individual differences in visual imagery and spatial ability

INTELLIGENCE 8, 93-138 (1984)

Individual Differences in Visual Spatial Ability* STEVEN E. POLTROCK

Bell Laboratories 600 Mountain Avenue

Murray Hill, NJ 07974

POLLY BROWN University of Denver 2030 S. York Street Denver, CO 80208

Imagery and

Spatial ability is generally assumed to involve construction, transformation, and interpretation of mental images. To explore the relationship between spatial ability and both image quality and image process efficiency, 79 subjects performed eight spatial tests, completed three imagery questionnaires, and participated in six laboratory tasks. These laboratory tasks were devised to measure image quality and the efficiency of image generation, image rotation, image scanning, adding and subtracting detail in images, and integration of images. Although ratings of imagery control and vividness were unrelated to spatial test performance, laboratory measures of process efficiency and image quality were strongly related to spatial test performance and weakly related to one another. A structural equation model identified a single spatial factor, Visu- alization ability, that can be decomposed into unique variance plus a linear combination of measures of image quality and image process efficiency. An interpretation of this model is that successful performance on spatial tests requires maintenance of a high-quality image and efficient image transformation and inspection processes.

When first attempting to solve Rubik's Cube a person may experimentallY rotate sections of the cube, and observe the effects of these rotations on several of the cube facets. After several hours of practice, a system of rules may be learned that allows effects of rotations to be predicted in a mental image. Using these rules and the corresponding images, the cube can eventually be solved.

*This research was supported by grant 80-0127 from the Air Force Office of Scientific Research and by grant R01 HD 23251 from the National Institute of Child Health and Human Development. We wish to thank John Horn, Marcy Lansman, Dennis Egan, and Franca Agnoli for their valuable feedback regarding both substantive and methodological aspects of drafts of this paper. We are also grateful to Jack McArdle for his statistical guidance and to Ralph Mason for technical assistance. Correspondence and requests for reprints should be sent to Steven E. Poltrock at MCC, 9430 Research Boulevard, Echelon Building #1, Austin, TX 78759.

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94 POLTROCK AND BROWN

The total time required to first solve Rubik's Cube could probably be predicted, in part, by measures of spatial ability. Indeed, some tasks designed to measure spatial ability require answering questions about colors on the facets of a cube. It is generally assumed by those who study spatial ability that, like solving Rubik's Cube, performing spatial ability tests involves construction, transformation, and interpretation of mental images. However, surprisingly little evidence exists linking spatial ability to particular imagery processes or structures.

Research on the nature of spatial ability has generally followed three approaches. First, factor analytic studies identified spatial ability, established its importance as a predictor of performance, and motivated competing theories of spatial ability. Second, the relationship between imagery and spatial ability has been studied using self-report measures of imagery ability. Third, researchers have recently developed and tested cognitive models of performance for specific spatial ability tests. This article briefly reviews the contributions of each of these approaches, then describes an investigation of the role of image quality and imagery process efficiency in spatial ability that combines these three approaches.

Factor Analytic Studies of Spatial Ability

Strengths and Weaknesses of Factor Analysis

There are both strengths and weaknesses in the factor analytic approach to studying individual differences. Because of its strengths, factor analysis has been widely used in the study of abilities in general and spatial ability in particular. Frequently used as a means of exploratory analysis, factor analysis reduces the number of variables required to represent test performance, and may suggest an organization of abilities that affect test performance. From a psychometric per- spective, factor scores from such an analysis provide an advantage over test scores as a measure of ability or aptitude because variance specific to a particular test is removed. Recently developed methods of confirmatory factor analysis permit tests of theories regarding the number and organization of abilities con- tributing to test performance.

Although factor analysis provides powerful methods for summarizing and organizing test results, psychologically meaningful interpretations of the organization may be elusive. When simple structure is obtained, each factor is defined in terms of the set of tests that correlate with (have substantial loadings on) the factor. To ascribe psychological attributes to the factor requires a theory of performance for each test. Given such theories, a factor can be defined as the processes that are common to all tests with substantial loadings. In practice, however, intuitions about test performance replace theory. Consequently, factor analysts have described spatial ability as an ability to use visual imagery, but have not developed detailed models of the processes required to solve spatial tests.

VISUAL IMAGERY AND SPATIAL ABILITY 95

If imagery is used in spatial tests, then subcapacities or abilities may exist that correspond to different imagery processes or structures. Factor analysis has not proven a successful means for identifying such subabilities, though some evidence exists for an ability to rotate images. The problem is that separate factors cannot be derived unless different tests depend primarily on different processes. If all spatial tests involve the same processes, then variability in the processes is combined in one factor.

Spatial Subabilities

One of the strengths of factor analysis is that it can suggest an organization of abilities. Indeed, much of the research on spatial ability has attempted to decompose spatial ability into a meaningful organization of subabilities. However, there is considerable disagreement regarding the number of spatial factors, their organization, and their interpretations. One reason for these disagreements is that there are many algorithms for determining both the number and structure of the factors obtained in a factor analysis. Thus, different investigators can reach very different conclusions when analyzing the same data.

Thurstone's (1938) study of Primary Mental Abilities exemplifies this problem. Thurstone (1938) administered 56 tests designed to measure a wide range of abilities to 218 volunteers. This rich data base has been analyzed many times yielding different numbers of spatial factors and different organizations of the factors (see Lohman, 1979 for a review of published analyses). Thurstone (1938) identified 13 orthogonal factors, including one factor, called Space, that he described as a facility for spatial or visual imagery. Using three different methods of factor analysis, Holzinger and Harman (1938), Spearman (1939), and Eysenck (1939) identified a general intelligence factor and specific ability factors including a factor for spatial ability. In contrast with these older analyses, Zim- merman (1953) identified no general factor but two spatial factors that Guilford and Lacy (1947) had called Spatial Relations (SR) and Visualization (Vz). It is unclear which of these five factor analyses best summarizes or describes Thurstone's data.

The disagreement about the number and organization of spatial ability factors is reflected in two recent reviews by McGee (1979) and Lohman (1979). McGee (1979) discussed evidence for two spatial factors: Visualization and Orientation. Visualization was described as an "ability to mentally manipulate, twist or invert a pictorially presented stimulus object" (p. 893). Orientation (a term McGee uses for Guilford and Lacy's SR factor) was described as an ability to com- prehend the arrangement of elements in a stimulus and remain unconfused by a change in orientation of the stimulus. Reviewing the same literature, Lohman (1979) concluded that there are three factors, Visualization, Orientation, and Spatial Relations. Lohman described Spatial Relations as the ability to rapidly and accurately rotate a mental image. He offered no psychological interpretation


for Visualization, but noted that it is defined by complex spatial tasks. The diversity of opinions on this issue is demonstrated by Guilford's (1956) theory of intelligence that includes 30 spatial abilities.

Conclusions

Despite the many areas of disagreement, there are some general points of agreement (Lohman, 1979; McGee, 1979). First, there is clear and consistent evidence for one or more spatial abilities. Second, one factor accounts for most of the common variance in spatial tests, though additional factors sometimes can be extracted. Third, spatial ability reflects the use of mental imagery to manipulate spatial representations.

Self-Report Imagery Studies

If mental imagery is a central component of performance in spatial tests, then individual differences in imagery should be related to spatial ability. Evidence for substantial individual differences in experienced vividness of images dates to Galton (1880), who also found that scientists report experiencing little or no imagery. Since scientists typically have good spatial ability, Galton's observa- tions argue against a relationship between imagery vividness and spatial ability. In more recent research, positive but surprisingly weak relationships have been found between spatial ability and characteristics of imagery (see reviews by Ernest, 1977; White, Sheehan, & Ashton, 1977).

Self-report questionnaires have been the most frequently used instruments for assessing individual differences in mental imagery. Questionnaires have been constructed to measure imagery vividness, imagery control, and preferred mode of thinking, verbal or visual. Self ratings on tests of vividness have been com- pared with paired-associate learning, recognition memory, free recall, speed to generate an image, speed to mentally rotate a figure, and speed to discriminate between two slightly different pictures (see Ernest, 1977 for a review). For the most part, vividness is unrelated to performance in these tasks. Vividness is apparently related to memory performance for verbal stimuli only when the memory test is unexpected (Janssen, 1976; Sheehan, 1973). Perhaps individuals with vivid imagery are more likely to encode the stimuli in images when no test is expected. However, only weak relationships with spatial test performance have been found.

Introspective reports of differences in ability to manipulate or control images led to development of tests of imagery control. Unlike vividness ratings, imagery control ratings have proven to be related to some measures of cognitive function- ing. For example, control was correlated with paired-associate learning (Morelli & Lang, 1971), speed of mental rotation, speed of spatial problem solving, and performance on some spatial tasks (Snyder, 1972). However, performance on


other spatial tasks is uncorrelated with imagery control ratings,, and significant correlations are usually weak.

In general, research with self-report measures has provided little evidence that spatial ability involves the use of imagery. Self-report imagery measures and spatial ability test performance are weakly correlated (r < .30), with somewhat higher correlations for measures of imagery control than imagery vividness (see Ernest, 1977 for a detailed review). Furthermore, self-report questionnaires and spatial tests load on different factors when factor analyzed (DiVesta, Ingersoll, & Sunshine, 1971; Forisha, 1975). If both self-report and spatial tests measure imagery, they apparently measure different aspects of imagery.

