a dissociation between object manipulation spatial ability...

Memory amp Cognition2001 29 (5) 745-756

Experimental studies of spatial reasoning providestrong evidence for a distinction between mental rotationand perspective-taking processes (eg Huttenlocher ampPresson 1973 1979 Presson 1982 Wraga Creem ampProfitt 2000) These studies compare tasks that require aperson to anticipate the appearance of an array of objectsafter it is rotated (rotation tasks) with tasks in which a per-son must anticipate the appearance of a fixed array aftera change in hisher perspective (orientation or perspec-tive tasks) Although these tasks are logically equivalentboth children and adults show different patterns of errorsfor the two tasks Perspective tasks lead to egocentric er-rors in which the participant describes the array fromhisher current perspective rather than the imagined per-spective whereas errors in mental rotation problems arenot systematic A distinction between orientation and ro-tation processes has also been found in object recognitiontasks so that people have difficulty recognizing changesin object arrays after the array rotates but not after theyphysically change their perspective with respect to thearray (Simons amp Wang 1998)

These results are consistent with behavioral and neuro-science evidence (D Bryant amp Tversky 1999 Easton ampSholl 1995 Muller Kubie Bostock Taube amp Quirk1991 OrsquoKeefe amp Nadel 1978 Paillard 1991 Rieser1989 Zacks Rypma Gabrieli Tversky amp Glover 1999)for a dissociation between knowledge of the spatial rela-tions among a set of stable reference objects (object-to-

object representational system) and knowledge of ob-jectsrsquo locations relative to the observerrsquos body (self-to-object representational system) Mental rotation of anobject or an array of objects involves imagining move-ment relative to an object-based frame of reference whichspecifies the location of one object (or its parts) with re-spect to other objects In contrast imagining a differentorientation (perspective) involves movement of the ego-centric frame of reference which encodes object loca-tions with respect to the front back left right andupdown axes of the observerrsquos body (D Bryant amp Tver-sky 1999 Easton amp Sholl 1995 Wraga et al 2000)Zacks et al (1999) have shown that egocentric perspec-tive transformations lead to increased cortical activityaround the left parietal-temporal-occipital junctionwhereas object-based spatial transformations such asmental rotation lead to an activation in posterior areasthat is greater in the right hemisphere than in the lefthemisphere

In this paper we examine whether a personrsquos ability tomentally manipulate objects from a stationary point ofview (involving an object-to object representational sys-tem) and hisher ability to imagine taking a different per-spective in space (involving a self-to-object representa-tional system) are separable mental abilities Althoughthe distinction between mental rotation and perspective-taking processes has been made in experimental and neu-roscience studies it does not necessarily imply a distinc-tion from an individual-differences perspective That isobject manipulation and perspective taking could be sep-arate processes but tap the same underlying ability in thesense that when an individual is good at object manipula-tion heshe is also good at spatial orientation and viceversa

The literature on individual differences up to now hasquestioned the separability of spatial abilities that involve

745 Copyright 2001 Psychonomic Society Inc

This research was supported by the Office of Naval Research undercontract N00014-96-10525 to the second author We thank Pam Freitasfor help with conducting the study and Nancy Collins for statistical ad-vice Correspondence concerning this article should be addressed toM Kozhevnikov Rutgers University Department of Psychology 101Warren St Smith Hall Newark NJ 07102 (e-mail mariapsychol-ogyrutgersedu)

A dissociation between object manipulationspatial ability and spatial orientation ability

MARIA KOZHEVNIKOV and MARY HEGARTYUniversity of California Santa Barbara California

We developed psychometric tests of spatial orientation ability in which people are shown a two-dimensional array of objects imagine taking a perspective within the array and indicate the directionto a target object from this perspective Patterns of errors on these tests were consistent with experi-mental studies of perspective taking Characteristic errors and verbal protocols supported the validityof the perspective-taking tests suggesting that people encoded the objects in the display with respectto a body-centered coordinate system when the imagined perspective was more than 90ordm different fromthe orientation of the display By comparing alternative models in a confirmatory factor analysis wefound that the ability to mentally rotate and manipulate an imagined object (as measured by tests ofspatial visualization and spatial relations) and the ability to reorient the imagined self (as measured bythe perspective-taking tests) are separable spatial abilities

746 KOZHEVNIKOV AND HEGARTY

imagining a change in onersquos own orientation in space fromspatial abilities that involve mentally manipulating anobject from a fixed perspective Psychometric studies ofspatial ability (eg Carroll 1993 Eliot amp Smith 1983Lohman 1988 McGee 1979) report evidence for severalmajor spatial abilities factors Two of these factors spatialvisualization and spatial relations require the ability tomentally manipulate spatial forms from a fixed perspec-tive and involve the object-to-object representational sys-tem Spatial visualization tasks require imagination of acomplex sequence of mental manipulations For examplethe Paper Folding Test (shown in the Appendix) and FormBoard Tests are typically loaded on the spatial visualiza-tion factor Spatial relations tasks (also called speeded ro-tation) involve simpler mental manipulations such as asingle-step mental rotation of a two-dimensional objectand emphasize speed of processing (Carroll 1993) Forexample the Card Rotation Test (shown in the Appen-dix) typically loads on the spatial relations factor For thepurposes of the present study we refer to tests of spatialvisualization and spatial relations collectively as objectmanipulation spatial tests1

