## 2 Experimental Methodology
### Experiments  
The psychophysical lateralization experiments were conducted inside a chamber with 40-dB sound attenuation. Stimuli were presented with an inter-stimulus interval of 3 seconds. There were always 10 degrees of azimuth difference between the reference and probe sounds of the stimulus and the participants' task was to report whether the probe sound was heard from the left or right side of the reference sound by pressing one of the two respective keys (Left/Right arrows) on a typical computer keyboard before the next stimulus. Stimulation sounds were presented by using a pair of Etiymotic Research 61-Martin Lane (Etymotic R-2A) audiological earphones with a flat frequency response that was driven by an external USB sound card (MUSE Mini DAC). The stimuli were presented to the participants using a MATLAB Graphical User Interface (GUI). During the experiments, the sound pairs with different reference azimuthal angles and shift directions were randomly presented so that the participants were not able  
Figure 2: A sample visualization of probe sounds from azimuth (\(\theta+10^{\circ}\)) for time-only (TO), level-only (LO), and time-level (TL) conditions where the reference sound is from azimuth (\(\theta\)) and direction of lateralization shift is outward. to learn and predict the type of the next pair of sounds in the stimulation sequence. An experiment with one subject was performed in three separate sessions for each of the TO, LO, and TL conditions. Table 1 shows all the stimulation pairs presented in the experiments. It should be noted that only the ones that were symmetric around the reference were used in the error rate calculations (In contrast to these azimuths, each of which has a pair of _outward_ and a pair of _inward_ trials, the azimuth 40 degree, has only one _outward_ and one _inward_ conditions, that is, \"30 to 40\" and \"40 to 30\". In order to maintain an equal number of samples for every azimuth, 40 degrees is excluded from the analysis.). Each session included 10 experimental blocks. Each block included 16 combinations of reference-probe sounds from 3 conditions (i.e., 16 TO, LO or TL) and each combination was repeated 10 times in a block. Hence, the test included 4800 judgments per subject. Since the experiment was in a two-alternative forced-choice (2 AFC) format, each response to the stimulus pair was taken as a HIT or a FALSE. If the participant was unable to answer the test in 2 s, a MISS was reported for the stimuli. The experimental data showed that the total MISS rate was 3 out of 24,000 trials (0.0125%), thus the MISS responses were discarded. The error rate was found over the total number of HIT and FALSE responses as,  
\[E_{r}=\frac{N_{F}}{N_{H}+N_{F}}, \tag{6}\]  
where \(N_{H}\) and \(N_{F}\) are respectively the total numbers of hit and false responses. The experimental SNR (Signal to Noise Ratio)values were then extracted from the error rate, \(E_{r}\), under the binary additive white-Gaussian noise channel model as,  
\[SNR=(\text{erfc}^{-1}(2E_{r}))^{2}, \tag{7}\]  
where \(\text{erfc}^{-1}()\) is the inverse of the complementary error function [35] defined as,  
\[\text{erfc}(\text{x})=\frac{2}{\pi}\int_{x}^{\infty}e^{-t^{2}}dt. \tag{8}\]  
The error rate at each azimuth \(\theta\) also defined based on whether the probe sound's azimuth is inward (towards the center) or outward (away from the center) with respect to the reference sound's azimuth. The inward and outward azimuth angles are defined as \(\theta_{in}=sign(\theta)(|\theta|-10^{\circ})\) and \(\theta_{out}=sign(\theta)(|\theta|+10^{\circ})\), where \(sign(\theta)\) is positive if the azimuth \(\theta\) is at the right side and negative if the azimuth is at the left side of the horizontal mid-line.