Additive effects in a rod-and-frame illusion estimated by response classification

Previous research has shown that not all segments of a square frame are necessary to produce the illusory tilt of an enclosed vertical line. Indeed, the presence of a single tilted line is often sufficient to induce the illusory tilt of a nearby vertical line (Carpenter & Blakemore, 1973). How do the four segments of a quadrilateral frame contribute to the illusory tilt if any one of them is sufficient to induce the illusion? Response classification (RC) was used in two experiments to examine the independent contributions of the four segments of a quadrilateral frame to judgments of the direction of tilt of an enclosed vertical line. Orientation perturbations were added independently to the four frame segments. The orientation of the top segment contributed most systematically to these judgments, whereas the orientation of the bottom segment contributed very little. Individual differences were observed with two of the four observers showing the largest apparent tilt of the test line for shear configurations of the quadrilateral in which the top and bottom segments were rotated in a direction opposite to the right and left segments. Logistic regression was used with a double-pass technique to estimate the relative importance of the four segments. Interactions between the segments were not systematically related to the observers' judgments. The results are discussed in terms of the utility of RC and logistic regression for studying perceptual phenomena whose mechanisms are thought to lie at levels such as orientation that are different from those typically examined with RC and pixel noise.