A third proposed spatial factor spatial orientation isdefined as the ability to imagine how a stimulus arraywill appear from another perspective For example theGuilfordndashZimmerman Spatial Orientation Test (Guilfordamp Zimmerman 1948) the most commonly used test ofspatial orientation requires a subject to identify the po-sition of a boat that would give a particular view of thelandscape (see an example of the task in the Appendix)In contrast to spatial visualization and spatial relationstests spatial orientation tests are designed to engage theself-to-object representational system Some researchers(eg McGee 1979) have argued that there is support forthe existence of the spatial orientation factor However amajor meta-analysis of the factor-analytic research (Car-roll 1993) failed to find evidence for the separability ofthis factor from spatial visualization (see also Borich ampBauman 1972 Price amp Eliot 1975)

Spatial orientation might be difficult to separate fromother spatial factors because tests designed to measurethis ability are often solved by mentally rotating the stim-ulus rather than by reorienting oneself (Barratt 1953Carpenter amp Just 1986 Carroll 1993) For example ina verbal protocol study Barratt found that the majority ofparticipants reported a mental rotation strategy on theGuilfordndashZimmerman task This would account for itstypically high loading on the spatial visualization factor(Carroll 1993) We suggest that the failure to find a dis-tinction between object manipulation and spatial orienta-tion abilities in the psychometric literature occurs becausethere are currently no pure psychometric tests of spatialorientation ability

One goal of this study was to develop valid tests ofspatial orientation ability On the basis of experimentalstudies of perspective taking (eg Hintzman OrsquoDell ampArndt 1981 Rieser 1989 Shelton amp McNamara 1997)we developed tests in which a person is shown a two-

dimensional array of objects imagines taking a perspectivewithin the array and indicates the direction to a target ob-ject from that perspective We analyzed patterns of er-rors on these tests and verbal protocols to examine whetherthe dominant strategy used in these tests involves imagin-ing reorienting oneself within the display rather thanmentally rotating the display

A second goal of the study was to examine the extentto which object manipulation abilities and spatial orien-tation ability are separable We analyzed performance ontests of object manipulation abilities and spatial orienta-tion abilities using confirmatory factor analysis (CFA)This method allowed us to test hypothesized factor struc-tures and compare alternative models statistically (Kline1998) If object manipulation and spatial orientationabilities tap the same underlying construct a model witha single spatial factor should provide a sufficiently goodfit to the data If however object manipulation and spa-tial orientation abilities are distinct a model with a singlespatial factor will significantly deviate from the data Incontrast a two-factor model that assumes their separabil-ity should provide a good fit to the data The correlationbetween these two factors then provides an estimation ofthe degree to which the two abilities are related

EXPERIMENT 1

MethodParticipants The participants were 71 undergraduate students

recruited from the psychology subject pool at the University of Cal-ifornia Santa Barbara

Materials The materials consisted of seven paper-and-penciltests of spatial abilities Object manipulation abilities were assessedby using the Card Rotation Test the Cube Comparison Test2 andthe Paper Folding Test (Ekstrom French amp Harman 1976) TheCard Rotation Test requires participants to view a two-dimensionaltarget f igure and judge which of the five alternative test figures areplanar rotations of the target figure (as opposed to its mirror image)as quickly and as accurately as possible In the Cube ComparisonTest each item presents two drawings of cubes with letters andnumbers printed on their sides Participants must judge whether thetwo drawings could show the same cube Items in the Paper FoldingTest show drawings of two or three folds made in a square sheet ofpaper The final drawing shows a hole being punched in the foldedpaper The task is to select one of five drawings that shows how thepunched sheet would appear when fully opened

The participants were presented with the GuilfordndashZimmermanSpatial Orientation Test as well (Guilford amp Zimmerman 1948)The test consists of items presenting two pictures of a lake andscenery as seen from looking out over the prow of a motorboatwhich has moved slightly between pictures The task is to select oneof five diagrams that represents how the boat has moved Each di-agram shows a dot representing the old position of the prow and adash representing the new position Changes include any combina-tion of heading change (ie rotation) and of forward translation andsideward translation of the boat

To measure studentsrsquo spatial orientation ability we developedtwo perspective-taking tests In the first test (the Object PerspectiveTest) a configuration of seven objects was drawn on a 85 3 11 insheet of paper (see Figure 1A) This display was fixed to the walldirectly in front of each participant and was visible at all timesEach participant also received an answer booklet with a separatepage for each of the test items On each item the participant was

OBJECT MANIPULATION VERSUS ORIENTATION 747

asked to imagine being at the position of one object in the display(the station point) facing another object (defining the imaginedheading or perspective within the array) and was asked to indicatethe direction to a third (target) object The page of the answer sheetfor each test item showed a picture of a circle in which the imag-ined station point was drawn in the center of the circle and the imag-ined heading was drawn as an arrow pointing vertically up The taskwas to draw another arrow from the center of the circle indicatingthe direction to the target object (eg ldquoimagine you are standingnear the stop sign facing the house point to the traffic lightrdquo) Theparticipants were prevented from physically rotating either the dis-play showing the object configuration or their answer sheets

In the second perspective-taking test (the Map Perspective Test)a map showing five landmarks was drawn on a 85 3 11 in sheetof paper (see Figure 1B) and was pinned to the wall in front of theparticipant The method of responding by drawing an arrow on acircle was the same as that for the Object Perspective Test

The direction of the target object relative to the heading was var-ied systematically by dividing the circle into eight sections (0ordmndash45ordm45ordmndash90ordm and so on) Both perspective-taking tests consisted of 10test items with the correct answer for at least 1 item being withineach of the eight sections The score for each item was the absolutedeviation in degrees between the participantrsquos response and the cor-rect direction to the target (absolute directional error) A partici-pantrsquos total score was the average deviation across all items If a par-ticipant did not point to any target direction a score of 90ordm wasassigned for that item (ie chance performance since the absoluteangular deviation can range from 0ordm to 180ordm) This occurred on 5of all observations

