## 4 Results
### Removing the Reverberant Parts in BRIRs  
Figure 9 shows the mean externalization ratings of the test stimuli for the \"RN\" (diamonds), \"RL\" (triangles), \"RR\" (circles), and \"RB\" (squares) conditions in different azimuth angles. For non-processed BRIRs (\"RN\" condition), the mean externalization ratings were overall high across different azimuth angles and highly consistent with the ratings for the \"SN\" condition. The degree of perceived externalization reduced substantially by removing the reverberant parts in BRIRs of both ears for all azimuth angles (\"RB\" condition).  
In the case of the \"RB\" condition, the mean externalization ratings increased as the sound source moved from frontal to lateral incidence angles, but they were overall lower than 1.0, corresponding  
Figure 9: Mean externalization ratings from zero (the sound is in my head) to three (the sound is externalized and at the position of the loudspeaker) across listeners for the “RN” (diamonds), “RL” (triangles), “RR” (circles), and “RB” (squares) conditions in different azimuth angles. The error bars indicate the standard deviations of the mean values.  
to sound sources being internalized or very close to subjects' heads. In addition, the ratings were lower than those for the other three conditions for all azimuth angles. For a frontal sound source, the externalization ratings were almost the same for the \"RL\" and \"RR\" conditions. In the case of negative azimuth angles, the externalization ratings were substantially higher for the \"RL\" condition than the \"RB\" and \"RR\" conditions and slightly lower than the \"RN\" condition. The ratings for the \"RR\" condition were a little higher than those for the \"RB\" condition. In contrast, for positive azimuth angles, the ratings were higher for the \"RR\" condition than the \"RB\" and \"RL\" conditions and a little lower than the \"RN\" condition. Furthermore, the ratings were slightly higher for the \"RL\" condition than the \"RB\" condition.  
An ANOVA with post-hoc-test (5% significance level with Bonferroni adjustment) was performed to show the significant differences of externalization ratings among the \"RN\", \"RL\", \"RR\", and \"RB\" conditions for each azimuth angle. In the case of the 0\({}^{\circ}\) sound source, no significant difference was observed between the externalization ratings for the \"RL\" and \"RR\" conditions (\(p\) = 0.8), but each of them differed significantly from the results for the \"RB\" and \"RN\" conditions. A significant difference was found between the results for the \"RN\" and each of the other three (\"RL\", \"RR\", and \"RB\") conditions (\(p\ll 0.05\)). For negative azimuth angles, there was generally no significant difference between the externalization ratings for the \"RN\" and \"RL\" conditions (\(p\) > 0.2), apart from one exception at the azimuth angle of \(-30^{\circ}\), where externalization was significantly higher for the \"RN\" condition than the \"RL\" condition (\(p\) = 0.03). However, the results for both conditions differed significantly from the results for the \"RR\" and \"RB\" conditions. Furthermore, there was no significant difference between the \"RR\" and \"RB\" conditions (\(p\) > 0.2). For positive azimuth angles, no significant difference was found between the externalization ratings for the \"RN\" and \"RR\" conditions (\(p\) > 0.2), and the results for both conditions differed significantly from the results for the \"RL\" and \"RB\" conditions (\(p\ll 0.05\)). Furthermore, there was no significant difference between the \"RL\" and \"RB\" conditions (\(p\) > 0.5).