Perceptin & Psychphysics 1976, Vl. 19 (1), 47-54 The induced asynchrny effect: Its rle in visual judgments f tempral rder and its relatin t ther dynamic perceptual phenmena C. E. COLLYER Princetn University, Princetn, New Jersey 085J,.0 A cntext-induced "illusin" in visual judgments f tempral rder, termed the induced asynchrny effect (IAE), is reprted. It cnsists f an apparent rdering in time f tw simultaneus light nsets, prduced by the preceding, asynchrnus ffsets f tw ther lights. The jint effect f a real stimulus nset asynchrny and a preceding stimulus ffset asynchrny n judgments f nset rder appears t be additive, given a Gaussian transfrmatin f respnse prbability. This result is shwn t be cnsistent with a simple statistical decisin mdel, which prvides a cnceptual framewrk fr drawing inferences frm tempral rder judgment data. Hwever, it is emphasized that certain interpretatins f such mdels are nt empirically testable n the basis f tempral rder data alne. An attempt is made t relate the IAE t three ther dynamic perceptual phenmena; all fur effects may reflect a tendency f bservers t perceive the velcity f apparent mtin as being cnstant. Questins raised by the demnstratin f the IAE are discussed, and directins fr further research are suggested. In the curse f designing stimulus displays fr use in experiments n apparent mtin, tempral rder, and masking. a rbust "illusin" in visual judgments f tempral rder was encuntered. Briefly, if tw stimuli are successively extinguished in the spatial vicinity ftw subsequent "test" stimuli, the apparent nset rder f the test stimuli is strngly influenced by the ffset rder f the tw preceding stimuli. Mre specifically, the nset f that test stimulus nearest the initially extinguished stimulus, tends t be judged earlier than the ther test stimulus nset. When the tw test nsets are really simultaneus, the ffset asynchrny f the tw preceding stimuli can be sufficient t induce a perceptin f nset rdering. This "illusin" is referred t as the induced asynchrny effect (lae). Tw experimentsare reprted in this paper; the first demnstrates the reliability f the IAE, while the secnd examines the jint influence f tw factrs n tempral rder judgments (TOJs): test stimulus nset asynchrny and preceding stimulus ffset asynchrny. EXPERIMENT I This experiment was designed t demnstrate the rbust and reliable nature f the IAE using an ptimal "inducing" prcedure. A questinnaire was emplyed t allw a number f bservers t characterize the apparent "nset rder" f tw lights which were actually illuminated simultaneusly in prximity t tw previusly extinguished "inducing" The authr wishes t thank R. A. Kinchla fr many valuable discussins and suggestins cncerning the present study in particular and relatins between thery and data in general. The authr's address is: Department f Psychlgy, Princetn University, Princetn, New Jersey 08540. lights. Three experimental cnditins were defined which differed nly in the ffset sequence f these inducing lights: Sequence L, in which the leftmst inducing light was extinguished first; Sequence R, in which the right light was extinguished first; and Sequence S, in which the inducing lights were extinguished simultaneusly. Methd Subjects. Twenty unpaid students and clleagues served as bservers. Apparatus and StimulI. Stimulus displays were presented n a Tektrnix Type 602 CRT display unit, cntrlled by a POP-12 cmputer (Digital Equipment Crpratin). The spatial cnfiguratin f the stimulus display and an example f the time curse f ne trial are shwn in Figure 1. The stimuli were i1iuminated rectangular patches cnsisting f a 6 by 4 matrix f clsely spaced pints. Three display prgrams were prepared, each f which presented a repeating series f identical trials in ne f the three previusly indicated sequences. In Sequence L, the time curse f stimulus events within a trial was as shwn in Figure Ib; that is, the ffset f Stimulus A ccurred 100 msec befre the ffset f Stimulus B, fllwed SO msec later by the simultaneus nsets f Stimuli C and D. Nte that ISO msec is usually cnsidered t brief t permit an vert fixatin shift t be initiated and cmpleted (Kmda, Festinger, Phillips. Duckman, & Yung. 1973). In Sequence R, the ffset f Stimulus B ccurred 100 msec befre the ffset