Perhaps self-report questionnaires provide a poor means of assessing individual differences in imagery. There are both methodological and theoretical reasons to be skeptical of the validity of these measures. Problems of validity with self-report measures are well known in the psychometric field. People may differ greatly in their experience of images, and may use very different criteria for judging vividness or control. Furthermore, tests of imagery vividness and control seem to have been motivated purely by introspections, not by any theory of how imagery is used. However, the notion that vividness is an important aspect of imagery seems to imply an unstated pictorial theory of imagery. Appar- ently, it is assumed that successful use of imagery requires a pictorial image that can be examined with an accompanying experience akin to the experience of viewing a picture. It is possible, however, that images can be manipulated and examined without any experience of "seeing" images. Indeed, people who claim to have no imagery are able to successfully use the method of loci as a mnemonic device. Thus, these tests may measure qualities of imagery that are not functionally related to the use of imagery in memory or problem solving.

Cognitive Models of Test Performance

In the past decade researchers have applied cognitive process methods and theories to the study of spatial ability. Models have been proposed of the cognitive processes required to solve particular spatial tests. By examining the relationship between spatial test performance and parameters of these models, individual differences in spatial ability can be attributed to particular cognitive processes.

Research by Shepard and Metzler (1971) and by Cooper and Shepard (1973) provided the groundwork for much of the research relating cognitive processes and spatial abilities. Shepard and his colleagues demonstrated that the time to compare two objects that are identical except for a rotation increases linearly with the angle of rotation, and they developed a model of task performance. According to this model the speed of mental rotation can be measured by computing the slope of the function relating latency find angle. Measurements of this rotation process are of interest because many spatial ability tests seem to involve


mental rotation, and rotation is identified with both the Cognition of Figural Transformations ability in Guilford's Structure of Intellect Theory and the Spa- tial Relations factor described in Lohman's (1979) review of spatial ability research.

Evidence that mental rotation is involved in complex spatial tests was first obtained by Snyder (1972) who found that the slope, intercept, and accuracy of mental rotation were correlated with performance on the Spatial Relations test of the Differential Aptitude Test. More recently, Lansman, Donaldson, Hunt, and Yantis (1982) found that mean rotation latency was highly correlated (r = .78) with the Visualization Factor (Gv) of Cattel's theory of crystallized and fluid intelligence (Cattell, 1963; Horn, 1968). This factor was defined by the common variance in six spatial tests that varied in complexity. Thus, mental rotation may be an important component of performance in many spatial tests.

Models of performance in spatial ability tests have generally included the mental rotation process as one component. For example, Egan (1979) proposed models for tests of three of the 30 spatial factors in Guilford's Structure of Intellect Model. One factor was defined by tasks that require deciding whether two rotated objects are the same or different. Egan's model for this mental rotation factor was borrowed from Just and Carpenter's (1976) analysis of image rotation. A similar model for the Hands test combined mental rotation with matching processes. Egan did not provide tests of these models, but proposed that the latencies of components of such models would provide a useful way of measuring spatial abilities.

Pellegrino and Kail (1982) reported a systematic study of the role of mental rotation in both simple and complex spatial tests. They studied mental rotation of letters, two-dimensional figures, and complex drawings of three-dimensional objects. For simple stimuli mental rotation was fast, and accuracy in a written form of the test was correlated with both the slope and intercept of the latency function. For complex stimuli rotation was substantially slower, and accuracy in a written test was correlated with slope, intercept, and error rate. Pellegrino (1983) has interpreted the error rate in tasks with complex spatial stimuli as an indicant of the precision or quality of stimulus representation. Thus, spatial ability test performance may depend on both image quality and rotation process efficiency.

Process Efficiency and Image Quality

The research reviewed above lends credence to the position that imagery is commonly used in performing spatial tests. Furthermore, it suggests that a subject's performance on many spatial tests is partly determined by the speed or efficiency of mental rotation. But do other imagery processes affect spatial ability test performance?

It is noteworthy that in every study investigating the relationship between


mental rotation and spatial ability, both intercept and slope of the latency function were correlated with criterion performance. These correlations suggest that the intercept measures the latency of some collection of processes that also contribute to spatial ability. Indeed, it is reasonable to expect spatial ability to be influenced by the operation of several imagery processes, not just mental rotation. Presumably the emphasis on mental rotation that has dominated recent research derives from the availability of procedures for measuring rotation rate. However, recent theoretical and empirical work by Kosslyn and his colleagues (reviewed in Kosslyn, 1980, 1981) suggests that properties of other imagery processes can be measured.

Kosslyn (1981) theorizes that images are constructed from information in long-term memory about the appearance of an object or objects. The constructed image is a data structure represented by points in a visual buffer in much the same way that a television picture is represented as points on a screen. The buffer is characterized by limited extent, limited resolution, and decreasing resolution with distance from its center or focus. These characteristics of the image buffer impose limitations on image quality.

An image is initially generated by a process that converts descriptive information in long-term memory into points in the image buffer. Details are integrated into an existing image by processes that ensure proper spatial relations are maintained. A search process determines the location in an image where a detail is to be integrated, and inspects images for other purposes as well. Images may be transformed by expansion, reduction, rotation, and scanning. The scanning transformation translates the image so that a new part moves to the center or focus of the image buffer. Evidence for these processes and descriptions of how they interact are provided by Kosslyn (1980; 1981; Kosslyn, Pinker, Smith, & Shwartz, 1979).

Kosslyn's theory suggests several hypotheses regarding sources of individual differences in imagery ability. There could be individual differences in (a) the descriptive information in long-term store, (b) limitations on image quality such as capacity of the visual buffer, or (c) the efficiency of the processes, such as mental rotation, that operate on these data structures. This article reports research investigating individual differences in the latter two of these potential sources of individual differences, image quality and process efficiency. If individual differences in imagery contribute to spatial ability, then relationships should be observable between spatial ability and measures of image quality and process efficiency.

The primary purpose of this research was to explore the hypothesized relationships between spatial ability and cognitive imagery processes and structures. Tasks were devised to measure the efficiency of processes involved in generating images, adding or subtracting detail, integrating images, and transforming images. Spatial ability was measured by factor analyzing performance on a battery of spatial tests. One goal of this research was to determine the contribution of


specific cognitive imagery processes to spatial ability. If this endeavor were successful, the individual differences in spatial ability could be understood as reflecting individual differences in the efficiency of particular imagery processes or the quality of image representations.

A secondary purpose of this research was to investigate the relationship between self-report tests of imagery and cognitive imagery processes. It is easy to generate hypotheses about the processes that might be related to self-reports. For example, image vividness might be related to image quality, and image control might be related to the efficiency of image transformation processes. Thus, self- report tests of imagery vividness, imagery control, and preferred mode of thinking were administered.

The remainder of this article consists of five sections. The first section describes the general method followed in obtaining cognitive, self-report, and spatial ability measures. The second section describes the tasks used to measure cognitive processes and image quality and their results. The third section describes the self-report measures and their relationship to the cognitive measures. The fourth section describes the procedures used to measure spatial ability and the relationship between spatial ability and both cognitive and self-report measures. These results are summarized and discussed in the last section.

GENERAL METHOD

Procedure

The ordering of tasks and the order of trials within tasks were the same for all subjects. The experiment consisted of two sessions on two different days. In the first session subjects were tested individually. This session required from 1.5 to 3.5 hours, depending on the subjects' speed in self-paced tasks. All the cognitive measures and a few spatial ability measures were obtained in the individual session. In the second session subjects were tested in groups. Group sessions lasted about two hours. Three self-report questionnaires and several more spatial tests were administered in the group session. (See Table 1 for the task order.) Subjects were paid at the end of the group session.

Equipment

In many of the tasks in the first session a computer-controlled slide projector was used to present stimuli. Stimuli were controlled and responses were col- lected by a Charles River Data Systems MF-211 computer with an LSI 11/03 central processor. ADAC Model 1300/HCO and 1616/CCI digital input and output panels provided the interface between the computer and other equipment. The computer controlled when a Kodak Ektagraphic slide projector advanced to the next slide through use of the projector's remote controls. The computer also controlled when each slide was presented through use of a Gerbrands Model 66 electronic shutter attached to the lens of the projector.


TABLE 1 Order of Tasks in Individual and Group Sessions

Individual Group Session Tasks Session Tasks

Picture VVIQ Rotate TVIC Add/Triangles VVQ Subtract/Triangles Designs Add/Stars Figures Subtract/Stars Paper Folding Scan Components Integrate Cube-Cutting Puzzles Mazes Space Relations

Slides were projected on a screen approximately 7 feet from the projector. Subjects sat just to the left and in front of the projector facing the screen. Subjects held two response buttons, one in each hand, while the experimenter held a third response button. The computer was programmed to recognize the experimenter's button as a signal to start either the experiment or the main trials after a set of practice trials. The subjects' response buttons were used to respond to each stimulus. After each response, the computer closed the shutter, advanced to the next slide, and after a programmed interval of I s the shutter was opened to present the slide. The interval between stimulus onset and the response was measured to the nearest hundredth of a second by a programmable clock.

In some tasks stimuli were presented auditorily. The stimuli were recorded in advance and presented by a Sony Model TC-252 tape recorder. Stimuli were presented through a speaker at a comfortable listening level.

Subjects Seventy-nine subjects were recruited from the University of Denver commu-

nity through campus newspaper advertisements, posters, and classroom an- nouncements. Each subject was paid $15 for participation in the experiment. There were 39 males and 40 females. All 79 subjects participated in the individual session, but only 77 subjects (39 males and 38 females) participated in the group session.

COGNITIVE IMAGERY TASKS

Measuring Process Efficiency The efficiencies of imagery processes were assessed by measuring latencies to

complete tasks involving these processes. The general strategy followed in this research was to use latency differences or linear regression slopes to separate the


contribution of a specific process from the total latency. Consider measurement of image rotation efficiency as an example. Following the method of Shepard and Metzler (1971), subjects were required to decide whether two figures were identical except for a simple rotation, The time to respond in this task increases with the angular difference between the two figures, suggesting that subjects mentally rotate the figures in a manner similar to physical rotation. The linear regression slope of the latencies provides a measure of the time to rotate a figure through a unit angle. Thus, a subject with a lower slope could be said to rotate more efficiently. The intercept of the linear regression function provides a measure of the time to encode the stimulus, generate an image, and respond. Thus, the intercept provides another measure of efficiency, but includes both imagery and nonimagery processes.