In addition the participants were administered the Santa Bar-bara Sense of Direction Scale (SBSOD Hegarty Richardson Mon-tello Lovelace amp Subbiah 2001) This self-report scale consists of15 statements designed to measure a personrsquos judgment of his orher own spatial orientation ability Examples of typical statementsare ldquomy sense of direction is very goodrdquo and ldquoI very easily get lostin a new cityrdquo Participants respond by circling a number from 1(strongly disagree) to 7 (strongly agree) to indicate their level ofagreement with each statement All the items were scored so that ahigher rating indicated a better self-report sense of direction (iethe scoring on negatively stated items was reversed)

Procedure The participants were tested in groups of up to 6 stu-dents per session They completed the Object Perspective Test theGuilfordndashZimmerman Spatial Orientation Test the Cube Compar-ison Test the Paper Folding Test the Card Rotation Test the MapPerspective Test and the SBSOD in that order Each of the testswas administered according to its standard instructions includingtime limits The participants were allowed 4 min to complete eachperspective-taking test Completion of the SBSOD was not timed

Results and DiscussionDescriptive statistics and measures of internal reliabil-

ity are given in Table 1First we examined whether the patterns of the partic-

ipantsrsquo responses on our paper-and-pencil perspectivetests were comparable with patterns of responses foundfor experimental perspective-taking tasks involving realarrays of objects

Note that the perspective-taking tasks involve mentaltransformations over two angles (1) the angle between theorientation of the array and the perspective to be imaginedand (2) the angle between the imagined perspective andthe direction to the target object Both of these transfor-mations contribute to task difficulty Errors and responsetimes increase with the angular deviation of the imagined

perspective from the orientation of the array (eg Hintz-man et al 1981 Rieser 1989 Shelton amp McNamara1997) and when imagining taking a particular perspec-tive people are faster and more accurate in naming andpointing to objects in front and behind them as comparedwith items to the right or left (eg D Bryant amp Tversky1999 Hintzman et al 1981) Therefore we examined howeach of these angles contributed to performance on ourpaper-and-pencil perspective-taking tests

Pointing accuracy as a function of imagined head-ing Consistent with experimental research (Hintzmanet al 1981 Rieser 1989 Shelton amp McNamara 1997)absolute angular error increased with the angular devia-tion of onersquos imagined heading (perspective) from the ori-entation of the array (see Figure 2) The data plotted inFigure 2 present mean absolute pointing error as a func-tion of this angular deviation combining items from thetwo tests The linear regression in Figure 2 was reliable[F(119) = 812 p 01]

Pointing accuracy as a function of pointing direc-tion We categorized all items from both perspective-taking tests as front right-front right and so forth accord-ing to the direction to the target from the participantrsquosimagined heading (eight sections of 45ordm) Figure 3 pre-sents absolute pointing error for targets in these eight sec-tions An analysis of variance showed a significant effectof pointing direction [F(7490) = 1293 p 001] Plannedcontrasts revealed that pointing accuracies for front andback responses were significantly higher than those forall the others (p 001) Front responses were also moreaccurate than back responses (p 01) and right-frontand left-front responses were significantly more accu-rate than right-back and left-back responses respectively( p 01) These results are very similar to the responseprofiles observed by Hintzman et al (1981) for a similarpointing task and by D Bryant and Tversky (1999) for timeto identify objects from an imagined perspective

In summary the results above provide evidence thaterror patterns on paper-and-pencil perspective-takingtests are similar to those on experimental perspective-taking tasks However this is not sufficient to establishthat the perspective-taking tests are solved by a strategythat involves mentally reorienting oneself rather than men-tally rotating the stimuli The increase in pointing error asa function of imagined heading is consistent with both aperspective-taking strategy and a mental rotation strat-egy Although the pattern of accuracy as a function ofpointing direction is suggestive of a body-centered coor-dinate system it is possible that front and back responsesare easier because they can be solved by a simpler strat-egy (ie noting that the three objects mentioned in an itemform a straight line)

Imagined perspective taking usually leads to systematicerrors that reflect the symmetry of the coordinate systemof the body whereas errors in rotation problems are notsystematic (Huttenlocher amp Presson 1973 1979 Pres-son 1982) In order to establish the validity of our paper-and-pencil perspective-taking tests we quantified errors


Figure 1 Configuration of objects presented to subjects in (A) the Object Perspective-Taking Test and(B) the Map Perspective-Taking Test

A

B


that reflect the symmetry of the coordinate system of thephysical body (left right and front back axes of the ob-serverrsquos body) We refer to these as reflection errors

Reflection errors We drew a circular plot of partici-pantsrsquo responses for each perspective-taking item For in-stance Figure 4A shows the distribution of responses onItem 1 from the Object Perspective Test (ldquoimagine youare standing at the house and facing the stop sign point tothe traffic lightrdquo) Each triangle represents the end of thearrow drawn by 1 participant This item requires the par-ticipant to imagine changing hisher orientation by 50ordmand the correct answer is in the upper right quadrant(quadrant I) As Figure 4A shows all the participantsrsquo re-sponses fall into the correct quadrant of the circle and theresponses are approximately normally distributed aroundthe modal response

