# The Effects of Augmented Reality Interaction Techniques on Egocentric Distance Estimation Accuracy
## 3 Results
### Task Completion Time and Throughput  
Figure 5 shows the mean completion time as functions of egocentric distance and ID. The repeated-measures ANOVA results showed that the task completion time for egocentric distances differed significantly (F [1.709, 22.217] = 37.382, \(p\)\(<\) 0.001). [PERSON] post-hoc tests further showed that the completion time was significantly different (\(p\)\(<\) 0.05) for all three distances. The completion time significantly increased when targets were displayed at the farthest distance of 150 cm (Mean = 18.342 s, SD = 0.930 s) as compared to 120 cm (Mean = 15.318 s, SD = 0.831 s) and 90 cm (Mean = 13.836 s, SD = 0.751 s). The completion time increased with ID for both direct pointing and indirect cursor techniques. The ANOVA confirmed that ID significantly affected completion time (F [2; 26] = 25.882, \(p\)\(<\) 0.001). The post-hoc [PERSON]'s analysis classified the independent variables into two groups. The results showed that the completion time was significantly higher (\(p\)\(<\) 0.01) when targets were displayed at high ID (mean = 17.020 s, SD = 0.893 s) than when they were displayed at medium (mean = 15.848 s, SD = 0.852 s) and low IDs (mean = 14.628 s, SD = 0.650 s). The post-hoc test did not indicate a significant difference between the low and medium IDs (\(p\)\(>\) 0.05) in task completion time. We found no significant main effect of interaction technique (F [1; 13] = 1.775, \(p\)\(>\) 0.05) on task completion time, and no significant (\(p\)\(>\) 0.05) two-way interaction effects of egocentric distance and interaction technique or ID and interaction technique. Furthermore, linear regression analyses showed that the movement time data were in agreement with Fitts' Law. The R\({}^{2}\) and the fitting equation of movement time for the direct pointing technique were 0.96 (MT = 1.75 + 0.10*ID), 0.85 (MT = 1.88 + 0.10*ID), and 0.87 (MT = 2.33 + 0.16*ID) for the distances of 90, 120, and 150 cm, respectively. The corresponding indirect cursor technique R\({}^{2}\) and the fitting equation of movement time were 0.83 (MT = 1.79 + 0.11*ID), 0.92 (MT = 1.75 + 0.27*ID), and 0.92 (MT = 2.02 + 0.29*ID) for the distances of 90, 120, and 150 cm, respectively.  
The results for throughput are illustrated in Figure 6. We found a weak main effect of interaction technique (F [1; 13] = 5.257, p = 0.039) on throughput. The overall throughput computed for the direct pointing technique was higher (mean = 2.314 bps, SD = 0.136 bps) than that for the indirect cursor technique (mean = 2.190 bps, SD = 0.095 bps). The ANOVA revealed a significant main effect of egocentric distance (F [1.989, 25.859] = 34.876, \(p\)\(<\) 0.001) on throughput. The post-hoc tests indicated that the throughput was significantly lower for the targets at 150 cm (\(p\)\(<\) 0.05) than for those at 120 cm and 90 cm. Similarly, we found a significant main effect of ID (F [1.548, 20.126] = 116.952, \(p\)\(<\) 0.001) on throughput. Tukey post-hoc tests further indicated that the throughputs were significantly different (\(p\)\(<\) 0.001) for all three IDs. The average throughput was significantly higher at the highest ID (Mean = 2.805 bps, SD = 0.157 bps) than at the medium ID (Mean = 2.172 bps, SD = 0.110 bps) and lowest ID (Mean = 1.779 bps, SD = 0.082 bps). We also found a marginally significant difference  
Figure 4: Results of accuracy measurement for direct pointing and indirect cursor interaction techniques with respect to egocentric distance (**A**) and index of difficulty (**B**). The error bar represents standard error of mean.  
between interaction technique and index of difficulty (F [1.987, 25.832] = 3.574, p = 0.043) on throughput, however, no significant difference was found between interaction technique and egocentric distance (F [1.795, 23.329] = 2.819, \(p>0.05\)).