Perceptualand MotorSkills, 1990, 70, 467-477.
O Perceptual and Motor Skills 1990
SEX DIFFERENCES AND THE ROLE O F FIGURAL COMPLEXITY IN DETERMINING T H E RATE O F MENTAL ROTATION ' M. I? BRYDEN, JULLA GEORGE, AND ROXANNE INCH University of Waterloo Summary.-Two experiments were conducted to investigate the effects of figural complexity on the rate of mental rotation of 3-dimensional Figures and to compare the performance of men and women. Complexity was manipulated in three ways: by changing the number of blocks in the Figure (7 or lo), by altering the number of turns (2 or 3), and by using outline or solid figures. In the first study, these factors were manipulated between groups of subjects. Women showed steeper slopes than men, but none of the complexity variables affected either slope or intercept for the mental rotation function. In the second study, number of nuns and number of blocks were manipulated within-subjects, using only the solid figures. There were significant sex differences in both slope and intercept, and the number OF blocks affected the slope of the rotation function. In both studies, a small percentage of the subjects showed nonlinear functions relating angular rotation to response time. Although the women consistently showed slower rotation functions, rate of rotation did not relate either to figural complexity or to nonlinearity. The results suggest that the rate of mental rotation is not affected by figural complexity, at least at the levels used i n the present study, and that men and women employ essentially similar strategies.
The hscovery that there is a linear relation between the time required to decide whether two complex figures are identical or not and the angular difference between them (Shepard & Metzler, 1971) is one of the landmarks of contemporary cognitive psychology. The Shepard and Metzler mental rotation experiments provided the impetus for a great deal of research on mental imagery and mental representation (e.g., Kosslyn, 1980; Metzler & Shepard, 1974; Pylyshyn, 1973, 1979; Shepard & Cooper, 1982). The basic phenomenon has been replicated many times and is now part of the standard knowledge of cognitive psychologists. One factor that should affect the rate of mental rotation is that of stimulus complexity (Folk & Luce, 1987). Complexity, however, has usually been studied with two-dimensional figures rotated in the picture plane, and most studies of this sort have not produced any systematic effects of complexity (Cooper, 1975; Cooper & Podgorny, 1976). There have been relatively few 'This research was supported by a strategic grant From the Natural Sciences and Engineering Research Council of Canada to the University of Waterloo (K. S. Booth, Principal Investigator). The authors thank m e Morgan and Kelly Booth of the Computer Graphics Laboratory for their work in reparing the stimulus materials. In addition, Margaret Ingleton and Daniel Voyer tested some o f t h e subjects, and Thomasin Adams-Webber and Leslie MacRae assisted with the data analysis. R. Inch is now at the University of Saskatchewan, and J. George is at the Women's Health Care Research Unit, London, England. Address requests for reprints to Dr. M. P. Bryden, Department of Psychology, University of Waterloo, Waterloo, Ontario, Canada N2L
3G1.
468
M. l? BRYDEN, ETAL.
attempts to study complexity in three-dimensional mental rotation. Metzler and Shepard (1974) used 2-turn 7-block configurations and reported that rate of rotation was much faster than with the more conventional 3-turn 10-block configurations. Yuille and Steiger (1982) added seven additional blocks to the original Shepard-Metzler figures to make complex 17-block figures. They reported that rotation rates were much slower for their complex figures than for the standard figures. Both of these studies, in contrast to those using figures in the picture plane (see Folk & Luce, 1987), suggest that rotation rate decreases with increasing complexity. In addition, mental rotation tasks are frequently used in the study of sex differences in spatial ability. Linn and Petersen (1985) have concluded that sex differences are larger on paper-and-pencil tests of mental rotation than on other spatial tasks. Under more rigorous experimental condtions, both Tapley and Bryden (1977) and Kail, Carter, and Pellegrino (1979) have reported that women rotate three-dimensional images more slowly than d o men. Voyer and Bryden (in press) have reported both sex differences and spatial ability differences in over-all performance in a laterahzed mental rotation task. The pervasiveness of such sex differences suggests that it is worth investigating individual differences in mental rotation more fully. The present study, therefore, has two objectives. First, we were interested in whether people mentally rotated stimuh varying in complexity at different rates. A relatively simple interpretation of Pylyshyn's (1973) propositional view, for instance, would argue that larger figures or figures that looked "heavier" would be rotated more slowly, because people would expect them to have greater inertia in the real world. Second, we were interested in individual differences in rates of mental rotation, especially those relating to sex differences. I n the following experiments, "complexity" was manipulated in three ways. First, the original Shepard and Metzler figures were outline drawings; we also produced solid figures having the same arrangement of blocks. Second, we constructed both 7-block and 10-block figures. T h r d , the original figures are what we shall call "3-turn" figures, that is, as one moves from one end of the block arrangement to the other there are three right-angle turns. However, to produce mirror-image pairs, it is only necessary to have some blocks lie on each of the X, Y, and Z axes, that is, a set of "2-turn" figures can also be constructed. Examples of the outline versions of the 2-turn and 3-turn figures are shown in Fig. 1; the solid figures were shaded and shadowed versions of the same figures, with the individual blocks clearly demarcated. These manipulations are not conventional ways of altering stimulus complexity, and we first verified that subjects actually did consider them effective. I n a two-alternative forced-choice situation, subjects judged the
STIMULUS COMPLEXITY AND MENTAL ROTATION
469
3-turn figures more complex than the 2-turn figures on 77% of the trials (p
O Perceptual and Motor Skills 1990
SEX DIFFERENCES AND THE ROLE O F FIGURAL COMPLEXITY IN DETERMINING T H E RATE O F MENTAL ROTATION ' M. I? BRYDEN, JULLA GEORGE, AND ROXANNE INCH University of Waterloo Summary.-Two experiments were conducted to investigate the effects of figural complexity on the rate of mental rotation of 3-dimensional Figures and to compare the performance of men and women. Complexity was manipulated in three ways: by changing the number of blocks in the Figure (7 or lo), by altering the number of turns (2 or 3), and by using outline or solid figures. In the first study, these factors were manipulated between groups of subjects. Women showed steeper slopes than men, but none of the complexity variables affected either slope or intercept for the mental rotation function. In the second study, number of nuns and number of blocks were manipulated within-subjects, using only the solid figures. There were significant sex differences in both slope and intercept, and the number OF blocks affected the slope of the rotation function. In both studies, a small percentage of the subjects showed nonlinear functions relating angular rotation to response time. Although the women consistently showed slower rotation functions, rate of rotation did not relate either to figural complexity or to nonlinearity. The results suggest that the rate of mental rotation is not affected by figural complexity, at least at the levels used i n the present study, and that men and women employ essentially similar strategies.