Now consider Figure 4B representing participantsrsquoresponses on Item 3 of the Object Perspective Test Thisitem asks the participant to imagine standing at the housefacing the flower and to point to the traffic light (148ordmdifference between the imagined perspective and the ori-entation of the array) The correct answer to this item falls

in the left upper quadrant (quadrant II) Although mostresponses are in this quadrant some responses also fallinto other quadrants Furthermore the incorrect responsesare not random but are grouped either in the right upperquadrant (quadrant I) suggesting a reflection throughthe vertical axis or in the lower left quadrant (quad-rant III) suggesting a reflection through the horizontalaxis Quadrant I errors would be produced if the partici-pants encoded the objects in a body-centered frame of ref-erence and confused left and right whereas quadrant IIIerrors would be produced if they confused front and backQuadrant IV errors would result if the participants con-fused between both left and right and front and back

To examine whether these errors are characteristic ofother trials we first classified a response as an error if itfell in the wrong quadrant We then classified errors oneach trial as reflection errors if they were within 20ordm ofa response that was a reflection of the correct responsethrough the horizontal vertical or both axes Figure 5shows the mean number of participants who made reflec-tion errors on items for different imagined headings andthe mean number of participants who made other errors(errors falling in the incorrect quadrant but not within 20ordmof a reflection of the correct answer) The number of re-flection errors increases significantly with the angular de-viation of imagined heading (perspective) from the ori-entation of the array whereas the number of other errorsdoes not Items involving perspective changes of less than90ordm resulted in significantly fewer reflection errors (meannumber of quadrant errors is 25 SD = 25) as comparedwith the items involving orientation changes of morethan 90ordm [mean number of quadrant errors is 1071 SD =57 F(119) = 1127 p 01] In contrast the number of

Table 1Descriptive Statistics and Measures of

Internal Reliability for the Spatial Abilities Measures

Test Mean SD Observed Range Reliability

Card Rotation 1109 338 0ndash156 80Cube Comparison 186 115 0ndash40 84Paper Folding 116 39 15ndash20 84GuilfordndashZimmerman 171 109 0ndash50 88Object Perspective 332 233 5ndash95 83Map Perspective 344 253 5ndash120 85Sense of Direction 35 16 1ndash6 88

Figure 2 Absolute pointing error as a function of the angular deviation of imaginedheading (perspective) from the orientation of the array (The solid curve represents theregression line)


other errors did not differ significantly with orientationchange [F(119) = 046]

The results above suggest that people use the egocen-tric frame of reference to solve perspective-taking tasksDifficulties in specifying rightndashleft and backndashfront di-rections to the target would not arise if the participantsperformed the task primarily with an object manipulationstrategy Furthermore if the participants gave up andguessed on difficult trials this would lead to an increasein all types of errors and not just reflection errors

There were few reflection errors for items involving aperspective change of less than 90ordm It is possible thatthese items were performed with a perspective-takingstrategy but were significantly easier than items involv-ing a larger change of perspective Alternatively the par-ticipants might have used other strategies to solve itemsinvolving a perspective change of less than 90ordm To dis-criminate between these alternatives in Experiment 2we asked participants to think aloud while they solvedperspective-taking items and classified the strategies thatthey reported

EXPERIMENT 2


who had not participated in Experiment 1 They were recruited fromthe psychology subject pool at the University of California SantaBarbara

Materials Two displays identical to those used in the ObjectPerspective and Map Perspective Tests were fixed on the wall di-rectly in front of the participant The participant received an answerbooklet with a page for each of 13 test items The format of theitems and the method of responding were the same as those in Ex-periment 1 Nine items referred to the object display and 4 items re-ferred to the map display Six items required the participant to

change hisher perspective less than 90ordm 2 required a change of 90ordmand 5 other items required a perspective change of more than 90ordm

Procedure The participants were first told to think aloud whilesolving each item and after answering they were also asked specif-ically whether they imagined changing their perspective or used an-other strategy We videotaped the participants in order to record ver-balizations hand movements and drawings

ResultsWe identified three strategies used by the participants

to perform the perspective-taking tasks1 Finding the angle Those participants who used this

strategy reported that they just saw the angle or tiltedtheir heads to see the angle but did not indicate any imag-ined perspective change or rotation of the array The fol-lowing transcripts are examples of responses that wereclassified as indicative of this strategy ldquoI could see theangle without imagining myself there rdquo ldquoI just tiltedmy head I saw the line and the angle I didnrsquot reallyimagine myself there rdquo ldquo I just see that the house stopsign and car form a straight line so I just think of it asthat and in this way put them on the circle rdquo

2 Mental rotation The participants were classified asusing this strategy if they reported that they mentally ro-tated the display or angle connecting three objects (stationpoint heading and target) The following examples illus-trate typical descriptions of the above strategy ldquoIf I didimagine something it was that the paper turned like thisand the line was here rdquo ldquoI imagined the paper turning actually the angle between three objects turning itrsquoseasier than imagining turning myself rdquo

3 Perspective taking The participants scored as usingthis strategy explicitly reported that they imagined re-orienting themselves while solving the task Typical re-sponses that were scored as perspective taking were as

Figure 3 Absolute pointing error as a function of the direction to the target fromonersquos imagined heading F front RF right front R right RB right back B backLB left back L left and LF left front


Figure 4 Distribution of participantsrsquo responses on (A) Item 1 of the Object Perspective Test and (B) Item 3of the Object Perspective Test Triangles represent the ends of the arrows showing the direction to the targetobject drawn by each subject

A

B


follows ldquoIrsquom trying to spin myself in my head rdquo ldquoIrsquomfacing the car and Irsquom trying to see where it would be inrelation to my right shoulder Irsquom trying to picture myselfthere rdquo ldquoI had to turn myself around because itrsquos fac-ing the opposite direction rdquo

