Perceptual and Motor Skills, 1976, 42, 625-626.
@ Perceptual and Motor Skills 1976
TIME DELAY IN ESTIMATION OF ANGLES DOUGLAS A. ROSS Indirma University of Pennsylvania Summary.-The hypotheses were that a 2-min. delay as opposed to a 2-sec. delay between observation and mechanical estimation of an acute angle will increase the likelihood of overestimation of that angle and that minimal-surround cue-conditions would produce greater overestimation than maximal cue-conditions. 40 subjects esrimated a 54" acute angle presented behind a 2-way mirror in one of the four treatment combinations in a 2 x 2 factorial design. A 2-min. time delay caused significantly larger estimates of the angle. Overestimation in the maximal cue-condition was significant but the underestimate in the minimal cue-conditions was not. Cue-conditions were not significantly different from one another. Fisher (1969) and Maclean and Stacey (1971) have shown that larger acute angles typically are underestimated using construction or reproduction techniques. Ross (1972) has confirmed the findings in a series of studies on angle estimation. The effect seems to hold for lengthened and shortened angle arms, with the angle viewed with broad vistas, or through an artificial pupil, in lighted or darkened surrounds, and with the plane of the angle either perpendicular to the line of sight or tilted away in depth. Ross (1972), however, found overestimates of ecological acute angles in a diagonalspace parking lot when drivers were forced to estimate the angle while parking in the snow. The finding was consistent for children between 3 and 11 yr. of age, using a simulated parking lot and "matchbox" cars. The method best matches a sequential reproduction technique like the original technique used by Jastrow (Fisher, 1969) to show underestimation of acute angles. Ross (1973) also showed that greater degrees of overestimation are related to the likelihood that a perceived angle represents a three-dimensional corner seen suspended in space. He argued that the use of such a variable is necessary to explain fully the relative overestimation of horizontally oriented angles described by Fisher (1969) and Maclean and Stacey ( 197 1 ) . The major untested variable in angle estimation studies is the time delay of the response. If the reliance upon long-term memory systems causes the driver to overestimate the parking angle then the implication is that cognitive events influence his perceptual judgment. In Ross' parking !ot studies the perception of the correct parking angle relied upon the driver's memory of that angle as seen on the previous days. Gregory (1971) and Segall, Campbell, and Herskovits (1966) both suggest that culturally based rectilinear ecologies influence perceptual responses. It follows that ang!e estimates should be overestimated in delayed-response conditions which require the subject to rely on his memory of the angle to be estimated. Maximum- and minimum-cue conditions were also explored (Maclean & Stacey, 1971) with the expectation that minimum-cue conditioas would lead to larger estimates. Forty men and women enrolled in general psychology were assigned to the treatment conditions randomly as they arrived for the study. The stimulus was produced by masking a light source so that a dim red 54" angle glowed on the far side of a two-way mirror. Angle arms were 11 mm in length; the subject sat in a darkened cubicle about 1 m from the window, with an angle another 20 mm beyond the window. For maximal-cue conditions the room containing the angle was illuminated allowing the subject to see Eoth the
626
D. A. ROSS
angle and assorted laboratory furniture in the background. In minimal-cue conditions only the glowing angle could be seen. The angle was displayed for 15 sec. and then was either estimated immediately or after a delay of 2 min. using a mechanical angle estimator containing one fixed and one moveable brass arm, each approximately 9 m m in length. By examining the reverse side of the estimator the experimenter could immediately read the estimate from the location of a coordinated pointer and a protractor which was etched on the aluminum panel. Subjects were told to observe the angle, and then estimate it when the experimenter returned. A 2 x 2 factorial analysis was followed by t tests of the hypothetical mean, i.e., the actual angle. Delayed presentation significantly increased angle estimation PI.^ = 9.91, P . 0 1 ) . Maximal and minimal cue conditions produced a nonsignificant difference ( K , , , = 2.35, P .05) as did the interaction (F1.n~= 3 7 , P . 0 5 ) . The overestimation was . 0 5 ) , but significantly larger than the angle ( M = 59.3, SEM = 1.91, t~ = 2.93, P the underestimation was not significantly smaller ( M = 53.4, SEA, = 1.63, ha = .37, P .05). The outcome confirms the hypotheses that time delay in angle estimation is a key variable in understanding differences reported by Ross (1972) and Fisher ( 1 9 6 9 ) and Maclean and Stacey ( 1 9 7 1 ) . Ecological cases of angle estimation (Ross, 1972) required the observer to rely on memory to park his car correctly on a snow-covered lot. When doing so, acute angles were overestimated. In laboratory studies of angle estimation using reproduction o r production methods, acute angles of 47" to 90" are underestimated when estimation techniques are immediately sequential to o r simultaneous with viewing the angle. T h e study shows that a time delay of 2 min. is sufficient to produce overestimation in the laboratory. It appears that such delays force the observer to rely o n memory structures which predispose interpretation of acute angles as representative of right angle corners positioned in depth. The absence of a significant difference between the maximum- and minimum-cue conditions suggests that the variable is not relative to the size of angle estimates. Previous studies by Ross ( 1 9 7 2 ) have also indicated the absence of overestimation in minimal-cue conditions. Maximal-cue conditions have regularly led to a pattern of overestimation of smaller angles, underestimates for angles between 40" and 80" and accurate estimation at 90". Ongoing studies are examining the generalizabiliry of the findings of overestimation for a wider range of angle sizes.
