Perceptual plane geometry: collinearity judgments probe the perceived orientation of an angle's sides

The task was to position a dot to lie one line length beyond the vertex of an angle by mentally extending one line segment forming the angle (and later the other line segment). Eight angles, variously oriented, provided judgmental errors attributable to the size of the subtended angle and line orientation. Collinearity errors are consistent with the hypothesis that the sizes of all subtended angles are underestimated. Horizontal-vertical assimilation describes the line-orientation effect. The largest error component is associated with the interaction of the two independent variables. Judgmental errors were modeled by a set of theoretically meaningful additive terms. Modeling was facilitated by symmetry assumptions (associated with odd and even mathematical functions) about the absolute magnitude and sign of judgmental errors that lead to the comparison of judgments derived from "interesting pairs" of stimuli.