U.S. copyright law (title 17 of U.S. code) governs the reproduction and redistribution of copyrighted material.

Transcription

1 U.S. copyright lw (title 17 of U.S. code) governs the reproduction nd redistribution of copyrighted mteril.

2 CGNITIVE PSYCHLGY Volume 10, Number 4, ctober 1978 Copyright 1978 by Acdemic Press, Inc. All rights reserved No prt of this publiction my be reproduced or trnsmitted in ny form or by ny mens, electronic or mechnicl, including photocopy, recording, or ny informtion storge nd retrievl system, without permission in writing from the copyright owner. The ppernce of the code t the bottom of the first pge of n rticle in this journl indictes the copyright owner s consent tht copies of the rticle my be mde for personl or internl use, or for the personl or internl use of specific clients. This consent is given on the condition, however, tht the copier py the stted per copy fee through the Copyright Clernce Center, Inc. (pertions Stff, P.. Box 765, Schenectdy, New York 12301), for copying beyond tht permitted by Sections 107 or 108 of the U. S. Copyright Lw. This consent does not extend to other kinds of copying, such s copying for generl distribution, for dvertising or promotionl purposes, for creting new collective works, or for resle. Copy fees for pre-1978 rticles re the sme s those shown for current rticles.

3 CGNITIVE PSYCHLGY 10, (1978) DISTRTINS F SPATIAL RELATINS 423 Distortions in Judged Sptil Reltions ALBERT STEVENS Bolt Bernek nd Newmn Inc. AND PATTY CUPE University of Cliforni, Sn Diego In three experiments, we explore distortions in subjects judgments of reltive geogrphicl reltions. People mke lrge systemtic errors in judging the geogrphicl reltions between two loctions tht re in different geogrphicl or politicl units. There is strong tendency to distort the judged reltion to conform with the reltion of the superordinte politicl unit. To ccount for this result, we present model in which sptil informtion is stored hierrchiclly. Sptil reltions between ny two loctions re stored explicitly only if those loctions re within the sme superordinte unit. Sptil reltions not stored re inferred by combining the reltions from between nd within superordinte units. Mdrid (Spin) is frther north thn shington (DC). Settle (USA) is frther north thn Montrel (Cnd). The bove two sttements re correct, yet they contrdict the opinions of most people. Mny people mke lrge errors in judging reltive geogrphicl reltions when the two loctions re in different geogrphicl or politicl units. The nomly is more thn plesnt curiosity; it revels the presence of internl structure in the representtion of geogrphicl informtion. Some reltionships re inferred, rther thn exmined directly. In ny informtion processing system, there is trde-off between memory nd computtion. If informtion is stored explicitly, little or no computtion is required but memory spce is incresed. If informtion is inferred, storge requirements re reduced but extr computtion is required. Moreover, if informtion is not stored explicitly, there is chnce This study is portion of PhD disserttion submitted to the University of Cliforni, Sn Diego by the first uthor. e would like to thnk Donld Normn, Dvid Rumelhrt, Mrc Eisenstdt, Lynn Cooper, Dedre Gentner, Jmes Levin, Jy McClellnd, Steve Plmer, nd Mike illims for vluble comments. This reserch ws supported by Grnt NS from the Ntionl Institute of Helth to Donld Normn. Reprint requests should be sent to Albert Stevens, Bolt Bernek nd Newmn Inc., 50 Moulton Street, Cmbridge, MA /78/ $05.00/0 422 Copyright 1978 by Acdemic Press, Inc. All rights of reproduction in ny form reserved. of mking errors in the inferences. Thus, by storing the informtion tht ll birds cn fly, one cn void storing the fct explicitly with the representtion of every bird in memory. But this svings in storge cn produce errors; some birds cnnot fly. Similr errors occur in judgments of geogrphicl loctions. By storing the informtion tht the Pcific Cost of the Americs is west of the Atlntic Cost, one cn sve the necessity of storing reltive est -west loctions for huge set of loction pirs. The price is occsionl errors: The Pcific entrnce of the Pnm Cnl ctully is est of the Atlntic entrnce (it is south-southest). In this pper we report three experiments which exmine the errors resulting from inferentil processes in sptil judgements. Experiment 1 exmines judgments bout rel world loctions which re in different politicl or geogrphicl units. Experiments 2A, 2B, nd 3 exmine judgments bout