species and testing azimuth had no significant effect on the localization errors (\(H_{0}\)). \(p\) denotes the probability of making mistakes regarding to rejecting \(H_{0}\). \(H_{0}\) was kept when the probability \(p\) was larger than \(\alpha\), while \(H_{0}\) was rejected when \(p\) was less than \(\alpha\). The result of ANOVA was listed in Table 8. As can be seen from Table 8, the HRTF species, testing azimuth and their interaction had significant effect on the localization errors. Consequently, the localization experiment was proved valid. Next, the Least Significant Difference (LSD) for independent samples was employed as the post-hoc of ANOVA to determine whether the individualized HRTFs performed better than the non-individualized ones in the binaural localization experiment. The localization errors of the testing HRTF species were hypothesized to be of no significant difference (\(H_{0}\)). \(p\) stands for the probability of making mistakes regarding to rejecting \(H_{0}\). \(H_{0}\) was kept when \(p\) was larger than \(\alpha\) while \(H_{0}\) was rejected when \(p\) was less than \(\alpha\).