Memory de Cognition1991. 19 (6), 558-567

Mental rotation of compound stimuli:The effects of task demands, practice,

and figural goodness

LISE PAQUETCarleton University, Ottawa, Ontario, Canada

Four experiments examined whether or not mental rotation of compound stimuli is a holisticprocess. Large letters (global aspect) composed of small letters (local aspect) were presented, andthe format (normal vs. reflected) of each aspect was manipulated independently. In Experiment 1,the rate of mental rotation was compared under divided- and focused-attention instructions. Theoverall rate of mental rotation was faster under focused-attention instructions than under divided­attention instructions. Also, contrary to previous findings, in the divided-attention task, the slopeof the rotation function was smaller when the stimulus configurations contained aspects withcongruent formats (both aspects were normal or mirror-reversed letters) than when they containedaspects with incongruent formats (one normal and one mirror-reversed letter). This pattern ofresults is unlikely to be caused by the subjects' level of familiarity with the divided-attentiontask (Experiment 2), by postrotation processes (Experiment 3), or by stimulus attributes (figuralgoodness) confounded with the format-congruency variable (Experiment 4). The implications ofthese results for models of mental rotation of compound stimuli are discussed.

Figure 1. Examples of the compound stimuli usedin the presentexperiments: (a) both, (b) global~nly, (c) local~nly, and (d) neitherreflection conditions.

aspect was rotated first, the global-only function wouldhave the largest slope because it would be the only con­dition requiring two rotations. Alternatively, the local­only condition would have the largest slope if the globalaspect was transformed first. However, the results failedto support the nonholistic hypothesis, and the observa­tion of parallel rotation functions for the global-only,local-only, and both-normal conditions suggested, instead,that a single holistic rotation is necessary to transform theglobal and local aspects of a compound stimulus.

Although the above result is consistent with holisticmodels, a nonholistic explanation of these data remainsplausible. In fact, with a divided-attention task such asthe one used by Robertson and Palmer (1983), parallelRT functionsmay also reflect the use of a serial-exhaustivestrategy (Sternberg, 1967), whereby both aspects of the

How do human observers mentally rotate hierarchicalstimuli? Robertson and Palmer (1983) assessed the fol­lowing nonholistic hypothesis: "Hierarchically structuredfigures might have to be rotated separately at the globaland local levels of structure" (p. 204). In their study,compound stimuli (cf. Navon, 1977)of the type displayedin Figure 1 were presented in various orientations (0°,±60°, and ± 120°). They used a divided-attention taskin which subjects were asked to respond "yes" if at leastone aspect (i.e., the global [larger letter], the local[smaller letters], or both) was a normal letter. The num­ber of rotations necessary to achieve a correct decisionwas manipulated. In the both-normal condition(Figure 1a), a single rotation of either the global or thelocal aspect could produce a "yes" response. However,depending on the processing order of the aspects, posi­tive decisions about the global-only (Figure 1b) and thelocal-only (Figure Ic) configurations could require tworotations.

Robertson and Palmer argued that nonholistic rotationwould be suggested if the slope of the function relatingreaction time (RT) to the orientation of the stimulus wassmaller in the both-normal condition than in at least oneof the other two conditions. For example, if the local

This research was supported by Grant Al247 from the NaturalSciences and Engineering Research Council of Canada. Thanks are ex­tended to Peter Boos for his invaluable computing advice and toEllen Corkery, Amy Dillon, Mark Hoestra, and Julie Parks for as­sistance in running the subjects. Requests for reprints should be sentto Lise Paquet, Department of Psychology, Carleton University, Ottawa,Ontario KIS 586, Canada.

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Copyright 1991 Psychonomic Society, Inc. 558

stimuli are sequentially rotated and compared with up­right representations, before response selection (Just &Carpenter, 1985; Yuille & Steiger, 1982).Therefore, thefinding of parallelRT functions in a divided-attention taskprovidesno clear-cutevidencein favorof the holistic view.

Given the theoretical ambiguity of Robertson andPalmer's (1983) results, the aim of Experiment 1 was todetermine whether rotation rate was affected by instruc­tions requiring subjects to attend either to both aspects(divided-attention instructions) or to a single aspect(focused-attention instructions)of the compound stimuli.The demonstration that the slopesof the rotationfunctionsare the same for divided- and focused-attention instruc­tions wouldsubstantiate holistic models of mentalrotation.

In Experiment 1, the results showedthat the attentionalmanipulation had a substantial impacton the rotationrate.More importantly, however, the basic pattern of resultsreported by Robertson and Palmer (1983)1 was not repli­cated. In Experiment 2, an attempt was made to link thisreplication failure to the extensive practice that Robert­son and Palmer's subjects had with the divided-attentiontask. However, their findings could not be reproduced,even with highly practiced subjects. Instead, it was ob­servedthat the both-normal and neither-normal conditions(which contained aspects with congruent formats) hadsmallerslopes than did the global-only and local-only con­ditions (which had aspects with incongruent formats). InExperiment 3, the hypothesis that the slopedifferencebe­tween congruent and incongruent configurations was theproduct of postrotational processes was discarded. Fi­nally, in Experiment 4, a holistic account of the format­congruency effect was rejected.

EXPERIMENT 1

The goal of Experiment 1 was to compare rotationratesunder divided- and focused-attention instructions. In thedivided-attention task, the subjectshad to decide whethera normal letter appeared at any of the aspects of a com­poundstimulus. In the focused-attention tasks, the instruc­tions were to attend to only one aspect (either local orglobal) of the stimulus and to decide whether a normalletter appeared at that level.

