# Auditory Coding of Reaching Space
## 3 Results  
Figure 4 exemplifies the reaching positions of all participants for one target point. The endpoints of the reaching movements spread around the target point.  
The mean absolute distance from the target point was 11.68 cm (SD: 2.46 cm) over all subjects, planes and conditions and therefore significantly lower than 18.60 cm, the value for the absolute distance expected at random reaching (t\({}_{(23)}\) = \(-\)13.49, \(p\) \(<\) 0.001). Accordingly, the averaged absolute differences between reaching and target point coordinates in the three directions in space over all subjects, axes and conditions was 7.25 cm (SD: 1.53 cm). This value is significantly lower than 11.75 cm, the value for the absolute axial differences expected at random reaching (t\({}_{(23)}\) = \(-\)14.13, \(p\) \(<\) 0.001).  
Figure 4: Reaching results for one target point in _xy_-plane. Target point: black, the participants’ pointing results: grey.  
This error remained stable over time, repeated measures ANOVA (3 sequences \(\times\) 4 blocks \(\times\) 9 trials, sorted chronologically) revealed no significant main effect or interaction for absolute distance to target point. Figure 5 shows the time course of the average absolute distance.  
In the following, the absolute differences between reaching and target point coordinates in the three directions in space are considered.  
For repeated measures ANOVA (3 axes \(\times\) 2 tablet sides \(\times\) 2 sonification classes \(\times\) 2 blocks, sorted by condition), main effect \"treatment\" did not reach level of significance (F\({}_{(1,\,22)}\) = 0.02, \(p\) = 0.887, \(\eta_{\text{p}}\)\({}^{2}\) \(<\) 0.01). The blindfolded group (M = 7.30 \(\pm\) 1.46 cm) did not reach significantly worse than the sighted group (M = 7.21 \(\pm\) 1.59 cm). None of the interactions with the factor \"treatment\" reached level of significance.  
There was a significant main effect \"axis\" (F\({}_{(2,\,44)}\) = 8.92, \(p\) = 0.001, \(\eta_{\text{p}}\)\({}^{2}\) = 0.29). The differences between the longitudinal axis and the transverse axis (\(p\) = 0.022) as well as between the longitudinal axis and the sagittal axis (\(p\) \(<\) 0.001) became significant, whereas the differences in the reaching precision between the transverse axis and the sagittal axis did not (\(p\) = 0.580) (see Figure 6). As the three axes were acoustically represented by three different sound parameters, this result cannot be interpreted purely regarding the spatial orientation.  
Figure 5: Time course of average absolute distance for the 12 blocks.  
Figure 6: Means and standard deviations of absolute differences for the three axes. Longitudinal axis corresponds to \(x\)-axis, transverse axis to \(y\)-axis and sagittal axis to \(z\)-axis in Figure 1.  
There was also a significant main effect \"sonification class\" (F\({}_{(1,\,22)}\) = 6.81, \(p\) = 0.016, \({\eta_{\rm p}}^{2}\) = 0.24) with a better reaching performance in conditions with mere discrete instruction and feedback than in conditions with additional continuous instruction and feedback, as depicted in Figure 7.  
Looking for interactions with the factor \"sonification class\", a significant interaction \"axis\" \(\times\) \"sonification class\" (F\({}_{(2,\,44)}\) = 5.47, \(p\) = 0.008, \({\eta_{\rm p}}^{2}\) = 0.20) was revealed. The difference in the reaching precision between discrete and additional continuous auditory feedback was significant only for the longitudinal axis (\(p<0.001\)). Figure 8 shows the interaction pattern.  
Main effect \"block\" (F\({}_{(1,\,22)}\) \(<\) 0.01, \(p\) = 0.955, \({\eta_{\rm p}}^{2}\) \(<\) 0.01) did not reach significance. The reaching performance in the discrete blocks in which both instruction and feedback took 1 s did not differ from that in the discrete blocks in which both instruction and feedback took as long as the continuous acoustic information did in the blocks with additional continuous information about the reaching movement.