# A Psychoacoustic Investigation on the Effect of External Shading Devices on Building Facades
## 3 Results and Discussion
### Analysis of Variance: Significance and Fixed Factors Effects
#### 3.2.1 Analysis of Variance and Effect of Size of the Loudness Comparisons  
The differences in loudness levels are statistically significant, looking at both the effects given by the louvres' tilt angle and the sound source position, while the interaction between the two factors is never significant. This result is repeated for both differences given by the traditional and the sound  
\begin{table}
\begin{tabular}{c c c c c c c c c} \hline \hline \multicolumn{2}{c}{**ANOVA Fixed Factors**} & \multicolumn{2}{c}{**\(\Delta\) in Loudness Levels**} & \multicolumn{2}{c}{\(\Delta\) **in Roughness**} & \multicolumn{2}{c}{\(\Delta\) **in Sharpness**} & \multicolumn{2}{c}{\(\Delta\) **in SPL**} \\ \cline{3-10}  & & **p.n.** & **traf.** & **p.n.** & **traf.** & **p.n.** & **traf.** & **-** \\ \hline \multirow{2}{*}{**Traditional**} & **Sound source pos.** & \(p\) \(<\) 0.001 & \(p\) \(<\) 0.001 & 0.021 & 0.048 & \(p\) \(<\) 0.001 & \(p\) \(<\) 0.001 & \(p\) \(<\) 0.001 \\  & **Louvres tilt angle** & \(p\) \(<\) 0.001 & \(p\) \(<\) 0.001 & \(p\) \(<\) 0.001 & \(p\) \(<\) 0.001 & \(p\) \(<\) 0.001 & \(p\) \(<\) 0.001 \\  & **Interaction** & 0.205 & 0.071 & 0.001 & \(p\) \(<\) 0.001 & 0.025 & 0.668 & 0.766 \\ \hline \multirow{2}{*}{**Sound**} & **Sound source pos.** & \(p\) \(<\) 0.001 & \(p\) \(<\) 0.001 & \(p\) \(<\) 0.001 & \(p\) \(<\) 0.001 & \(p\) \(<\) 0.001 & \(p\) \(<\) 0.001 \\  & **Louvres tilt angle** & \(p\) \(<\) 0.001 & \(p\) \(<\) 0.001 & 0.348 & \(p\) \(<\) 0.001 & 0.044 & \(p\) \(<\) 0.001 & \(p\) \(<\) 0.001 \\  & **Interaction** & 0.067 & 0.123 & 0.985 & 0.004 & 0.215 & 0.369 & 0.977 \\ \hline \hline \end{tabular}
\end{table}
Table 1: \(p\)-values calculated from the analysis of the variance for each data set of the calculated \(\Delta\)s. The term “Interaction” is to be intended as the interaction between the sound source position and the louvres’ tilt angle.  
Figure 10: Average differences in Sound Pressure Levels (Insertion Loss in dB) due to the presence of the traditional louvres compared to the sound absorbing louvres. The bars in the figure are listed in function of the source positions used for the measurements (S1, S2, and S3). Error bars reports the doubled standard deviations for each average.  
absorbing louvres. This means that the shading device plays an important role in the variations of the loudness levels, and both the sound source position and the louvres' tilt angle are important.  
The comparison of the effect of size (\(\eta_{\text{p}}\)\({}^{2}\)) on the loudness differences (Figure 11) shows that the louvres' tilt angle of the standard louvres has a greater effect on the loudness variations compared to the sound source position, while the opposite behaviour is observed for the sound absorbing louvres. The loudness level attenuation given by the traditional louvres is quite poor, if not negative (Figure 7). Tilting the louvers produces greater effects on the facade loudness levels than changing the sound source position, because they become transparent to the generated acoustic field (Figure 11a). The reverse situation observed with the sound absorbing louvers (Figure 11b) is due to the fact that the sound absorbing material plays an important role independently of the louvres' tilt angle, because the material quantity in the shading system does not change. In this case the sound source position seems to have a greater effect because the free space between the louvres, seen from the position of the sound source, becomes smaller as the angle between the loudspeaker and the facade plane is reduced (Figure 5a,c). Similar behaviours in \(\eta_{\text{p}}\)\({}^{2}\) are observed for both studied signals.