## 4 Results
### Size Estimation  
Two participants failed to complete this task appropriately. Further, for each study condition, outliers were dropped from the analyses, which resulted in the exclusion of about 13% of the data. The remaining data from 23 participants was entered into the analyses. In the environment with maximum visual and gravitational cues, participants underestimated the depth dimension of the near target (Mrelative error (near) = 0.19, SD = 0.27) but accurately estimated the depth of the far target (Mrelative error (far) = 0, SD = 0), while overestimating the height (Mrelative error (near) = \(-\)0.46, SD = 0.64; Mrelative error (far) = \(-\)0.40, SD = 0.55) and length (Mrelative error (near) = \(-\)0.54, SD = 0.69; Mrelative error (far) = \(-\)0.40, SD = 0.54) of both the near and far targets. Similarly, under the environment with a moderate level of cues, there was a tendency for underestimation of depth of the near target (Mrelative error (near) = 0.21, SD = 0.23) but accurate estimation of the depth of the far target (Mrelative error (far) = 0, SD = 0). However, there was an overestimation of height (Mrelative error (near) = \(-\)1.02, SD = 1.45; Mrelative error (far) = \(-\)0.99, SD = 1.34) and length (Mrelative error (near) = \(-\)0.85, SD = 1.21; Mrelative error (far) = \(-\)0.94, SD = 1.23) of both the near and far targets. Depth perception was accurate under the environment with minimum cues for both the near and far targets (Mrelative error = 0, SD = 0), whereas the height (Mrelative error (near) = \(-\)1.50, SD = 1.27; Mrelative error (far) = \(-\)0.80, SD = 0.82) and length (Mrelative error (near) = \(-\)1.16, SD = 0.99; Mrelative error (far) = \(-\)0.82, SD = 0.98) were overestimated for both the near and far targets. Similar to the analyses of distance estimation data, the sign of relative errors was removed for further analyses of size estimation data. A 3 (maximum vs. moderate vs. minimum visual and gravitational cues) \(\times\) 2 (near vs. far) \(\times\) 3 (depth vs. height vs. length) repeated measures ANOVA was performed to examine the effects of the within-subject variables of the environmental condition, proximity of the target, and dimension of the cuboid, respectively, on the absolute relative error of size estimation. The analysis revealed significant main effects of the environmental condition (F (1.54, 33.85) = 3.60, \(p\) = 0.036, \(\eta^{2}_{\text{P}}\) = 0.14; Greenhouse-Geisser correction), target proximity (F (1, 22) = 9.56, \(p\) = 0.005, \(\eta^{2}_{\text{P}}\) = 0.30), and cuboid dimension (F (1.24, 27.17) = 29.02, \(p\) < 0.001, \(\eta^{2}_{\text{P}}\) = 0.57; Greenhouse-Geisser correction). The two-way interaction between the main effects of environmental condition and dimension was also significant (F (1.73, 37.94) = 3.87, \(p\) = 0.035, \(\eta^{2}_{\text{P}}\) = 0.15; Greenhouse-Geisser correction). Most importantly, the three-way interaction between environmental condition, dimension, and target proximity was significant (F (2.44, 53.56) = 5.05, \(p\) = 0.006, \(\eta^{2}_{\text{P}}\) = 0.19; Greenhouse-Geisser correction). None of the other effects reached significance (see Figure 5). To break down the significant three-way interaction, simple two-way interaction analyses between environmental condition and dimension were conducted within each level of target proximity, using Bonferroni correction (i.e., \(p\) < 0.025). The interaction between environmental condition and dimension was only significant in size estimation of the near target (F (1.6, 35.21) = 5.035, \(p\) = 0.017, \(\eta^{2}_{\text{P}}\) = 0.186; Greenhouse-Geisser correction) but not the far target (\(p\) > 0.025). Figure 5: Relative error in size estimation by environmental condition (maximum, moderate, and minimum) and target proximity (near and far). Error bars represent SE. We followed up with simple effects analyses of the environmental condition within each level of dimension for the near target, using Bonferroni correction (\(p<0.017\)).