Limits of focused attention in three-dimensional space

Transcription

1 Perception & Psychophysics 1993, 53 (6), Limits of focused ttention in three-dimensionl spce GORG J. ANDRSN University of liforni, Riverside, liforni nd ARTHUR F. KRAMR University of Illinois, Urbn hmpign, hmpign, Illinois The present experiment exmined the shpe of the ttentionl grdient in three-dimensionl spce. Subjects performed response-comptibility tsk in which they were instructed to respond to centrlly locted trget nd ignore flnking distrctors. The irrelevnt distrctors were presented t combintions of seven different depths, three different horizontl seprtions, nd three different verticl seprtions reltive to the trget. Depth ws vried in stereoscopic disply viewed through polrized glsses. Overll, the size of the response-comptibility effect decresed with incresed seprtion in ll three dimensions. Interestingly, the response-comptibility effect ws lrger for horizontl seprtions thn for verticl seprtions nd ws lrger for crossed disprities thn for uncrossed disprities. The results suggest n ellipticl focus of ttention, with steeper grdients in the verticl dimensions thn in the horizontl dimensions. In ddition, the results suggest, long the verticl dimension, steeper grdient for objects locted beyond the focus of ttention reltive to tht for objects locted between the observer nd the focus of ttention. Over the pst two decdes, there hs been considerble interest in the dynmics ofvisul ttention. An importnt focus of this body of reserch hs been the reltion between the size of the ttentionl focus nd processing efficiency. For exmple, models bsed on spotlight nlogy hve rgued tht stimuli tht fll within the bem of the spotlight receive full processing, wheres stimuli tht re locted outside of the boundries of the spotlight re ignored (Brodbent, 1982; Posner, Snyder, & Dvidson, 198; Shulmn, Remington, & McLen, 1979). Within these models, the requirement to process informtion t different loctions in the visul field necessittes movement of the spotlight. Although the spotlight models provide resonble ccount of results obtined in sptil priming, focused ttention, nd dul-tsk studies (Bshinski & Brrch, 198; B. A. riksen &. W. riksen, 1974; Hoffmn & Nelson, 1981), they cnnot esily ccommodte findings tht suggest tht efficient processing cn occur over either nrrow or wide re of the visul field. For exmple, LBerge (1983; LBerge & Brown, 1986; see This reserch ws supported by grnts from the Ntionl Science Foundtion (BNS 92181), the Office of Nvl Reserch (N14-89-J- 1493), nd Honeywell Inc. The uthors would like to thnk Dvid LBerge, Steven Yntis, Lester Krueger, nd n nonomous reviewer for comments on n erlier drft of the mnuscript nd Andri Glsser for running the subjects Reprint requests should be sent to either G. J. Andersen, Deprtment of Psychology, University of liforni, Riverside, A or A. F. Krmer, Deprtment of Psychology, University of Illinois, 63. Dniel St., hmpign, IL lso Jonides, 1983) found tht the size of the ttentionl focus could be vried by using single letter or word to precue different size regions of the visul field. Similrly, other reserchers hve found tht ttention could be directed to either smll or lrge res of the visul field on the bsis of cues such s color, contour, nd proximity (Hrms & Bundesen, 1983; Humphreys, 1981; Krmer & Jcobson, 1991; Pomerntz & Schwitzberg, 1975). Two relted models hve been proposed to ccommodte these findings.. W. riksen nd St. Jmes (1986;. W. riksen & Yeh, 1985) rgued tht zoom lens provides n pt nlogy for the dynmic nture of ttention in the visul field. Within the zoom-lens model, ttention cn be dynmiclly llocted long continuum from tightly focused re to widely distributed re. The resolution of the ttentionl system is inversely relted to the width of the ttentionl focus. Thus, while reltively esy discrimintions cn be mde with diffuse focus of ttention, difficult discrimintions require concentrted bem of ttention. Grdient models re similr to the zoom-lens model in tht they rgue tht processing efficiency vries over the visul field (Downing & Pinker, 1985; Hughes & Zimb, 1985; LBerge & Brown, 1989). However, rther thn shifting the focus from nrrowly to widely distributed res, grdient models suggest tht processing efficiency declines in continuous fshion from the center to the periphery of the ttentionl field. LBerge nd Brown (1989) hve suggested tht the shpe of the ttentionl grdient is determined on the bsis of informtion concerning the size nd probble loction of n expected object. opyright 1993 Psychonomic Society, Inc. 658

