## 3 Auditory Perception Study of Sound Field in Closed Spaces with Different Structural Parameters
### Experimental Results
#### 3.3.2 Analysis of Variance  
The listening test in the current research is of a two-factor interactive design. To be specific, when considering the effect of space volume, the inner surface absorption coefficient and space shape are held constantly, while the volume and the position of receiving point are changed. When considering the effect of inner surface absorption coefficient, the space volume and shape are held constant, while the absorption coefficient and the receiving point position are changed. When considering the effect of space shape, the space volume and the absorption coefficient are held constantly while the shape and the receiving point position are changed. Consequently, at the significant level of \(\alpha\) = 0.05, a two-factor nonrepetitive experimental variance analysis is conducted to test whether the volume, inner surface absorption coefficient, shape of the closed space, and the position of the receiving point have significant impacts on auditory perception. The results of the analysis are shown in Table 8.  
From the results of the variance analysis, it can be seen that the change of inner surface absorption coefficient has a significant impact on the auditory perceptions of all the three testing musical sounds, which is consistent with our reasoning. The change of volume of closed spaces has a significant impact the auditory perception of flute and violin music, and the change of closed space shape has a significant impact on the auditory perception of the violin music. Besides, the change in position of the receiving point has no significant impact on the auditory perceptions of all the three testing musical sounds. At significant level of \(\alpha\) = 00.05, the post-hoc of the above ANOVA is conducted to explore whether there is significant difference among the observing samples. The evaluation results for each simulated model were taken as the observing sample. The results of the post-hoc are shown in Table 9. It can be seen from Table 9 that the auditory perception of flute and violin music has a significant difference among most simulated models. The auditory perception of flute music has no significant difference only between models b and h. The auditory perception of violin music has no significant difference between models b and c. However, the auditory perception of symphony music has no significant difference when space volume and shape change except models b and h. When the absorption coefficient changes, the auditory perception of all the testing music type changes significantly. \begin{table}
\begin{tabular}{c c c c c c c c c c c c} \hline \hline \multirow{2}{*}{**Signal Type**} & \multicolumn{3}{c}{**F**} & \multicolumn{3}{c}{**F**} & \multicolumn{3}{c}{**F**} \\ \cline{2-11}  & \multirow{2}{*}{**Volume**} & **Receiving** & **Absorption** & **Receiving** & **Shape** & **Receiving** \\  & & **Point** & **Coefficient** & **Point** & **F(2,8)** & **4.46** & **F(3,8)** & **4.46** & **F(3,8)** & **4.47** \\ \hline Flute & 12.37 & 0.15 & 145.89 & 0 & 3.52 & 0 \\ Violin & 9.05 & 0 & 14.77 & 0.09 & 14.77 & 0.09 & 14.77 & 0.09 \\ Symphony & 2.13 & 0 & 63.81 & 0 & 0.81 & 0 \\ \hline \hline \end{tabular}
\end{table} 
Table 8: Results of two-factor nonrepetitive experimental variance analysis. F(n\({}_{1}\),n\({}_{2}\)) denotes the value in the F distribution table with freedom degree of n\({}_{1}\) and n\({}_{2}\). It is hypothesized that the factors have no significant impact on the auditory perception. When the calculated F is less than F(n\({}_{1}\),n\({}_{2}\)), the hypothesis is accepted. When the calculated F is larger than F(n\({}_{1}\),n\({}_{2}\)), the hypothesis is rejected; the factor is considered to impact auditory perception significantly.