# Examining User Perception of the Size of Multiple Objects in Virtual Reality
## 4 Discussion
_The points of subjective equality for all conditions are all less than 1.4 mm and less than 2% of the target width._ These results support the findings of the height judgement tasks that virtual reality is a suitable design tool to allow users to understand the width of control objects, such as dials and levers. \begin{table}
\begin{tabular}{l r r r r r} \hline \hline \multicolumn{6}{c}{**Difference of Final and Target Height in mm**} \\ \hline Height & 10 & 30 & 50 & 70 & 90 \\ \hline Total & 0.1117 & \(-\)0.2741 & 0.0455 & 0.6168 & 0.3284 \\ \hline Shrink & 0.2752 & \(-\)0.03913 & 0.1502 & 0.7484 & 0.3409 \\ Grow & \(-\)0.0517 & \(-\)0.5090 & \(-\)0.0592 & 0.4851 & 0.3160 \\ \hline \hline \end{tabular}
\end{table} 
Table 7: Difference from the final mean and target height in mm for height adjustment. Figure 10: Difference from the final mean and target in mm for width adjustments (error bars depict standard error of the overall mean values). \begin{table}
\begin{tabular}{l r r r r r} \hline \hline \multicolumn{6}{c}{**Percentage of Final and Target Height**} \\ \hline Height & 10 & 30 & 50 & 70 & 90 \\ \hline Total & 1.12\% & 0.91\% & 0.09\% & 0.88\% & 0.36\% \\ \hline Shrink & 2.75\% & 0.13\% & 0.30\% & 1.07\% & 0.38\% \\ Grow & 0.52\% & 1.70\% & 0.12\% & 0.69\% & 0.35\% \\ \hline \hline \end{tabular}
\end{table} 
Table 8: Percentage from the final mean and target height in mm for height adjustment. Figure 9: Difference of final and target height in mm for height adjustment (error bars depict standard error of the overall mean values). Just-noticeable difference is the amount that height or diameter must be changed in order for a difference to be noticeable, detectable at least half the time by the participants. The just-noticeable difference for both height and width indicates users notice a greater difference for larger sizes, see Figures 11 and 12. In the case of the height judgement, the just-noticeable difference was less than 1.6 mm. The judgement for width was less than 2.4 mm. As previously mentioned, these results are similar those found by [PERSON] et al. (2018) for Fish Tank Virtual Reality displays. One possible explanation for this result is both HMD-based and Fish Tank VR support users changing their point of view when performing the size judgements. Motion parallax is a power distance visual cue, and users might be relaying this form of perception in their size judgement. As with the point of subjective equality, the two colours did not appear to affect the results of just-noticeable difference. For height judgement, the mean across all heights is 1.1981 mm (SD 0.3293) and for the width judgement is 1.3990 mm (SD 0.7134). The values for each task represent in the smaller sized object noticeable difference of less than 1 mm. In the larger sized objects, noticeable difference was approximately 2.5% of the object's target size. This leads to confidence that the different coloured objects will be interpreted within an acceptable range. This will allow different controls of different colours to be placed on a control panel with confidence the user would understand the spatial relationship between the controls. There is a question of why the just-noticeable difference width judgement was slightly worse than the height judgement. One possible explanation is the stereo and head parallax depth cues may function more effectively for the height judgements. It was noticed some users moved they head more during the width adjustment tasks. The viewing angle might be a second reason for this difference. While the user's viewed the cylinders at an approximate 45\({}^{\circ}\) viewing angle (equal for both tasks), this position might favour the height adjustment task as it might be more understandable for the participants.