2 ATTNTION IN THR-DIMNSIONAL SPA 659 Thus, the ttentionl grdient will be nrrowly focused if the expected trget is smll nd its loction is precisely known. On the other hnd, the grdient will be wide when the trget loction is not well defined. Although t first glnce it my pper tht these two models cn be discriminted on the bsis of empiricl dt, two proposls one concerning the zoom-lens model nd the second concerning the grdient model mke it difficult to distinguish between these concepts of ttention.. W. riksen nd St. Jmes (1986), in their description of the zoom-lens model, hve suggested tht the edge of the ttentionl focus is not discontinuity, but is rther grded drop-off in processing resources corresponding to Willim Jmes s conception of focus, mrgin, nd fringe (p. 233). Thus, even the zoom lens incorportes grdient of processing. The fct tht both clsses of models incorporte the notion of grdient mkes it difficult to contrst the models, t lest with regrd to the selective processing of subset of items in the visul field. While the theory nd dt described bove suggest tht there is some consensus bout the importnt properties of visul ttention, it is importntto note tht our knowledgebout ttention is, for the most prt, bsed on studies tht hve been conducted within two-dimensionl (2-D) world. Reltively little reserch hs been conducted to exmine how ttention is distributed in 3-D spce. One exception is study reported by Downing nd Pinker (1985), who employed the vlid/invlid cuing procedure populrized by Posner et l. (198). The subjects tsk ws to respond whenever they detected light flsh t one of eight loctions. The lights were rrnged in two rows in depth, with the subject s fixtion directed between the rows. Shortly prior to the flsh, subjects were cued to shift their ttention to one loction. On 8% of the trils, the cue ws vlid; on 2% of the trils, the flsh occurred t n uncued loction. Reltive to control condition in which none of the loctions were cued, ttentionl costs defined s invlid rection time (RT) minus control RT were lrger when subjects were required to shift to different depth, reltive to the sme horizontl position t the sme depth. Attentionl costs were lso greter when subjects were required to shift from ner to fr positions, reltive to shift from fr to ner positions. A similr series of studies were reported by Gwryszewski, Riggio, Rizzoltti, nd Ulmità (1987). In their first experiment, subjects responded to the occurrence of light tht could pper t either ner or fr position, reltive to fixtion. A vlid/invlid cuing procedure ws used similr to tht used in the study by Downing nd Pinker (1985). The RTs were greter for invlid s compred to vlid cue trils, suggesting tht subjects did not simultneously ttend to positions locted t different depths. The vlid/invlid RT differences were lso significntly greter for ttention shifts to fr loction thn to ner loction. These results were interpreted in terms of model in which ttention is llocted, in viewer-centered fshion, from the observer to the precued position in depth. The chrcteristics of ttention in depth hve lso been exmined in series of visul serch studies. In one such study, Nkym nd Silvermn (1986; see lso Steinmn, 1987) presented subjects with stereoscopic disply in which they serched for trget defined by conjunction of disprity nd motion. The RTs were reltively invrint cross different distrctor set sizes, suggesting tht the subjects were ble to restrict their ttention to single depth plne nd discriminte between the trget nd distrctors on the bsis of single feture. Thus, consistent with the sptil priming results described bove, it ppers tht ttention is distributed in reltively restricted region in depth. Although the sptil priming nd visul serch studies suggest circumscribed distribution of ttention in depth, the fct tht these studies presented stimuli t only two different depths limits our knowledge of the shpe of the ttentionl focus. This issue ws ddressed by Andersen (199) in response comptibility tsk in which subjects were instructed to respond to centrlly locted trget nd ignore the surrounding distrctors. On some trils, the distrctors were comptible with the response of the trget (e.g., identicl to the trget), wheres, on other trils, the distrctors were incomptible with the response of the trget (e.g., the distrctors required different response when they served s trgets). Across trils, the distrctors ppered t seven different depths: three loctions between the observer nd the trget, the sme depth s the trget, nd three depths frther thn the trget. The displys were rndom dot stereogrms tht were viewed through stereoscopic prism viewer. The size of the interference effect (e.g., incomptible distrctor minus comptible distrctor RT) incresed, in monotonic fshion, with decreses in the disprity between the trget nd distrctors. Interestingly, this interference effect ws symmetric with respect to the position of the trget. Distrctors tht were locted frther from the trget (e.g., uncrossed disprity) produced lrger interference effect thn did distrctors locted in front of the trget (e.g., crossed disprity). As result of the symmetric pttern of interference, Andersen (199) suggested tht depth of focus of ttention might function in mnner similr to the depth of focus of cmer lens. Tht is, the depth of focus is nrrower for ner objects thn it is for fr objects. Andersen s finding of symmetric depth effects is consistent, in generl, with the symmetric ttention movement effects obtined in vlid/invlid cuing prdigm (Downing & Pinker, 1985; Gwryszewski et l., 1987). However, the symmetries of the study by Andersen nd of the studies by Downing nd Pinker (1985) nd Gwryszewski et l. (1987) re in opposite directions. Thus, while Andersen (199) found lrger interference effects for the distnt distrctors, suggesting steeper grdient of ttention