Two independent raters who were unaware of the pur-pose of the study viewed the videotapes and classified par-ticipantsrsquo responses on each item as using one of the threestrategies The agreement between raters regarding thetype of strategy used was 89 Disagreements were set-tled by consensus of the two raters

The first two strategies finding the angle and mentalrotation might be classified as object manipulationstrate-gies Those who reported the angle strategy seemed toretrieve the interobject relations from the initial orienta-tion of the array and then impose them on the orientationof the answer circle Those who used the mental rotationstrategy explicitly described computing the angle betweenthe station point heading and target and then rotating theangle

In contrast participants reporting the perspective-taking strategy mentioned changes of their own orienta-tion Their protocols indicated that they encoded the ob-jects in the array or map with respect to their own bod-ies (selfndashobject representational system) as thefollowing examples illustrate ldquoIrsquom standing here myshoulders face here and I see the stop light in relation tomy shoulders Once I position my shoulders I can judgethe angles and right from left rdquo ldquoI had to think morebecause it was on different sides I had to think which is

my arm pointing tordquo Reports of leftndashright or backndashfrontdiscrimination accompanied the majority of trials inwhich a participant reported a perspective-taking strat-egy (52 out of 64 reports) When other strategies wereused no left-right or back-front discriminations were re-ported

As is shown in Table 2 most participants reported theangle strategy for items requiring reorientation of less than90ordm However for tasks requiring a perspective change ofmore than 90ordm the dominant strategy was perspective

Table 2Number of Participants Who Were Classified

as Using the Different Strategies for IndividualPerspective-Taking Items in Experiment 2

Perspective Pointing Strategy

Item Change (ordm) Direction Perspective Angle Rotation

1 45 right-front 3 5 02 45 front 2 6 03 45 right-front 2 6 04 50 back 3 5 05 50 right-back 4 4 06 70 left-back 3 5 07 90 right-front 6 1 18 90 left-front 6 1 19 130 left 7 0 1

10 130 back 7 0 111 145 left-front 7 0 112 145 left-back 7 0 113 150 right-front 7 0 1

NotemdashItems are classified by the change of perspective required by theitem and the direction of pointing from the imagined heading

Figure 5 The mean number of reflection errors and other errors as a function of the devia-tion of imagined heading from the orientation of the display Error bars represent the standarderror of the mean


taking (Only 1 of the 8 participants changed from theangle strategy to mental rotation) A paired-sample t testrevealed that the proportion of perspective-taking strate-gies reported by the participant on items with an orienta-tion change of more than 90ordm (M = 88 SD = 24) wassignificantly higher than the proportion of perspective-taking strategies reported by the participants to itemswith an orientation change of less than 90ordm [M = 35SD = 18 t (7) = 991 p 001)

ConclusionsThe results of the protocol study support the validity

of the perspective-taking tests as tests of spatial orienta-tion by showing that the dominant strategy used on theseitems is to imagine oneself reoriented within the arrayHowever this is true only for items that require a per-spective change of more than 90ordm In contrast most itemsthat require a perspective change of less than 90ordm aresolved by object manipulation strategies

CONFIRMATORY FACTOR ANALYSIS

Having established the validity of the perspective-taking tests we now turn to the second goal of the studywhich is to examine whether spatial orientation abilityas measured by our perspective-taking tests is separablefrom object manipulation abilities (ie spatial visual-ization and spatial relations) To examine this questionwe performed a CFA on the data from Experiment 1 Onthe basis of the results of the protocol analysis we ex-cluded items requiring a perspective change of less than90ordm from this analysis (five items in the Object Perspec-tive Test and three items in the Map Perspective Test)Scores on the restricted set of items were linearly trans-formed so that higher values corresponded to better per-formance (by subtracting the average error score for eachparticipant from 180ordm) The internal reliability of the re-sulting Object Perspective Test was 82 (M = 13726SD = 3277) and of the resulting Map Perspective Test was82 (M = 14522 SD = 2827)

Table 3 shows the correlations between the different spa-tial ability tests The measures are significantly correlatedwith each other (with the exception of the SBSOD whichdoes not correlate with Card Rotation or Paper Folding)

According to our model there are two separable spatialfactors object manipulation ability and spatial orientationability We assumed that Card Rotation Cube Compari-son and Paper Folding would load on the object manip-ulation spatial factor and that Object Perspective andMap Perspective would load on the spatial orientationfactor The SBSOD was also assumed to load on the spa-tial orientation factor because similar self-report mea-sures have been shown to correlate with an ability to takea perspective in a familiar environment and point to a land-mark in that environment (K Bryant 1982 Sholl 1988)

There has been doubt about whether the GuilfordndashZimmerman Spatial Orientation Test measures spatialorientation rather than other spatial abilities (Barratt1953 Carpenter amp Just 1986 Carroll 1993) To examinethis question we tested a preliminary two-factor modelin which this test was allowed to load on both factorsand found that it loaded significantly only on the objectmanipulation factor (15 overlapping variance) Thus inour final version of the two-factor model we consideredthis test as loading only on object manipulation

The estimated two-factor model complete with factorloadings is illustrated in Figure 6 The numbers abovethe straight single-headed arrows are standardized factorloadings and the arrows at the end of the shorter single-headed arrows represent error terms All these numberscan be interpreted as standardized regression coefficients

Values of fit indices for the two-factor model are re-ported in Table 4 All indices suggest that the two-factormodel fits the data This model produced a nonsignifi-cant c2(13) = 1316 p = 44 indicating that the model didnot significantly deviate from the data In addition theBentler Comparative Fit Index (CFI) is 99 well abovethe commonly used criterion of 90 for a good fit and thestandardized root-mean square residual (SRMR) is 012well below the criterion of 05

