## 2 Materials and Methods
### Experimental Design  
Three different reverberation times and four acoustic parameters were employed to evaluate changes in perceptual thresholds of reverberation, so the whole experiment is divided into three groups and each group includes four parts as shown in Table 1. All 12 parts were presented in a random order and a 30 s rest time is set between each part to reduce fatigue and experimental error caused by sustained concentrated listening. The measurement of perceptual thresholds for each parameter was established using an AB blind test [28] and the staircase method [29]. An AB blind test is a method that can compare two sensory stimuli to judge detectable differences between them [28]. Sample 'A' as a reference audio sample and sample 'B' as a test audio sample are provided to a subject. The subject compares 'A' and 'B' and then judges them as the same or not, providing the responses 'Yes' or 'No'. Staircases usually begin with a detectable difference between a reference and test stimulus. This difference is then reduced with predetermined repeat intervals until the participant provides a negative response. At this point, the staircases reverse and the difference increases with predetermined repeat intervals until the participant makes a different response again, triggering another reversal. Predetermined repeat intervals can be set to be the same or different, and this process can be repeated  
Figure 4: The time frequency spectrum of the BRIRs used in the listening test. (**a**) The time frequency spectrum of the BRIR with 0.31 s reverberation time. (**b**) The time frequency spectrum of the BRIR with 0.91 s reverberation time. (**c**) The time frequency spectrum of the BRIR with 1.51 s reverberation time. as needed, until the stimuli reach an asymptotic level. Then, they hover around the plateau as long as the conditions remain unchanged [29]. The staircase method has three predetermined conditions, the start point, the step sizes and the stop point. In this listening test, participants were asked to listen to and compare reference audio samples to audio samples rendered with a single variable acoustic parameter. They responded 'Yes' or 'No' to the question 'Are audio samples A and B the same?'. This experiment involves threshold detection for four BRIR parameters, RER, ITDG, FER and LR. The extended start points of ITDGs were empirically set to 40 ms as it was quite apparent to the authors that the effect could clearly be heard at this large interval for all rooms. Similar to ITDG, the reverse removal start points of ERs are all set as 50 ms, and the forward removal start points of ERs are all set as 35 ms. Reverberation time is closely related to LR, so there are great differences in removal start points of LRs for BRIRs with different reverberation times. Through listening and confirmation of pilot tests, thresholds that produced clearly distinguishable differences from the reference reverberation were set as LR was removed by 465 ms for the BRIR with short reverberation time (0.31 s), 780 ms for the BRIR with medium reverberation time (0.91 s) and 1250 ms for the BRIR with long reverberation time (1.51 s), respectively. By averaging these results, the removal start points of LRs were set as 465 ms for the BRIR with short reverberation time (0.31 s), 780 ms for the BRIR with medium reverberation time (0.91 s) and 1250 ms for the BRIR with long reverberation time (1.51 s), respectively. The step sizes are not fixed. They are adjusted according to the experimental results. The initial step sizes are 5 ms in ITDG, RER and FER tests. After three 'Yes' responses appear, the step sizes are adjusted to 3 ms, and after five 'Yes' responses appear, the step sizes are adjusted to 1 ms. For LR tests, the test start point is large with initial step sizes set to 10 ms. After three 'Yes' responses appear, the step sizes are adjusted to 5 ms, and after five 'Yes' responses appear, the step sizes are adjusted to 3 ms. There are two kinds of stop conditions.