## 2 Experimental Methodology
### Experiments
\begin{table}
\begin{tabular}{c c c c c c c c c c} \hline \hline \(\mathbf{P}\backslash\mathbf{R}\) & \(\mathbf{-40}\) & \(\mathbf{-30}\) & \(\mathbf{-20}\) & \(\mathbf{-10}\) & \(\mathbf{0}\) & \(\mathbf{+10}\) & \(\mathbf{+20}\) & \(\mathbf{+30}\) & \(\mathbf{+40}\) \\ \hline \(-40\) & \(-\) & * & \(-\) & \(-\) & \(-\) & \(-\) & \(-\) & \(-\) & \(-\) \\ \hline \(-30\) & * & \(-\) & * & \(-\) & \(-\) & \(-\) & \(-\) & \(-\) & \(-\) \\ \hline \(-20\) & \(-\) & * & \(-\) & * & \(-\) & \(-\) & \(-\) & \(-\) & \(-\) \\ \hline \(-10\) & \(-\) & \(-\) & * & \(-\) & * & \(-\) & \(-\) & \(-\) & \(-\) \\ \hline \(0\) & \(-\) & \(-\) & \(-\) & * & \(-\) & * & \(-\) & \(-\) & \(-\) \\ \hline \(+10\) & \(-\) & \(-\) & \(-\) & \(-\) & * & \(-\) & * & \(-\) & \(-\) \\ \hline \(+20\) & \(-\) & \(-\) & \(-\) & \(-\) & \(-\) & * & \(-\) & * & \(-\) \\ \hline \(+30\) & \(-\) & \(-\) & \(-\) & \(-\) & \(-\) & * & \(-\) & * & \(-\) \\ \hline \(+40\) & \(-\) & \(-\) & \(-\) & \(-\) & \(-\) & \(-\) & \(-\) & * & \(-\) \\ \hline \hline \end{tabular}
\end{table} 
Table 1: The reference (columns) and the probe (rows) sounds from azimuth angles that are used in the tests: (*) conditions are used in the error rate calculations for the azimuth \(0\), \(10\), \(20\), \(30\) and \(40\) degrees. Right and left azimuth angles are respectively denoted by positive and negative signs. \(N_{F}(\theta_{r},\theta_{p})\) is used to define the number of false responses for the azimuth of the reference and probe stimuli for \(\theta_{r}\) and \(\theta_{p}\), respectively. In this case, the number of false responses for inward \(N_{F}^{in}(\theta)\), and outward \(N_{F}^{out}(\theta)\), cases are defined as,  
\[N_{F}^{in}(\theta) =N_{F}(\theta_{out},\theta)+N_{F}(\theta,\theta_{in}), \tag{9}\] \[N_{F}^{out}(\theta) =N_{F}(\theta,\theta_{out})+N_{F}(\theta_{in},\theta), \tag{10}\]  
for all non-zero \(\theta\) values, that is, \(\theta=\pm 10,\pm 20,\pm 30\) degrees. The number of hit responses for inward and outward cases can be computed similarly and represented as \(N_{H}^{in}(\theta)\) and \(N_{H}^{out}(\theta)\). Considering the symmetry of the left and right sides of the horizontal mid-line, the number of false and hit responses can be calculated for absolute azimuth angles over both the left and right sides. The number of false responses around an absolute azimuth \(\theta\) in inward and outward directions are found at absolute azimuth values, \(\theta=10^{\circ},20^{\circ},30^{\circ}\) as follows:  
\[N_{F}^{in}(|\theta|) =N_{F}^{in}(\theta)+N_{F}^{in}(-\theta), \tag{11}\] \[N_{F}^{out}(|\theta|) =N_{F}^{out}(\theta)+N_{F}^{out}(-\theta). \tag{12}\]  
Similarly, \(N_{H}^{in}(|\theta|)\) and \(N_{H}^{out}(|\theta|)\) can be defined for hit responses. At \(\theta=0^{\circ}\), the inward and outward false responses are defined as,  
\[N_{F}^{in}(\theta) =N_{F}(10^{\circ},\theta)+N_{F}(-10^{\circ},\theta), \tag{13}\] \[N_{F}^{out}(\theta) =N_{F}(\theta,10^{\circ})+N_{F}(\theta,-10^{\circ}). \tag{14}\]  
Finally, the error rates for inward (in) and outward (out) cases are defined at absolute azimuth values, \(\theta=0^{\circ},10^{\circ},20^{\circ},30^{\circ}\) as follows:  
\[E_{r}^{in}(|\theta|) =\frac{N_{F}^{in}(|\theta|)}{N_{F}^{in}(|\theta|)+N_{H}^{in}(| \theta|)}, \tag{15}\] \[E_{r}^{out}(|\theta|) =\frac{N_{F}^{out}(|\theta|)}{N_{F}^{out}(|\theta|)+N_{H}^{out}(| \theta|)}. \tag{16}\]