The two-factor model indicates that perspective takingand spatial visualization are highly correlated with eachother as would be expected But are these factors identi-cal We considered an alternative single-factor model inwhich the correlation between the two factors was fixedto 1 The fit indices for this model are shown in Table 4The overall chi-square for the single-factor model wassignificant [c2(14) = 3568 p = 001] indicating that the

Table 3Correlations Between the Spatial Ability Measures

(Pearson Correlation Coefficients N = 71)

Object Map Cube Card PaperTask Perspective Perspective Comparison Rotation Folding GuilfordndashZimmerman SBSOD

Object ndash 72dagger 50dagger 27dagger 47dagger 34dagger 28daggerMap ndash 249dagger 18 45dagger 32dagger 19Cube ndash 52dagger 57dagger 38dagger 29daggerCard ndash 46dagger 28dagger 09Paper ndash 35dagger 12GndashZ ndash 25

NotemdashScores on the Object and Map Tests reported in the table are for a restricted set of items (morethan 90ordm) and are linearly transformed so that higher values correspond to better performanceSBSOD Santa Barbara Sense of Direction Scale p 05 daggerp 01


model significantly deviates from the data In additionthe values of CFI (86) and SRMR (139) do not meet thecriteria for a good fit Thus the single-factor model doesnot explain the data Moreover a chi-square differencetest comparing the fit of the two models indicates thatthe overall fit of the two-factor model is significantlygreater than that of the single-factor model [c2(1) =2253 p 01]

GENERAL DISCUSSION

We developed new spatial orientation tests based ontasks used in experimental studies of perspective takingThe patterns of studentsrsquo responses on our tests are verysimilar to response profiles found in previous experimen-tal studies Furthermore we quantified errors character-istic of a perspective-taking strategy that involve confusionbetween left right as well as backfront pointing direc-tions The number of these errors increased significantlywhen the angle between the orientation of the array and

the perspective to be imagined exceeded 90ordm These re-sults suggest that people use a perspective-taking strategyto solve items that require changing imagined heading bymore than 90ordm These systematic errors would not be pre-dicted if people performed the perspective-taking tasksmainly with an object manipulation strategy

The results of the protocol analysis also support theclaim that perspective taking is the prevalent strategy usedto solve Object Perspective and Map Perspective itemsthat involve a perspective change of more than 90ordm Al-though it is possible to solve these items by mentally ro-tating the display rather than by imagining oneself re-oriented in space 7 of the 8 participants interviewed inExperiment 2 reported a perspective-taking strategy

The second goal of our study was to establish whetherobject manipulation spatial abilities (ie spatial visual-ization and spatial relations) can be dissociated fromperspective-taking spatial abilities The CFA indicatedthat a model assuming that these are separate abilities isa better fit to the data than a model that assumes a single

Figure 6 The results of the confirmatory factor analysis


spatial factor Although they are correlated object manip-ulation and spatial orientation abilities can be separated

In contrast the GuilfordndashZimmerman Spatial Orien-tation Test which is the most commonly used test of spa-tial orientation ability could not be distinguished fromobject manipulation spatial abilities We suggest that theGuilfordndashZimmerman Test is a less valid test of spatialorientation because it does not involve large changes inperspective (only differences of about 30ordm) Our data sug-gested that people do not use a perspective-taking strat-egy for items less than 90ordm Consistent with this inter-pretation Barratt (1953) found that many people reportsolving items in the GuilfordndashZimmerman Test by an ob-ject manipulation strategy It seems that in order to mea-sure individual differences in spatial orientation abilitiesit is necessary to test people on items that involve orien-tation changes of 90ordm or more

The fact that SBSOD loads on the perspective-takingfactor is very preliminary evidence that performance inour pencil-and-paper perspective-taking tests might be re-lated to perspective taking in large-scale space This ev-idence is relatively weak because the loading is not high and SBSOD is not a direct measure of performanceFurther research is required to examine the relation of perspective-taking tests to other spatial tasks such astaking a perspective in an array of real objects and navi-gation in large-scale space

In conclusion this research indicates that a personrsquosability to mentally manipulate a visual stimulus from a sta-tionary point of view (object manipulation ability) doesnot reflect hisher ability to reorient himherself in space(spatial orientation ability) Although they are highly cor-related object manipulation and perspective-taking testsdo not appear to reflect the same construct Failure to finda distinction between these abilities in the psychometricliterature to date might be attributed to the fact that previ-ous spatial orientation tests used were not pure measuresof this ability

REFERENCES

Barratt E S (1953) An analysis of verbal reports of solving spatialproblems as an aid in defining spatial factors Journal of Psychology36 17-25

Borich G D amp Bauman P M (1972) Convergent and discriminantvalidation of the French and GuilfordndashZimmerman spatial orienta-tion and spatial visualization factors Educational amp PsychologicalMeasurement 32 1029-1033

Bryant D amp Tversky B (1999) Mental representations of perspec-tive and spatial relations from diagrams and models Journal of Ex-perimental Psychology Learning Memory amp Cognition 25 137-156

Bryant K (1982) Personality correlates of sense of direction and ge-

ographical orientation Journal of Personality amp Social Psychology43 1318-1324

Carpenter P A amp Just M A (1986) Spatial ability An information-processing approach to psychometrics In R J Stenberg (Ed) Ad-vances in the psychology of human intelligence (Vol 3 pp 221-252)Hillsdale NJ Erlbaum

Carroll J (1993) Human cognitive abilities A survey of factor-analytical studies New York Cambridge University Press