We reasoned that, if a single holistic rotation of the en­tire stimulusis performed, then the rate of rotationshouldbe unaffectedby the attentionalinstructions. On the otherhand, if rotation of each aspect can occur separately, thenthe rate of rotationmightbe faster in the focused-attentiontasks. This prediction is based on the idea that divided­attention instructionsmay induce subjects to preserve andsequentially transform both aspects of the stimuli. How­ever, since less structural information is relevant for thefocused-attentiontask, decisions may be based on the ro­tation of a single aspect (Folk & Luce, 1987; Yuille &Steiger, 1982). In sum, while Robertson and Palmer's(1983) results shouldbe replicated under divided-attentioninstructions, the rotationfunctions obtainedunder focused

MENTAL ROTAnON 559

attention might have shallower slopes than those of thedivided-attention conditions.

MethodSubjects. Twenty-three subjects participated for course credits

in three sessions of approximately I h each. Data for 5 subjectswere discarded because their overall error rate exceeded 20%.

Stimuli and Apparatus. The stimuli were identical to those usedby Robertson and Palmer (1983): large letters (F or R) made ofsmaller letters (F or R). The global letters measured 2.9° of visualangle; the local letters subtended a 0.34° visual angle.

Sixteen compound stimuli were used and consisted of all combi­nations of four variables: identity of the global aspect (F or R),Identity of the local aspect (F or R), format of the global aspect(normal or reflected), and format of the local aspect (normal orreflected). Each of the 16 stimuli was drawn in SIX orientations:0°. 60°, 120°, 180°. 240° (-120°), and 300° (-60°). Thecomputer-generated stimuli were plotted with a laser printer, andslides were made. The slides were back-projected onto a translu­cent screen by a carousel projector.

The presentation of stimuli and collection of responses were con­trolled by an Apple II+ microcomputer interfaced with a Gerbrandsshutter through a Gerbrands tachistoscope/Apple interface. A re­sponse box containing three keys was positioned in front of the sub­ject. The center key (pressed with the thumbs) served to initiatestimulus presentation. The left key, pressed with the left index finger,indicated a . 'yes" response; the nght key (pressed with the rightindex finger) signaled a "no" response. RTs from display onsetwere measured by the computer.

Procedure. The experiment involved three sessions administeredon 3 consecutive days. On the 1stday. half of the subjects performedthe divided-attention task; on the 2nd and 3rd days, they receivedthe focused-attention tasks (global- or local-directed session). Thisorder was reversed for the remaining subjects, who first performedthe focused-attentiontasks. The order of presentation of the focused­attention sessions was counterbalanced across subjects.

In each testing session, four reflection conditions were presentedby combining the format (normal vs. reflected) of each aspect ofthe stimulus. For the both condition, the global andthe local aspectswere both normal letters (Figure la). Only the global aspect wasnormal for the global-only condition (Figure Ib); only the localaspect contained a normal letter for the local-only condition(Figure Ic). As shown 10 Figure Id, the neither condition presentedreflected letters at each aspect of the stimulus.

At the beginning of each trial, following an auditory warning sig­nal, the experimenter gave a verbal "ready" signal. The subjectsinitiated the stimulus display by pressing the start key. A stimuluswas then displayed in the center of the screen until the subjectsresponded. The beginning of the next trial was indicated by the au­ditory warning signal. Between each block of trials, a brief restperiod was provided. In each session, the subjects were requiredto respond as quickly as possible while minimizing errors.

Divided-attention session. The divided-attention task was simi­lar to Robertson and Palmer's (1983) procedure, with the excep­tion thata single session, insteadof three sessions, was administered.The subjects were instructed to press the "yes" button if the global,the local, or both aspects were normal letters. The session consistedof three blocks of 120 trials. Within each block, 72 trials requireda positive response and 48 trials required a negative response. Onethird of the positive trials consisted of stimuli in which bothaspectswere normal (both), one third in which only the global aspect wasnormal (global-only), and one third in which only the local aspectwas a normal letter (local-only).

Focused-attention sessions. In the global-directed session, the sub­jects were required to decide whether the global aspect was a nor-

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mal letter and to ignore the local aspect. In the local-directed ses­sion, the subjects were required to indicate whether the local aspectwas a normal letter and to ignore the global aspect. Each focused­attention session was composed of three blocks of 96 trials. Foreach block, 48 trials required a positive response and 48 trials re­quired a negative response. For the global-directed session, halfof the positive trials included stimuli from the both-reflection con­dition and the other half was composed of stimuli from the global­only condition. The negative trials consisted of stimuli from thelocal-only and the neither conditions. Similarly, during the local­directed session, 24 positive trials presented the both condition andthe remaining 24 positive trials showed stimuli from the local-onlycondition. The negative trials were composed of stimuli from theglobal-only and the neither conditions. For each focused-attentionsession, the order of presentation of the various reflection condi­tions was randomized.

ResultsFor each session andeach subject, median RTs for each

rotationangle (0°, ±60 0, ± 120°, 180°)andeach reflec­

tioncondition (both, global-only, local-only, neither) werecomputed. The RT data- were then evaluated by threeseparate analyses: one analysis involved the conditionsused in the divided-attention task, andthe second and thirdanalyses involved the conditions for the global-directedand local-directed focused-attention tasks, respectively.

Divided attention. The mean median correct RT andpercentageof error for eachreflection condition andeachangular orientationare presentedin Table 1. A repeatedmeasures analysis ofvariance (ANOVA)wasusedtoevalu­ate theeffects of angleof rotation andreflection conditions.