loctions on simple mps lerned in the lbortory. In the discussion, we suggest model of the representtion nd inference process to ccount for the results of these experiments. EXPERIMENT 1 The first experiment ws designed to ssess to wht extent distortions like the necdotes of the introduction relly do exist. e exmined subjects knowledge bout the direction between geogrphicl loctions in North nd Centrl Americ. e chose pirs of loctions so tht their geogrphicl direction ws different from the generl direction of their superordinte politicl or geogrphicl units. Subjects were sked to estimte the direction between the pirs. For exmple, the stte of Nevd is est of the stte of Cliforni, but the direction from the city of Sn Diego (Cliforni) to the city of Reno (Nevd) is north-northwest. Method Mterils. Five loction pirs (listed in Fig. 1) chosen ccording to the bove criteri nd 15 filler pirs were presented to subjects in questionnire. The filler items were constructed using southwestern US cities nd sttes. Ech pir ws presented on seprte pge. ne member of ech pir ws lbelled with the word from, the other with the word to. A circle, 5.08 cm in dimeter, with verticl line, 0.32 cm in length, intersecting the top of the circle on its verticl bisector ws printed next to ech pir of loctions. The verticl line ws lbelled N. The pges of the questionnire were rndomized for ech subject with the restriction tht t lest one filler question occurred between ny two test questions. Subjects. The subjects were 10 undergrdute students t the University of Cliforni, Sn Diego who volunteered in response to cmpus dvertisement. They were pid $2.00 n hour. Procedure. Subjects were instructed to indicte the direction from the loction lbelled from to the loction lbelled to by drwing line from the center of the circle, intersecting the edge in the estimted direction. They were told to do this by imgining tht the loction lbelled from ws t the center of the circle nd then drwing line in the stright-line direction towrd the second loction. They were told tht N ment north.

4 424 STEVENS AND CUPE DISTRTINS F SPATIAL RELATINS 425 more, the result does not seem to rely on unfmilirity with the loctions being judged. The experiment ws done in Sn Diego, yet subjects were s poor t judging the Sn Diego-Reno direction s they were for those less fmilir to them. Portlnd,re. to Toronto (United Sttes to Cnd) Sn Diego to Reno (Cliforni to Nevd) Q -+ Montrel to Settle Atlntic entrnce o the (Cnd to United Sttes) Pnm Cnl to Pcific entrnce (Atlntic cen to Pcific cen) Portlnd, re. to Portlnd, Me, (Pcific Cost to Atlntic Cost) 7 ACTUAL DIRECTIN - - SUPERRDINATE FIG. 1. Response distributions for Experiment 1. Judged loctions re listed under ech polr-coordinte histogrm. The superordintes re indicted in prentheses. For ll grphs, north is verticl. Results Ech response ws mesured to the nerest five degrees. For ech pir of loctions, shown in Fig. 1, the responses re plotted on polr coordinte histogrm. The ctul directions, determined from Miller cylindricl projection, re indicted by solid rrows nd the directions between the superordinte units of the loctions re indicted by dotted rrows. All of the verged responses nd ll but two of the 50 individul responses re distorted in the direction of the superordinte units. Exmintion of the results show no other systemtic tendencies. The results confirm the necdotl evidence. There is strong tendency to distort direction reltions towrd the direction of the superordinte reltionships. Further- EXPERIMENT 2A If the interprettion we hve proposed is correct, then we should find tht geogrphicl judgements re inferred when the items being judged re in different units. To demonstrte this, we need simply devise stimuli tht cuse the subjects to form nd use internl units. The stimuli turn out to be very simple; we need only three cities nd two superordinte regions. Method Subjects. The subjects were 10 University of Cliforni, Sn Diego undergrdutes different from those in the previous experiment who volunteered in response to cmpus dvertisement. They were pid $2.00 n hour. Mterils. Prototypicl stimuli re shown in Fig. 2. n ech of these mps there re two key cities, lbelled x nd y, nd filler city, lbelled z. There re two sets of stimuli, one in which we tested subjects memory for the reltive direction of the key cities long the verticl dimension nd the other in which we tested their memory for reltive direction long the horizontl dimension. The key city configurtions differ in these two conditions