3 66 ANDRSN AND KRAMR between the observer nd the ttended object, Downing nd Pinker (1985) nd Gwryszewski et l. (1987) found greter RT costs when ttention ws moved from ner to fr thn from fr to ner positions, suggesting steeper grdient beyond the focus of ttention in depth. A potentil explntion for the discrepncy in the sign of the symmetric ttentionl effects in the vlid/invlid nd response comptibility studies concerns the viewing conditions employed in the studies. In the Andersen (199) study, subjects viewed the stereo imges through prism stereoscope. Under these viewing conditions, the opticl xes of the eyes re ligned in prllel nd the convergence ngle is zero. Without informtion from convergence, bsolute distnce might be derived from other sources of informtion, such s ccommodtion. Under the close viewing conditions used in the Andersen (199) study, smll vritions in pprent distnce would hve reltively lrge effect on the perceived size of the distrctors. Thus, the size of the fr distrctors might hve been overestimted, cusing them to produce lrger interference effect thn tht produced by the ner distrctors (Wtson, 1981). In the study by Downing nd Pinker (1985), subjects monoculrly viewed the rows of lights. Depth cues vilble to the subject included texture, ccomodtion, nd liner perspective. Since subjects in the Gwryszewski et l. (1987) study viewed the lights binoculrly, convergence informtion ws lso vilble. Despite the vilbility of vriety of depth cues in these studies, it is conceivble tht the differences in intensity of the lights locted t the two depths might hve bised the results to fvor the ner loction (i.e., ssuming tht the ner lights were perceived s brighter thn the fr lights nd therefore were esier to perceive). Oneof the gols ofthe present study ws to further exmine the nture of the symmetric ttentionl effects. To tht end, we hd subjects view stereoscopic imges on computer screen through pir of polrized glsses. Under these viewing conditions, the opticl xes of the eyes converge on the disply nd bsolute distnce informtion cn be derived. This llows for direct derivtion of the simulted reltive distnce between the items on the disply. Furthermore, other less relible sources of distnce informtion (e.g., ccommodtion) would hve little influence on the perceived bsolute distnce since the viewing distnce in the present study ws considerbly greter (i.e., 14 cm) thn the distnce used in Andersen (i.e., 21 cm). Finlly, the presenttion of computergenerted stereoscopic imges rther thn ctul objects elimintes the potentil problem of chnges in illumintion with distnce. A second objective of the present study ws to more finely mp the distribution of ttention in 3-D spce. This is in contrst to previous studies of ttention in depth tht hve exmined verticl, horizontl, nd depth xes in seprte experiments (Gwryszewski et l., 1987), exmined limited rnge of depth with severl horizontl positions (Downing & Pinker, 1985), or fixed the position of distrctors in horizontl nd verticl dimensions while investigting lrge number of positions in depth (Andersen, 199). In the present study, response distrctors were locted t seven positions in depth, three horizontl seprtions, nd three verticl seprtions in n effort to provide more extensive exmintion of the sptil chrcteristics of ttention in 3-D spce. MTHOD Subjects The subjects were 1 undergrdute students t the University of Illinois t Urbn-hmpign who were pid $4 per hour for their prticiption. All subjects hd norml or corrected-to-norml vision nd were nive s to the purpose of the study. All subjects were tested for stereoscopic vision using the Rndot test nd were required to hve disprity sensitivity of 2 sec of rc. Design Five independent vribles were exmined: type of trget (X or ), type of distrctor (comptible or incomptible), difference in disprity between the trget nd the distrctors ( 6.8, 3.4, 1.7,, 1.7, 3.4, nd 6.8 mm of rc), 2-D distrctor direction (verticl or horizontl), nd 2-D distrctor seprtion (horizontl nd verticl seprtions:.59 nd.67 [close],.71 nd.8 [intermedite], or 1.19 nd 1.34 [fr]). Stimuli The displys consisted of two imges, lterntely presented on computer screen t 12 Hz, tht were viewed through polrized glss plte. The subjects viewed displys through pir of polrized glsses such tht one eye received one imge nd the other eye received the other imge. The disply consisted of chromtic elements displyed ginst blck bckground. The response disply consisted of trget with two djcent distrctors, one on either side of it, presented