THREE-DIMENSIONAL SETS IN ESTIMATION OF ANGLES

Summary.-The hypothesis was that an acute angle preceded by a threedimensional set will increase the likelihood of overestimation of that angle both absolutely and relative to the same angle preceded by a two-dimensional set or none. 60 subjects, using a mechanical estimator, estimated a 34" stimulus angle from a photograph in one of the three conditions in a one-way analysis of variance design. The three-dimensional set generated significantly larger estimates of the angle. Fisher (1969), using verbal estimation, indicated that acute angles displayed in a horizontal orientation produced overestimation both absolutely and relative to vertically oriented acute angles. Maclean and Stacey (1971) confirmed this finding and noted further that, while response mode had a significant effect in the estimation of horizontally oriented angles, the difference between response modes, matched reproduction and verbal estimation was least for vertically oriented angles. Ross (1973), in attempting to explain these distortion patterns inherent in the estimation of horizontal angles, concluded that these angles suggest a corner seen in depth (Gregory, 1962, 1963) and as such create an illusion as suggested by Segall, Campbell, and Herskovits (1966) in their carpentered-world hypothesis. The suggestion was that, if a three-dimensional set could be produced in subjects prior to the display of the stimulus angle, a maximal effect of learned reailinearity could be created. If culrurally based rectilinear ecologies influence perceptual responses, it follows that a stimulus angIe preceded by a three-dimensional set should be overestimated both absolutely and relative to a stimulus angle preceded by a two-dimensional set. A no-set condition was expected to produce estimates of the stimulus angle consistent with findings of Maclean and Stacey (1971). Sixty men and women enrolled in general psychology were randomly assigned to the treatment conditions. The experimental stimuli were five 4%- X 6%-in. photographs displaying angles symmetrical around the Cartesian axis.' The three-dimensional set stimuli were a series of three black and white photographs of a ping pong table. The first photograph in the series was a view of the entire table displaying two 34' acute angles representing right angles, made by white lines on the table top, seen in depth. The second was a magnified view of the center of the table focusing on the intersection and the two 34" angles, and the third, or test angle, was a magnification displaying only one 34' angle with the table edges no longer visible. Shown alone, the photograph appeared to be of a white 34" angle on a textured dark gray surface. The two-dimensional stimuli were two photographs of a standard institutional clock face measuring 13 in. in diameter. The first bladc and white photograph was a view of the entire clock whose hands formed a 34" angle at approximately 11% min. past 3 o'clock. The second was a magnified view that displayed only the hands and approximately one-third of the clock face. The third photograph was the same test photograph used as the third stimulus in the three'Photographs are on file in Document NAPS-03039. Order from Microfiche Publications. P. 0. Box 3513. Grand Central Station. New York. New York 10017. Remit $3.00 for fiche or $8.00 fir photocopy.