The analysisconfirmed Robertson and Palmer's (1983)finding of main effects dueto reflection condition [F(3,51)= 48.93, MS. = 114,729,P < .001] and angle of rota-

tion [F(3,51) = 72.06, MS. = 140,200, p < .0001].More importantly, however, contrary to Robertson andPalmer's results, the analysis revealed a significant inter­actionbetweenthe two factors [F(9,153) = 4.93, MS. =28,194, p < .0001].

Polynomial contrastsinvolving the slopeof the rotationfunction for each reflectionconditionrevealed that rota­tion speedwas faster under the both condition(271 °/sec)thanunderthelocal-only condition (181 °/sec) [F(1, 153) =19.27, P < .01]. The differencein rotationrate betweenthe both condition (271 a/sec) and the global-onlycondi­tion (198°/sec) also reached significance [F(1,153) =10.51 ,p < .01]. However, noreliable difference emergedbetween theglobal-only condition (181 °/sec)andthelocal­onlycondition (198°/sec) [F(1,153) = 1.32].On the otherhand, the neither condition(264°/sec) was rotated fasterthantheglobal-only condition [F(1,153) = 9.00,p < .01]and the local-only condition [F(I,153) = 17.21, p <.0001], while no difference was found between the bothand the neither conditions (F < 1).

To sum up, the most important aspect of the presentresults is the failure to replicate Robertson and Palmer's(1983)finding of parallel RT functions under the variousreflection conditions of the divided-attention task. Instead,the rate of mental rotation was faster under the both andthe neither conditions than underthe local-only andglobal­only conditions. A fuller discussion of this finding willfollow the presentation of Experiment 2.

Focused attention: Global-directed session. Themeans of the median RTs for correct responses are dis­played in Table 2. There were main effects of reflectioncondition [F(2,34) = 13.47, MS. = 51,888, p < .001]

Table 1Reaction Times, Percent Errors, and Rotation Rates in the Divided-Attention Session of Experiment 1

Orientation

0° 60° 120° 180° RotationReflection RT PE RT PE RT PE RT PE Rate

Both 852 0.04 883 0.0 1,039 0.02 1,540 2.3 271Global-only 1,054 4.2 1,122 3.3 1,343 3.7 1,989 11.6 198Local-only 1,167 3.2 1,291 2.8 1,519 4.4 2,195 17.6 181Neither 1,460 2.8 1,544 1.6 1,807 2.1 2,130 6.7 264

Note-Reaction times are given in milliseconds. Rotation rates are given in degrees per second. PE = percent error.

Table 2Reaction Times, Percent Errors, and Rotation Rates in tbe Focused-Attention Sessions of Experiment 1

Orientation

0° 60° 120° 180° RotationReflection RT PE RT PE RT PE RT PE Rate

Global-Directed Session

Both 729 2.3 756 1.4 898 1.6 1,226 2.3 368Global-only 836 3.7 857 3.0 1,054 2.8 1,327 6.5 361Neither 876 2.3 916 1.6 1,172 2.0 1,431 6.5 310

Local-Directed Session

Both 825 0.0 875 2.1 987 2.3 1,392 6.0 331Local-only 959 6.0 1,023 3.2 1,146 3.5 1,508 6.0 339Neither 996 2.1 1,043 1.6 1,273 2.4 1,688 8.8 259

Note-Reaction times are given in milliseconds. Rotation rates are given in degrees per second. PE = percent error.

and of orientation of the stimulus [F(3,51) = 53.45, MSe

=56,881,p < .0001]. However, no interaction was un­covered between these factors [F(6, 102) = 1.07, MSe =15,992, P > .1].

Focused attention: Local-directed session. The resultsare displayed in Table 2. There were significant main ef­fects of reflection condition [F(2,34) = 23.22, MSe =41,367, p < .001] and of orientation of the stimulus[F(3,51) = 31.72,MSe = 126,429,p < .0001]. The in­teraction between the factors was significant [F(6, 102) =2.65, MSe = 12,900, p < .01].

Polynomial contrasts revealed equivalent rotation speedsunder the both reflection condition (331 °/sec) and thelocal-only reflection condition (339°/sec) (F < 1). How­ever, there was a difference in rotation rate between theboth condition (331 °/sec) and the neither condition(259°/sec) [F(1,I02) = 9.05, p < .01] and between theneither condition and the local-only condition (339° /sec)[F(1,102) = 10.56, p < .01].

Evaluation of the effect of task requirements. Fur­ther polynomial comparisons revealed that the both reflec­tion condition (271°/sec) from the divided-attention sessionhad a slower rate of rotation than did the both conditionof the global-directed session (368° /sec) [F(1,306) = 5.47,p < .05]. However, the difference between the local­directed both stimulus and the divided-attention both condi­tion was not significant. On the other hand, the global-onlyrotation rate was faster under focused attention (361°/sec)than under divided attention (198°/sec) [F(1,306) = 29.91,p < .0001]. Similarly, the local-only condition was ro­tated at a faster rate under focused-attention instructions(339°/sec) than under divided-attention instructions (181°/sec) [F(1,306) = 38.62, p < .0001].

DiscussionThe present results do not confirm the prediction that

mental rotation should be unaffected by the nature of thetask. Instead, it made a difference, in terms of the slopesof the rotation functions, whether the subjects were re­quired to preserve one or two aspects of the stimuli. Thisresult is consistent with previous findings (Yuille &Steiger, 1982) that demonstrated that rotation performanceis improved when processing of complex figures can berestricted to limited parts. Therefore, the present data arein agreement with the view that the aspects of a hierar­chical stimulus can be rotated separately, at least whenit is required by the task.