either verticlly or horizontlly reltive to the trget. Trils were either comptible (distrctors nd trget were identicl) or incomptible (distrctors nd trget were different). The position of the distrctors ws shifted in equl increments in both imges to mintin constnt visul ngle seprtion between the trget nd the distrctors. Vritions in the depth positions ofthe distrctors were produced by shifting the positions of the items reltive to the trget. Shifting the distrctors in the nsl direction produced crossed disprity reltive to the trget; shifting the distrctors in the temporl direction produced uncrossed disprity reltive to the trget. The disprity vlues of the distrctors, reltive to the trget, were 6.8, 3.4, 1.7,, 1.7, 3.4, nd 6.8 mm of rc of disprity. Negtive disprity vlues indicte crossed disprity; positive disprity vlues indicte uncrossed disprity. The disprity vlues used in the present study were within the rnge of Pnum s fusion re (Schumer & Julesz, 1984). Three types of stereoscopic displys were used on ech tril: fusion disply, precue disply, nd response disply (see Figure 1). The fusion disply consisted of colon : symbol. The dimensions of the : symbol were.44 wide horizontlly x.51 high verticlly. The precue disply ws either verticl br (.44 high x.26 wide) orhorizontl br (.22 high x.51 wide). The response disply consisted of trget (either n X or n ) nd two distrctors. The dimensions of the X nd were ech.44 wide X.51 high. The distnce between the subject nd the monitor ws 141 cm. The durtion of the precue ws 5 msec. The durtion of theresponse disply ws lso 5 msec. The interstimulus intervl between the displys ws 3 msec. Thus, the totl durtion ofech tril ws 13 msec, which ws below the minimum time required to initite

4 Fusion : Precue Trget xxx~ I H Time (msec) Figure 1. A schemtic digrm of ech tril, indicting the presenttion order nd durtion of the fusion, precue, nd response displys. The totl disply durtion ws 13 msec. vergence eye shift (Rshbss & Westheimer, 1961; Westheimer & Mitchell, 1969). The stimuli were presented on Tektronix stereoscopic color monitor under the control of n IBM P AT. Procedure The subjects were told to position their hnds on the keybord s if typing nd to press the spce br on ech tril s soon s they hd cler percept of the : symbol. Once the spce br ws pressed, either verticl or horizontl br ppered t the sme loction s the : symbol. If the subjects sw verticl br, they were not to respond to the trget tht would follow. Trils with verticl br precue served s ctch trils nd ccounted for 6.6% of the totl number of trils. The purpose of the ctch trils ws to ensure tht the subjects were ttending to the centrl position t the beginning of the stimulus presenttion. The disprity vlue of the distrctors for ctch trils ws equl ( disprity) to the disprity of the trget. Ifthe subjects sw horizontl br, they were to respond to the trget tht followed t the sme loction, pressing either the z key or the I key. For hlf ofthe subjects, the z key ws used s the response for n trget, wheres the I key ws used s the response for the X trget. For the other hlfof the subjects, the response ssignment ws reversed. The subjects were instructed to respond s quickly s possible, but lso to be s ccurte s possible. They were lso told tht they might see other items locted djcent to the trget, but tht they should ignore these items. The subjects received 4 blocks of trils over 1-dy period. The first block oftrils on the first dy ws used for prctice. ch block contined single presenttion of ech disply condition (2 trget types x 2 distrctor types x 7 disprity levels x 2 distrctor directions x 3 distrctor seprtions) nd 12 ctch trils (trils in which the verticl br precued the trget) for totl of 18 trils. Thus, the totl number of trils over the 1-dy period ws 7,2 trils per subject. The ctch trils consisted of 6 comptible nd 6 incomptible distrctor trils, with one tril for ech of the close, intermedite, nd fr seprtions t verticl nd horizontl loctions. The subjects were given rest hlfwy through ech block nd following the completion of ech block. The subjects viewed the displys in drk room. Trils in which the RT ws less thn 1 msec or exceeded 1 sec were not included nd were replicted t the end of the block. Men RT ws computed for correct trils only. RSULTS ATTNTION IN THR-DIMNSIONAL SPA 661 A preliminry nlysis of trget type indicted no significnt differences for RT or percentge of correct responses. Thus, ll dditionl nlyses were collpsed cross this vrible. The remining nlyses re orgnized in terms of men RT nd men percentge of response errors. Rection Time The men RT for ech subject for ech condition ws tbulted nd nlyzed in four-wy (type of distrctor x disprity difference x 2-D distrctor direction x 2-D distrctor seprtion) nlysis of vrince (ANOVA). The min effect for distrctor type ws significnt [F( 1,9) = 71.6, p <.1], nd so ws tht for 2-D distrctor seprtion [F(2,18) = 45.2, p <.1]. Distrctor type intercted significntly with 2-D distrctor