# Binaural Rendering with Measured Room Responses: First-Order Ambisonic Microphone vs. Dummy Head
## 2 Experiment I: Dynamic Rendering of Multiple-Orientation Binaural Signals
### Results and Discussion  
The statistical analysis below uses pooled data for each attribute; see Figure 3. For timbre and spatial mapping, ratings of four directions were pooled, and both virtual loudspeaker directions were pooled for continuity. Please note that throughout the article we use a Wilcoxon signed-rank test [29] with a Bonferroni-Holm correction [30] to determine \(p\)-values of pair-wise comparisons between test conditions and define \(p<0.05\) as significantly different. We employ non-parametric statistics as we do not assume a normal distribution of the ratings due to severe clustering at the limits of the scale. _Timbre:_ Per MOBRIR resolution, there is a clear advantage of the LISHPh method in the settings proposed compared to broadband linear interpolation. The \(p\)-values (significance level) given in the upper triangle of Table 1 indicate that there are four groups, which are significantly different from each other. The LISHPh interpolations with settings \(8^{\circ}/4\)k and \(15^{\circ}/2\)k are not significantly different (\(p=0.11\)) to the \(1^{\circ}\) reference condition and perform significantly better than all other conditions. For the coarser resolutions, the quality of the LISHPh interpolation decreases significantly with spacing. However, for all orientation resolutions, LISHPh performs significantly better than linear interpolation (\(p<0.005\)). The best linear interpolation conditions \(8^{\circ}\)lin and \(15^{\circ}\)lin are comparable to the worst LISHPh condition \(60^{\circ}/1\)k (\(p>0.36\)). _Spatial Mapping:_ The results for spatial mapping, i.e., localization and distance impression, indicate that there is no significant difference between the ref and \(8^{\circ}/4\)k, and \(15^{\circ}/2\)k (\(p>0.13\)) conditions, cf. lower triangle in Table 1. For coarser resolutions, the quality of spatial mapping decreases significantly. Again, the LISHPh conditions clearly outperform the linear interpolation. However, the best linearly interpolated conditions \(8^{\circ}\)lin and \(15^{\circ}\)lin are significantly better than the worst LISHPh condition \begin{table}
\begin{tabular}{c c c c c c c c c c} \hline \hline
**Method** & ref & \(8^{\circ}/4\)k & \(15^{\circ}/2\)k & \(30^{\circ}/2\)k & \(60^{\circ}/1\)k & \(8^{\circ}\)lin & \(15^{\circ}\)lin & \(30^{\circ}\)lin & \(60^{\circ}\)lin \\ \hline ref & - & **0.11** & **0.11** & 0.00 & 0.00 & 0.00 & 0.00 & 0.00 & 0.00 \\ \hline \(8^{\circ}/4\)k & **0.13** & - & **0.95** & 0.00 & 0.00 & 0.0 & 0.00 & 0.00 & 0.00 \\ \hline \(15^{\circ}/2\)k & **0.58** & **0.35** & - & 0.00 & 0.00 & 0.00 & 0.00 & 0.00 & 0.00 \\ \hline \(30^{\circ}/2\)k & 0.00 & 0.02 & 0.00 & - & 0.00 & 0.00 & 0.00 & 0.00 & 0.00 \\ \hline \(60^{\circ}/1\)k & 0.00 & 0.00 & 0.00 & 0.00 & - & **0.72** & **0.36** & 0.00 & 0.00 \\ \hline \(8^{\circ}\)lin & 0.00 & 0.00 & 0.00 & 0.00 & 0.00 & - & **0.95** & 0.03 & **0.16** \\ \hline \(15^{\circ}\)lin & 0.00 & 0.00 & 0.00 & 0.01 & 0.01 & **0.58** & - & 0.00 & 0.00 \\ \hline \(30^{\circ}\)lin & 0.00 & 0.00 & 0.00 & 0.00 & 0.02 & 0.00 & 0.00 & - & **0.95** \\ \hline \(60^{\circ}\)lin & 0.00 & 0.00 & 0.00 & 0.00 & 0.00 & 0.00 & 0.00 & **0.13** & - \\ \hline \hline \end{tabular}
\end{table} 
Table 1: \(p\)-values (Wilcoxon signed-rank test with Bonferroni–Holm correction) for ratings of timbre and spatial mapping of Experiment I. The upper triangle corresponds to timbre, the lower triangle to spatial mapping. Insignificant differences (\(p\)-values \(\geq\) 0.05) are indicated by bold numbers. Figure 3: Median (markers) and 95% confidence interval (solid lines) of ratings from all 10 subjects for testing the perceived difference to the reference (linearly interpolated BRIRs on a \(1^{\circ}\) resolution). Settings of the algorithm are indicated by \(\Delta\varphi/f_{c}\), where _lin_ denotes a broadband linear interpolation. \(60^{\circ}/1\)k. This is caused by its low crossover frequency at \(f_{c}=1\)kHz which is set to avoid comb filtering (cf.