## 5 Results  
Each subject's ratings were normalized with respect to mean value (0) and standard deviation as recommended by ITU-R BS.1284-1 [25]. The combined ratings for each attribute were then normalized to a maximum absolute value of \(\pm 1\). The responses to each stimuli are presented as box plots in Figure 10 in order of mean preference. Stimuli are identified by either the anchor they represent, or by the subject whose HRTFs were used to render the signals. To preserve anonymity, human subjects are referred to as H[3; 4; 5; 6; 7; 8; 9; 10; 11; 12; 13; 14; 15; 16; 17; 18; 19; 20]. Included on the plots are the ratings given to each stimuli by the owner of the respective HRTFs. This is referred to as the _Personal Rating_. The average values and narrow ranges of the _thin_, _dark_ and _bright_ anchors (stereo tracks) validate the participants understanding of the attributes. The results of the _mono_ anchor are surprisingly optimistic. Despite averaging amongst the lowest scores in both externalisation and preference, the confidence intervals and error bars extend to well within the ranges of higher scoring HRTF sets. This indicates the significance of timbre in rendering systems. The responses to each stimuli were tested for normality with a Lilliefors test which failed to reject the null-hypothesis of normality at the 5% significance level. The significance of the ratings given to each stimuli for each attribute were explored by one-way repeated measure ANOVA with post hoc analysis. Violations of the assumption of sphericity were identified by [PERSON]'s tests and Greenhouse-Geiser corrections were applied in the calculations of \(p\)-values. Results are presented in Table 4.  
A \(p\)-value of below 5% indicates that we may say with 95% confidence that the average results do truly vary. Greatest significance is seen with respect to preference, followed by timbral attributes: brightness and richness. A significant difference is not seen with respect to externalisation. Together with Figure 10, these results reinforce that timbre must play a considerable role in HRTF selection. \begin{table}
\begin{tabular}{c c c} \hline \hline
**Attribute** & **Greenhouse-Geiser Estimation of \(\epsilon\)** & \(p\)**-Value (with Greenhouse-Geiser Correction) (\%)** \\ \hline
**Brightness** & 0.418 & 1.1 \\
**Richness** & 0.435 & 0.78 \\
**Externalisation** & 0.448 & 9.1 \\
**Preference** & 0.461 & 0.065 \\ \hline \hline \end{tabular}
\end{table} 
Table 4: A Greenhouse-Geiser estimation of \(\epsilon\) and the results of a corrected one-way repeated measure ANOVA applied to the ratings given to each stimuli with respect to attribute. A \(p\)-value below 5% was considered significant. A post hoc pairwise comparison of the mean ratings given to each stimuli was undertaken using [PERSON]'s Honestly Significant Difference test procedure. This revealed seven significant differences between stimuli with respect to preference, two with respect to richness and five with respect to brightness. Zero significant results were seen with respect to externalisation. A summary is given in Table 5.  
Figure 10: Subject ratings of stimuli in order of mean preference. A personal rating reflects a subject’s rating of their own measurements. By virtue of the fact that diffuse field equalised HRTFs were used throughout the test, these differences in timbral and spatial features must be attributed to the individual spectral notches of the HRTFs and not to any general frequency response of the individual. The correlation of brightness, richness and externalisation with respect to preference is plotted in Figure 11. The graph directly compares the attribute ratings given by each participant to each stimuli. Anchors and anomalies identified in Figure 10 are excluded from this plot. Second order polynomial lines of best fit indicate a positive correlation between richness, externalisation and preference. A slight preference for neutral brightness can be seen.