## 6 Discussion
For both experiments, including subjects' random intercept in the linear mixed effects models improved the models significantly. This confirms findings of other psychoacoustic laboratory experiments [8; 28; 40; 41]. Furthermore, this shows the general interindividual differences in the preferences and sensibilities of human observers to background sounds [42]. It should be noted that including subjects' age and gender in the models, i.e., Equations (2) and (3), did not improve the models significantly. Similar further analyses were carried out with \(L_{\text{AE,S}}\), \(L_{\text{ASmax,S}}\), or \(L_{\text{Aeq,S}}\) instead of \(L_{\text{AE,F}}\) in the linear mixed effects models. This was done to investigate whether--beside the differences caused by the background type--the subjects were annoyed mainly by the flight event levels (F) or by the level of the mixture of flight and background sound (S). All the linear mixed effects models with \(L_{\text{AE,S}}\), \(L_{\text{ASmax,S}}\), or \(L_{\text{Aeq,S}}\) led to higher AIC and BIC than the same models with \(L_{\text{AE,F}}\), which indicates that \(L_{\text{AE,F}}\) was a better predictor of short-term annoyance. Table 6 shows Pearson correlation coefficients for bivariate correlations between annoyance and these level variables. Table 6 confirms the above analysis: annoyance correlated more strongly with the flight event sound exposure level (\(L_{\text{AE,F}}\)) than with the stimulus level variables. The outcome of this study strengthens the theories of urban sound design. Enabling the presence of less eventful background sounds (such as water stream, birds, and vegetation) of mid \(L_{\text{Aeq,B}}\) range should be effective in reducing perceived annoyance from noise sources in living areas which are affected by them. The highest annoyance rating in experiment 1 was given for \begin{table}
\begin{tabular}{l l l l l l} \hline \hline  & \(\mathbf{L_{\text{AE,F}}}\) & \(\mathbf{L_{\text{AES}}}\) & \(\mathbf{L_{\text{ASmax,S}}}\) & \(\mathbf{L_{\text{Aeq,S}}}\) \\ \hline Annoyance (experiment 1) & 0.571 ** & 0.569 ** & 0.562 ** & 0.569 ** \\ Annoyance (experiment 2) & 0.629 ** & 0.604 ** & 0.611 ** & 0.604 ** \\ \hline \hline \end{tabular}
\end{table} 
Table 6: Pearson’s \(r\) for correlations between a series of sound level variables and annoyance. \begin{table}
\begin{tabular}{l l l l l l l} \hline \hline  & \multicolumn{2}{c}{**No Background**} & \multicolumn{2}{c}{**Less Eventful**} & \multicolumn{2}{c}{**Eventful**} \\ \cline{2-7}  & **Mean** & **Median** & **Mean** & **Median** & **Mean** & **Median** \\ \hline Annoyance (experiment 1) & 5.41 & 5 & 5.42 & 5 & 5.68 & 6 \\ Annoyance (experiment 2) & 5.57 & 6 & 5.34 & 5 & 5.58 & 6 \\ \hline \hline \end{tabular}
\end{table} 
Table 5: Mean and median annoyance for different background sound types. the stimuli with the eventful church bell in background. Similarly, [PERSON] and [PERSON] [43] reported that natural and culture-related sounds (e.g., music) were preferred compared to artificial sounds. More importantly, [PERSON] and [PERSON] [44] reported that, in particular, water and bird sounds have been usually evaluated as the most effective and most favorable sounds to improve urban sound environments [11; 12]. The results of the present study indicate that, for background sounds to be effective in reducing perceived annoyance and improving the soundscape, not only it is important that they are natural, e.g., from water and birds, but also they should exhibit a low degree of eventfulness. Furthermore, their sound pressure levels should not be too low or too high. On the other hand, if the goal is, for example in a psychoacoustic experiment or in virtual acoustic demonstrations, not to affect the perception of the foreground sound (i.e., noise)--and hence to avoid a weakening in the validity of the experiment--the data suggest to use relatively low-level natural background sounds with a low degree of eventfulness.