Four tasks were developed in an attempt to separate the processes required to generate an image structure from those required to add, subtract, or integrate detail. In the first task subjects were simply asked to press a key when an image was formed. In two other tasks details were added to or subtracted from an image. In a fourth task several parts were integrated to form a complete image.

Efficiency of two image transformation processes, scan and rotate, were studied. Transformation processes permit an image to be manipulated in much the same way as an actual visual scene. For example, through use of rotate and scan transformations an architect could examine an image of a building in much the same way that a physical model would be examined. One might expect the efficiency of these functions to influence the amount of control over images that a subject experiences.

Measuring Image Quality

In many of these tasks accuracy was measured. The interpretation of accuracy measures in cognitive tasks such as these is difficult. However, measures of accuracy may permit evaluation of the importance of our second hypothesized source of individual differences in imagery ability, limitations in image quality. Suppose that subjects differ in the quality or quantity of the information available in the visual buffer. These characteristics of the image data structure are likely to influence the accuracy of the outcome of imagery functions, but may not affect the time required by processes operating on the data structures. Furthermore, the capacity of the visual buffer is likely to influence accuracy in every task that requires imagery. If these hypotheses are correct, then accuracy on different cognitive tasks should be positively correlated, and provide a measure of image quality (see Pellegrino, 1983, and Pellegrino & Kail, 1982, for similar interpretations of accuracy).

Picture Task

The efficiency of image generation was assessed by asking subjects to form an image of a verbally-described object or objects. The subject was required to press


a button when the image was formed, and the time was measured from stimulus onset to the subject's response. In a similar experiment Kosslyn (1980) found that the time to form an image increased by about 125 ms per object as the number of objects to be imaged increased from two to four.

In our task, subjects were simply asked to form visual images of verbally described scenes, and the time to form each image was measured. No objective measure of performance was obtained. The number of objects in each scene was manipulated, but over a smaller range than that used by Kosslyn (1980); some scenes consisted of only one object while others consisted of two objects.

Method

Materials. Twenty phrases, verbal descriptions of scenes, were constructed. Half the phrases described only one object and half described two objects. In addition, four practice phrases were constructed. All phrases were photographed and presented separately on slides as white words on a black background. The order of presentation of the 20 descriptions was randomized, but remained constant for all subjects.

Procedure. Subjects were instructed to form "a mental picture or visual image" of the scene described on each slide. As soon as subjects could clearly " s ee" the scene described, they pressed a button. After each response the slide projector automatically advanced, and the next slide was presented. Subjects completed four practice slides and 20 experimental slides.

Results and Discussion

The mean times to create an image were longer for two objects (2511 ms) than for one object (2122 ms), t(78) = 2.99, p < .005. Generation of an image of two objects required 389 ms more than an image of one object, suggesting that this interval represents the time to generate each object. This interval of 389 ms is somewhat longer than the value of about 125 ms per object obtained by Kosslyn (1980), but much less than the value of 2520 ms obtained by McGlynn, Hofius, and Watulak (1974). Unfortunately, the 389-ms interval cannot be un- ambiguously interpreted. The verbal descriptions of two-object images were somewhat longer, requiring more reading time. The difference between the two conditions could be largely due to the difference in reading times.

We had intended to use the latency difference between one- and two-object images to separate image generation time from the time to encode the stimulus and initiate the response. Realizing that the number of objects was confounded with description length, we decided to use overall mean latencies to measure the efficiency of the picture function. Descriptive statistics regarding mean latency,


presented in Table 2, indicate that the mean time to create an image was highly reliable.

Add Task

The purpose of the Add Task was to assess ability to add detail to visual images. In the Add Task subjects were asked to mentally add dots at specified locations in a base form. First the base form was presented, followed by five pictures of the base form and a dot in some location. Subjects controlled the rate of dot presentation by pressing'a button when ready for the next dot. After the last dot was added subjects were required to identify the resulting image among a set of alternatives so that accuracy could be measured. There were two levels of difficulty; the simpler level required adding dots to a triangle and the more difficult level required adding dots to a six-pointed star.

Method

Materials. Twenty-eight problems were constructed. Each problem required adding five dots, one at a time, to a base form. The base form was a triangle for one set of 14 problems and a six-pointed star for a second set of 14 problems. The first two problems from each set of 14 were practice problems and the remaining 12 were test problems. The positions where dots were to be added were chosen randomly from 13 positions on the triangle and 25 positions on the star, as shown in Figs. l(b) and 2(b). All pictures were photographed and presented separately on slides as white figures on a black background.

The first picture of each problem presented the base form without any dots. The next five pictures each showed the base form with one dot in some position on the form. The height of the triangles in these pictures subtended a visual angle of approximately 5.5 deg.; the height of the stars subtended a visual angle of approximately 6 deg. The seventh picture showed six figures, labeled 1 to 6, containing the base form and five dots. (Figures l(a) and 2(a) illustrate sample problems.) One of these six figures represented the correct image; that is, the five dots were in the positions indicated on the five previous pictures. In the other five figures four dots were in the correct positions and a fifth dot was in a wrong position; the correct position for this fifth dot differed for each of the five distractor figures. The target (correct) figure appeared with the labels 1, 2, 3, 4, 5, and 6 in this last picture an equal number of times.

Procedure. Subjects were instructed to form a "mental picture" of the triangle and add the dots to this picture. The pace of the task was controlled by the subject pressing a button when ready for the next slide. Subjects were not informed that latencies were measured. Responses to the last slide were given


FIG. 1. task.

STUDY SLIDES

TEST SLIDE (b)

(o)

Add/triangle task: ('a) sample problem; (b) 13 dot positions utilized in the

orally and recorded by the experimenter. All subjects completed two practice and 12 test triangle problems, then two practice and 12 test star problems.


Proportion Correct. The mean number of correct responses for 12 problems was 9.01 for triangles and 9.46 for stars. According to a repeated measures Analysis of Variance there was no significant difference in accuracy for the two base forms, F(1, 78) = 3.31, p > .05. Of course, neither the presence nor the absence of an effect is interpretable because the base forms were confounded with practice. The stars were always presented after the triangles. Descriptive statistics are presented in Table 2.


STUDY SLIDES

TEST SLIDE (b)

(a)

FIG. 2. Add/star task: (a) sample problem; (b) 25 dot positions utilized in the task.

Mean Response Times. Mean RTs are presented in Table 3 as a function of the base form (triangle or star) and the ordinal position of the dot to be added. Subjects were considerably slower when adding dots to a star despite the effects of practice, F(1, 78) = 39.92, p < .001. Furthermore, subjects slowed with the addition of each new dot, producing a highly significant Position main effect, F(4, 4t2) = 60.86, p < .001. The increase in time with each succeeding dot was considerably greater for stars than for triangles, resulting in a significant interaction, F(4, 412) = 10.47, p < .001. For both the triangles and stars mean RT increased approximately linearly with dot ordinal position, resulting in a correlation between mean RT and dot ordinal position of 0.991.

Why is there a linear relationship between mean RT and ordinal dot position? Perhaps when a new dot is presented the subject refreshes the image before adding the dot. To refresh the image the subject must generate the base form


TABLE 2 Summary Statistics for Cognitive Measures

Task Measure M SD Split-Half ct

Picture Mean RT (ms) 2316 1916 Add Prop. Correct 0.770 0.167

Mean RT 3386 1730 0.993 a Slope 566 544 0.937 a Intercept 1690 1217 0.919a

Subtract Prop. Correct 0.780 0.180 Mean RT 3508 1600 0.964 a Slope 599 528 0.919 a Intercept 1711 1552 0.935 '~

Integrate Prop. Correct 0.686 0.210 Mean RT 3825 t600 0.915 a Slope -473 719 0.458 a Intercept 4772 2280 0.598 a

Rotate Prop. Correct 0.827 0.124 Mean RT 7591 4270 0.958 b Slope 27.4 25.6 0.675 b Intercept 4842 3208 0.837 b

Scan Mean RT 2113 1310 0.972 c Slope 49.0 83.7 0.888 c Intercept 1590 881 0.851 c

.852

.777

.819

.655

.839

aSplit-half reliabilities were obtained by correlating odd and even num- bered problems and correcting the correlation by means of the Spearman- Brown formula.

bMeasures were split into two halves by first ordering all test items by object instance and angle of rotation, then dividing them into odd and even items in this ordering.

cMeasums were split into two halves by ordering the items according to distance between pair members, then dividing them into odd and even items in this ordering.

(triangle or star), then insert each previous ly presented dot into the image. Such a

sequence o f operat ions would result in the observed l inear funct ion with a slope

corresponding to the t ime required to regenerate and insert each dot and an

intercept corresponding to the t ime required to encode the st imulus, generate the

base form, and initiate a response. This interpretation is consistent with the

introspect ive reports o f our subjects who c la imed to rehearse the image when

inserting each new dot. G iven this interpretation, the slope measures the eff ic ien-

cy o f processes required to add a single feature to an image at a specif ied posit ion.

