# Examining User Perception of the Size of Multiple Objects in Virtual Reality
## 4 Discussion  
A closer investigation into the mean values of the points of subjective equality, the difference of the mean values from the target values, is presented in the Table 7. These values fall well below 1 mm. Figure 9 depicts these values as a graph, and these fit into a tight band. The point of subjective equality for the height of a 30 mm diameter cylinder for a range of heights (10 mm, 30 mm, 50 mm, 70 mm and 90 mm) are all very close the target values, as also shown in the Table 8 as the percentage of final and target values for the height adjustment conditions. Users can accurately judge the height of a virtual object when compared to a second virtual object. _All points of subjective equality are under 1 mm for the height judgement task._ These results show users can understand the height of control objects, such as dials and levers. \begin{table}
\begin{tabular}{l r r r r r} \hline \hline \multicolumn{6}{c}{**Just Noticeable Difference (JND)**} \\ \hline Width & 10 & 30 & 50 & 70 & 90 \\ \hline JND & 0.5234 & 0.7938 & 1.6562 & 1.8011 & 2.2207 \\ \hline Shrink & 0.5244 & 0.7766 & 1.9791 & 1.9029 & 2.1148 \\ Grow & 0.5224 & 0.8110 & 1.3332 & 1.6992 & 2.3265 \\ \hline \hline \end{tabular}
\end{table} 
Table 6: Just noticeable difference width in mm for width adjustment. \begin{table}
\begin{tabular}{l r r r r r r} \hline \hline \multicolumn{6}{c}{**Width Point of Subjective Equality**} \\ \hline  & **Point of Subjective Equality** & **Std. Dev.** & **Minimum** & **Maximum** & **Range** & **Graph** \\ \hline Width 10 mm Shrink & 29.7026 mm & 1.1528 & 26.9380 mm & 35.3506 mm & 8.4125 mm & Figure A11 \\ Width 10 mm Grow & 29.5704 mm & 1.2033 & 26.2231 mm & 33.0424 mm & 6.8192 mm & Figure A12 \\ \hline Width 30 mm Shrink & 29.7026 mm & 1.1528 & 26.9380 mm & 35.3506 mm & 8.4125 mm & Figure A13 \\ Width 30 mm Grow & 29.5704 mm & 1.2033 & 26.2231 mm & 33.0424 mm & 6.8192 mm & Figure A14 \\ \hline Width 50 mm Shrink & 51.0674 mm & 2.9364 & 43.6741 mm & 61.000 mm & 17.3259 mm & Figure A15 \\ Width 50 mm Grow & 50.9046 mm & 1.9781 & 46.4467 mm & 55.9687 mm & 9.5219 mm & Figure A16 \\ \hline Width 70 mm Shrink & 71.2485 mm & 2.8233 & 65.9305 mm & 78.2263 mm & 12.2957 mm & Figure A17 \\ Width 70 mm Grow & 71.5205 mm & 2.5211 & 65.4601 mm & 75.9389 mm & 10.4786 mm & Figure A18 \\ \hline Width 90 mm Shrink & 89.1925 mm & 3.1377 & 81.8442 mm & 97.2569 mm & 15.4127 mm & Figure A19 \\ Width 90 mm Grow & 91.2312 mm & 3.4518 & 85.2544 mm & 101.3365 mm & 16.0821 mm & Figure A20 \\ \hline \hline \end{tabular}
\end{table} 
Table 4: Width judgement for tasks of 10 mm to 90 mm for height point of subjective equality. \begin{table}
\begin{tabular}{l r r r r r} \hline \hline \multicolumn{6}{c}{**Just-Noticeable Different (JND) for Height Judgens**} \\ \hline Height & 10 & 30 & 50 & 70 & 90 \\ \hline JND & 0.6462 & 1.1510 & 1.3327 & 1.4500 & 1.4108 \\ \hline Shrink & 0.6158 & 0.9999 & 0.9806 & 1.3423 & 1.3273 \\ Grow & 0.6765 & 1.3020 & 1.6847 & 1.5576 & 1.4943 \\ \hline \hline \end{tabular}
\end{table} 
Table 5: Just noticeable difference height in mm for height judgements. With a deeper examination of the results, the difference of the mean values from the target values is presented in the Table 9. These values are greater than the height adjustment values, but they fall below the absolute value of 1.4 mm. Figure 10 depicts these values as a graph, and they also fall into a tight band of values. The point of subjective equality for the width of a 50 mm tall cylinder for a range of widths (10 mm, 30 mm, 50 mm, 70 mm and 90 mm) is close the target values, as also shown in the Table 10 as the percentage of final and target values for the width adjustment conditions. Users are able to accurately judge the width of a virtual object when compared to a second virtual object.