seprtion [F(1,9) = 23.3, p <.1], 2-D distrctor direction [F(2,18) = 14.9, p <.1], nd disprity [F(6,54) = 2L3,p <.5]. There were significnt three-wy interctions of distrctor type, distrctor seprtion, nd disprity [F(6,54) = 2.9, p <.51 nd of distrctor type, distrctor direction, nd disprity [F(12,18) = 2.4, p <.1]. The four-wy interction of distrctor type, distrctor seprtion, distrctor direction, nd disprity ws significnt [F(12,18) = 2.5, p <.5]. There were no other significnt min effects or interctions. As shown in Figure 2, men RT ws longer for incomptible distrctors (37 msec) thn for comptible distrctors (359 msec). The men RTs for the close, intermedite, nd fr seprtions were 37, 364, nd 361 msec, respectively. The incresed RTs for incomptible trils decresed with incresed horizontl, verticl, nd depth seprtion between the distrctors nd the trget. One interesting finding ws the significnt interction between distrctor type nd distrctor direction (see Figure 3). According to this result, there ws greter overll interference (difference between RTs for the comptible nd incomptible distrctors) for horizontl distrctors thn for verticl distrctors. This suggests tht ttention is not symmetricl in the horizontl nd verticl directions. One could rgue tht this effect is due to the slightly different visul ngle vlues used for the close, intermedite, nd fr seprtions for horizontl nd verticl loctions. However, the difference between horizontl nd verticl loctions t the three seprtions were.8,.9, nd.15.it is unlikely tht these smll differences could hve resulted in the interction. A more rigorous test of this effect would be to compre the results for horizontl nd verticl distrctor conditions cross different visul ngles. Four different F rtios were clculted to exmine these conditions. Two F rtios compred the close (.67 )verticl condition with the intermedite (.71 )horizontl condition for crossed nd Uncrossed disprities. The other F rtios compred the intermedite (.8 )verticl condition with the fr (1.19 ) horizontl condition for crossed nd uncrossed disprities. If significnt differences were found for these comprisons, it would suggest horizontl distrctors locted t greter 2-D seprtions produced greter interference thn did verticl distrctors positioned closer to the trget. The F rtios for crossed disprity conditions were nonsignificnt

5 662 ANDRSN AND KRAMR A U Ut I Horizontl Distrctors.59 deg.. ~- Incomptible f3 omptible B In (U Horizontl Distrctors.71 deg... s. Incomptible omptible In Horizontl Distrctors 1.19 deg. Incomptible 6 omptible w t ) 15 1 U. ~ 5 ~15 ~ 1 ) 15 1 U Fr Ner Disprity (mm. rc) Fr Ner DIsprity (mm, rc) ) Fr Ner Disprity (mm. rc) D Verticl Distrctors.67 deg. Verticl Distrctors.8 deg. F Verticl Distrctors 1.34 deg. 39. Incomptible 8 omptible 39.- Incomptible 8 omptible 39 ~ ~R Incomptible.~. omptible U) In In ~ t~i 15 ) 1,. ~ 5 ) ) 15 1 U. ~ Fr Ner Fr Ner Fr Ner Disprity (mi n. rc) Disprity (ml n. rc) Disprity (ml n. rc) Figure 2. ffect of incomptible nd comptible distrctors on men RT nd men percentge error s function ofdisprity. Seprte grphs re presented for horizontl distrctors with 2-D sptil seprtions of (A).59,(B).71,nd () 1.19,nd for verticl distrctors with 2-D sptil seprtions of (D).67,().8,nd (F) 1.34.Positive nd negtive disprity refer to ner nd fr distnces, respectively.

6 ) ~ ) to c 1 I.). ~ 5 to lncorcpt~bie ~ orcpot~bio Figure 3. ffect of distrctor type nd distrctor direction on men RT nd men percentge error. (p <.5). However, different pttern of results occurred for uncrossed disprity conditions. The comprison between close/verticl nd intermedite/horizontl distrctors ws significnt [F(l,9) = 9.43,p <.25]. The men interference for the close/verticl nd intermedite/horizontl conditions ws 8 msec nd 16.8 msec, respectively. The comprison between intermedite/verticl nd fr/horizontl condition pproched significnce [F(l,9) = 4.51, p <.7]. The men interference for the intermedite/verticl nd fr/horizontl distrctor conditions ws 5.6 msec nd 1.6 msec, respectively. These results suggest tht interference vried s function of verticl, horizontl, nd depth positions. In ddition, the significnt four-wy interction mong the distrctor type, distrctor seprtion, distrctor direction, nd disprity vribles suggests tht the mgnitude of interference vried for different positions long the horizontl, verticl, nd depth dimensions. An importntgol of the present study ws to determine the chnge in interference for different seprtions between the distrctors nd trget in the verticl, horizontl, nd depth dimensions. In order to exmine this issue, series of dditionl nlyses of prtil interctions were conducted. The nlyses exmined contrst effects for the distrctor conditions t different disprity vlues by subtrcting the RTs for comptible nd incomptible conditions s function of disprity (see Keppel, 1991, for discussion of contrst effects nd interctions). The difference in men RT for comptible nd incomptible conditions provides mesure of the differentil