Easton R D amp Sholl M J (1995) Object-array structure framesof reference and retrieval of spatial knowledge Journal of Experi-mental Psychology Learning Memory amp Cognition 21 483-500

Ekstrom R B French J W amp Harman H H (1976) Manual forKit of Factor Referenced Cognitive Tests Princeton NJ EducationalTesting Service

Eliot J amp Smith I M (1983) An international directory of spatialtests Windsor Berkshire UK NFER-Nelson

Guilford J P amp Zimmerman W S (1948) The GuilfordndashZimmermanAptitude Survey Journal of Applied Psychology 32 24-34

Hegarty M Richardson A E Montello D R Lovelace K ampSubbiah I (2001) The Santa Barbara Sense of Direction Scale Un-published manuscript University of California Santa Barbara

Hintzman D L OrsquoDell C S amp Arndt D R (1981) Orientationin cognitive maps Cognitive Psychology 13 149-206

Huttenlocher J amp Presson C C (1973) Mental rotation and theperspective problem Cognitive Psychology 4 277-299

Huttenlocher J amp Presson C C (1979) The coding and transfor-mation of spatial information Cognitive Psychology 11 375-394

Kline R B (1998) Principles and practice of structural equationmodeling New York Guilford

Lohman D F (1988) Spatial abilities as traits processes and knowl-edge In R J Sternberg (Ed) Advances in the psychology of humanintelligence (pp 181-248) Hillsdale NJ Erlbaum

McGee M G (1979) Human spatial abilities Psychometric studiesand environmental genetic hormonal and neurological influencesPsychological Bulletin 86 889-918

Muller R U Kubie J L Bostock E M Taube J S amp QuirkG J (1991) Spatial firing correlates of neurons in the hippocampusformation of freely moving rats In J Paillard (Ed) Brain and space(pp 269-333) Oxford Oxford University Press

OrsquoKeefe J amp Nadel L (1978) The hippocampus as a cognitive mapOxford Oxford University Press

Paillard J (1991) Brain and space Oxford Oxford University PressPresson C C (1982) Strategies in spatial reasoning Journal of Ex-

perimental Psychology Learning Memory amp Cognition 8 243-251Price L amp Eliot J (1975) Convergent and discriminant validities of

two sets of measures of spatial orientation and visualization Educa-tional amp Psychological Measurement 35 975-977

Rieser J J (1989) Access to knowledge of spatial structure at novelpoints of observation Journal of Experimental Psychology Learn-ing Memory amp Cognition 15 1157-1165

Shelton A L amp McNamara T P (1997) Multiple views of spatialmemory Psychonomic Bulletin amp Review 4 102-106

Sholl M J (1988) The relation between sense of direction and men-tal geographic updating Intelligence 12 299-314

Simons D J amp Wang R F (1998) Perceiving real-world viewpointchanges Psychological Science 9 315-320

Wraga M Creem S H amp Profitt D R (2000) Updating displaysafter imagined object and viewer rotations Journal of ExperimentalPsychology Learning Memory amp Cognition 26 151-168

Zacks J Rypma B Gabrieli J D E Tversky B amp Glover G H

Table 4Comparison of the Single-Factor and Two-Factor Models

Model c2 df c2 df c2difference dfdifference CFI NNFI SRMR

Singlendashfactor 3568 14 262 ndash ndash 86 80 14Twondashfactor 1316 13 016 2252 1 99 93 01

NotemdashCFI Bentler Comparative Fit Index NNFI BentlerndashBonett Non-Normed FitIndex SRMR standardized root-mean squared residual p 01


(1999) Imagined transformations of bodies An fMRI investigationNeuropsychologia 37 1029-1040

NOTES

1 Although there is strong evidence for a dissociation between testsof spatial visualization and speeded rotation in the psychometric liter-ature (Carroll 1993) several tests of each type must be included in afactor analysis in order for these abilities to emerge as separate factors

In this study we were more concerned with the dissociation betweenobject manipulation and spatial orientation abilities so we did not in-clude enough tests for spatial visualization and speeded rotation toemerge as separate factors Therefore we refer to these tests collectivelyas tests of object manipulation ability

2 The Card Rotation and Cube Comparison Tests classif ied asspeeded rotation tests by most researchers (see Carpenter amp Just 1986Carroll 1993 Eliot amp Smith 1983 Lohman 1988) were called spa-tial orientation tests by Ekstrom French and Harmon (1976)

APPENDIX

Instructions and a Sample Item From the Paper Folding Test (Ekstrom et al 1976)In this test you are to imagine the folding and unfolding of pieces of papers The figures on the left repre-

sent a square piece of paper being folded and the last of these figures has one or two small circles drawn onit to show where the paper has been punched One of the five figures on the right shows where the holes willbe when the paper is unfolded You are to decide which one of these figures is correct

Instructions and Sample Items From the Card Rotation Test (Ekstrom et al 1976)Each problem in this test consists of one card on the left of a vertical line and eight cards on the right You

are to decide whether each of eight cards on the right is the same as or different from the card at the left Markthe box beside the S if it is the same as the one at the beginning of the row Mark the box beside the D if it isdifferent from the one at the beginning of the row

Instructions and Sample Items From the GuilfordndashZimmermanSpatial Orientation Test (Guilford amp Zimmerman 1948)

In each item you are to note how the position of the prow of the boat has changed in the second picture fromits original position in the first picture To work each item First look at the top picture See where the motorboat is headed Second look at the bottom picture and note the CHANGE in the boatrsquos heading Third selectand mark one of five diagrams to represent how the boat has moved Each diagram shows a dot representingthe old position of the prow and a dash representing the new position