only by rottion of 90 degrees. For both of these tested dimensions there re three types of superordinte informtion. In the homogenous condition, the cities re shown s prt of single homogenous unit without county informtion. In the congruent condition, the superordinte county direction is the sme s the city direction long the dimension tested. Thus, for the congruent horizontl stimulus in Fig. 2, city x is in Alph, city y is in Bet, city x is west of city y, nd Alph is west of Bet. In the incongruent condition, the superordinte county direction is opposite from the city direction long the dimension tested. Thus, for the incongruent horizontl stimulus in Fig. 2, city x is in Bet, city y is in Alph, city x is west of city y, but Bet is est of Alph. Ech of the conditions in Fig. 2 ws tested twice by including the configurtions illustrted nd six dditionl stimuli formed by rotting ech of the originls 180 degrees. In the finl stimulus set, ech city ws lbelled with letter of the lphbet, immeditely below it in the horizontl condition, or immeditely to its right in the verticl condition. The lbels were chosen rndomly for ech stimulus. Counties were lwys lbelled with Greek letter, spelled out, plus the word county. A smll compss rose tht displyed the four mjor geogrphicl dimensions ws shown in the lower right corner of ech mp. Ech mp ws 21.6 x 21.6 cm squre. The two key cities were lwys seprted by 1.27 cm long the dimension tested nd 12.7 cm long the other. In both the congruent nd incongruent conditions, the cities were.64 cm from the border. A set of questions ws constructed for ech mp. Ech set included key question which sked the direction of the key cities long the test dimension. For the stimuli in Fig. 2 in the horizontl condition, this question is Is x est or west of y? ithin condition, est nd west or north nd south were tested eqully often. There were four filler questions deling with direction nd county loction of cities for ech mp in the congruent nd incongruent conditions. For the homogenous condition, there ws single filler question. The questions were rndomized within ech set. Procedure. Subjects were told tht we were interested in how much they could remember bout simple mps. They were told tht while ech mp ws in front of them they were to try to memorize it becuse they would be sked questions bout it.

5 426 STEVENS AND CUPE DISTRTINS F SPATIAL RELATINS 427 DI MENSIN HRIZNTAL TESTED VERTICAL TABLE 1 ERRR PRPRTINS FR EXPERIMENT 2A Dimension tested CNGRUENT Congruent Incongruent Homogenous Horizontl Verticl Men Men INCNGRUENT HMGENUS FIG. 2. Prototypicl stimuli for Experiment 2A. Subjects were run individully, seted t tble cross from the experimenter. For ech tril the experimenter sid redy then plced the stimulus mp on the tble in front of the subject. After 20 sec the experimenter removed the mp nd plced sheet contining the questions in front of the subject. The subject nswered the questions on seprte sheet, tking s much time s necessry. hen done, the nswer sheet nd questions were removed nd the next tril begn. No feedbck ws given. The mps were presented in rndom order, subject to the restriction tht no two of the sme type of county orgniztion ppered in succession. The entire session lsted bout 20 min. Results The results support the view tht subjects encoded the mps in terms of superordinte units; subjects mde bout three times s mny errors in judging the reltive directions in the incongruent condition thn in the other two. The percentge of errors for ech condition is shown in Tble 1. These dt were nlyzed using n nlysis of vrince. The only significnt effect ws tht due to superordinte informtion [F(2,18) = 6.08, p <.01]. Dimension tested ws not significnt fctor [F( 1,9) < 1] nor +E ws its interction with superordinte informtion [F(2,18) < 1]. Newmn-Keuls tests show tht s predicted, the incongruent condition is significntly different from both the congruent condition [Q(3,18) = 4.44, p <.05] nd the homogeneous condition, [Q (2,18) = 4.07, p <.01]. ne possible explntion of these results is tht they re due to perceptul illusion. e sked six different subjects (not prt of ny other experiments) to nswer the incongruent questions while the stimuli were present in front of them; the subjects were perfect. Experiment 2A provides dditionl support for the ide tht mps re represented in terms of superordinte units in memory. Even for these simple stimuli, there is substntil effect of superordinte structure on the memory for subordinte sptil reltions. EXPERIMENT 2B