## 4 Results
### Egocentric Distance Perception  
One participant failed to complete this task, so was not included. In addition, we screened for outliers by condition (there were about 23% outliers). As a result, data from 24 participants were used for the final analyses.  
The data showed a tendency for underestimation of distance in environments with maximum cues (Mrelative error (near) = 0.60, SD = 0.22; Mrelative error (far) = 0.57, SD = 0.23) and minimum visual and gravitational cues (Mrelative error (near) = 0.56, SD = 0.35; Mrelative error (far) = 0.58, SD = 0.32). However, for the moderate cue environment participants tended to _overestimate_ the distance between themselves and the targets (Mrelative error (near) = \(-\)6.67, SD = 26.55; Mrelative error (far) = \(-\)5.46, SD = 20.23).  
For further analyses, absolute relative errors were used to represent inaccurate estimation, regardless of direction, under each environmental condition (i.e., overestimation or underestimation). However, in terms of the magnitude of error, a negative relative error is just as different from zero (i.e., accurate estimation) as an equivalent positive relative error. A 3 (maximum vs. moderate vs. minimum visual and gravitational cues) \(\times\) 2 (near vs. far) repeated measures ANOVA was performed to investigate the effects of the within-subject variables of environmental condition and proximity of the target, respectively, on the absolute relative error of distance estimation. The results showed no main effect of environmental condition or target proximity. The interaction of the two variables was not significant, either (all \(p\) > 0.05, Greenhouse-Geisser correction; see Figure 4).  
Because there was no significant effect of target proximity, we increased the power of the analyses by combining the data from the near and far targets by averaging the absolute relative error of the two proximity conditions for each participant. For participants whose data point for either the near or far condition was an outlier, we used the data point that was not an outlier. This resulted in omission of fewer data points (\(\sim\)16%) and the remaining data from 26 participants was entered into this analysis. A repeated measures ANOVA was conducted on the effect of environmental condition on the relative error of distance perception. The effect of the environmental condition approached significance, F (1, 25) = 2.92, \(p\) = 0.10, \(\eta^{2}\)p = 0.11; Greenhouse-Geisser correction. The relative error was larger under the environment with a moderate level of visual and gravitational cues (Mrelative error = 10.71,  
Figure 4: Relative error in distance estimation by environmental condition (maximum, moderate, and minimum). The left \(y\) axis represents the maximum and minimum conditions and the right \(y\) axis the moderate condition. Near and far bars represent the egocentric distances between the participant and each target. Allocentric bars represent the distance between the two targets. Error bars represent SE.  
SD = 30.11) than the environment with minimum cues (Mrelative error = 0.62, SD = 0.21) or relative to the environment with maximum cues (Mrelative error = 0.57, SD = 0.21).  
To examine whether the absolute relative error of egocentric distance perception under each environmental condition was significantly greater than zero, we conducted one-sample \(t\)-tests (one-tailed) against zero for each environmental condition. The results revealed significant deviation from zero, i.e., an accurate estimation under all environments with maximum (t (25) = 13.60, \(p\) < 0.001, d = 2.67), moderate (t (25) = 1.81, \(p\) = 0.04, d = 0.36), and minimum (t (25) = 14.99, \(p\) < 0.001, d = 2.94) visual and gravitational cues.