One unexpected result was the failure to observe parallelRT functions under the various reflection conditions inthe divided-attention task. Instead, the time taken for therotation of compound stimuli was affected by the con­gruency of the format (normal vs, mirror-reversed) of thelocal and global aspects. Thus, steeper slopes-reflectinglonger rotation times-were found when only one aspectwas a normal letter (i.e., conflicting format) than whenboth aspects were either normal or mirror-reversed let­ters (i.e., congruent format). However, before consider­ing the implications of this finding for the nature of therotation process, the reason for the discrepancy between

MENTAL ROTATION 561

our results and those of Robertson and Palmer (1983) mustbe explored.

EXPERIMENT 2

One important difference between our study and Robert­son and Palmer's (1983) experiment is the amount ofprac­tice that subjects received in the divided-attention task.We administered a single session in our study, whereasRobertson and Palmer tested their subjects during threeexperimental sessions. In light of recent proposals (Bethel­Fox & Shepard, 1988; Finke, 1985; Finke & Shepard,1986; Kosslyn, 1980) that the ability to transform an im­age holistically requires extended practice, it is impera­tive to assess whether the low level of practice that oursubjects had with the task was responsible for our repli­cation failure. Therefore, in Experiment 2, three consecu­tive divided-attention sessions were administered. Thepractice hypothesis predicts that our previous findingsshould only be replicated on the first testing session inwhich subjects are unfamiliar with the stimuli and the task.On the other hand, by the third session, holistic process­ing should have developed, and parallel rotation functionsshould emerge across reflection conditions.

MethodSubjects. Twenty-four new subjects were recruited to partici­

pate in three I-h sessions, in return for course credits. Data for4 subjects, who could not maintain an overall accuracy of 80%,were eliminated.

Procedure. The procedure was identical to the divided-attentionsession of Experiment I, with the exception that the subjects weretested for 3 days.

ResultsThe results for each session are displayed separately

in Tables 3-5. The statistical analysis revealed that over­all latency decreased as a function of testing sessions[F(2,38) = 83.85, MSe = 186,933, P < .0001]. Ourprevious findings of main effects due to reflection condi­tions [F(3,57) = 55.64, MSe = 105,300, p < .001] andto angle of rotation [F(3,57) = 52.36, MSe = 362,492,p < .0001] were replicated. There was a significant inter­action between testing sessions and reflection conditions[F(6,114) = 7.00, MSe = 19,365, p < .0001], as theoverall latency difference between the various conditionsdecreased with practice. Also, a significant interaction wasfound between testing session and orientation [F(6,114) =16.97, MSe = 37,965, p < .0001]. This interactionreflects the fact that rotation rate increased from Session 1(226° /sec) to Session 2 (327° /sec) to Session 3 (411°/sec).In agreement with Experiment 1, there was a significantinteraction between the angle of rotation and the reflec­tion conditions [F(9,17l) = 13.12, MSe = 23,338, p <.0001]. More critically, the three-way interaction involv­ing session, reflection conditions, and orientation was notsignificant [F(18,342) = l.09,MSe = 14,259,p > .1].

The rotation rates displayed in Tables 3-5 show thatall of the critical fmdings of Experiment 1 were replicatedfor each testing session. Polynomial contrasts confirmed

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Table 3Reaction Times, Percent Errors, and Rotation Rates in the First Session of Experiment 2

Orientation

0 0 600 1200 1800

RotationReflection RT PE RT PE RT PE RT PE Rate

Both 902 1.3 920 1.0 1,091 0.1 1,552 7.5 283Global-only 1,081 2.9 1,100 4.2 1,347 4.0 1,991 10.8 202Local-only 1,180 5.4 1,220 6.9 1,437 5.2 2,188 23.3 185Neither 1,322 3.1 1,361 3.3 1,529 2.5 2,025 5.8 264

Note-Reaction times are given in milliseconds. Rotation rates are given in degrees per second. PE = percent error.

Table 4Reaction Times, Percent Errors, and Rotation Rates in the Second Session of Experiment 2

Orientation

0 0 60 0 1200 1800

RotationReflection RT PE RT PE RT PE RT PE Rate

Both 746 0.1 790 0.1 877 1.5 1,198 5.4 416Global-only 866 1.3 925 2.1 1,088 2.3 1,445 3.8 316Local-only 980 2.9 1,003 1.9 1,167 2.1 1,746 15.5 244Neither 1,050 2.9 1,088 2.1 1,192 1.5 1,526 2.3 392

Note-Reaction times are given in milliseconds. Rotation rates are given in degrees per second. PE = percent error.

Table 5Reaction Times, Percent Errors, and Rotation Rates in the Third Session of Experiment 2

Orientation

0 0 600 1200 1800

RotationReflection RT PE RT PE RT PE RT PE Rate

Both 680 0.8 708 0.0 793 1.0 975 5.8 617Global-only 782 2.5 820 1.25 946 4.8 1,191 3.8 444Local-only 846 2.5 879 2.1 1,003 5.0 1,497 16.6 289Neither 882 2.7 928 2.3 1,013 1.2 1,331 2.7 419

Note-Reaction times are given in milIiseconds. Rotation rates are given in degrees per second. PE = percent error.