There re some potentil objections to Experiment 2A. The incongruent condition hd two counties, wheres the homogenous condition did not. This difference in informtion might invlidte tht comprison. In ddition, the incongruent county lines rn t slight digonl, so subjects might hve used them to lign geogrphicl dimensions, ccounting for their errors. Experiment 2B remedies these objections. In ddition we exmined subjects confidence in their responses. Method Subjects. The subjects were 12 University of Cliforni, Sn Diego undergrdutes different from those in the previous experiments. They were recruited with cmpus dvertisement nd were pid $2.00 n hour. Mterils. The stimuli were similr to those used in Experiment 2A with minor exceptions. The county lines for the incongruent condition were djusted so tht they were precisely verticl except for the curved prt seprting the key cities. The homogenous condition ws modified by dding county line identicl in shpe to tht used for the incongruent condition but plced so tht it did not pss between the key cities. An extr city ws dded to ech configurtion (mking totl of four cities) so tht there ws lwys t lest one city in ech

6 428 STEVENS AND CUPE county in ll conditions. Cities nd counties were lbelled in n identicl mnner to Experiment 2A except tht we used niml nmes insted of Greek letters for the counties. The number nd types of stimuli, dimensions of the mp, key city seprtion, nd key city reltionship to the county borders were identicl to Experiment 2A. Questions were identicl in form to those used in the incongruent nd congruent conditions of Experiment 2A. The stimulus mps were rrnged in booklets, one for ech subject. The stimuli in ech booklet were rrnged in different rndom order with the constrints tht order of ech stimulus in reltion to the others of its orgniztion type ws blnced cross subjects, nd stimuli representing the sme type of orgniztion were seprted by t lest one other mp. Eight filler mps were included which did not resemble ny of the stimulus mps nd contined no incongruent conditions. Procedure. Subjects were given instructions similr to those of the previous experiment. A 5-point confidence rting scle ws explined to them (1 corresponding to just guessing nd 5 to bsolutely positive ). The confidence scle ws lso written on blckbord in cler view of ech subject. Subjects were run in groups seted t lrge tble with the stimuli nd questions presented in booklets. For ech tril, the experimenter sid redy, pused nd then sid begin. Subjects immeditely turned to the next mp in their booklet. At the end of 20 sec, the experimenter sid stop nd the subjects immeditely turned to the questions, tking s long s necessry to nswer them. The complete session lsted bout 30 min. Results Errors. The results confirm Experiment 2A. Subjects gin mde more errors in the incongruent condition thn in the other two (Tble 2). The only significnt effect in these dt from n nlysis of vrince is tht due to superordinte structure [F(2,22) = 11.07, p <.01]. Neither the effect of dimension [F( 1,ll) < 1], nor its interction with orgniztion [F(2,22) = 1.72, p <.20] were significnt. Newmn-Keuls tests show tht s predicted, the incongruent condition is significntly different from both the congruent condition [Q(3,16) = 6.43, p <.1] nd the homogenous condition [Q(2,16) = 3.54, p <.05]. A Newmn-Keuls test lso suggests tht the congruent condition is different from the homogenous condition [Q(2,16) = 2.89, p <.10]. However, this difference should be interpreted with cution since it did not pper in Experiment 2A. It could be explined by ssuming tht subjects encode the sptil reltionships of the superordintes prior to or more ccurtely thn the sptil reltionships of the subordintes. The overll pttern of results replictes nd supports the conclusions drwn from Experiment 2A. Confidence rtings. The confidence rtings show no difference cross orgniztion condition (Tble 2). Superordinte structure hd no relible effect [F(2,22) = 1.91, p >.10]. However, specific contrst (Congruent vs Incongruent nd Homogenous) suggests there my be difference [F( 1,16) = 5.23, p <.05], so this should be interpreted with cution. There ws relible effect due to dimensions [F( 1,ll) = 6.80, p <.05]. Subjects were more confident when questions delt with the verticl dimension. The interction between superordinte nd dimension ws not significnt [F(2,22) = 2.36, p >.10]. DISTRTINS F SPATIAL RELATINS 429 TABLE 2 ERRR PRPRTINS AND CNFIDENCE RATINGS FR EXPERIMENT 2B Dimension tested Horizontl