## 4 Experiment 1
### Results  
In total, 1280 annoyance ratings were collected (32 subjects \(\times\) 40 stimuli), each of which was assigned to a particular subject and a specific stimulus (of the total 78 stimuli). The results of experiment 1 are illustrated in Figure 4.  
The following simple linear mixed effects model was found to be effective to predict annoyance:  
\[y_{ik}=\mu+\tau_{\rm B,i}+\beta\cdot L_{\rm AE,F}+\theta\cdot S_{ik}+u_{k}+ \epsilon_{ik}. \tag{1}\]  
In Equation (1), \(y_{ik}\) is the dependent variable annoyance, predicted for each background type and subject at different helicopter sound exposure levels and playback number. \(\mu\) is the overall grand mean and \(\tau_{\rm B,i}\) denotes the categorical variables background type (three levels: \(i=1,2,3\)). Parameters \(\beta\) and \(\theta\) are regression coefficients for \(L_{\rm AE,F}\) and \(S_{ik}\), respectively. The (unstructured) random effect term \(u_{k}\) is subjects' random intercept--for \(k=1,\ldots,32\). Finally, the error term \(\epsilon_{ik}\) is the random deviation between observed and expected values of \(y_{ik}\). Model coefficients are listed in Table 2.  
Figure 3: \(L_{\rm AS,F}\) as a function of time for the six flight events (no added background sounds) used in experiment 1. Helicopter type and \(L_{\rm AE,F}\) of each individual flight event is indicated in the box. The main predictor of annoyance was flight event's sound exposure level, \(L_{\text{AE,F}}\) (\(p<0.001\)). Annoyance increased with increasing \(L_{\text{AE,F}}\). Background type was a further significant predictor of annoyance (\(p<0.05\)). Whereas no significant difference was found between average annoyance ratings \begin{table}
\begin{tabular}{l l l l l} \hline \hline
**Parameter** & **Symbol** & **Coeff.** & **95\% CI** & \(p\)** \\ \hline Intercept & \(\mu\) & \(-25.173\) & \([-26.867;-23.479]\) & 0.00 \\ Background type & \(\tau_{\text{B,i}}=\text{No}\) & 0 \({}^{a}\) & \\  & \(\tau_{\text{B,i}}=\text{L}\) & 0.063 & \([-0.225;0.350]\) & 0.67 \\  & \(\tau_{\text{B,j}}=\text{E}\) & 0.280 & \([-0.006;0.567]\) & 0.06 \\ \(L_{\text{AE,F}}\) & \(\beta\) & 0.414 & [0.392;0.435] & 0.00 \\ Playback No. & \(\theta\) & 0.017 & [0.011;0.024] & 0.00 \\ \hline \hline \end{tabular} \({}^{a}\) Redundant coefficients are set to zero.  
\end{table} 
Table 2: Experiment 1, model 1: model coefficients (Coeff. ), their 95% confidence interval (CI), and probabilities (\(p\)) of the linear mixed effects model for annoyance. The parameters and symbols are explained in Equation (1). Figure 4: Results of experiment 1: mean acoustic comfort ratings across subjects (and their 95% confidence intervals) are shown as a function of \(L_{\text{AE,F}}\) (**above**) or for different background types (**middle**) and \(L_{\text{Aeq,B}}\) (**below**). for stimuli without background sounds and those with less eventful background sounds, stimuli containing eventful background sounds were found to be more annoying on average than the other two categories. Furthermore, annoyance increased slightly, however significantly, with the playback number (\(p<0.001\)). A second more complex linear mixed effects model was found to be optimal to predict annoyance:  
\[y_{ik}=\mu+\tau_{\text{B},i}+\beta\cdot L_{\text{AE,F}}+\gamma\cdot L_{\text{ Aeq,B}}+\theta\cdot S_{ik}+\gamma_{\text{B},i}\cdot L_{\text{Aeq,B}}+u_{k}+ \epsilon_{ik}. \tag{2}\]  
In Equation (2), \(y_{ik}\), \(\mu\), \(\tau_{\text{B},i}\), \(\beta\), \(\theta\), \(u_{k}\), and \(\epsilon_{ik}\) are the same parameters as in Equation (1). \(\gamma\) is the regression coefficient for \(L_{\text{Aeq,B}}\) and \(\gamma_{\text{B},i}\) represents interaction between background type and background level \(L_{\text{Aeq,B}}\). Model coefficients are listed in Table 3.  
The main effect of the background level (\(L_{\text{Aeq,B}}\)) on annoyance was not significant (\(p>0.05\)).