interference between these conditions nd represents the fcilittion of comptible distrctors nd the interference of incomptible distrctors. This type of nlysis ws performed for ech distrctor direction in the horizontl nd verticl dimensions. ATTNTION IN THR-DIMNSIONAL SPA 663 Seprte grphs of men differentil interference for different visul ngles long the horizontl nd verticl dimensions is presented in Figure 4. A significnt effect of disprity ws found for horizontl distrctors t the close (.59 )seprtion [F(6, 18) = 3.18, p <.5] nd intermedite (.71 )seprtion [F(6,l8) = 5.2, p <.51. A significnt effect of disprity ws lso found for verticl distrctors t the close (.67 )seprtion [F(6, 18) = 4.6, p <.5] nd intermedite (.8 ) seprtion [F(6,18) = 2.97, p <.5]. There were no significnt effects found for either the horizontl-fr or the verticl-- fr seprtions [F(6,18) < 1]. As shown in Figure 4, there ws n overll decrese in the mount of interference ccording to the horizontl or verticl seprtion of the distrctors. The gretest mount of interference occurredt the closest seprtion, with interference decresing with n increse in the seprtion between the trget nd distrctors. These results re similr to the results obtined by B. A. riksen nd. W. riksen (1974), who found decrese in interference for incresed 2-D sptil seprtions between distrctors nd trgets. Of prticulr interest in the present study ws whether the pttern of results suggests tht ttention vried ccording to grdient in the depth dimension for different 2-D sptil seprtions. In order to ssess the overll interference of distrctors vrying in depth, series of correltions were derived for different 2-D seprtions. If ttention is distributed s grdient long the depth dimension, then interference should be negtively correlted with distnce. The strength of the correltions, s well s the slope of liner regression equtions, should decrese with n increse in 2-D sptil seprtion between the trget nd distrctors. Seprte correltions nd liner regression equtions were derived for crossed nd uncrossed disprity conditions for both distrctor directions in order to determine whether interference vried for distrctors locted closer to or frther from the observer. The disprity vlues used for these nlyses included the four bsolute disprity vlues of, 1.7, 3.4, nd 6.8 mm of rc. The results of the correltions, significnce tests for the correltions, nd slopes nd intercepts of the regression equtions re presented intble 1. We will begin by contrsting the crossed nd uncrossed disprity functions for the verticl distrctor loctions. As cn be seen in Tble 1, the correltions were significnt for both the crossed nd the uncrossed close distrctor positions. However, the slope ws substntilly steeper for the uncrossed disprity. The difference in the slopes ws not function of speed ccurcy trdeoffs, since correltions between disprity vlues nd error rtes (see Tble 2) were equivlent for the uncrossed nd crossed disprities t the close distrctor loction (slopes =.77 nd.7 for uncrossed nd crossed disprities, respectively). For the horizontl loctions, the correltions were significnt for the close, intermedite, nd fr crossed disprity conditions, s well s for the close uncrossed disprity condition. Furthermore, it cn be seen in Tble 1 tht the slopes re more negtive for the crossed horizontl

7 664 ANDRSN AND KRAMR A B Ii) 3 2 U U) t * V..U7deg. ~ tj V..Uodeg. ~ V.1.34 dog. 1 U) ~ O ~gt O ~ Fr Ner Disprity (mm. rc) Fr Ner Disprity (mm. rc) 8 Figure 4. The differentil interference (in milliseconds nd percentge error) of ttention s function of the disprity vlueof distrctors. Seprte grphs re presentedfor horizontl (H) nd verticl (V) distrctor conditions t different 2-D sptil seprtions. Positive nd negtive disprity vlues refer to ner nd fr distnces, respectively. loction thn for the uncrossed horizontl loctions. At first glnce, these results seem to belie our finding of steeper ttentionl grdient for the uncrossed disprities t the verticl distrctor loctions. However, this pprent discrepncy between the grdients obtined for the horizontl nd verticl loctions cn be resolved by n exmintion of the error rte dt. As indicted bove, the RT nd error rte functions were consistent in indicting steeper grdient (e.g., more negtive slopes) for the uncrossed disprities for the verticl distrctor loctions. However, such is not the cse with the horizontl loctions. Although the RT functions suggest steeper grdient t the crossed loctions, the error rte slopes suggest steeper grdient for the uncrossed loctions. The slopes of the error rte regression functions for the uncrossed close, intermedite, nd fr horizontl loctions Tble 1 orreltion nd Liner Regression Anlyses of Interference (in Milliseconds) s Function of Distrctor Loction Horizontl Loction Verticl Loction lose Intermedite Fr lose Intermedite Fr rossed Disprity Men r score 2.45* 2.82* 2.8* 959* Men Slope Men Intercept Uncrossed Disprity Men r score 3.69*, Men Slope Men Intercept *Significnt sc ore, p <.5.