Verticl Men Errors Conf. Errors Conf. Errors Conf. Congruent Incongruent Homogenous Men The fct tht the confidence rtings were generlly high suggests tht responses in the incongruent condition were not the result of guessing or confusion. Rther, subjects were quite confident of their responses. This would be expected if subjects integrte the informtion they hve stored in norml mnner to rrive t their responses. Subjects think these tsks re esy; they do not relize they re mking errors in the incongruent condition. EXPERIMENT 3 Gibson (1929) hs demonstrted tht under certin conditions lines re remembered s strighter thn they ctully re. Suppose tht subjects remember the city loctions in reltion to the border nd then remember the lines s strighter thn they were. This could possibly ccount for the results of the previous experiments. In this experiment, we exmine memory for direction when ll boundries re stright. Method Subjects. The subjects were 14 undergrdutes from the University of Cliforni, Sn Diego different from those in the previous experiments. They prticipted s prt of course requirement. Mterils. Prototypicl stimuli for ech of the mjor conditions re shown in Fig. 3. There re two different superordinte directions: one in which the counties re est-west of ech other (the E condition) nd the other in which they re north-south of ech other (the NS condition). The second fctor is the mount the reltive direction of the key cities (lbelled x nd y) differs from the superordinte direction. There re three levels of devition: 15 degrees, 45 degrees, nd 75 degrees. Exmples of ech of these for both superordinte directions re illustrted in Fig. 3. Ech mp contined two filler cities dded with the constrint tht single city ws in ech of the four qudrnts of ech mp. As control for sptil symmetries, we used the sme physicl configurtions of cities in the 15 degree E nd 75 degree NS conditions, in the 75 degree E nd the 15 degree NS conditions, nd in both of the 45 degree conditions. Note tht in Fig. 3, the reltive directions of the key cities in the E condition ll devite

7 430 STEVENS AND CUPE DISTRTINS F SPATIAL RELATINS 43 1 n I- R 3 V) z V) œ 45 (3 Y z I- o 15 SUPERRDINATE DIRECTIN EAST-EST Alph. X Alph Alph X Bet y 1: Bet NRTH-SUTH Bet FIG. 3. Prototypicl stimuli for Experiment 3. from the superordinte direction in counterclockwise direction but in the NS condition, they ll devite in clockwise direction. To control for ny possible bises this might introduce we lso included six dditionl stimuli so tht ech level of devition ws lso represented s clockwise devition for the E condition nd s counterclockwise devition for the NS condition. Pirs of configurtions corresponding to those of Fig. 3 were lso physiclly identicl. In order to present ll 12 stimuli to ech subject without repeting the sme physicl configurtion of cities we constructed second set of stimuli by reflecting ll 12 originls bout the horizontl xis. Two different sets of stimuli were constructed from the totl set of 24 so tht within ech set, ll three devitions were represented in both clockwise nd counterclockwise directions for both superordinte conditions. Identicl physicl configurtions were not repeted in either set. Cities nd counties were lbelled in mnner similr to tht of Experiments 2A nd 2B, except tht county nmes were tken from the nmes of smll midwestern US towns. A set of questions ws constructed for ech of the stimulus mps. These sked wht county ech city ws in nd the directions between three different pirs of cities, one of which ws lwys the key pir. A 2.5 cm circle with dot in the center ws printed beside ech direction question. A booklet of questions, with one pge for ech stimulus ws prepred for ech subject. The questions were rndomly ordered on ech pge. The order in which the two key cities were presented for the direction estimte ws blnced cross subjects. b Procedure. Subjects were given generl instructions similr to those of Experiments 2A nd 2B. Subjects were told to nswer the direction questions by drwing line from the center of the djcent circle, intersecting its edge in the estimted direction. The experimenter gve two exmples on the blckbord using fictitious cities. The subjects were run in two groups of seven. Ech of the groups received one of the stimulus sets presented in rndom order. The stimulus mps were projected on screen in the front of the room. The projected size of ech mp ws bout 1 m by 1 m nd key cities were lwys bout.5 m prt. Subjects were from 1.5 m to 3 m from the screen. For ech