## 4 Experimental Investigations
### Subjective Experiments for Discrimination Degree of Given Azimuths
#### 4.2.3 Results and Analysis  
Figure 11 gives the results of the subjective experiment for discrimination degree of given azimuths, in which an upper and shorter box implies a better evaluation results. As shown in Figure 11, stimuli with individualized HRTFs are evidently easy to discriminate the azimuth information. Despite that the stimuli at directions of \(90^{\circ}\) and \(270^{\circ}\) are easy to discriminate with non-individualed HRTFs, the individualized ones even improve the discrimination degree. At azimuths of \(30^{\circ}\) and \(45^{\circ}\), the performance of the individualized HRTF species is obviously superior to the non-individualed species in the 25 th percentiles, the median and the 75 th percentiles. Moreover, the stimuli with azimuths in front of the listening subject (left part of Figure 10(a) and right part of Figure 10(b) are noted easy to discriminate than the ones at the back of the listener (right part of Figure 10(a) and left part of Figure 10(a)). This is caused by the human auditory nature of being sensitive to the front directions. \begin{table}
\begin{tabular}{c c c c c c} \hline \hline
**Discrimination Degree** & **Unconspicuous** & **Detectable** & **Obvious** & **Very Obvious** & **Extremely Obvious** \\ \hline Class & 1 & 2 & 3 & 4 & 5 \\ \hline \hline \end{tabular}
\end{table} 
Table 4: Directional discrimination degree class. Figure 11: Box-plot for results of the subjective experiment for discrimination degree of given azimuths. (**a**) and (**b**) represent the azimuths in right and left of the subject, respectively. X-axis and Y-axis denote the testing azimuths and the discrimination degree showed in Table 4, respectively. Red and blue boxes denote the HRTF species of the presented individualization method and KEMAR dummy head. Box edges mark the 25 th and 75 th percentiles, black dots in a circle mark the median. Outliers are indicated by +. To determine whether the individualized HRTFs perform better than the non-individualized ones in this subjective experiment, statistical analysis was made. First of all, a two-way repeated variance analysis (ANOVA) was made under the significance level of \(\alpha\) = 0.05 to verify the validity of the experimental results. It was hypothesized that both the testing HRTF species and azimuths had no significant effect on the subjects (\(H_{0}\)). The hypothesis was kept if \(p\) was larger than \(\alpha\) (\(p\) stands for the probability of making mistakes regarding to rejecting \(H_{0}\)). The hypothesis was rejected if \(p\) was less than \(\alpha\), the factor was thus considered to have significant effect on the subjects. The result of ANOVA was shown in Table 5. As can be seen from Table 5, both the HRTF species and the testing azimuth had significant effect on the participants, while the interaction of HRTF species and azimuth had no significant effect on the participants. Consequently, the psychoacoustic experiment was considered to be 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 this experiment. It was hypothesized that there was no significant difference between the evaluation results of individualized HRTFs and non-individualized ones (\(H_{0}\)). \(p\) 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 \(\alpha\). Under the significant level of \(\alpha\) = 0.05, the result of LSD was given in Table 6 and Figure 12. As can be seen from Table 6, the evaluation results were significantly different between individualized HRTFs and the non-individualized ones. The mean class of the individualized HRTFs was larger than that of the non-individualized ones. The individualized HRTFs were consequently considered performing better than the non-individualized ones in this psychoacoustic experiment.