# Enhancing Street-Crossing Safety for Visually Impaired Pedestrians with Haptic and Visual Feedback
## 3 Study 1: Haptic and Visual Feedback for Visually Impaired Pedestrians Crossing at Traffic Signals
### Results
#### 4.2.1 Cross Rate, Decision Time, and User Behavior Data in Study  
**Cross rate. **  
Main effects were found for frequency (\(\chi^{2}(3)=49.27,p<0.001\)), size (\(\chi^{2}(1)=52.41\), \(p<0.001\)), state (\(\chi^{2}(1)=3.88\), \(p<0.05\)). Additionally, we observed significant interaction effects between feedback and frequency (\(\chi^{2}(3)=24.88\), \(p<0.001\)) and feedback and size (\(\chi^{2}(1)=4.64\), \(p<0.05\)). The mean cross rate across feedback modalities, frequencies, sizes, directions, and states is illustrated in Figure 10a. Post hoc Bonferroni pairwise comparisons showed that the cross rate of frequency 0.5 Hz (0.76) was significantly more than that of frequency 2.0 Hz (0.15) (\(p<0.01\)) and frequency 4.0 Hz (0.09) (\(p<0.01\)); that of frequency 1.0 Hz (0.60) was significantly more than that of frequency 2.0 Hz (0.15) (\(p<0.01\)) and frequency 4.0 Hz (0.09) (\(p<0.01\)). The cross rate of the small size (0.51) was significantly more than that of the medium size (0.24) (\(p<0.01\)). **Decision time. **  
Main effects were found for feedback (\(\chi^{2}(1)=12.81,p<0.001\)), frequency (\(\chi^{2}(3)=51.94\), \(p<0.001\)), size (\(\chi^{2}(1)=11.07,p<0.001\)), and state (\(\chi^{2}(1)=33.28\), \(p<0.001\)). Additionally, we observed significant interaction effects between feedback and size (\(\chi^{2}(1)=33.28\), \(p<0.05\)) and between feedback and state (\(\chi^{2}(1)=63.03\), \(p<0.001\)). The mean decision time across feedback modality, frequency, size, direction, and state is illustrated in Figure 10b. Post hoc Bonferroni pairwise comparisons showed that the decision time of the visual feedback (3.78 s) was significantly longer than that of the haptic feedback (3.07 s) (\(p<0.01\)). The decision time of frequency 4.0 Hz (2.85 s) was significantly faster than that of frequency 0.5 Hz (4.10 s) (\(p<0.01\)), frequency 1.0 Hz (3.63 s) (\(p<0.01\)), and frequency 2.0 Hz (3.17 s) (\(p<0.01\)); that of frequency 2.0 Hz (3.17 s) was significantly faster than that of frequency 0.5 Hz (4.10 s) (\(p<0.01\)) and frequency 1.0 Hz  
Figure 10: Mean cross rate and decision time. (**a**) Mean cross rate; (**b**) mean decision time. (3.63 s) (\(p<0.01\)); that of frequency 1.0 Hz (3.63 s) was significantly faster than that of frequency 0.5 Hz (4.10 s) (\(p<0.05\)). The decision time of the medium size (3.28 s) was significantly faster than that of the small size (3.53 s) (\(p<0.01\)). The decision time of the state dynamic (3.73 s) was significantly longer than the static state (3.11 s) (\(p<0.01\)). **Head rotation angle. **  
We recorded the total head rotation angle during the decision time. The main effect was found for frequency (\(\chi^{2}(3)=56.30,p<0.001\)) and state (\(\chi^{2}(1)=7.94,p<0.01\)). No other main or interaction effect was found. The mean decision across feedback modalities, frequencies, sizes, directions, and states is illustrated in Figure 11a. Post hoc Bonferroni pairwise comparisons showed that the total head rotation angle of frequency 0.5 Hz (8.07 degree) was significantly longer than that of frequency 1.0 Hz (5.51 degree) (\(p<0.05\)), frequency 2.0 Hz (5.13 degree) (\(p<0.05\)), and frequency 4.0 Hz (4.64 degree) (\(p<0.01\)); that of frequency 1.0 Hz (5.51 degree) was significantly longer than that of frequency 4.0 Hz (4.64 degree) (\(p<0.05\)). The head rotation angle of the dynamic state (6.38 degree) was significantly longer than that of the static state (5.11 degree) (\(p<0.05\)). **Head movement distance. **  
We recorded the total head movement distance during the decision time. The main effect was found for feedback (\(\chi^{2}(1)=4.05,p<0.05\)), frequency (\(\chi^{2}(3)=344.99,p<0.01\)), and size (\(\chi^{2}(1)=27.22,p<0.001\)). The mean decision across feedback modalities, frequencies, sizes, directions, and states is illustrated in Figure 11b. Post hoc Bonferroni pairwise comparisons showed that the total head movement distance of the small size (2.80 cm) was significantly longer than that of the medium size (1.56 cm) (\(p<0.01\)).