We next evaluated spatial errors to determine participants’ proficiency in intercepting the target, and to determine whether there were any patterns in the participants’ reaches. For this and all following analyses, we included both trials with no errors and out-of-box errors. To assess spatial errors, we generated average 95% CI ellipses centered on the average x,y locations of the interception locations for each condition as shown in
Figure 5a. Visual inspection of this figure suggests several notable features. First, the constant errors indicate the endpoints were similar across conditions along the horizontal (x) axis, always to the right of the ball, consistent with the left-right direction of the ball's motion. However, constant errors differed between conditions along the vertical (y) axis, with lower positions for the upright conditions than the inverted conditions. Participants may be accustomed to aiming below a ball to intercept it in everyday life; given that the upright parabola condition is more natural than the upright tent, the effect of anticipating the ball's future location is more pronounced in this condition. Second, the pattern of variable errors indicated differences in the elongation and orientation of the error ellipses. Upright conditions showed trial endpoints scattered along the approximate orientation of the final trajectory. Presumably, in the upright conditions, participants were more attuned to the axis of the ball's final trajectory, especially when the trajectory was parabolic. During inverted conditions, error patterns were less elongated suggesting less influence of systematic errors. All of these effects were supported by statistical testing as follows.
A three-factor ANOVA on the data for the average x location of interception identified no significant main effects or interactions; however, the average position across conditions was significantly to the right of the ball's location (one-tailed
t test comparing x values vs. 0,
t23 = 5.77,
p < 0.001,
d = 1.18). A three-factor ANOVA on the data for the average y location of interception (
Figure 5b) identified a three-way interaction between
Orientation,
Shape, and
Visual Field,
F(1, 23) = 14.03,
p = 0.001,
η2p = 0.38, along with an interaction between
Orientation and
Shape,
F(1, 23) = 19.51,
p < 0.001,
η2p = 0.46, an interaction between
Orientation and
Visual Field,
F(1, 23) = 30.85,
p < 0.001,
η2p = 0.57), and a main effect of
Orientation (
F1,23 = 29.15,
p < 0.001,
η2p = 0.56). Inspection of the three-way interaction revealed that the modulation by
Visual Field did not qualitatively alter the interpretation of the interaction between
Orientation and
Shape (
Supplementary Figure S2a). The interaction supports the observation that average reach locations were lower for upright than inverted conditions, although the difference was modulated by
Shape. The two-way interaction between
Orientation and
Visual Field is depicted in
Supplementary Figure S2b for completeness.
Statistical testing of variable-error ellipse properties supported the observations from
Figure 5a. A three-factor ANOVA on the data for the length of the major axis (
Figure 5c) identified a main effect of
Orientation, with longer ellipses for upright than inverted conditions,
F(1, 23) = 8.68,
p = 0.007,
η2p = 0.27, and a main effect of
Shape with longer ellipses for parabola than tent
F(1, 23) = 99.89,
p < 0.001,
η2p = 0.81, but no interactions. Thus, for the more natural conditions, upright and parabolic trajectories, participants likely benefitted from stronger expectations about the ball's trajectory. A three-factor ANOVA on the data for the anisotropy of the ellipses (i.e., whether they are more elongated or circular;
Figure 5d) identified a main effect of
Orientation,
F(1, 23) = 15.47,
p < 0.001,
η2p = 0.40, with higher anisotropy for upright conditions and a main effect of
Shape,
F(1, 23) = 64.03,
p < 0.001,
η2p = 0.74, with higher anisotropy for parabola conditions. The most natural orientation, the upright parabola, yielded the highest anisotropy, providing statistical support for the observations from
Figure 5a regarding the major axis.
A two-factor ANOVA (using the Harrison-Kanji test for circular statistics; factors of
Orientation and
Shape) on the angle of the ellipse identified an interaction between
Orientation and
Shape (
F = 7.45,
p = 0.007), along with a main effect of
Orientation (
F = 13.52,
p < 0.001) and a main effect of
Shape (
F = 22.76,
p < 0.001). These results provide statistical support for the visual observations from
Figure 5a that endpoints for the upright condition were scattered along the direction of the ball's trajectory, while during inverted conditions they were scattered in the direction of the ball's trajectory for parabola but not tent trials.