Ind i v idua l Di f f e rences . Individual differences in R T and accuracy could be

due largely to a speed-accuracy tradeoff. Howeve r , the correlat ion be tween

overal l mean R T and proport ion correct was nonsignif icant , r = .208, p > .05,


TABLE 3 Add and Subtract Mean Latencies (ms)

as a Function of Base Form and Ordinal Position of Dot

Task

Ordinal Position of Dot Base Form 1 2 3 4 5

Add

Subtract

Triangle 2183 2205 2906 3587 3754 Star 2542 3265 3561 4581 5277 Mean 2363 2735 3234 4084 4516 Triangle 2513 2559 3545 4202 4413 Star 2565 2412 3455 4750 4663 Mean 2539 2486 3500 4476 4538

suggesting that a speed-accuracy tradeoff was not the only source of individual differences. Thus, individual differences in accuracy may reflect differences in image quality, and not just speed-accuracy strategy differences.

To measure the efficiency of the add process, linear regression slopes and intercepts were computed for the RTs of each subject (see Table 2 for summary statistics). To ensure that the linear relationship observed for group data applied to individuals, the correlation of mean RT and ordinal dot position was computed for each subject. The average of these correlations was .744 indicating that a linear relationship held reasonably well for individuals. Both slope and intercept were highly reliable as shown in Table 2.

Subtract Task

The purpose of the Subtract Task was to assess ability to mentally delete parts of an image. The procedure for each problem was similar to that followed in the Add Task. A base form was presented with dots in 13 positions, followed by a sequence of self-paced pictures indicating the dot to be subtracted from the image. At the end of the sequence subjects were required to identify the resulting image among a set of alternatives. Task difficulty was manipulated by including both triangles and stars as base forms. Both accuracy and the time to view each slide were measured.

Method

The four practice and 24 test problems were similar to those presented in the Add Task (see Figs. 3 and 4 for examples). The first picture of each problem showed the base form with all 13 dots. The next five pictures indicated the positions where a dot was to be subtracted. The final test pictures were constructed in a manner analogous to the final pictures in the Add Task.


STUDY SLIDES

TEST SLIDE

FIG. 3. Sample subtract/triangle problem.


Because of computer failure during the Subtract Stars Task, the data for two subjects were discarded. These two subjects were excluded from all analyses involving the Subtract Task.

Proportion Correct. The mean number correct for 12 problems was nearly identical for triangles (9.34) and for stars (9.38), F < 1. Descriptive statistics are presented in Table 2.

Mean Response Times. Mean RTs are presented in Table 3 as a function of base form (triangle or star) and ordinal position of the dot to be subtracted. The effect of the base form was negligible, F < 1. Mean RT increased nearly .5 s for each additional dot resulting in a significant Position main effect, F(4, 304) -=


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80.20, p < .001. A significant Form x Position interaction, F(4 ,304) = 4.54, p < .01, is probably due to the nonmonotonicity of the RTs for star~. Nonetheless, the correlation between mean RT and dot position was .949, indicating that the relationship is reasonably linear.

As in the Add Task, we interpret the linear relationship as due to the time required to regenerate or rehearse the image before subtracting each new dot. Thus, the slope measures the efficiency of processes required to subtract a dot, and the intercept measures the time required to encode the stimulus, generate the base form, and initiate a response.

Individual Differences. Overall, the results were similar to those obtained in the Add Task. Again, the correlation between mean latency and accuracy was nonsignificant, r = .165, p > .05, suggesting that a speed-accuracy tradeoff was not a major source of individual differences. More importantly, the mean correlation between RT and ordinal dot position, r = .701, indicates the linear


STUDY SLIDE

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RED GREEN

TEST SLIDE

FIG. 5. Sample integrate problem. (Words and arrows identify regions that were colored in the original problem.)

relationship observed in the group results was a reasonable description of individual results. Descriptive statistics for linear regression slopes and intercepts are presented in Table 2.

Integrate Task

The purpose of the Integrate Task was to assess ability to integrate successive images into a complete image. In each problem of the Integrate Task a series of pictures was presented. Subjects were asked to mentally fuse the shapes presented in the picture series to form a new, whole image. As in the Add and Subtract Tasks, subjects controlled the pace of the task by pressing a response button when ready for the next picture. After integrating all pieces of the image, subjects were required to identify a picture corresponding to the resultant image.

Method

Two practice problems and 12 test problems were conducted following the procedure of the Add and Subtract Tasks. In each problem five pictures of outline forms such as the example in Fig. 5 were presented. The outline form in the first picture was composed of blue, red, green, and/or black segments. The next three pictures showed a different outline form to be integrated with the first picture. In these three pictures one form was blue and black, one red and black,


and one green and black. The red, green, or blue part of each form matched the part of the original form of the same color. The order of the three colors varied for different problems. The fifth picture showed four outline forms labeled 1 to 4. Only one of these forms was the outline of the shape that would result from fusing the four previous forms as indicated by the colors. The other three forms were distorted in the area of either the blue, red, or green portion; the location of the distortion was different for each distractor outline. The target (correct) outline form appeared with the labels 1, 2, 3, and 4 in this last picture an equal number of times. All pictures were separately photographed on slides and appeared as black and color line drawings on a white background. The average height of the first four pictures of a problem subtended a visual angle of approximately 5.5 deg.


Proportion Correct. This task proved to be difficult for our subjects. The mean proportion correct averaged over all subjects and problems was only 0.69 (see Table 2).

Mean Response Time. The mean time between slides was 3.82 s. In- terestingly, the mean time decreased as more pieces were added. The slide viewing times were 4.20, 4.01, and 3.25 s for the second, third, and fourth slides, respectively. A repeated measures Analysis of Variance established that the effect of slide position on viewing time was highly significant, F(2, 156) = 25.53, p < .001.

Again, we need to ask why latency should decrease linearly with slide order. Two possible reasons come to mind. First, the decreases may be due to reduced uncertainty regarding the position where an image part must be integrated. In the first slide the locations where parts were to be integrated were marked by red, blue, and green segments. As each new part is integrated, the number of positions where a part can be integrated is reduced. Perhaps the correct location is more quickly located as the number of alternative locations decreases.

Another possibility is that latency decreases as the integrated image becomes simpler. The red, blue, or green segments in the first picture were irregular and jagged. As each part is integrated the resulting image boundaries become simpler, and less color information need be retained. Perhaps a new part can be integrated more quickly as the total image becomes simpler.

According to these admittedly post hoc explanations the slope of the latency function represents sensitivity to positional uncertainty or image complexity. Although it was not our intention to measure these qualities of the imagery processes, the linearity of the observed relationship suggests measuring slopes and intercepts for each subject. These two measures contain all the information


to be found in the mean reaction time, and may measure different sources of imagery ability.

Individual Differences. There was no evidence of a speed-accuracy tradeoff; the correlation between proportion correct and mean RT was only .04. The mean correlation between slide viewing time and ordinal slide position was - .627 , suggesting that linear regression would describe the results of individuals reasonably well. Descriptive statistics regarding the regression slopes and intercepts are given in Table 2. As Table 2 shows, the reliabilities of these measures were low.

Rotate Task

Rotation of part or all of an image is often required in tests of spatial ability. It is accomplished by a transformatibn process in Kosslyn's theory of imagery. To measure rotation efficiency subjects were required to determine whether two rotated objects were the same or different.

Method

The materials were selected from the stimuli used by Shepard and Metzler (1971), and kindly provided by Roger Shepard. Each stimulus consisted of two line drawings of three-dimensional, geometric objects. Fifty stimulus pictures and eight practice pictures were selected from the complete set. These stimuli were photographed and presented as white line drawings on a black background.

Half the 50 stimulus pictures depicted two identical objects (same set) and the other half depicted two objects that were mirror images of one another (different set). There were five distinct objects and there were five instances of each of these distinct objects within both the same and different sets. Each instance depicted an object paired with itself (or its mirror image) rotated in depth. The angular differences in spatial orientation between pair members were 20, 60, 100, 140, and 180 deg.

Each subject completed eight practice problems and 50 stimulus problems. Subjects indicated whether the objects were the same or different by pressing one of two keys.


Proportion Correct. This task proved more difficult for our subjects than for Shepard and Metzler's highly practiced subjects; the mean proportion correct was only 0.83. Table 4 presents proportion correct as a function of rotation angle and whether the objects were the same or different. Accuracy decreased as the angle of rotation increased, producing a highly significant effect of angular difference, F(4, 312) = 11.22, p < .001. In addition, accuracy was greater


TABLE 4 Rotate Proportion Correct as a Function of Angular Difference

and Same/Different Objects

Angular Difference (deg,)

20 60 100 140 180 M

Same .96 .89 .82 .80 .85 .864 Different .84 .77 .80 .77 .78 .792 M .90 .83 .81 .785 .815 .833

when the objects were the same rather than different, F(1, 78) = 18.17, p < .001. Finally, angular difference affected accuracy more for objects that were the same than for those that were different, F(4, 312) = 4.15, p < .01. Table 2 presents descriptive statistics for proportion correct averaged over all conditions.

Mean Response Time. The mean RTs are presented in Figure 6 as a function of rotation angle and same or different objects. Mean RT for the same pairs increased with angle of rotation, producing a highly significant effect of angle, F(4, 312) = 22.25, p < .001. Furthermore, the correlation between mean RT and angle of rotation was 0.958, indicating that the relationship was approximately linear.

The mean response time for different pairs was substantially longer than the mean for same pairs, F(1, 78) = 69.63, p < .001. Furthermore, the angle of

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rotation had little effect on mean RT to different pairs, yielding a highly significant interaction, F(4, 312) = 30.01, p < .001. This interaction is not surprising because the angle of rotation is not well defined for different pairs; different objects cannot be rotated into congruence.