tril, the experimenter sid redy, checked to ensure tht ll subjects were wtching the screen, nd then displyed the stimulus. The stimulus remined on for 20 sec nd ws then removed. The subjects immeditely turned to the next pge in their response booklets nd nswered the questions. hen they finished, they turned their booklets fce down nd the next tril begn. No feedbck ws given. The entire session lsted bout 30 min. Results Errors. The responses re distorted towrd the superordinte county direction nd the mount of distortion increses s the devition of the stimulus direction from the superordinte increses. e scored the dt using two different procedures. In the first, responses were scored s degrees of devition from the originl stimulus. Devitions were counted s positive if they were on the verticl side of the originl stimulus direction nd negtive if they were on the horizontl side. The second scoring procedure ws motivted by pilot dt. Even with well lerned mps, some responses occur which re bout 180 degrees different from the correct direction. About 3% of the responses in the present experiment fll in this ctegory. This is n interesting phenomenon but it obscures the present nlysis. Therefore, in the second procedure, we scored the responses s undirected lines deviting by 0-89 degrees from the originl stimulus direction. Devitions on the verticl side of the originl stimulus were counted s positive, those on the horizontl side s negtive. The dt from the second nlysis re shown in Fig. 4. The horizontl xis indictes stimulus devition from the superordinte; the verticl xis indictes response devition from the originl stimulus. Perfect performnce would result in ll points flling on the horizontl xis. Performnce which used only superordinte informtion would result in ll points flling long the digonls. The grph illustrtes tht subject s responses re compromise between the ctul direction nd the direction of the superordinte counties. An nlysis of vrince shows tht there is significnt effect due to superordinte direction [F( 1,13) = 23.16, p <.001], tht mount of stimulus devition hs no relible min effect [F(2,26) = 1.82, p >,10], nd tht there is significnt interction of superordinte direction with stimulus devition [F(2,26) = 10.29, p <.001]. An nlysis bsed on the

8 432 STEVENS AND CUPE n u) / in 40L / / / NRTH-SUTH u) 2 o c / SUPERRDINATE (3 Y x 0 z E! t- -20 I- -4t CI) \ EAST-EST \ SUPERRDINATE \ I I I I I I I I l \ STIMULUS DIRECTIN (DEGREES FRM SUPERRDINATE) FIG. 4. Men response distortions for Experiment 3. Distortions is mesured s degrees of devition from the originl stimulus. Positive distortions indicte those more verticl thn the originl; negtive distortions re those more horizontl. first scoring procedure shows the sme pttern. Superordinte direction is significnt [F( 1,13) = 17.88,p <.001], stimulus devition is not significnt [F(2,26) = 1.98, p >.l0], nd the interction between these two fctors is significnt [F(2,26) = 5.44, p <,025]. It is possible tht these results re due to guessing strtegies. Most of the time the subjects my know the direction but when they do not, they might guess bsed on their knowledge of the generl county direction. e exmined this possibility by conditionlizing the responses on the bsis of confidence level. Figure 5 shows only the high confidence responses (confidence levels 4 nd 5) scored using the second procedure. This represents 29% of the dt; only one response is ffected by differences in the scoring n u) DISTRTINS F SPATIAL RELATINS r I- CI) 40 z LL CI) 20 (3 o 0 Y Z o t- o[: -20 I- 2 D -40 V) z -80 CNFIDENCE RESPNSES / NRTH-SUTH SUPERRDINATE STIMULUS DIRECTIN (DEGREES FRM SUPERRDINATE) FIG. 5. Men response distortions for high confidence responses of Experiment 3. Positive distortions re more verticl. thn the originl, negtive distortions re more horizontl. procedures. It is pprent tht the high confidence responses follow the sme pttern s the reminder. Thus, the observed responses re probbly not due to guessing strtegies. It is unlikely tht errors in this experiment re due to perceptul illusion. Induction effects on perceived orienttion show mximl effect of bout 10 degrees for lines which devite from mjor sptil xis by bout 45 degrees. Angles ner the verticl or horizontl tend to be perceived s distorted towrd the nerest mjor xis (Boum & Andriessen, 1970). In this experiment, mximl distortion ws observed for ngles nerest mjor sptil xis nd then the distortion ws wy from the mjor sptil xis. Confidence rtings. The men confidence rtings for ll six conditions

