## 3 Results and Discussion
### Chi-Square Test Calculations  
In order to apply the conclusions that were made for this sample (68 participants) to the whole population, it is necessary to apply a certain and appropriate statistical method, which is in this concrete case is the chi-square (\(\chi^{2}\)) test [43]. A \(\chi^{2}\)-test is a very practical statistical tool which is used when it is necessary to determine whether some of the obtained or observed values differ from the values that would be expected under a certain research hypothesis. The \(\chi^{2}\)-test calculations are similar to the correlation coefficient calculations in terms of showing if there is a link between the two variables. However, in these cases there is also a significant difference between the correlation coefficient calculations and the \(\chi^{2}\)-test. The correlation coefficient calculations show the degree of correlation between the two variables, while the \(\chi^{2}\)-test shows the probability of the correlation. Thus, in almost all the cases (provided that some additional corrections sometimes need to be made or it is more practical to use another formula that abbreviates computation), the \(\chi^{2}\)-test is calculated according to the following expression:  
\[\chi^{2}=\sum\frac{\left(f_{0}-f_{t}\right)^{2}}{f_{t}} \tag{3}\]  
where \(f_{0}\) is the observed frequencies and the \(f_{t}\) is the expected (theoretical) frequencies. \begin{table}
\begin{tabular}{c c c c} \hline \hline  & **AMPLITUDE (0-1)** & **DURATION (0-2)** & **AMPLITUDE** \\  & & **GROWTH RATE (0-1)** \\ \hline CHILDREN’S SCREAMS & 0.51 & 1.10 & 0.55 \\ \hline A CAR PASSING BY & 0.42 & 0.98 & 0.63 \\ \hline SOUND OF A GRINDER & 0.47 & 0.92 & 0.54 \\ \hline MEAN OF EACH DISTRACTING SIGNAL & 0.47 (15.1 sones) & 1.00 (1.8) & 0.57 (16.73 sones/s) \\ \hline RANGE OF VARIATION [min, max] & 0.19–0.63 & 0.89–1.21 & 0.48–0.79 \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Study results for the sound of the children’s screams, a car passing by and a grinder (number of study participants = 68). In this particular study, it was expected (e.g., the null hypothesis was) that the listeners will be annoyed with the amplitude, the duration and the amplitude growth rate of the short signal, however, not necessarily in the same ratio. Bearing in mind the defined intervals in this experiment, the expected values would be: for amplitude 0.40, for duration 1.20, and for amplitude growth rate 0.60. The expected values were obtained in the following way. Considering the results of our previous research [31; 40], a signal's amplitude is the most important parameter in determining the signal's irritability, so its expected value is equal to the mean value of the range reduced by a correction value of 0.10 (i.e., the majority of participants will be annoyed at a lower level i.e., 10% of the entire range lower from the mean value of the range which is \(0.50-0.10=0.40\)). The correction value of 0.10 was not chosen randomly. If we look at Table 1, in particular the amplitude parameter for each startling sound change and we take into account the range of its change, 0.10 \"covers\" the whole difference change and in addition, it represents \"one step\" in adjusting the sliders. Thus, following the same methodology, the expected frequencies for the duration and the amplitude growth rate were also adjusted. Since the duration turned out to be less important than the loudness, its expected value was obtained by adding the 0.20 to the midpoint of the corresponding interval. In the end, the least important parameter e.g., the amplitude growth rate, was obtained by adding the 0.20 to the range's mean value due to the fact that previous research [31; 40] showed that for the listeners this was not the \"crucial\" parameter in terms of annoyance. For example, if the duration and the amplitude growth rate were equally important, then the expected value for the loudness growth rate would be obtained by adding 0.10 or in particular the expected value would be 0.60.