The mental processes required to perform this task have been the subject of considerable study (e.g., Just & Carpenter, 1976; Metzler & Shepard, 1974). According to Just and Carpenter (1976) search, transformation, and comparison processes align and compare representations of the two objects. Increases in angular disparity affect the time required by all three processes, but have the greatest effect on the transformation time. Thus, regardless of the model adopted for this task, the slope of the RT function represents the efficiency of mental rotation. The intercept is an estimate of the latency of processes that do not depend on orientation.

Individual Differences. The correlation between overall mean RT and proportion correct was - . 10, suggesting that differences in accuracy are not due to a speed-accuracy tradeoff. Thus, individual differences in accuracy may reflect differences in image quality.

Linear regression slopes and intercepts were computed for the RTs of each subject to measure efficiencies of rotation process and those processes that are independent of rotation angle (see Table 2 for summary statistics). The mean correlation between RT and angle was an unimpressive 0.378, suggesting that the models of Metzler and Shepard (1974) or Just and Carpenter (1976) may not provide a good description of the performance of some subjects. Thus, the slope may be measuring some combination of rotation efficiency and adoption of the assumed imagery strategy.

Scan Task

An imagery scanning process plays an important role in Kosslyn's (1978; 1980; 1981) theory of imagery because of hypothesized characteristics of the imagery buffer. The buffer has limited extent, limited resolution, and decreasing resolution with distance from its center. Thus, inspection of a portion of an image often requires translating the image or, equivalently, scanning across the image to bring the attended portion into the region of greatest resolution.

Kosslyn, Ball, and Reiser (1978) developed a method for studying the scan function. First, subjects were required to memorize a map of an island with several prominent landmarks. Then subjects were asked to scan from one land- mark to another in the image. They found that the time to complete this subjec- tive scan increased linearly with the distance between the landmarks on the map. We used the same stimuli and method to determine the function relating scanning time to distance for each subject. The slope of this function should provide a measure of the efficiency of the scan process.


Method

Design. A black-and-white drawing of a fictional island was copied after the island used by Kosslyn et ai. (1978). There were seven objects on the island: a hut, grass, sand, a rock, a well, a tree, and a pond. A small red dot was drawn on each of the seven objects. The dots in the seven objects were located on the island such that the distance between pairs of dots varied from 2.1 cm to 20.7 c m .

A list of 21 object pairs was constructed by pairing each object with every other object. The ordering of objects within pairs was randomly determined with the constraint that each of the seven objects was first and second equally often. A list of 14 additional pairs was constructed by pairing the seven objects with six other objects that did not appear on the island (e.g., a church). The first member of these pairs was always an object on the island (all seven objects were in 2 of the 14 pairs).

These 35 pairs were recorded on tape with five seconds between first and second pair members and ten seconds between the second member of a pair and the first member of the next pair. The order of pairs on the tape was randomly determined with the constraints that no object could occur twice within three consecutive pairs, there could be no more than four island-island pairs in a row, and no more than three island-non-island pairs in a row.

Procedure. First, subjects studied the island until they could draw and label all seven red dots on a blank island within 0.5 cm of the actual locations. Next, subjects were asked to maintain an image of the island in their minds while listening to the tape, and to focus on the location of the dot for the first object mentioned in each stimulus pair. When the second object was named subjects decided whether this object was on the island. If the second object was not on the island, subjects pressed the left-hand button. Alternatively, if the object was on the island, subjects were told to imagine a "black speck traveling in a fast, straight line from the first member to the second member of the pair." Subjects pressed the right-hand button when the black speck arrived at the location of the dot for the second object.

Ten practice pairs were conducted using a mental map of the United States. At the end of the practice, the subject briefly studied the map of the island again. During the task, the experimenter started the computer's timer by pressing a button simultaneously with presentation of the first member of a pair, and the subject stopped the timer when he/she pressed a button after hearing both pair members. The interval between the onsets of pair members was measured and subtracted from all the response times.


Proportion Correct. The analysis was restricted to the 21 problems requiring a scan from one object to another. The mean number of errors was only 0.945. Because the error rate was so low no further analysis of accuracy was conducted.


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Mean Response Time. Mean RT averaged over all subjects is shown in Fig. 7 as a function of distance between the objects on the map. Clearly, mean RT tended to increase with distance between the objects. However, the relationship was not as systematically linear as that obtained by Kosslyn et al. (1978). Whereas, they obtained a nearly perfect linear relationship (r --- .97), we observed a correlation of 0.801 between mean RT and distance. This correlation increased to 0.822 when the extreme point corresponding to the shortest distance was eliminated.

Why do our results show so much greater variability from a linear function? One possibility is that our latency measurements were insufficiently precise. Kosslyn et al. used a voice key to start a timer at the onset of the second stimulus. In contrast, our experimenter started the timing by pressing a button when the first word was spoken, introducing random error. In addition, we had half the number of trials used by Kosslyn et al. per subject, but we had many more subjects.

Another possibility is that the linear relationship does not hold for all subjects. Richman, Mitchell, and Reznick (1979) demonstrated that latencies in a scan task may be influenced by implicit distance cues in the instructions to use mental imagery. In collaboration with Richman, Goldston (1982) found considerable variability in the adequacy of a linear fit to the relationship between latency and distance. Interestingly, he found the best linear fit for subjects who had (1) guessed that distance and time should be related and (2) scored high on a social


desirability test. The mean correlation between latency and distance for subjects with a low social desirability score was 0.62.

Individual Differences. In fact, the results for individual subjects were not in good agreement with Kosslyn's theory. The mean correlation between RT and distance was only 0.265, and this correlation was quite variable over subjects; the standard deviation of the correlation was 0.370. Despite the low average correlation, linear regression slopes and intercepts were computed to represent the scanning efficiency of each subject (see Table 2 for summary statistics). These measures proved reasonably reliable, eliminating random error as an ex- planation for the low correlations. Unfortunately, it is not clear how these slopes should be interpreted. The slope may represent some mixture of scan efficiency and adoption of a strategy consistent with Kosslyn's theory.

Intercorrelations of Cognitive Measures

Correlations

The correlations among 15 latency and accuracy measures are presented in Table 5. Correlations with accuracy have been reflected to establish a positive manifold; accuracy measures are more appropriately conceptualized as error measures when considering the correlations. Equivalently, one can consider the latencies, including slopes and intercepts, to be reflected so Table 5 presents correlations between measures of speed and accuracy. The communalities in the diagonal of the correlation matrix were determined by a Principal Axis Factor Analysis described below. The correlations and communalities presented in Table 5 are based on data from 77 subjects.

The correlations among accuracy measures in Table 5 are consistent with the hypothesis that accuracy in every task is affected by limitations' in image quality. This hypothesis requires a positive correlation between all accuracy measures. In fact, all correlations between accuracy scores from the Add, Subtract, Integrate, and Rotate Tasks were significantly correlated with a mean correlation of .454.

Correlations between accuracy scores and mean latencies (not shown in Table 5) suggest that accuracy and latency measure different facets of imagery. Of the 24 correlations between mean latencies and reflected accuracies only five were significant (p < .05). The mean of these 24 correlations was only - .002 .

Although accuracy scores were not related to mean latencies, there were consistent relationships with the RT slopes and intercepts. In all four tasks providing these measures, reflected accuracy correlated negatively with slope (mean r = - .303) and positively with intercept (mean r = .226). The correlations with the intercepts suggest that subjects who quickly encode the stimulus, generate an image, and perform other functions that are independent of the experimental manipulation tend to be more accurate. Surprisingly, subjects with

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low slopes tend to be less accurate. This observation raises problems for the interpretation of slope as a measure of the efficiency of imagery functions. It suggests that differences in slope represent a speed-accuracy tradeoff rather than efficiency differences.

An alternative interpretation is that slope measures were contaminated by strategy differences. Suppose a subject failed to follow the imagery strategy implicitly assumed when computing the regression functions. In the extreme case the subject might just respond randomly. The latencies of such a subject would not dePend on the experimental manipulation and the error rate would be relatively high. On the other hand, subjects who consistently follow an imagery strategy would show a relatively steep slope and high accuracy.

Regardless of whether the observed correlations between slopes and accuracies arise from a speed-accuracy tradeoff or strategy differences, the correlations pose a probIem for the interpretation of the slopes as measures of efficiency. This problem can be ameliorated by removing the linear effect of accuracy from each slope. Removing this linear effect ensures that accuracies and the corresponding corrected slopes are uncorrelated, facilitating interpretations of the slopes. A later section describes such a correction to two slope measures.

The pattern of correlations among latency measures can be readily interpreted in terms of Kosslyn's theory of imagery. First, consider the efficiency of image generation as measured by latency in the Picture Task. The Picture latency was significantly correlated with three of the four accuracy measures. Subjects who quickly generated images tended to be more accurate~ These correlations suggest a relationship between image quality and image generation efficiency. In addition, Picture latency was significantly correlated with the Scan and Rotate intercepts and with the Rotate slope. The correlations with the intercepts suggest that subjects must generate mental images of the stimuli before transforming them by rotation or scanning. Perhaps the correlations with intercepts from other tasks were smaller (though positive) because the stimuli were simpler and images were easier to generate. In these other tasks image generation contributed less than other processes to the intercept variance.

The Add and Subtract Tasks were devised to measure the efficiency of the processes involved in adding and subtracting detail in an image. Corresponding measures from these two tasks (slopes, intercepts, and accuracies) were all highly correlated, suggesting that these two tasks measure the same or similar processes. We expected the Integrate Task to involve similar processes since integration of two images is conceptually similar to adding detail to an image. In fact, the mean latency for the Integrate Task was significantly correlated with mean latency for both the Add Task (r = .413) and the Subtract Task (r = .484), suggesting that similar processes were measured. However, as Table 5 shows, Integrate slope and intercept were not significantly correlated with the Add or Subtract slope and intercept.