9 434 STEVENS AND CUPE DISTRTINS F SPATIAL RELATINS 435 re shown in Tble 3. All vlues re pproximtely 3, hlfwy between just guessing nd bsolutely positive on the scle. An nlysis of vrince shows no significnt effects. The rtings re generlly lower thn those of Experiment 2B, but the direction estimte required in this experiment is much more precise thn the simple ctegoricl responses of Experiment 2B. The confidence rtings show tht subjects were not wre when they were distorting the originl informtion. DISCUSSIN Superordinte structure systemticlly distorts how sptil reltionships re remembered. The judged direction between geogrphicl loctions tht re in different units reflects both the ctul reltionships nd the reltionships of the superordinte units. This result holds for rel world loctions (Experiment 1) nd for simple mps lerned in the lbortory (Experiments 2A, 2B, nd 3). Furthermore, s the devition between the ctul direction nd the superordinte direction increses, the mount of response distortion lso increses. e believe these results reflect the storge-computtion trde-off. e propose tht sptil informtion is stored hierrchiclly s in Fig. 6. This figure shows forml representtion for sptil informtion bout six regions: the sttes hio nd Colordo, nd the cities Cincinnti, Columbus, Denver, nd Pueblo. The nottion is tht of semntic networks (see Normn, Rumelhrt, & the LNR Reserch Group, 1975). Concepts, representing regions, re represented by nodes (nd thus pper s ngulr brckets). Reltions, representing sptil reltionships mong regions, re represented by sptil predictes (nd thus pper s ellipses). The nodes they relte re indicted by rrows lbelled from nd to. The specil reltion which holds between region nd its subregions is indicted by n rrow lbelled Prt-of. In order to del with the storge-computtion trdeoff, we ssume tht two principles of storge nd inference govern the representtion of sptil informtion in terms of these structures: TABLE 3 MEAN CNFIDENCE RATINGS FR EXPERIMENT 3 Stimulus devition from superordinte direction Superordinte direction Men North-south Est-west Men < U. S. > x % BU S > FIG. 6. A hierrchicl representtion of sptil informtion bout loctions within the US. (1) Generlly informtion bout sptil reltionships between regions is stored only for regions encoded s prt of the sme superordinte unit. (2) Reltions between two regions not stored explicitly must be inferred. The inference process combines the reltions between superordintes with the reltions of the subregions within their respective superordintes. Thus, Fig. 6 represents the informtion tht the US is n immedite superordinte of both hio nd Colordo, tht Colordo is n immedite superordinte of Denver nd Pueblo, nd tht hio is n immedite superordinte of Cincinnti nd Columbus. Becuse three pirs hve common superordintes, they hve sptil informtion stored bout their reltionships to ech other. e hve represented direction nd distnce reltions which hold between ech respective pir of regions. Note tht none of the 12 possible dditionl pirs hs common immedite superordinte, so no sptil informtion is explicitly stored bout their reltionships. This mens tht in order to infer the reltionship between Columbus nd Denver, three sources of informtion must be combined: the superordinte reltions holding between Colordo nd hio; the reltion of Columbus to the rest of hio (only prtilly represented in the figure); nd the reltion of Denver to the rest of Colordo (gin only prtilly represented). Generlly the reconstructed informtion will be ccurte enough for most purposes. nly under specil circumstnces, such s those selected for our experiments do serious distortions occur. The importnt properties of this representtion re its hierrchicl structure nd corresponding inference process. The experiments we report sy little bout the types of sptil reltions tht hold between units. In ddition to representing ll pirwise reltions within given unit, there re severl other possibilities. Ech region could be orgnized round few distinguished points such s key lndmrks or geometricl fetures like the center of region (Plmer, 1975). Direction nd distnce reltions would connect ech unit to one or more of these lndmrks or fetures. Ech re-