f Stimulus A; the duratins f Stimuli and A and B were 1,100 and 1.000 msec, respectively. In Sequence S, the ffsets f Stimuli A and B were simultaneus; the duratins were bth 1.000 msec, In all three sequences. the nsets f C and 0 were simultaneus; a brief SO-msec dark interval elapsed between the last ffset (f A r B) and the simultaneus nsets (f C and 0). An interval f 2,000 msec elapsed between successive presentatins f the identical stimulus patterns in each f the three cnditins. In additin t the three IAE sequences, a prgram was prepared which cntrlled the display f a stimulus pair, in which the nset rder f the stimuli culd be selected by the experimenter. Using a Teletype keybard t initiate single trials, the experimenter culd present the tw stimuli, in a "right first" (by SO msec), "left first" 47
48 COLLYER B.J A 0 0 i C 0 0 0 1000 msec 1100 msec 1 ')0' (a) ')0 msec~ +- n...-----ff c...j1 ')00 msec L 0 ---1 1 ')00 msec L Time (b) Figure 1. (a) Spatial cnfiguratin f stimulus psitins in the IAE eiisplay f Experlmmt I. (b) TIme cune f IIDDilnatin f atimallin the lae eiisplay f Experiment I, fr Sequence 1. ) B '3'), (by SO msec), r "simultaneus" rder. The tw stimuli were laterally separated by l SQ' visual angle at a viewing distance f 30 in.; a fixatin pint was psitined midway between them, and remained illuminated thrughut the trial. The nset f the fixatin pint preceded the nset f the first stimulus by 1,000 msec; the duratin f the stimulus illuminated secnd was SOO rnsec. Prcedure. Subjects were run individually. All subjects were instructed that the experimenter was interested in verifying the reliability f bservers' tempral rder impressins, using stimulus patterns that wuld be emplyed in a subsequent experiment. Examples f "right first," "left first," and "simultaneus" stimulus pairs were first shwn t the subject, t acquaint him with the magnitude f "asynchrnies" being used as well as with what the experimenter meant by "simultaneus." Then the experimenter presented a randm series f nine stimulus pairs, three f each type, asking the subject t respnd "right first," "left first," r "simultaneus" t identify each pair. A perfrmance criterin f at least eight crrect respnses was required n this pretest series in rder fr an bserver t be included in the final IAE tests, althugh subjects were nt infrmed f this cntingency. (Only ne subjects, wh made three errrs, was rejected in this way.) The 20 subjects wh satisfied the pretest criterin, were divided int tw grups. Thse in Grup I were shwn Sequences Land S; thse in Grup II were shwn Sequences Rand S. Half f the subjects in each grup were shwn Sequence S first. and half secnd. Subjectswere given the fllwing printed instructins prir t bserving each sequence: "On the screen befre yu, there is a repeating display cnsisting f a fixatin pint and fur stimulus lights in the fllwing cnfiguratin: (A diagram similar t Figure 1a was n the instructin sheet.) Observe this display fr as many repetitins as yu wish. In a future experiment, bservers will be asked t judge the rder in which lights C and D cme n. What! d yu think their respnse tendency will be? (Please chse ne f the fllwing 3 alternatives): (i) Observers will have a strng impressin that C came n first; (ii) Observers will have a strng impressin that D came n first; (iii) Observers will have the impressin that C and D came n at abut the same time." It was hped that by making the subject's respnse a "predictin" ffuture bservers' respnses, he wuld be mre likely t give his wn "immediate perceptual impressin" rather than sme lgically deduced hypthesis abut what the experimenter might really be presenting. Results The chices made by the 20 bservers are shwn in Table 1. Each rw f Table 1 is a frequency distributin ver the three respnse alternatives given a particular sequence (L. R, r S), rder f presentatin (Sequence S presented first r secnd). and grup (I, which judged Sequences Sand L, r II, which judged Sequences Sand R). All 20 subjects judged that Sequence S gave an impressin f nset "simultaneity." Ofthe 10 subjects in Grup I, 9 judged that Sequence L gave "a strng impressin" f "left first" nset rdering. f the 10 subjects in Grup II, 7 judged that Sequence R gave "a strng impressin" f "right first" nset rdering. Recalling that the tw test nsets in all three sequences were actually simultaneus, these data indicate cnsiderable cntrl f the nset rder judgment by the ffset asynchrny f the tw preceding stimuli. THEINTERPRETATION OF TEMPORAL ORDERJUDGMENTS Having demnstrated that the ffset asynchrny f preceding cntextual stimuli is a factr influencing visual judgments f nset rder. it seems natural t examine hw this factr cmbines with real nset asynchrny t determine such judgments. This will be the purpse f Experiment II. Table 1 Distributins f Chices: Experiment "Left First" Chice Simultaneus "Right First" Grup I Sequence S S,L Order 0 5 0 L,S Order 0 5 0 Sequence L S,L Order 5 0 0 L,5 Order 4 0 1 Grup II Sequence S S,R Order 0 5 0 R.S Order 0 5 0 Sequence R S,R Order 0 4 R,S Order I 3
INDUCED ASYNCHRONY EFFECf 49 First, hwever, it will be useful t develp a simple mdel fr tempral rder judgments, which frmalizes an interpretatin f hw bservers cnvert "real" stimulus asynchrnies int respnses. The mdel will facilitate the discussin f Experiment II. Generally speaking, the mdel characterizes the perceptual prcess as a "statistical decisin" based n a "nisy" internal representatin f the real nset asynchrny. Thus, it includes a measure f the hypthetical "nise level," and distinguished between the bserver's respnse bias and sensitivity. Frmally, the mdel is specified as fllws: Let X =A' + P-C, where A' (the "effect" f nset asynchrny), P (perceptual errr), and C (decisin r "criterin" errr) are mutually independent randm variables with expected values UA, Up, and uc, respectively. Let the randm variable X be Gaussian, with variance ai, and let UA = A, the nset asynchrny. Let the discrete variable R (the respnse) equal I if and nly if X<O, and let R equal 2 therwise. This mdel applies t tempral rder tasks in which A, the nset asynchrny f tw test stimuli, is an independent variable, and in which the bserver's tw respnse alternatives are "Stimulus 1 first" (RJ and "Stimulus 2 first" (RJ. This mdel predicts that the psychmetric functin (that is, the prprtin f Rz respnses as a functin f A) will be a nrmal give. The value f that nrmal deviate exceeded with prbability P(Rz I A) will be I Z(Rz I A) = - a(a + Up - uc), that is, a linear functin f A. This linear functin has a slpe f -(1/0), and assumes a value f zer when the nset asynchrny is am = Uc - Up. Since the parameters ax and am are independent, the mdel is ne which characterizes the slpe and the lcatin (r A intercept) f the psychmetric functin as separate aspects f perfrmance. Experimental manipulatins ther than varying A, may influence the slpe r the lcatin f the psychmetric functin, r bth. Changes in slpe are attributed in the mdel t changes in ax, that is, in the ttal "nise" level. Changes in the lcatin f the functin may be due either t changes in respnse bias (uc) r t changes in the mean perceptual errr (up), r t bth. Only am, whse value depends n bth, can be estimated frm TOJ data. This inseparability f the tw different surces f errr has nt ften been emphasized, althugh mdels similar t the present ne have been emplyed in analyzing tempral rder data. Barn's (1969) "nise thery" is similar in many respects t the present mdel, except fr his cntentin that "failures t crrectly discriminate the rder f tw stimuli" are due slely t a type f perceptual errr. Hwever, if ne carefully cnsiders his use f a rating respnse in the tempral rder task, and his interpretatin f ratings as reflecting multiple criteria, it becmes clear that the value f Uc must als be respnsible fr failures t discriminate rder crrectly. Rutschmann's (1966) analysis f the effect f bservers' vert rientatin n TOJs emplyed a versin f the present mdel in which tic was implicitly assumed t equal zer. With am then theretically equal t Up, lim was interpreted as the mean difference in "arrival latency" between the fixated and peripheral test stimuli. While it is very plausible t interpret Up as the mean difference in arrival latency (r in "transmissin times"), there culd be additinal cmpnents f the variable P whse means are nnzer. Hence, using am as a measure f latency difference depends n the tw assumptins (i) that there are n such ther cmpnents fp, and (li) that Uc = O. The