Two tasks, Rotate and Scan, were included to measure efficiency of image


transformation functions. The mean latencies for these two tasks were significantly correlated (r = .254) suggesting some commonality in the processes required by these tasks. However, correlations among the slopes and intercepts were low; suggesting that different processes were primarily involved. In fact, the Scan slope and intercept were not significantly correlated with any other measures except for the correlation between Scan intercept and Picture latency discussed above. In contrast, the Rotate slope and intercept were significantly correlated with several other measures including picture latency. The Rotate intercept was correlated with both the Add and Integrate intercepts. The Rotate slope was correlated with both the Add and Subtract slopes.

Factor Analysis

A Principal Axis Factor Analysis of the 15 varialbles listed in Table 5 identified five factors with corresponding eigenvalues that exceeded one. These five factors account for 68.7% of the total variance in the variables. Varimax rotation yielded a factor matrix, presented in Table 6, with a structure that is readily interpreted by simply noting factor loadings that exceed 0.5 in absolute value.

The first factor corresponded to the number correct in each task, suggesting that this factor represents limitations in image quality as hypothesized. The second and fourth factors were clearly defined by Add and Subtract measures. The Add and Subtract slopes defined the second factor and the Add and Subtract intercepts defined the fourth factor. It is encouraging that these slopes and

TABLE 6 Varimax Rotated Factor Matrix for Cognitive Imagery Measures (x 100)

Factors: 1 2 3 4 5

PIC -27 7 3 4 73* ASL 37 86* 3 -20 15 AIN -14 -8 3 98* -4 ANC -78* -11 -13 13 -9 SUS 42 80* -7 -13 15 SUI -38 -17 15 56* -2 SUN -83* -23 -7 4 12 ISL 11 5 -83* 2 -1 IIN 4 15 91" 18 21 INC -54* 4 16 6 6 RSL 10 16 7 -14 36 RIN - 1 2 -10 14 24 60* RNC -52* -10 9 22 -2 SSL 6 -29 -3 0 6 SIN 1 -4 -1 -7 38

*Value of factor loading exceeds 0.50.


intercepts corresponded to different factors because the slopes and intercepts were calculated from the same data, resulting in an operational dependency that negatively inflates the correlations between these measures. Such biases in the correlations would tend to produce a single factor for both the slope and intercept.

The third factor corresponded to the slope and intercept of the Integrate Task. This slope and intercept were highly correlated (r = - . 76 ) suggesting that the slope and intercept did not measure distinct abilities. The last factor corresponded to the Picture latency and Rotate intercept, a relationship discussed in the previous section. Three variables, the slope and intercept for the Scan Task and the slope for the Rotate Task, had low communalities and did not have loadings greater than 0.4 on any factor.

Composite Measures

The factor analysis confirmed that some of the measures from different tasks assessed the same imagery processes. Thus, composite measures formed by standardizing and summing equivalent measures can be computed without loss of any important information about individual differences. The computation of such composite measures has several benefits. The most obvious consequence is that the number of variables to be considered is reduced. Furthermore, composite measures are more reliable than the measures from which they are computed, and should have simpler interpretations in terms of the cognitive theory.

The correlations among the accuracy measures and their loadings on the first factor suggest combining these scores to form a single accuracy measure. The average accuracy on the Add, Subtract, Integrate, and Rotate Tasks is interpreted as a measure of image quality.

The high correlations between the Add and Subtract slopes and intercepts and the loadings on the second and fourth factors suggest computation of a single slope and intercept to represent performance in these two tasks. The intercept measures the time required to encode the stimulus, generate the base form, and initiate a response. The slope is interpreted as a measure of the processes required to add detail to an image. The correlation between the resulting slope and accuracy on the Add and Subtract Tasks was highly significant (r = .48). As noted earlier, a positive correlation between slope and accuracy poses a problem for interpretation of the slope as a measure of efficiency. To eliminate this problem, the linear effect of accuracy on the slope was removed.

The third factor indicated that the Integrate slope and intercept measured equivalent sources of individual differences. Thus, these measures were replaced with the mean latency for that task. This latency is presumed to measure efficiency of the processes required to integrate two images.

Because the fifth factor accounted for only eight % of the variance accounted for by all five factors, the two measures that loaded on this factor, Picture mean


R T and Rotate intercept, were not combined. The linear effect of the Rotate accuracy on the Rotate slope, although small (r = . 112), was removed in the same manner and for the same reasons that the linear effect of accuracy was removed from the Add and Subtract slope.

The correlations among the remaining nine measures are presented in Table 7. It is noteworthy that the correlations among these measures are low; only eight of the 36 correlations are statistically significant. There are two implications of these low correlations. First, there was relatively little commonality in the processes measured by the latencies, slopes, and intercepts in different tasks. Sec- ond, the efficiencies of different imagery processes and image quality are largely independent. Thus, these different processes and image quality may make separate contributions to spatial ability.

SELF-REPORT TESTS

Self-rating questionnaires were given to assess vividness, control, and strategy preference. Vividness was assessed by the Vividness of Visual Imagery Ques- tionnaire (VVIQ) developed by Marks (1973), imagery control was assessed by the Test of Visual Imagery Control (TVIC) developed by Gordon (1949), and preference for visual or verbal strategies was assessed by the Verbalizer-Visu- alizer Questionnaire (VVQ) developed by Richardson (1977a). We expected imagery control to be related to the efficiency of imagery processes because these processes permit manipulation of images. We expected vividness to be unrelated to the efficiency of processes, with the possible exception of image generation. In addition, vividness may be related to image quality. The inclusion of the preference questionnaire was exploratory.

TABLE 7 Correlations for Cognitive Imagery Composite Measures (x 100)

PIC SSL SIN ACC SLP INT RSL RIN IRT

- 1 1 25 29 17 6 27 52 23 PIC 11 0 -20 6 18 5 -10 SSL

1 9 - 4 17 19 1 SIN -6 39 -2 22 -12 ACC

-26 29 -1 22 SLP -9 20 21 INT

12 10 RSL 35 RIN

PIC: Picture Mean Time; SSL: Scan Slope; SIN: Scan Intercept; ACC: Number Correct for All Tasks; SLP: Add & Subtract Slope Corrected for Accuracy; INT." Intercept for Add and Subtract Tasks; RSL: Rotate Slope Corrected for Accuracy; RIN: Rotate Intercept; and IRT: Integrate Mean Time.


All three self-rating questionnaires were given, one at a time, at the beginning of the group session. Subjects read the instructions accompanying each questionnaire, and the experimenter reviewed the instructions and answered any questions. Subjects were allowed as much time as they wanted to complete each questionnaire.

Resul~

Vividness

A rating on a 5 point scale was provided by each subject to each of the 16 items. The mean rating for each subject provided a measure of imagery vividness; the higher the rating, the less vivid the imagery. Because other rating tests yielded higher scores for greater use of imagery, the VVIQ scores were reflected so that a higher rating would correspond to greater vividness. The mean rating averaged over subjects was 2.32 and the standard deviation of the mean ratings was 0.562. The reliability of the mean ratings, a = 0.828, was about the same as the reliability obtained by Marks (1973).

Visualizer/Verbalizer

Each of 15 questions was answered by marking true or false. These answers were assigned values of one or zero such that one corresponded to a response of a visualizer and zero corresponded to a response of a verbalizer. The sum of these values represents the degree to which a subject preferred the cognitive style of a visualizer, The mean score averaged over subjects was 9.44 and the SD of the scores was 2.21. The VVQ scores had low reliability, ot = 0.524. Indeed, this reliability is notably lower than the test-retest reliabilities of about 0.9 obtained by Richardson (1977a).

Control

Each of 20 questions was answered by marking yes, no, or unsure. A no response was assigned the value zero, an unsure response was assigned the value one, and a yes response was assigned the value two. The sum of these values over the 20 questions represents the amount of control over imagery that a subject reports experiencing; the higher the sum, the greater the reported control of visual imagery. The mean score averaged over subjects was 20.09 and the SD was 3.72. The scores were moderately reliable, et = 0.707.

Intercorrelations

Scores on the preference test were uncorrelated with scores on the v.ividness test (r = - .013) and the control test (r = .045). However, subjects who reported more vivid imagery also tended to report more control, r = .329, p = .002. This


result is consistent with previous research using other scales of vividness and control (e.g., Morris & Gale, 1974; Starker, 1974); greater vividness is associated with greater control.

The relationships were weak between these self-report measures and the cognitive imagery measures. Neither vividness nor control responses were significantly correlated with any of the cognitive measures (p > .05 for all measures). Preference responses were significantly correlated (p < .05) with the Add and Subract slope, r = - .245 , and with the Rotate slope, r = - .254. Thus, it appears that self reports of being a visualizer are weakly related to the efficiency of processes involved in adding image detail and rotating images.

SPATIAL ABILITY TESTS

Spatial tests were selected to measure the broad spatial ability called Visualiza- tion by McGee (1979). Visualization represents an "ability to mentally manipulate, twist, or invert a pictorially presented object" (p. 893). It is equivalent to the general visualization ability (Gv) in Cattell's theory of crystallized and fluid intelligence (Horn, 1968). To measure Visualization ability, eight tests were chosen that broadly vary complexity, the required mental processes, and the method of testing.

Two of these tests require searching for embedded figures. Thurstone's De- signs Test requires identification of figures that contain the upper case Greek Letter sigma. The more difficult Components Test (Flanagan, 1953) requires finding one of five model figures in extremely complex designs.