that the slopes of the both rotation functions were smallerthan (1) the slopes of the local-only functions [Session I,F(1,171) = 23.58, p < .0001; Session 2, F(I,171) =30.61, P < .0001; Session 3, F(I,171) = 73.96,p < .0001] and (2) the slopes of the global-only func­tions [Session I, F(1,171) = 13.78,p < .001; Session 2,F(1,171) = 6.09,p < .05; Session 3, F(1,17l) = 8.72,p < .01]. A similar pattern was found when comparingthe slopes of the neither conditions with that of the global­only conditions [Session I, F(1,171) = 9.28, p < .01;Session 2, F(1,171) = 3.91,p < .05; Session 3 was anexception, F < 1] and the local-only conditions [Ses­sion I, F(1,171) = 17.56, p < .0001; Session 2,F(1,171) = 25.41, p < .0001; Session 3, F(1,171) =25 .10, p < .0001]. Furthermore, with the exception ofSession 3 [F(1,171) = 12.89,p < .001], no differencein rotation rate was found between the congruent patterns(both vs. neither). On the other hand, the analysis revealedthat, for Sessions 2 and 3 [Session 2, F(l,l71) = 9.39,P < .01; Session 3, F(1,171) = 31.89,p < .0001], thelocal-only conditions had larger slopes than did the global­only stimuli.

DiscussionContrary to the data reported by Robertson and Palmer

(1983), the results showed a faster rotation rate for theboth than for the global-only and local-only conditions.Given that their procedure was reproduced as preciselyas possible, this repeated finding raises serious questionsabout their study. In addition, this finding has importantimplications for models that assume that a serial­exhaustive strategy was adopted to perform the divided­attention task. As pointed out in the introduction, sucha strategy should have resulted in rotation functions withequivalent slopes across reflection conditions. This wasnot the case.

At first glance, serial self-terminating accounts seemconsistent with our results. First, the finding that the slopeof the both function was shallower than the slopes of theglobal-only and the local-only conditions could be under­stood by assuming that only one aspect was rotated in theformer condition, whereas more than one rotation wasperformed in the latter conditions. Second, the equalityof the global-only and local-only slopes after one testingsession may indicate that the local aspect was rotated first

MENTAL ROTAnON 563

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MethodSubjects. Eighteen subjects participated for course credits in two

sessions administered on 2 consecutive days. Data for 3 subjects,who were unable to maintain an overall accuracy of 80%, werediscarded.

Stimuli and Apparatus. The 16upright (0°) stimuli used previ­ously were presented during the encoding phase of the experiment.For the rotation phase, one of the two arrows shown in Figure 2was displayed. The comparison phase employed standard lettersdrawn using Franklin Gothic Condensed Letraset (36point size).

Sixteen practice encoding stimuli were also used to familiarizethe subjects with the apparatus and the general procedure. Thesestimuli consisted of standard letters which were drawnusing FranklinGothic Letraset. The apparatus was the same as in Experiments 1and 2.

subjects are unfamiliar with normal-mirror judgments,there is uncertainty about the outcome of the rotationprocess when an incongruent stimulus has been trans­formed. Moreover, if decision latency is influenced bythe level of uncertainty, and if the level of uncertaintyincreases as a function of the angular orientation of thestimulus, then rotation and decision times would affectthe slope of the orientation functions. Since, by this ar­gument, it is not necessarily the rotation stage that is af­fected by format congruency but rather the postrotationstages, then Robertson and Palmer's (1983) conclusionthat rotation rate is unaffected by reflection conditioncould prevail.

To settle this issue, the paradigm developed by Bethel­Fox and Shepard (1988) was chosen, because it permitsthe investigation of the effect of format congruency onthree separate latency measures presumed to reflect,respectively, (1) the time to form an image (encodingstage), (2) the duration of the mental rotation of the en­coded stimulus (rotation stage), and (3) the decision lat­ency concerning the transformed stimulus (postrotationstages). The postrotation hypothesis predicts that effectsof format congruency should be observed for the encod­ing and decision latencies, but not for the rotation latency.On the other hand, the two accounts presented earlierpredict that rotation latency should also be affected by for­mat congruency.

on some trials, whereas the global aspect was rotated firston other trials. Finally, the observation that, by the sec­ond testing session, global-only stimuli were rotated fasterthan were local-only stimuli may suggest that, with ex­tended practice, there is a tendency to rotate the globalaspect first.

However, a key prediction of this account was discon­firmed: the neither rotation function should have exhibitedthe steepest slope, because negative decisions should al­ways have been based on two rotations. This was not thecase. Instead, the slope of the neither condition was gener­ally (1) shallower than the conditions with a single nor­mal letter and (2) equal to the both condition. It is there­fore unlikely that the task was performed by sequentiallyrotating the aspects of the stimuli.

How could we account for the puzzling observation thatthe orientation functions had shallower slopes when thestimuli were made of two aspects with congruent formats(i.e., the both and the neither conditions) than when theformats were incongruent (i.e., local-only and global­only)? One possibility is that a single aspect was rotatedfor the congruent stimuli but that the incongruent stimuliwere transformed through a nonholistic, level-by-levelprocess that often required more than one rotation.

Alternatively, the difference in slope may be explainedby assuming that a single holistic rotation was always per­formed but was executed at a slower rate when the globaland the local aspects had incongruent, rather than con­gruent, formats. What factor could induce these differentrotation rates? One speculation is that, perhaps because ofa difference in the good continuation of the vertical lineforming the global letters (for a review of Gestalt princi­ples of perceptual organization, see Pomerantz & Kubovy,1986), incongruent configurations (Figures lb and lc) arelower quality patterns than are congruent stimuli (Figuresla and ld). According to this suggestion, more time maybe required to form, maintain, and transform an imageof the "poorer" (incongruent) configurations than thatrequired to form, maintain, and transform an image ofthe "better" (congruent) configurations (Jolicoeur,Regehr, Smith, & Smith, 1985; Kosslyn, 1980; Pylyshyn,1979). In sum, it could be argued that the process of rotat­ing a compound stimulus was affected by format con­gruency simply because this factor was confounded withstimulus attributes such as figural goodness.