(Manuscript received August 4 2000revision accepted for publication February 2 2001)


imagining a change in onersquos own orientation in space fromspatial abilities that involve mentally manipulating anobject from a fixed perspective Psychometric studies ofspatial ability (eg Carroll 1993 Eliot amp Smith 1983Lohman 1988 McGee 1979) report evidence for severalmajor spatial abilities factors Two of these factors spatialvisualization and spatial relations require the ability tomentally manipulate spatial forms from a fixed perspec-tive and involve the object-to-object representational sys-tem Spatial visualization tasks require imagination of acomplex sequence of mental manipulations For examplethe Paper Folding Test (shown in the Appendix) and FormBoard Tests are typically loaded on the spatial visualiza-tion factor Spatial relations tasks (also called speeded ro-tation) involve simpler mental manipulations such as asingle-step mental rotation of a two-dimensional objectand emphasize speed of processing (Carroll 1993) Forexample the Card Rotation Test (shown in the Appen-dix) typically loads on the spatial relations factor For thepurposes of the present study we refer to tests of spatialvisualization and spatial relations collectively as objectmanipulation spatial tests1

A third proposed spatial factor spatial orientation isdefined as the ability to imagine how a stimulus arraywill appear from another perspective For example theGuilfordndashZimmerman Spatial Orientation Test (Guilfordamp Zimmerman 1948) the most commonly used test ofspatial orientation requires a subject to identify the po-sition of a boat that would give a particular view of thelandscape (see an example of the task in the Appendix)In contrast to spatial visualization and spatial relationstests spatial orientation tests are designed to engage theself-to-object representational system Some researchers(eg McGee 1979) have argued that there is support forthe existence of the spatial orientation factor However amajor meta-analysis of the factor-analytic research (Car-roll 1993) failed to find evidence for the separability ofthis factor from spatial visualization (see also Borich ampBauman 1972 Price amp Eliot 1975)

Spatial orientation might be difficult to separate fromother spatial factors because tests designed to measurethis ability are often solved by mentally rotating the stim-ulus rather than by reorienting oneself (Barratt 1953Carpenter amp Just 1986 Carroll 1993) For example ina verbal protocol study Barratt found that the majority ofparticipants reported a mental rotation strategy on theGuilfordndashZimmerman task This would account for itstypically high loading on the spatial visualization factor(Carroll 1993) We suggest that the failure to find a dis-tinction between object manipulation and spatial orienta-tion abilities in the psychometric literature occurs becausethere are currently no pure psychometric tests of spatialorientation ability

One goal of this study was to develop valid tests ofspatial orientation ability On the basis of experimentalstudies of perspective taking (eg Hintzman OrsquoDell ampArndt 1981 Rieser 1989 Shelton amp McNamara 1997)we developed tests in which a person is shown a two-

dimensional array of objects imagines taking a perspectivewithin the array and indicates the direction to a target ob-ject from that perspective We analyzed patterns of er-rors on these tests and verbal protocols to examine whetherthe dominant strategy used in these tests involves imagin-ing reorienting oneself within the display rather thanmentally rotating the display

A second goal of the study was to examine the extentto which object manipulation abilities and spatial orien-tation ability are separable We analyzed performance ontests of object manipulation abilities and spatial orienta-tion abilities using confirmatory factor analysis (CFA)This method allowed us to test hypothesized factor struc-tures and compare alternative models statistically (Kline1998) If object manipulation and spatial orientationabilities tap the same underlying construct a model witha single spatial factor should provide a sufficiently goodfit to the data If however object manipulation and spa-tial orientation abilities are distinct a model with a singlespatial factor will significantly deviate from the data Incontrast a two-factor model that assumes their separabil-ity should provide a good fit to the data The correlationbetween these two factors then provides an estimation ofthe degree to which the two abilities are related

EXPERIMENT 1


recruited from the psychology subject pool at the University of Cal-ifornia Santa Barbara

Materials The materials consisted of seven paper-and-penciltests of spatial abilities Object manipulation abilities were assessedby using the Card Rotation Test the Cube Comparison Test2 andthe Paper Folding Test (Ekstrom French amp Harman 1976) TheCard Rotation Test requires participants to view a two-dimensionaltarget f igure and judge which of the five alternative test figures areplanar rotations of the target figure (as opposed to its mirror image)as quickly and as accurately as possible In the Cube ComparisonTest each item presents two drawings of cubes with letters andnumbers printed on their sides Participants must judge whether thetwo drawings could show the same cube Items in the Paper FoldingTest show drawings of two or three folds made in a square sheet ofpaper The final drawing shows a hole being punched in the foldedpaper The task is to select one of five drawings that shows how thepunched sheet would appear when fully opened

The participants were presented with the GuilfordndashZimmermanSpatial Orientation Test as well (Guilford amp Zimmerman 1948)The test consists of items presenting two pictures of a lake andscenery as seen from looking out over the prow of a motorboatwhich has moved slightly between pictures The task is to select oneof five diagrams that represents how the boat has moved Each di-agram shows a dot representing the old position of the prow and adash representing the new position Changes include any combina-tion of heading change (ie rotation) and of forward translation andsideward translation of the boat

To measure studentsrsquo spatial orientation ability we developedtwo perspective-taking tests In the first test (the Object PerspectiveTest) a configuration of seven objects was drawn on a 85 3 11 insheet of paper (see Figure 1A) This display was fixed to the walldirectly in front of each participant and was visible at all timesEach participant also received an answer booklet with a separatepage for each of the test items On each item the participant was


















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APPENDIX

























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a dissociation between object manipulation spatial ability...

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