Several tests seem to involve mental rotation. In the Figures Test subjects mark the figures that are simple rotations of a model figure. The Paper Folding Test (French, Ekstrom, & Price, 1963) and the Space Relations Test (Bennett, Seashore, & Wesman, 1974) are more complex; they seem to require a combination of several imagery processes including integration and adding detail. In the Paper Folding Test subjects determine the appearance a square piece of paper would have after folding it in certain ways, punching a hole through it, and unfolding it. In the Space Relations Test subjects must mentally fold a flat figure to construct a three-dimensional object, then identify this object from a set of alternatives.

The Cube-Cutting Test was adapted from Richardson (1977b). This test consisted of four questions about a colored cube. Before starting the test, a cube was drawn on a blackboard and described as composed of a white substance on the inside and painted red on the outside. Subjects were then shown how two hori- zontal cuts and four vertical cuts were made in the cube to result in 27 smaller cubes. The experimenter then erased the blackboard, and subjects read and answered four test questions. The questions were: (1) How many cubes have three faces painted red?; (2) How many cubes have two faces painted red?; (3) How many cubes have one face painted red?; and (4) How many cubes have no


faces painted red? The Cube-Cutting Test requires subjects to maintain a clear image while examining the image from different perspectives. We expected this test to require image generation, rotation, and inspection.

In addition to the standard tests described above, two new spatial tests were administered. These tests were administered to eliminate method specific variance associated with the paper and pencil tests described above. In these tests latency was measured rather than accuracy. In the first test subjects were required to assemble portions of jigsaw puzzles, a task that appears to require mental rotation and integration of images. The second test required subjects to follow a specified path out of a maze, but the path was rotated so subjects must mentally rotate the path and integrate it with the maze. The procedure followed in these two tests is described below.

Puzzles Test

The Puzzles Test was similar to the standard Form Board Test (Likert & Quasha, 1941). Subjects completed five jigsaw puzzles, and the latencies were measured. A jigsaw puzzle requires finding pieces with complimentary outlines. Typically, pieces must be rotated, mentally or physically, to match the orienta- tions of candidate pieces. Following rotation, identification of the matching pieces requires integration of the piece outlines.

Materials

Five jigsaw puzzles were constructed, including one practice and four test puzzles. Each puzzle consisted of nine jigsaw puzzle pieces that fit together to form a three-by-three matrix. Because the nine pieces were chosen from the interior of a large jigsaw puzzle, the outline of each completed puzzle was irregular (non-rectangular) in shape. The pieces were all upside-down so their color would be a uniform gray. The edges of puzzle pieces that comprised the outline were colored red; thus, a completed puzzle was gray with a red border.

Procedure

Each puzzle was presented with the nine pieces in a random arrangement that was constant for all subjects. The instructions explained that the red border defined the outside edge of the puzzle, and emphasized the importance of solving the puzzle mentally. That is, subjects were instructed to avoid using a trial-and- error approach to connect puzzle pieces. They were encouraged to decide that two pieces fit together by visual inspection before attempting to join them. A practice puzzle and four test puzzles were completed. A stopwatch was used to measure the time required to solve each puzzle.


Mazes Test

The Mazes Test was developed to simulate the processes involved in finding a route marked on a map. Complex printed mazes and, on a separate page, rotated solutions through the mazes were presented. The test required drawing the indicated path through the maze. Thus, subjects were required to mentally rotate and

integrate images.

Materials

Five mazes, one practice and four experimental, were selected from a book of mazes. Each maze was a line drawing with one point labeled “start” and another labeled “finish.” The solution for each maze (a line connecting the “start” and “finish” points) accompanied the maze on a separate piece of paper; the solution sheet did not include a drawing of the maze itself. Every solution was rotated (relative to the maze itself) between 0 and 90 deg. and the side of the solution corresponding to the top of the page on the maze was labeled “top” so that subjects could see how the solution had been rotated.

Procedure

The task required drawing a continuous line from “start” to “finish” without crossing any lines on the maze. The instructions emphasized that subjects were not to use their usual strategy for solving mazes, but were to follow the route shown on the solution much as they would follow a map. The rotation of the

solution relative to the maze was explained to subjects. Each subject completed one practice and four test problems. The subject was

timed with a stopwatch from the time the maze and its solution were presented until the subject reached the “finish” point. The experimenter watched the subject while he/she worked and required correction of any illegal moves (crossing a line on the maze) when they occurred.


The means, standard deviations, and reliabilities of performance on the spatial tests are presented in Table 8. In many of the tests subjects were supposed to mark some items and avoid marking others. For these tests the number of incorrect responses are also reported in Table 8. The number of correct responses was used as the performance score for the Designs, Paper Folding, and Compo- nents Tests. For the Figures and Space Relations Tests the performance score was adjusted by correcting for guessing.

The intercorrelations among the spatial test measures are presented in Table 9. In this table correlations with the Puzzles and Mazes latencies were reflected to reveal a positive manifold. Thus, the Puzzles and Mazes measures should be


TABLE 8 Summary Statistics for Spatial Ability Tests

Test Measure M SD Split-Half et

Designs N Correct 21.53 6.73 0.924 N Incorrect 0.143 0.663 0.879

Figures N Correct 20.66 5.66 0.878 N Incorrect 1.53 2.90 0.790

Paper Folding N Correct 10.18 4.23 0.897 N Incorrect 3.32 3.31 0.420

Components N Correct 10.78 4.69 0.888 N Incorrect 1.93 2.01 0.400

Space Relations N Correct 41.29 12.7 0.945 N Incorrect 5.72 5.91 0.885

Cube-Cutting N Correct 2.48 !.42 Puzzles M RT (s) 92.34 36.16 Mazes M RT (s) 105.88 44.96

0.736 0.737 0.665

conceptua l ized as speed rather than latency. All correlat ions were posi t ive and

significant , ranging in absolute value f rom 0.35 to 0 .65.

A Principal Axis Factor Analys is o f the spatial test measures ident i f ied only

one factor with an e igenva lue greater than one (h = 4.3) . This single factor

accounted for 54% o f the c o m m o n var iance among the measures . The c o m m u -

nalities based on this one-fac tor solut ion are l isted on the diagonal o f the matr ix

in Table 9. The factor loadings are s imply the square root o f these c o m m u -

nalities. It is apparent f rom Table 9 that all measures , including Puzzles and

Mazes speed, have substantial factor loadings, indicat ing that the factor repre-

sents a broad Visual izat ion ability.

TABLE. 9 Correlations and Communalities of Spatial Ability Tests (× 100)

CMPNT PRFLD FGURS DSGNS SPCRL CUBCT PUZLS MAZES

62 60 40 52 62 65 47 48 CMPNT 44 40 39 60 40 37 41 PRFLD

41 42 54 42 49 46 FGURS 40 57 40 35 43 DSGNS

74 55 55 58 SPCRL 46 41 43 CUBCT

38 36 PUZLS 42 MAZES

CMPNT: Components; PRFLD: Papeffolding; FGURS: Figures; DSGNS: Designs; SPCRL: Space Relations; CUBCT: Cube-Cutting; PUZLS: Puzzles; MAZES: Mazes.


TABLE 10 Correlations Between Self-Report

and Spatial Test Measures (x 100)

VVQ VVIQ TVIC

CMPNT 20 31 1 PRFLD 18 13 10 FGURS 14 2 3 DSGNS 25 18 6 SPCRL 30 -5 -6 CUBCT 12 11 9 PUZLS 34 2 1 MAZES 18 9 4

Relationship with Self-Report Measures

Correlations between the spatial ability and imagery self-report measures are presented in Table 10. As before, correlations With the vividness test and the Puzzles and Mazes latencies were reflected to reveal a positive manifold. In- terestingly, the strongest relationships were obtained with the VVQ, a test of preferred mode of thought. Preference for a visual mode of thought was significantly related to higher performance in three tasks (criterion r = .23, p = .05), and in the expected direction for every task. In contrast, rated imagery control (TVIC) was not significantly related to performance in any task, and rated vividness (VVIQ) was significantly related to performance in only one task.

Relationship with Cognitive Imagery Measures

The relationship between spatial ability and both imagery process efficiency and image quality is the primary issue addressed in this article. If spatial tests are performed through use of imagery, then spatial ability reflects, in part, imagery ability. The finding of Lansman et al (1982) that rotation latency is correlated with Visualization ability is consistent with this hypothesis. This correlation is somewhat difficult to interpret, however, because rotation latency measures the efficiency of a collection of processes, presumably including image rotation, generation, and inspection.

The contribution of imagery processes to performance on specific spatial tests has been explored by Pellegrino and his colleagues (summarized in Pellegrino & Kail, 1982). Pellegrino, Mumaw, Kail, and Carter (1979) found that performance on a test similar to the Figures Test was correlated with both the slope and intercept of rotation latency functions. Mumaw, Pellegrino, and Glaser (1980) found that performance on the Minnesota Paper Form Board Test was highly correlated with a linear combination of accuracy and latency measures from problems designed to decompose the processes required by the Form Board Test. Although these analyses identify processes that contribute to performance on


specific spatial tests, it does not necessarily follow that these processes contribute to spatial ability. The processes may contribute to performance variance that is specific to these tests rather than the common variance represented as spatial ability.

The correlations between spatial test performance and cognitive imagery measures, shown in Table 11, are consistent with the hypothesis that spatial ability reflects the operation of imagery processes. Performance on every spatial test was significantly correlated with several cognitive measures, and nearly every task was significantly correlated with cognitive Accuracy, Rotate intercept, and Add and Subtract intercept. Correlations with other cognitive measures were more variable.

Two features of these correlations are particularly noteworthy. First, the average correlation between spatial test performance and cognitive measures is approximately twice the average correlation among the cognitive measures. Thus, the observed relationships between cognitive measures and spatial tests are, to some extent, independent. Second, cognitive task Accuracy was significantly correlated with performance on every spatial test, suggesting that image quality is an important determinant of performance on spatial tests. These correlations cannot be interpreted as a trivial demonstration that accuracy measures correlate highly with accuracy measures because latencies were the dependent variable in the Puzzles and Mazes spatial tests.