8 Men r score Men Slope Men Intercept Men r score Men Slope Men Intercept ATTNTION IN THR-DIMNSIONAL SPA 665 Tble 2 orreltion nd Liner Regression Anlyses of Interference (rror Rte) s Function of Distrctor Loction Ho rizontl Loction Verticl Loction lose Intermedite Fr lose Intermedite Fr * * *significnt t sc ore, p <.5. rossed Disprity * 2.12* Uncrossed Disprity * iJ* * * * were.84,.2, nd.31. The slopes for the crossed close, intermedite, nd fr horizontl loctions were.21,.26, nd.33. Thus, it would pper tht the steeper RT slopes for crossed horizontl loctions were due to speed-ccurcy trdeoff. In summry, the results of the verticl distrctors provide evidence tht ttention is symmetriclly distributed long the line of sight, s ws found in previous reserch (Andersen, 199; Downing & Pinker, 1985; Gwryszewski et l., 1987). However, one importnt difference between the present results nd those obtined by Andersen (199) is the direction of the symmetry. In the Andersen study, greter interference ws obtined for uncrossed (fr) disprity conditions. The results of the present study suggest tht greter interference occurred for crossed (ner) disprity conditions, consistent with the results of Downing nd Pinker (1985) nd Gwryszewski et l. (1987). An explntion for this pttern of results is provided in the Discussion section. rrors The men percentge of errors for ech subject for ech condition ws nlyzed in four-wy (distrctor type x disprity X 2-D distrctor direction x 2-D distrctor seprtion) ANOVA. The min effect for distrctor type ws significnt [F(1,9) = 28.8, p <.1]. The men percentge of errors for the comptible nd incomptible distrctors were 9.8 nd 12.9, respectively. The min effect of 2-D distrctor direction ws lso significnt [F(1,9) = 12.5, p <.1], s ws the min effect ofdisprity [F(6,54) = 2.S9,p <.5]. As shown in Figure 2, error rtes were greter for the verticl distrctors thn for the horizontl distrctors. rror rte ws gretest when distrctors were locted t the sme distnce s the trget. Incresing the depth seprtion between the trget nd distrctors resulted in decrese in the error rte. There were significnt two-wy interctions between distrctor type nd distrctor seprtion [F(2, 18) = 11.6, p <.1] nd between distrctor type nd distrctor direction [F(1,9) = 11.5, p <.1]. There were no other significnt min effects or interctions. One interesting finding ws the significnt interction between distrctor type nd distrctor direction (see Figure 3). According to this result, subjects hd greter difference in error rte (between comptible nd incomptible distrctor conditions) for horizontl distrctors thn for verticl distrctors. This result provides further evidence tht interference ws not symmetricl long the horizontl nd verticl xes. DISUSSION Two relted issues were investigted within the context of focused ttention in depth. The first issue concerned the sptil dimensions of focused ttention in 3-D spce. This issue ws ddressed by instructing the subjects to respond to centrlly locted trget nd ignore flnking distrctors tht could pper t combintions of seven different depths, three horizontl seprtions, nd three verticl seprtions. The difference between RTs nd error rtes obtined for response-comptible nd responseincomptible distrctors served s the bsis for evluting the shpe of the ttentionl focus. Overll, our results re consistent with the notion of grdient of ttention in 3-D spce (Andersen, 199; Downing & Pinker, 1985; LBerge & Brown, 1989). The difference in RT nd ccurcy between responsecomptible nd response-incomptible trils decresed s distrctors were locted frther from the trget. This effect ws observed for the horizontl, verticl, nd depth dimensions. It is interesting to note tht the shpe of the grdient ws different in the horizontl nd verticl dimensions. The response comptibility effect ws significntly greter, for both RT nd error rtes, for distrctors positioned long the horizontl dimension thn for those positioned long the verticl dimension. This effect is consistent with the difference between vlid nd invlid cue trils for the horizontl nd verticl conditions in the Gwryszewski et l. (1987) studies. The RT differences s function of cue vlidity were 43 msec for the horizontl conditions nd 13 msec for the verticl conditions. Thus, the results obtined in two different ttention pr-

9 666 ANDRSN AND KRAMR digms, cue vlidity nd response comptibility, suggest tht the shpe of the ttention grdient is ellipticl, with steeper grdient in the verticl dimension. The second issue ddressed in the present study concerned the discrepncy between the findings of symmetries of ttention long the depth xis. Investigtions of ttention using vlid/invlid cuing prdigms hve found tht the reorienttion of ttention occurs more quickly when shifting from distnt loction to ner loction thn when shifting from ner loction to distnt loction (Downing & Pinker, 1985; Gwryszewski et l., 1987). This pttern of results cn be interpreted in terms of steeper grdient beyond the focus of ttention in depth. Thus, it might be ssumed tht ttention is distributed, in viewer-centered fshion, from the observer to fixtion. Therefore, the processing of objects between the observer nd fixtion should be reltively esy, wheres the processing of objects beyond fixtion my necessitte the redeployment of ttention. It is importnt to note, however, tht the differences in pprent illumintion between ner nd fr distrctors might hve been t lest prtilly responsible for the symmetry of cuing effects long the depth xis. Thus, it is conceivble tht the brighter ner lights might hve been esier to perceive, thereby resulting in fster shift from the fr position to the ner position thn from the ner position to the fr position. ontrry to the findings obtined in the vlid/invlid cuing prdigm, Andersen (199) found lrger interference effects for further distrctors in focused ttention prdigm. These results could be interpreted in terms of steeper ttentionl grdient between the observer nd