10 436 STEVENS AND CUPE DISTRTINS F SPATIAL RELATINS 437 gion could be encoded s set of subregions determined by perceptul grouping of elements or in terms of geometricl divisions such s top hlf, bottom left qudrnt, etc. This scheme simply requires dditionl levels in the bsic hierrchy. Finlly, ech region could be encoded in terms of corse grid or polr coordinte system which llowed smll number of ctegories for ech coordinte. The present experiments do seem to rule out schemes which use reltively precise informtion. For exmple, the precise polr coordinte representtion proposed by Kosslyn nd Schwrtz (1977) seems to predict tht people would not mke errors of the type we report. Given hierrchicl representtion, there re t lest two wys tht the inference process might operte. The first weights higher level informtion more hevily thn lower level informtion. If reltions representing direction nd distnce re encoded bout the reltionships of units, then informtion t higher levels typiclly will be bsed on more instnces thn tht t lower levels. Thus, it would be resonble for the reconstructive processes to weight the higher level informtion more hevily. A second possible inference procedure cn be considered to be levels of processing nlysis (Crik & Lockhrt, 1972). If the representtions of regions re structured hierrchiclly in terms of geometricl units like top-hlf, top-left-qudrnt, top-left-qudrnt-of-the-top-leftqudrnt, then sptil informtion cn be stored nd inferred to n rbitrry level of precision, given enough time nd effort. Distortions rise becuse the level of processing necessry for precise encoding or inference is typiclly not performed. Thus, people might encode northern city ner the western border of county s simply being in the northwest qudrnt or encode detiled informtion but not bother to pply inference procedures below the level of northwest qudrnt, thereby erring when sked the direction between the city nd city in different unit. The distortions presented in this pper re difficult to ccount for in terms of representtions bsed on imgery metphors (e.g., Kosslyn, 1973, 1975; Kosslyn & Pomerntz, 1977; Pivio, 1975). Simple imgery models fil to del with the multilevelled structuring necessry to ccount for our results. The hybrid nlog/propositionl model proposed by Kosslyn & Schwrtz (1977) cn in principle ccount for our dt. To do this requires tht the propositionl component include hierrchicl structuring nd tht the inference processes construct the nlog imge from the hierrchiclly structured informtion. However, the imge itself would ply no substntive role in this explntion nd it is difficult to see ny role tht it could ply. rgniztionl units need not lwys be bsed on politiclly defined regions. The orgniztion of sptil informtion must depend on the ultimte use of the stored informtion. Thus, irline pilots re likely to use both routes nd politicl units to orgnize loctions, creting errors tht re quite different from those we report. e hve induced subjects to use politicl units, but it is likely tht different tsk demnds would induce different orgniztions. Similrly, there re probbly other inference mechnisms tht people use. For exmple, if people re specificlly sked to recll shpe informtion, then the types of errors we observed might be minimized. Regrdless of the units used, or of the existence of other inference strtegies, the principles of hierrchicl representtion nd reconstruction re of criticl importnce in the wy tht people encode sptil informtion. Higher order orgniztionl structure cnnot be ignored. This structure cuses systemtic errors in judgments bout sptil reltionships. REFERENCES Boum, H., & Andriessen, J. J. Induced chnges in the perceived orienttion of line segments. Vision Reserch, 1970, 10, Crik, F. I. M., & Lockhrt, R. S. Levels of processing: A frmework for memory reserch. Journl of Verbl Lerning nd Verbl Behvior, 1972, 11, Gibson, J. J. The reproduction of visully perceived forms. Journl of Experimentl Psychology, 1929, 12, Kosslyn, S. M. Scnning visul imges: Some structurl implictions. Perception und Psychophysics, 1973, 14, Kosslyn, S. M. Informtion representtion in visul imges. Cognitive Psychology, 1975, 7, Kosslyn, S. M., & Pomerntz, J. R. Imgery, propositions, nd the form of internl representtions. Cognitive Psychology, 1977, 9, Kosslyn, S. M., & Schwrtz, S. P. A simultion of visul imgery. Cognitive Science, 1977, 1, Normn, D. A., Rumelhrt, D. E., & the LNR Reserch Group. Explortions in cognition. Sn Frncisco:. H. Freemn, Pivio, A. Perceptul comprisons through the mind s eye. Memory nd Cognition, 1975, 3, Plmer, S. E. Visul perception nd world knowledge: Notes on model of sensory-cognitive interction. In D. A. Normn, D. E. Rumelhrt, & the LNR Reserch Group (Eds.), Explortions in cognition. Sn Frncisco:. H. Freemn, (Accepted April 12, 1978)