The hypothesis that spatial ability reflects imagery process efficiency and image quality can best be examined through use of an explicit statistical model, represented pictorially in Fig. 8, This unusual model is essentially a combination of two quite ordinary models, multiple linear regression and common factor analysis with one factor. According to the common factor model performance on each spatial test is determined by a single common factor (Visualization ability) and a test specific factor. All correlations between spatial tests are a consequence of their relationships with Visualization ability.

The remainder of the model depicted in Fig. 8 represents Visualization ability as a linear combination of image quality and process efficiency. These traits are represented by the nine cognitive measures. Because the correlations among these cognitive measures are low, each latency measure is assumed to correspond closely to a trait. According to this part of the model, all correlations of cognitive measures with spatial test performance are due to the contributions of imagery process efficiency and imagery quality to Visualization ability. In other words, all contributions of process efficiency and image quality to the specific variance of spatial tests are assumed to be negligible.

Maximum likelihood methods of confirmatory factor analysis (McArdle & McDonald, 1982) were used to test the complete model represented in Fig. 8. The data tested by this model are the correlations among all the spatial tests and the correlations between the spatial tests and the cognitive measures. The model provided an excellent fit to these data as indicated by a chi-square close to its

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expected value (X 2 = 88.10, df = 83). Maximum likelihood estimates of the path coefficients or regression weights are presented in Fig. 8. When interpreting these coefficients it is important to recognize that all the latency measures (including slopes and intercepts) have been reflected and should be conceptualized as measures of speed.

Consider the values of the path coefficients displayed in Fig. 8. The coefficients on the paths connecting Visualization ability to the spatial tests represent factor loadings, and the square of the coefficients represent the proportion of test variance attributable to this ability. The coefficient to the right of each spatial test is the proportion of test variance attributable to error and processes specific to that test. The value of these coefficients indicates that the contribution of visualization ability to the spatial tests is about equal to the sum of measurement error and other unique contributions to performance. This part of the model confirms that the spatial tests measure a single spatial ability.

The coefficients on the paths connecting cognitive imagery measures to Visu- alization ability represent standardized multiple linear regression weights. The multiple correlation of Visualization ability with the linear combination of cognitive measures was 0.80. The proportion of variance unaccounted for by this linear combination (0.36) is displayed in Fig. 8 as specific variance.

Six of the nine path coefficients relating cognitive measures and Visualization ability were significantly different from zero according to z-tests. The processes measured by Scan slope, Scan intercept, and Add and Subract slope did not contribute significantly to Visualization ability. The strongest contribution to Visualization ability was provided by image quality, as measured by accuracy. In addition, the efficiency of image rotation, image generation, integration, and processes measured by Rotate intercept and Add and Subract intercept were related to Visualization ability.

Surprisingly, the relationship between image generation efficiency (Picture latency) and Visualization ability was opposite the expected direction. Longer picture latencies were associated with greater ability. Apparently Picture latency is acting as a suppressor variable (the path coefficient and the simple correlation between Picture latency and Visualization ability have opposite signs), obscuring the true relationship between image generation efficiency and Visualization ability. Picture latency is significantly correlated with several other cognitive imagery measures, particularly Rotate intercept and Accuracy. These correlations suggest that Rotate intercept includes the time to generate an image and Ac- curacy reflects the ease of image generation. If Visualization ability does not depend on image generation efficiency, then the negative coefficient removes variance in generation efficiency added indirectly through these other variables.

When the spatial tests included in this research were chosen, we had specific hypotheses about the imagery processes required in each task. In particular, we hypothesized that image rotation was required to solve all tests except Designs and Components; image integration was required to solve Puzzles, Mazes, and


Space Relations; and adding detail was required to solve Paper Folding. We considered the possibility that the unique variance for each test may arise from requirements for specific imagery processes. The Figures Test, for example, may require image rotation to a greater degree than any other test. Despite the excellent fit to the data provided by the model in Figure 8, we decided to test these specific hypotheses by adding direct links between each spatial test and the cognitive measures of the processes hypothesized to be involved in that test. Of course the model provided a good fit to the data (×2 = 52.4, df = 50), but the improvement over the model depicted in Fig. 8 was nonsignificant (×2 = 35.7, df = 33). Furthermore, all the path coefficients for the direct connections to the spatial tests were small and nonsignificant. Thus, we conclude that the Visualiza- tion factor includes all the imagery ability that affects spatial test performance.

Although most of the variance in the Visualization factor was predictable by a linear combination of cognitive imagery measures, about a third of the variance was not predictable. This unique variance could arise from many sources. For example, it could be due to the fact that spatial tests and cognitive tests were conducted on different days. More interestingly, the spatial tests may involve fluid intelligence as suggested by Horn (1979), whereas the cognitive tasks measure components of imagery ability. This hypothesis could have been examined if tests of fluid intelligence had been included.

GENERAL DISCUSSION

Three approaches to the study of individual differences in imagery ability were used in this research: self-report questionnaires, spatial tests, and cognitive imagery tasks. Each approach derives from a different view of the nature of imagery and provides different information about the underlying structures that comprise imagery ability. Comparisons of the results from these different approaches suggest that imagery ability can be decomposed into independent cognitive processes. Consider the results from each of these approaches.

Self-Report Questionnaires

Self-report questionnaires remain the most frequently used approach to the study of individual differences in imagery ability. Typically, questionnaires are used to assess imagery vividness or imagery control. Although previous research is far from consistent, moderate relationships have been observed between rated vividness and memory performance and between rated control and spatial test performance (Ernest, 1977; White et al., 1977).

Although the ratings of imagery vividness and control that we obtained were reliable and significantly correlated with one another, neither measure was related to the cognitive or spatial test measures. The only significant correlation was between rated imagery control and the Components spatial test. The fact that we


failed to observe the moderate relationships that others have obtained underlines the problems inherent in use of ratings as an assessment method.

The frequent use of these rating procedures suggests that researchers have adopted a theory of imagery in which images are conceptualized as mental pictures. If an image was like a picture, then more information could be extracted from a more vivid image. However, the experience of imagery as a picture may be epiphenomenal. We have observed people use the Method of Loci as a mnemonic who claim to be unable to form a visual image. Thus, we suggest that information can be stored in and extracted from a visual image without the experience of "seeing" the image.

Unlike the ratings of vividness and control, the rated preferred mode of thought proved to be related to both cognitive and spatial test measures. Efficient mental rotation and addition and subtraction of details were associated with a preference for a visual mode of thought. These results suggest that people are aware, to some degree, of their cognitive strengths and weaknesses, and prefer to use a mode of thought at which they excel. Alternatively, people may become more efficient using their preferred mode of thought.

One of the many problems associated with the use of such self-report measures is the coarse nature of the response. Self-reports do not provide fine- grained information that could lead to a theory of imagery. However, if a gross assessment of imagery ability is desired, the VVQ preference test is appropriate. It simply asks whether the subject tends to use imagery.

Cognitive Imagery Measures

The cognitive measures were derived from Kosslyn's theory of mental imagery (Kosslyn, 1980, 1981; Kosslyn et al., 1979). Tasks were constructed to provide measures of image quality and the efficiency of image generation, adding detail, integration, rotation, and scanning. Although each process could not be uniquely identified with a single measure, a set of nine measures were defined that were loosely interpreted in terms of Kosslyn's model.

One could disagree with the interpretations offered for these measures or even with the theory upon which they were based. Nonetheless, it is clear that the nine variables listed in Table 7 measure reasonably independent aspects of imagery ability. The correlations in Table 7 are remarkably low considering the sim- ilarities among the tasks, and are not even consistently positive. Thus, these measures provide a means for decomposing imagery ability into subprocesses by examining the correlations between performance in tasks that require imagery and these cognitive measures.

Spatial Ability Tests

Analysis of spatial test performance yielded a single factor accounting for most of the common variance that corresponds to the Visualization ability described by Horn (1979). Summarizing research on spatial ability, McGee (1979)


characterized Visualization ability as involving mental manipulation, rotation, twisting, or inversion of a pictorially presented stimulus object. Needless to say, this description of visualization ability is simply a summary of the processes that investigators believed were involved in the spatial tests that defined the factor.

There is no doubt that the spatial tasks require these processes, but there is no evidence that these processes limit performance in the tasks. It is possible, for example, that all subjects are readily able to rotate mental representations of objects, but subjects differ greatly in their ability to maintain the mental representation after it has been rotated. More realistically, it is possible that imagery ability reflects the efficiency of a constellation of processes, and Visualization ability is influenced by imagery abilities as well as other abilities.

The model depicted in Fig. 8 reflects this view. In this model Visualization ability is defined by performance on the spatial tests through factor analysis. Simultaneously, Visualization ability is decomposed into unique variance plus a linear combination of cognitive imagery measures. The model suggests that the most important determinant of Visualization is not rotation efficiency but image quality. Successful completion of spatial tests requires maintaining a high-quality representation of the stimulus. Efficiency of rotation is an important component of Visualization ability, but efficiency of image integration processes are also important.

Precise interpretations of some of the cognitive measures requires further research. In particular, sources of variance in the Add and Subtract intercept and the Rotate intercept are poorly understood. However, the structure of the results in Fig. 8 is important regardless of the interpretation of the cognitive measures. The model depicted in Fig. 8 establishes that Visualization ability can be decomposed into relatively independent measures though traditional methods of abilities research have been unsuccessful at decomposing it. By using the methods of cognitive psychology to provide more precise interpretations of the cognitive measures, a richer understanding of Visualization ability may be obtained.

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