@ Perceptual and Motor Skills 1976
TIME DELAY IN ESTIMATION OF ANGLES DOUGLAS A. ROSS Indirma University of Pennsylvania Summary.-The hypotheses were that a 2-min. delay as opposed to a 2-sec. delay between observation and mechanical estimation of an acute angle will increase the likelihood of overestimation of that angle and that minimal-surround cue-conditions would produce greater overestimation than maximal cue-conditions. 40 subjects esrimated a 54" acute angle presented behind a 2-way mirror in one of the four treatment combinations in a 2 x 2 factorial design. A 2-min. time delay caused significantly larger estimates of the angle. Overestimation in the maximal cue-condition was significant but the underestimate in the minimal cue-conditions was not. Cue-conditions were not significantly different from one another. Fisher (1969) and Maclean and Stacey (1971) have shown that larger acute angles typically are underestimated using construction or reproduction techniques. Ross (1972) has confirmed the findings in a series of studies on angle estimation. The effect seems to hold for lengthened and shortened angle arms, with the angle viewed with broad vistas, or through an artificial pupil, in lighted or darkened surrounds, and with the plane of the angle either perpendicular to the line of sight or tilted away in depth. Ross (1972), however, found overestimates of ecological acute angles in a diagonalspace parking lot when drivers were forced to estimate the angle while parking in the snow. The finding was consistent for children between 3 and 11 yr. of age, using a simulated parking lot and "matchbox" cars. The method best matches a sequential reproduction technique like the original technique used by Jastrow (Fisher, 1969) to show underestimation of acute angles. Ross (1973) also showed that greater degrees of overestimation are related to the likelihood that a perceived angle represents a three-dimensional corner seen suspended in space. He argued that the use of such a variable is necessary to explain fully the relative overestimation of horizontally oriented angles described by Fisher (1969) and Maclean and Stacey ( 197 1 ) . The major untested variable in angle estimation studies is the time delay of the response. If the reliance upon long-term memory systems causes the driver to overestimate the parking angle then the implication is that cognitive events influence his perceptual judgment. In Ross' parking !ot studies the perception of the correct parking angle relied upon the driver's memory of that angle as seen on the previous days. Gregory (1971) and Segall, Campbell, and Herskovits (1966) both suggest that culturally based rectilinear ecologies influence perceptual responses. It follows that ang!e estimates should be overestimated in delayed-response conditions which require the subject to rely on his memory of the angle to be estimated. Maximum- and minimum-cue conditions were also explored (Maclean & Stacey, 1971) with the expectation that minimum-cue conditioas would lead to larger estimates. Forty men and women enrolled in general psychology were assigned to the treatment conditions randomly as they arrived for the study. The stimulus was produced by masking a light source so that a dim red 54" angle glowed on the far side of a two-way mirror. Angle arms were 11 mm in length; the subject sat in a darkened cubicle about 1 m from the window, with an angle another 20 mm beyond the window. For maximal-cue conditions the room containing the angle was illuminated allowing the subject to see Eoth the
626
D. A. ROSS
angle and assorted laboratory furniture in the background. In minimal-cue conditions only the glowing angle could be seen. The angle was displayed for 15 sec. and then was either estimated immediately or after a delay of 2 min. using a mechanical angle estimator containing one fixed and one moveable brass arm, each approximately 9 m m in length. By examining the reverse side of the estimator the experimenter could immediately read the estimate from the location of a coordinated pointer and a protractor which was etched on the aluminum panel. Subjects were told to observe the angle, and then estimate it when the experimenter returned. A 2 x 2 factorial analysis was followed by t tests of the hypothetical mean, i.e., the actual angle. Delayed presentation significantly increased angle estimation PI.^ = 9.91, P . 0 1 ) . Maximal and minimal cue conditions produced a nonsignificant difference ( K , , , = 2.35, P .05) as did the interaction (F1.n~= 3 7 , P . 0 5 ) . The overestimation was . 0 5 ) , but significantly larger than the angle ( M = 59.3, SEM = 1.91, t~ = 2.93, P the underestimation was not significantly smaller ( M = 53.4, SEA, = 1.63, ha = .37, P .05). The outcome confirms the hypotheses that time delay in angle estimation is a key variable in understanding differences reported by Ross (1972) and Fisher ( 1 9 6 9 ) and Maclean and Stacey ( 1 9 7 1 ) . Ecological cases of angle estimation (Ross, 1972) required the observer to rely on memory to park his car correctly on a snow-covered lot. When doing so, acute angles were overestimated. In laboratory studies of angle estimation using reproduction o r production methods, acute angles of 47" to 90" are underestimated when estimation techniques are immediately sequential to o r simultaneous with viewing the angle. T h e study shows that a time delay of 2 min. is sufficient to produce overestimation in the laboratory. It appears that such delays force the observer to rely o n memory structures which predispose interpretation of acute angles as representative of right angle corners positioned in depth. The absence of a significant difference between the maximum- and minimum-cue conditions suggests that the variable is not relative to the size of angle estimates. Previous studies by Ross ( 1 9 7 2 ) have also indicated the absence of overestimation in minimal-cue conditions. Maximal-cue conditions have regularly led to a pattern of overestimation of smaller angles, underestimates for angles between 40" and 80" and accurate estimation at 90". Ongoing studies are examining the generalizabiliry of the findings of overestimation for a wider range of angle sizes.