Although these two accounts are based on differentviews of mental rotation, both imply that it is the rotationprocess itself that is affected by the format-congruencyvariable. Therefore, both accounts could be discarded ifthis assumption was shown to be incorrect.

Does the difference in the slopes of the congruent­incongruent functions indicate a difference in rotationrates? An alternative explanation! is that it largely reflectsdifferences in postrotation decision latency (Carpenter & Figure 2. Examples of the (a) 90° and (b) 180° arrows used inJust, 1978). In particular, it could be argued that, because the rotation phase of Experiments 3 and 4.

EXPERIMENT 3

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Table 6Reaction Times and Rotation Rates in Experiment 3

Both 1,429 1,713 317Global-Only 1,418 2,015 151Local-Only 1,453 2,053 150Neither 1,493 1,808 285

Note-Reaction timesare given in milliseconds. Rotation ratesare givenin degrees per second.

DiscussionThe results provide no support for the ideathat the slope

difference observed across reflection conditions is sim­ply the productof differences in the decisionstages. Ac­cording to this argument, the comparisonlatency of Ex­periment 3 should have been affected by the angle ofrotation, being slowerfor largertransformations. Clearly,the data provideno evidencefor this prediction. Anotherpredictionfrom this view is that rotation rate should beunaffected by the format congruency. In contrast, theresults showedthat the rate of rotationwas slower whenthere was a conflictbetweenthe formatsof the local andglobal aspects of the stimuli.

Rotation latency. Median correct RTs were com­puted for each subject, each congruency level, and eachorientation. The latencies for congruent patterns(1,587 msec) were shorterthan thosefor incongruent pat­terns (1,735 msec) [F(1,14) = 7.6, MSe = 43,661,p < .05]. The angle of rotation also had a significanteffect [F(1,14) = 13.96, MSe = 190,842,p < .01]. Ro­tation time was shorter for the 90° transformations(1,450 msec) than for the 180° transformations(1,872 msec). From this 422-msec difference, a rate ofrotation of 213°/sec is obtained. More critically, a sig­nificant interaction was observed between format con­gruency and orientation [F(1,14) = 6.67, MSe = 49,067,p < .05]. The data showed faster rotationrates for con­gruent stimuli (328°/sec) than for incongruent stimuli(158°/sec).

To comparetheserateswiththoseobtained previously,medianRTs were computed for each reflectioncondition(both, gIobal-only, local-only, andneither) and eachorien­tation. The mean medianRTs are displayed in Table 6.

Thesedata showed a marginaleffect of reflectioncon­dition [F(3,42) = 2.73, MSe = 79,460, p < .1] and amain effect of orientation [F(1,14) = 12.29, MSe =491,606, P < .01]. As before, the reflection X orienta­tion interaction wasalsosignificant [F(3,42) = 2.93, MSe= 76,490, p < .05].

Comparison latency. An ANOVA was conductedonmedianRTs to determineif the comparisonstage was in­fluenced by format congruency. The congruent stimuli(1,041 msec)were comparedfaster than were the incon­gruent configurations (1,366 msec) [F(1,14) = 24.03,MSe = 65,888,p < .01]. As already mentioned, no othereffect was significant.

RotationRate180°

Orientation

90°Reflection

Procedure. Each of the 32 trials of a block consisted of threeevents: inspection, rotation, andcomparison. When the experimentergave the ready signal, the subjects initiated the trial by pressingthe start key on the response box. An inspection stimulus was thenpresented; the subjects inspected it until they could remember everyaspect of it. The subjects pushed the start key when they completedstimulus inspection. The inspection stimulus disappeared, and la­tency from the stimulus onset to the subject's response was recordedas inspection latency.

When the second ready signal was given, the subjects pressedthe start key again. An arrow was presented, and the subjects wereinstructed to rotate the pattern they had just imagined either 90°clockwise if the arrow was the one displayed in Figure 2a or 180°clockwise if the arrow shown in Figure 2b was displayed. The sub­jects pressed the start key when they were able to imagine the pat­tern in the requested orientation. Following the keypress, the ar­row disappeared and the rotation latency was recorded.

After the third ready signal, the subjects pressed the start buttonagain. A comparison stimulus (probe) was displayed, and the sub­jects pressed the •'yes" button if the probe was identical in orien­tation, format, and identity to either the large letter or the smallletters of the imagined rotated pattern. If the probe was differentfrom both letters, the subjects were required to push the "no" but­ton. After the subjects responded, the probe disappeared and thecomparison latency was recorded. This was the end of one trial.

Each session consisted of 16 practice trials and two blocks of32 experimental trials. An 88%accuracy rate had to be maintainedduring the practice trials. The subjects who failed to reach this cri­terion after three blocks of practice trials were not tested further.As soon as the accuracy criterion was achieved, the experimentaltrials began.

Sixteen trials of each experimental block required a •'yes"response, and 16 required a "no" response. Each compound stimu­lus (four both, four global-only, and four neither) was randomlypresented twice, once requiring a positive response and once be­ing associated with a negative response.

ResultsBethel-Fox and Shepard(1988) statedthree conditions

for interpreting the rotation latency as the time to men­tally transform the encoded pattern. First, the compari­son decision should be accurate, with an average errorrate of approximately 6% or 7%. We met this conditionsince the overall error rate was 5.5%. Second, the com­parison latency shouldbe quick. A possible baseline maybe that thecomparison latency should be closeto theaver­age latency observed (1,032 msec) in the upright (0°)orientation condition of our previous divided-attentionconditions. Hence, thepresent 1,062-msec average latencyshould be viewed as "quick." Third, andmorecritically,the comparison timeandaccuracy should bothbe indepen­dent of the angle of rotation. Two ANOVAs were con­ducted, and both analyses failed to uncover orientationeffects on either comparison latency [F(1, 14) = 1.81,P > .1] or comparison accuracy [F(1, 14) = 1.47,P > .1].