The hscovery that there is a linear relation between the time required to decide whether two complex figures are identical or not and the angular difference between them (Shepard & Metzler, 1971) is one of the landmarks of contemporary cognitive psychology. The Shepard and Metzler mental rotation experiments provided the impetus for a great deal of research on mental imagery and mental representation (e.g., Kosslyn, 1980; Metzler & Shepard, 1974; Pylyshyn, 1973, 1979; Shepard & Cooper, 1982). The basic phenomenon has been replicated many times and is now part of the standard knowledge of cognitive psychologists. One factor that should affect the rate of mental rotation is that of stimulus complexity (Folk & Luce, 1987). Complexity, however, has usually been studied with two-dimensional figures rotated in the picture plane, and most studies of this sort have not produced any systematic effects of complexity (Cooper, 1975; Cooper & Podgorny, 1976). There have been relatively few 'This research was supported by a strategic grant From the Natural Sciences and Engineering Research Council of Canada to the University of Waterloo (K. S. Booth, Principal Investigator). The authors thank m e Morgan and Kelly Booth of the Computer Graphics Laboratory for their work in reparing the stimulus materials. In addition, Margaret Ingleton and Daniel Voyer tested some o f t h e subjects, and Thomasin Adams-Webber and Leslie MacRae assisted with the data analysis. R. Inch is now at the University of Saskatchewan, and J. George is at the Women's Health Care Research Unit, London, England. Address requests for reprints to Dr. M. P. Bryden, Department of Psychology, University of Waterloo, Waterloo, Ontario, Canada N2L
3G1.
468
M. l? BRYDEN, ETAL.
attempts to study complexity in three-dimensional mental rotation. Metzler and Shepard (1974) used 2-turn 7-block configurations and reported that rate of rotation was much faster than with the more conventional 3-turn 10-block configurations. Yuille and Steiger (1982) added seven additional blocks to the original Shepard-Metzler figures to make complex 17-block figures. They reported that rotation rates were much slower for their complex figures than for the standard figures. Both of these studies, in contrast to those using figures in the picture plane (see Folk & Luce, 1987), suggest that rotation rate decreases with increasing complexity. In addition, mental rotation tasks are frequently used in the study of sex differences in spatial ability. Linn and Petersen (1985) have concluded that sex differences are larger on paper-and-pencil tests of mental rotation than on other spatial tasks. Under more rigorous experimental condtions, both Tapley and Bryden (1977) and Kail, Carter, and Pellegrino (1979) have reported that women rotate three-dimensional images more slowly than d o men. Voyer and Bryden (in press) have reported both sex differences and spatial ability differences in over-all performance in a laterahzed mental rotation task. The pervasiveness of such sex differences suggests that it is worth investigating individual differences in mental rotation more fully. The present study, therefore, has two objectives. First, we were interested in whether people mentally rotated stimuh varying in complexity at different rates. A relatively simple interpretation of Pylyshyn's (1973) propositional view, for instance, would argue that larger figures or figures that looked "heavier" would be rotated more slowly, because people would expect them to have greater inertia in the real world. Second, we were interested in individual differences in rates of mental rotation, especially those relating to sex differences. I n the following experiments, "complexity" was manipulated in three ways. First, the original Shepard and Metzler figures were outline drawings; we also produced solid figures having the same arrangement of blocks. Second, we constructed both 7-block and 10-block figures. T h r d , the original figures are what we shall call "3-turn" figures, that is, as one moves from one end of the block arrangement to the other there are three right-angle turns. However, to produce mirror-image pairs, it is only necessary to have some blocks lie on each of the X, Y, and Z axes, that is, a set of "2-turn" figures can also be constructed. Examples of the outline versions of the 2-turn and 3-turn figures are shown in Fig. 1; the solid figures were shaded and shadowed versions of the same figures, with the individual blocks clearly demarcated. These manipulations are not conventional ways of altering stimulus complexity, and we first verified that subjects actually did consider them effective. I n a two-alternative forced-choice situation, subjects judged the
STIMULUS COMPLEXITY AND MENTAL ROTATION
469
3-turn figures more complex than the 2-turn figures on 77% of the trials (p
