# Diffuse-Field Equalisation of Binaural Ambisonic Rendering
## 4 Evaluation
### Perceptual Listening Tests
#### 4.3.2 Results  
No participants results were excluded, based on the criteria of rating the hidden reference less than 90% for more than 15% of trials or rating the mid-anchor higher than 90% for more than 15% of trials. The results from both listening tests were tested for normality using the Kolmogorov-Smirnov test, which showed all data as non-normally distributed. As a result, all statistical analysis was conducted using non-parametric methods.  
The median results of the MUSHRA test, conducted to determine whether DFE reduces the differences in timbre between binaural Ambisonic rendering and HRIR convolution, are shown in Figure 8 for each condition across all test sound locations, with non-parametric 95% confidence intervals (CI) [50].  
[PERSON]'s Analysis of Variance (ANOVA) tests showed a statistically significant difference (\(\chi^{2}(5)=247.6,p<0.05\)) between standard and DFE binaural Ambisonic rendering for all tested orders and sound locations. 1 st-order Ambisonics showed the most improvement, followed by 5 th and 3 rd.  
The perceptual effect of DFE was found to vary with test sound location, with a [PERSON]'s ANOVA showing this variation to be statistically significant (\(\chi^{2}(7)=127.8,p<0.05\)). Figure 9 shows the median results with non-parametric 95% CI for each test sound location \(\psi\).  
Post-hoc Wilcoxon signed-rank tests determined which test conditions with DFE produced a significant improvement in timbre; the results of which are shown in Table 6. For both 1 st and 5 th-order Ambisonics, DFE was shown to bring the timbre of binaural Ambisonic rendering closer to HRIR convolution with statistical significance for 5 of the 8 test sound locations. Results for 3 rd-order were much less clear and only significant for one test sound location.  
Figure 8: Median MUSHRA results with non-parametric 95% CI across all test sound locations. Score indicates perceived timbral similarity between test stimulus and HRIR reference.  
The median results of the second listening test, the AB comparison conducted to determine whether DFE improved the consistency of timbre between Ambsonic orders, are shown in Figure 10 for both conditions across all test sound locations, with non-parametric 95% CI.  
\begin{table}
\begin{tabular}{c c c c c c c c c} \hline \hline \(\mathbf{\psi}\) & **1** & **2** & **3** & **4** & **5** & **6** & **7** & **8** \\ \hline \(h\) (M = 1) & 1 & 1 * & 0 & 1 * & 1 * & 0 & 1 * & 0 \\ \(h\) (M = 3) & 0 & 0 & 0 & 0 & 0 & 1 * & 0 & 0 \\ \(h\) (M = 5) & 1 * & 1 * & 0 & 0 & 1 & 1 * & 1 * & 0 \\ \hline \hline \end{tabular}
\end{table}
Table 6: Hypothesis test results of the MUSHRA test results of the three Ambsonic orders for each test sound location using Wilcoxon signed-rank test (1 indicates statistical significance at \(p<0.05\); * indicates \(p<0.01\)).  
Figure 9: Median multiple stimulus test with hidden reference and anchor (MUSHRA) results with non-parametric 95% confidence intervals (CI) for each test sound location (\(\psi\)): (**a**) \(\psi=1\), (**b**) \(\psi=2\), (**c**) \(\psi=3\), (**d**) \(\psi=4\), (**e**) \(\psi=5\), (**f**) \(\psi=6\), (**g**) \(\psi=7\) and (**h**) \(\psi=8\). Reference and anchor scores omitted. Score indicates perceived timblar similarity between test stimulus and HRIR reference.