Inspection latency. Median correct RTs were com­puted for each subjectand each format congruency. AnANOVA revealed that it took longer to form an imageof the incongruent patterns [F(I,14) = 22.55, MSe =18,577, P < .001]. An inspection time of 1,963 msecwas found for congruentstimuli, whereas an inspectiontime of 2,199 msec was found for incongruent patterns.

MENTAL ROTAnON 565

Table 7Reaction Times and Rotation Rates in Experiment 4

The observation that the average rotation rate for thecongruent configurations (328° /sec) is about twice thatfor the incongruent stimuli (158°/sec) is consistent withthe nonholistic explanation of the congruency effect onrotation rate. However, this evidence is insufficient to ruleout the holistic figural-goodness account, and a more strin­gent test is required.

Orientation

Reflection 900 1800

Both 1,339 1,773Global-Only 1,587 2,481Local-Only 1,587 2,782Neither 1,540 2,373

RotationRate

20710175

108

EXPERIMENT 4

The holistic figural-goodness hypothesis was assessed"by distorting the congruent configurations (both andneither). As illustrated in Figure 3, every second elementof the vertical line forming the global letters was displacedto the left by 0.1 0. On the other hand, the incongruentpatterns were left unchanged. We assumed that this manip­ulation would reduce the figural goodness of the congruentpatterns below that of incongruent stimuli." A straight­forward prediction of the figural-goodness hypothesis isthat, because the figural goodness of congruent and in­congruent patterns are now reversed, we should also ob­serve a reversal in the pattern of results previously obtainedin favor of the incongruent patterns. In other words, ro­tation rates should now be faster for incongruent patterns.

MethodSubjects. Seventeen paid subjects served in two I-h sessions.

Data for 4 subjects were discarded because their error rate exceededthe criterion.

Procedure. The general procedure was identical to that of Ex­periment 3, with the following exceptions. First, the congruentstimulus displays were distorted in the manner described above.Second, the stimuli were presented on a Zenith VGA monitor con­trolled by a Zenith computer.

Results and DiscussionAs in Experiment 3, all the conditions defined by Bethel­

Fox and Shepard (1988) were met. In short, the compar­ison latencies were accurate (6.5% error rate), reasonablyfast (1,253 msec), and, more critically, independent ofthe angle of rotation [F(1,12) = 1.24, P > .25].

Inspection latency. The results replicated those ob­tained in Experiment 3, and the subjects encoded stimu­lus configurations with incongruent formats (2,556 msec)

R RRRR RR RRRRR

R RR RR R

Figure 3. A distorted large R composed of small Rs, as used inExperiment 4.

Note-Reaction timesare given in milliseconds. Rotation ratesare givenin degrees per second.

more slowly than they encoded those with congruent for­mats (1,986 msec) [F(I,12) = 16.7, MSe = 126,637, P< .01].

Rotation latency. The analysis yielded significant maineffects of format congruency [F(1,12) = 8.16, MSe =163,446, P < .05] and of angle of rotation [F(1,12) =12.24, MSe = 653,205, P < .01]. Also, the two-wayinteraction involving these factors was marginally signifi­cant [F(1,12) = 3.67, MSe = 89,197, P < .08]. Moreimportantly, however, the results indicate that, despite ageneral decrease in rotation rate (rotation rate was115°/sec, which is slower than that of Experiment 3), thecongruent stimuli were still rotated faster (144°/sec) thanwere the incongruent stimuli (95°/sec). Thus, contraryto the prediction of the figural-goodness hypothesis, noreversal in the rotation rate of the congruent and incon­gruent configurations took place.

The rotation rates for each reflection condition are pre­sented in Table 7. An inspection of these data reveals thatthe speed of rotating the both stimulus condition (207°/sec)remained faster than the speed of transforming the global­only configurations (101a/sec) and the local-only config­urations (75°/sec). Finally, the fact that the rotation rateof the neither condition (108°/sec) was not slower thanthat of the local-only and global-only stimuli also runscounter to the holistic figural-goodness hypothesis.

Comparison latency. The analysis failed to uncovereffects of format congruency on the comparison time[F(1,12) = 2.8, MSe = 583,520, p > .2].

GENERAL DISCUSSION

The ambiguity of previous evidence (Robertson &Palmer, 1983) on the mental rotation of compound stimuliled us to compare rotation rates for divided- and focused­attention tasks. Ifcompound stimuli were rotated holisti­cally, then rotation rates should not have been affectedby this manipulation. However, rotation rates were fasterfor focused-attention conditions. This finding suggests thatonly one aspect was transformed under focused attention,whereas more than one aspect was rotated under dividedattention. This account is consistent with the idea that taskrequirements determine the amount of structural infor­mation that is mentally transformed.

This interpretation is strengthened by two results. First,in the focused-attention tasks, no difference in rotationrates was found (1) between the global-directed both and

566 PAQUET

global-only stimuli or (2) between the local-directed bothand local-only stimuli. This is to be expected if only oneaspect is preserved and transformed. Second, a differentpattern of results emerged in the divided-attention task,where stimuli from the both reflection condition are ro­tated at a faster rate than are stimuli from the global-onlyand the local-only conditions. This finding is consistentwith the notion that divided-attention instructions inducesubjects to preserve and transform all of the availablestructural information concerning the compound stimuli.

