# Perceptual Similarities between Artificial Reverberation Algorithms and Real Reverberation
## 4 Results
### Statistical Analysis
#### 4.2.2 Post Hoc Test  
Post hoc tests were performed to confirm where differences between groups occurred. Pairwise Comparison in Multiple Comparison was performed to determine which two groups were significantly different from each other. The post hoc test results reveal whether the highest-scoring reverberation algorithm is significantly different from the other reverberation algorithms. Tables 13-15 present the Pairwise Comparison post hoc test results. The values presented in Tables 13-15 are \(p\)-values. Those p-values less than 0.05 indicate significant differences. As described in Section 4.1, the algorithms with the highest scores are shown in bold in Table 11. Reverberation algorithms that are not significantly different from the highest scoring reverberation algorithm are marked in bold italics in Table 11.  
It can be seen that at short reverberation times, although HMS achieved the highest scores in simulating all three stimuli except female singing, overall there were no significant differences between the HMS, Gardner, and Schroeder reverberation algorithms in simulating the four stimuli in the experiment. At medium reverberation times, there was no significant difference between the HMS and Schroeder reverberation algorithms, although HMS scored highest when simulating real reverberation. At long reverberation times, the Gardner reverberation algorithm performed best. \begin{table}
\begin{tabular}{c c c c c c c c c} \hline \hline
**Stimuli** & **Reverberation** & **Déttoro** & **DFDN** & **FDM** & **Gardner** & **Moorer** & **HMS** & **Schroeder** \\ \cline{2-10}  & **Time** & **0.266 s** & 29.10 & 50.65 & 64.10 & **85.05** & 72.65 & **73.05** & **73.90** \\ \hline
**Female singing** & **0.95 s** & 30.35 & 31.70 & 53.45 & 57.25 & 58.00 & **81.25** & **74.90** \\  & **2.34 s** & 36.45 & 15.65 & **69.50** & **77.10** & 37.60 & 56.10 & **65.80** \\ \hline
**Male speech** & **0.266 s** & 17.45 & 51.00 & **62.25** & **57.15** & 51.00 & **69.90** & **57.90** \\  & **0.95 s** & 24.15 & 19.30 & 38.85 & 40.50 & 56.10 & **72.15** & **68.35** \\  & **2.34 s** & 29.15 & 11.35 & 28.10 & **64.10** & 37.85 & **49.00** & 43.25 \\ \hline
**Cello piece** & **0.266 s** & 49.95 & 65.10 & **75.70** & **77.05** & **77.05** & **80.40** & **65.90** \\  & **0.95 s** & 45.20 & 35.45 & 59.45 & 57.40 & 65.60 & **82.85** & **70.90** \\  & **2.34 s** & 54.60 & 22.20 & 62.70 & **78.40** & 45.85 & **66.20** & 48.55 \\ \hline
**Drumbeat** & **0.266 s** & 17.70 & 35.50 & **52.90** & 57.45 & 59.70 & **60.15** & **53.60** \\  & **0.95 s** & 13.50 & 11.85 & 34.15 & 42.00 & 63.55 & **68.55** & **56.15** \\  & **2.34 s** & 24.00 & 11.55 & 22.15 & **48.85** & **46.05** & **42.15** & **42.35** \\ \hline \hline \end{tabular} Note 1  
\end{table} 
Table 11: The mean scores of the above reverberation algorithms simulating the female singing, male speech, cello piece, and drumbeat at short (0.266 s), medium (0.95 s), and long reverberation times (2.34 s), respectively. \begin{table}
\begin{tabular}{c c} \hline \hline
**DF = 6** & **_p_ Value** \\
**Significance Level = 0.05** & **_p_ Value** \\ \hline
0.266 s female singing & \(<\)0.001 \\
0.266 s male speech & \(<\)0.001 \\
0.266 s cello piece & \(<\)0.001 \\
0.266 s drumbeat & \(<\)0.001 \\
0.95 s female singing & \(<\)0.001 \\
0.95 s drumbeat & \(<\)0.001 \\
2.34 s female singing & \(<\)0.001 \\
2.34 s male speech & \(<\)0.001 \\
2.34 s cello piece & \(<\)0.001 \\
2.34 s drumbeat & \(<\)0.001 \\ \hline \hline \end{tabular}
\end{table} 
Table 12: Kruskal-Wallis ANOVA test results for all seven reverberation algorithms.