fixtion. However, the method used to view stereoscopic imges in the Andersen (199) study might hve resulted in perceived size vritions for distrctors t different depths. Since subjects viewed the stereo imges through prism stereoscope, the opticl xes of their eyes were ligned prllel, thereby producing convergence ngle of zero. Without convergence informtion, perceived bsolute distnce might hve been determined from ccommodtion. Under the close viewing conditions used in the Andersen study, vritions in perceived reltive distnce from disprity might hve cused the subjects to gretly overestimte the size of the fr distrctors, thereby producing lrger interference effect for the fr distrctors thn for the ner distrctors. In the present study, we ttempted to resolve the inconsistent findings obtined in the cue-vlidity nd responsecomptibility prdigms by instructing subjects to view stereoscopic imges on computer screen through pir of polrized glsses. Under these viewing conditions, the opticl xes of the eyes converge on the disply nd bsolute distnce cn be derived. The presenttion of computer-generted imges rther thn ctul objects lso elimintes the potentil problem of chnges in illumintion cross different depths. onsistent with the results found in the cue-vlidity prdigm, we found lrger response comptibility effects t crossed (ner loctions) disprities thn t uncrossed (fr loctions) disprities. In ddition, the slope relting interference to trget/distrctor seprtion in depth ws significntly more negtive for the uncrossed (fr) disprities thn for the crossed (ner) disprities for the verticl distrctors. The results for horizontl distrctors were less cler, with speed ccurcy trdeoff occurring cross vritions in disprity. The result for verticl distrctors is consistent with steeper grdient beyond the focus of ttention in depth. Given these results, it would pper tht the lrger response comptibility effect obtined by Andersen (199) for the uncrossed disprities my be ttributed to n overestimtion of the size of the fr distrctors. RFRNS ANDRSN, G. J. (199). 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10 POSNR, M., SNYDR,., & DAVIDSON, B. (198). Attention nd the detection of signls. Journl ofxperimentl Psychology: Generl, 19, RASHBASS,., & WSTHIMR, G. (1961). Independence of conjugte nd disjunctive eye movements. Journl ofphysiology, 159, SHUMR, R., & JULSZ, B. (1984). Binoculr disprity modultion sensitivity to disprities offset from the plne offixtion. Vision Reserch, 24, SHULMAN, G., RMINGTON, R., & MLAN, J. (1979). Moving ttention through visul spce. Journl of xperimentl Psychology: Humn Perception & Performnce, 5, STINMAN, 5. (1987). Seril nd prllel serch in pttern vision. Perception, 16, WATSON, H. D. (1981). The effects ofobjective nd perceived size properties on visul form mtching. Journl ofxperimentl Psychology: Generl, 11, WSTHIMR, G., & MITHLL, D.. (1969). The sensory stimulus for disjunctive eye movements. Vision Reserch, 9, NOT ATTNTION IN THR-DIMNSIONAL SPA An lterntive explntion ofthe results is tht the decrese in comptible RT minus incomptible RT with incresing trget/distrctor disprity cn be ttributedto decreses in distrctor cuity. This nonttentionl hypothesis ws exmined in n dditionl experiment. In this experiment, the subjects were presented with three stereoscopic displys on ech tril: fusion disply, precue disply, nd response disply. These displys were identicl to those used inthe originl experiment with the following exceptions. The response disply consisted of only two letters rther thn three letters, s were used in the originl experiment. These letters, which were either Os or Xs on ny prticulr tril, were rryed.59 (e.g., the closest horizontl seprtion used in the originl study) to the left nd the right of the fusion point. The subject s tsk ws to press one response button if the letters were Os nd nother responsebutton ifthe letters were Xs. Five subjects prticipted in 1-h prctice session nd second session in which they performed 6 trils of the letter identifiction tsk for ech disprity vlue exmined in the originl experiment. If differentil cuity for the distrctors t the seven trget/distrctor disprities ws responsible for the chnges in comptible RT minus incomptible RT in the originl study (i.e., the decresed comptible RT minus incomptible RT difference s function of incresed trget/distrctor disprity), we would expect increses in RT s the subjects were required to identify distrctors t incresing disprities reltive to the fusion point. On the other hnd, if the comptible effects obtined in the originl experiment were due to the restricted focus of ttention, we would expect little or no chnge in RT or error rte t different disprity vlues. The dt obtined in this experiment were consistent with the ltter prediction. There were no significnt differences in either RT orerror rte s function of the disprity of letters from the fusion point. (Mnuscript received July 12, 1991; revision ccepted for publiction November 23, 1992.) Dedline for submissions to the Bulletin of the Psychonomic Society revised After 1993, the Psychonomic Society will no longer be publishing the Bulletin ofthe Psychonomic Society. The Society s Publictions ommittee hs decided tht its originl purpose tht of providing n outlet for quick, brief, unrefereed rticles in experimentl psychology t time when publiction lgs were generlly very long hs been fulfilled nd is no longer needed. The 1993 volume hs been filled sooner thn expected, nd the dedline for submissions to the Bulletin hs been revised ccordingly. Mnuscripts must be received by June 3, 1993 to be considered for publiction in the journl. The journl stff in Austin will mke every effort to include ll mnuscripts received before the dedline in the finl volume, but will return ny mnuscript received fter tht dte to the uthor. Authors who wish to submit mnuscripts before the June 3 dedline should consult recent issue of the Bulletin for informtion bout publiction policies.