One unexpected result was our failure to replicateRobertson and Palmer's (1983) finding that, for divided­attention tasks, rotation rate is unaffected by format con­gruency. Instead, we repeatedly observed that congruentpatterns (both and neither) are rotated faster than are in­congruent stimuli (global-only and local-only). Follow­ing Experiment 1, we hypothesized that our subjects' un­familiarity with the divided-attention task could haveprevented them from performing a holistic transforma­tion (Bethel-Fox & Shepard, 1988; Finke & Shepard,1986). However, the results of Experiment 2 do not sup­port this possibility, since a robust format -congruency ef­fect is obtained with highly practiced subjects.

An attempt was made to link the format-eongruency ef­fect to differences in figural goodness between congruentand incongruent configurations. On the basis of Experi­ment 4, there is no reason to believe that figural good­ness is a crucial factor. Hence, distorted congruent stimulithat had been judged to be poorer patterns than incon­gruent stimuli were nevertheless rotated at a faster rate.

What mechanisms may underlie the format-eongruencyeffect obtained under divided-attention instructions? Theresults cast doubt on several possible accounts. As notedpreviously, the format-congruency effect is particularlyinconsistent with either a serial-exhaustive approach ora holistic model of the type proposed by Robertson andPalmer (1983), because both accounts predict parallel ro­tation functions across reflection conditions. On the otherhand, although sequential self-terminating models providea reasonable account of the positive responses, the predic­tion that the slowest rotation rate should be that of theneither condition was not observed. Instead, the neitherrotation rate was generally faster than the global-only andthe local-only rates, and it was often very close to the rateof the both condition.

At this point, two speculations can be offered to accountfor the results of the divided-attention task. The first waspresented earlier and relies on the notion that a mixtureof strategies may have been used (for related ideas, seeKoriat & Norman, 1989). For instance, it is possible thata single rotation (either of a single aspect or of the entireconfiguration) was performed for the congruent formatstimuli, but that the incongruent stimuli were transformedthrough a part-by-part process requiring more than onerotation. Although this hypothesis is consistent with ourresults, its plausibility rests on the assumption that informa­tion concerning format congruency becomes available at

encoding, before subjects mentally rotate the stimulus. Theobvious next question would be, what source of informa­tion could be used to establish the format congruency?

One candidate is the direction in which the letters face.Thus, an examination of Figure 1 reveals that, with theletter F, the congruent stimuli (both and neither) alwayspresented local and global aspects facing in the same direc­tion (i.e., to the right for the both stimulus and to the leftfor the neither configuration), whereas the incongruentstimuli always showed local and global aspects facing inthe opposite direction. The same held true for the letter R.However, one difficulty is that, while it is reasonable tothink that the detection of similar formats could lead torotating a single aspect, it is unclear as to why the detec­tion of aspects facing opposite directions should lead totwo sequential rotations. One interesting direction for fur­ther work would be to separate format congruency anddirection of facing, perhaps, by using letter pairs suchas J and F. This would allow the presentation of congruentformat stimuli having aspects facing in opposite directionsand incongruent format stimuli with aspects facing in thesame direction. If our speculation is correct, a reversalin the rotation rates of congruent and incongruent stimulishould be observed.

An alternate explanation is also plausible. It can be ar­gued that the local and global aspects were transformedby two parallel operations (see Robertson & Palmer, 1983)whose output feed into a common decision stage (seeMiller, 1981). If we assume that, as information aboutthe outcome of each rotation gradually accumulates, it alsopartially activates its response (for evidence concerningthis type of continuous model of information processingsee Eriksen & Schultz, 1979; McClelland, 1979; Miller,1988; Meyer, Yantis, Osman, & Smith, 1985), then, earlyin the process, incongruent stimuli would produce con­siderable response competition, while no such competi­tion would be experienced for congruent stimuli. If thepresence of response competition during early outputreduces the speed of the ongoing rotations, then rotationrates would be faster for congruent stimuli, because theabsence of response competition would allow rotation toproceed at the same speed until its completion. However,further experiments are required to disentangle these andany other remaining explanations of the present results.

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NOTES

I. In Experiments 1-2 and in a pilot study, this replication failurewas also obtained when the lSO° disorientation stimuli were omittedfrom analyses.

2. It shouldbe notedthat, althoughwe report only theanalysesbasedon latencydata, additionalanalysesperformed on error data of Experi­ments 1-2 mirrored that of the RT ANOVAs. Thus, the present find­mgs were not due to a speed-accuracy tradeoff.

3. 'The authorwouldliketo thankan anonymous reviewerof an earlierversion of this paper for emphasizingthe importance of ruling out thisalternative explanation.

4. The author thanks Pierre Jolicoeur for this suggestion.5. To obtain independentevidence that the distortion manipulation

effectively reduced the figural goodness of the congruent patterns, 51subjectswho did not participate in Experiment 4 were asked to rate thesimilarity (by choosing a number between I [extremely similar] to 9[barely similar)) of each of the 16 compound stimuli used in Experi­ment 4, with letter fonts that they chose to be the best examples of themost typical and familiar letters (F, R, mirror-F. and mirror-R) thatthey could imagine. The results indicated that the congruent distortedstimuliwere rated as poorer exemplars of thetypical letters (6.18) thanthe incongruent configurations (3.54)[F(I,50) = 61.49,p < .01]. Thedetails of this study can be obtained from the author.

(Manuscript received August 27, 1987;revision accepted for publication March 15, 1991.)