use f cnverging evidence, reactin time data f Gibbn and such as the Rutschmann (1969), in cnjunctin with tempral rderdata seems a desirable practice in attempting t infer the rle f arrival latencies in tempral rder judgments. As fr respnse bias, Gibbn and Rutschmann attributed lcatin discrepancies between their bserved psychmetric functins and thse predicted frm RT data, t biased respnse criteria, which is plausible. Strictly speaking, hwever, the discrepancies culd have arisen frm surces f perceptual errr (cmpnents f P) t which the RT analysis was insensitive. In shrt, the inseparability f Up and tic pses a prblem fr the interpretatin f tempral rder data. A related prblem is that the ttal nise, ai, cannt be attributed arbitrarily t nly ne cmpnent f X, such as the perceptual errr. One purpse f this paper is t draw attentin t these cnstraints n permissible inference. If the variable P is interpreted as the difference in arrival latencies between stimuli, then the present mdel may be viewed as a special case f the apprach summarized by Sternberg and Knll (1973). Their representatin f the psychmetric functin as the cnvlutin f a decisin functin with an arrival latency difference distributin leads t the recgnitin f prblems similar t thse psed by the additivity f the means and variances f A', P, and C in the present develpment f the mdel (cf, sectin II-D f their paper). The present mdel is an imprtant special case fr three reasns: (i) It makes the generally
50 COLLYER acceptable assumptin that ttal errr is Gaussian distributed; (ii) It emplyes the "deterministic" decisin rule. which is the simplest f the rules cnsidered by Sternberg and Knll; (iii) it prvides a simple. but mathematically explicit. ratinale fr a methd f data representatin (i.e., treating the psychmetric functin as a nrmal give) which has frequently been applied t tempral rder judgment data (d. Hirsh. 1959; Rutschmann, 1966). EXPERIMENT II This experiment examines the jint effect f preceding stimulus ffset asychrny, and test stimulus nset asynchrny, n perfrmance in an nset rder judgment task. T specify these tw independent variables mre precisely, let the test nset asynchrny be dented A l, and defined by T L and T R are the (clck) nset times f the left and right test stimuli (Stimuli C and D in Figure la), respectively. Similarly, let the preceding stimulus ffset asynchrny be dented Az, defined by A 2 =T~ - T:. Tt and T: are the (clck) ffset times f the left and right preceding stimuli (Stimuli A and B in Figure Ia), respectively. The main purpse f the experiment was t reveal the effects f Az n the slpe and lcatin f the psychmetric functin, in an "IAE cnditin," in which A l and Az were varied factrially. A cmparisn between these functins and thse btained in a mre cnventinal tempral rder task (the "simple cnditin") is als described. The mdel is used t draw preliminary cnclusins abut the rle f the IAE in tempral rder judgments. Methd Subjects. The authr and tw paid undergraduate assistants served as bservers. 1 Prcedure. The display and cntrl apparatus have been described fr Experiment I. Details f the IAE cnditin will be described first. The spatial cnfiguratin f stimulus displays was as in Figure Ia. The sequence f events within a trial was as fllws: (i) bth preceding stimuli were illuminated fr 1,000 msec; (ii) either light A alne r light B alne, r neither inducing light, remained illuminated fr anther 50 msec (these three pssibilities crrespnd respectively t A, = +50 msec, Az = -SO msec, and Az = 0 msec): (iii) an "all dark" interval f SO msec was presented; (iv) either light C alne r light D alne, r neither test light, was illuminated fr SO msec (these three pssibilities crrespnd, respectively t Al = -SO msec, A, = +SO msec, and Al = msec); and (v) bth test stimuli were illuminated tgether fr 500 msec, These five time "frames" were immediately cnsecutive and nnverlapping; thus the ttal duratin f the stimulus pattern was a cnstant 1,6SO msec. The central fixatin pint (see Figure la) remained illuminated thrughut the five "frames." The "dark" interval between inducing stimulus ffset and test stimulus nset n either side (left r right> f the display culd be SO, 100, r ISO msec, depending n the stimulus pattern defined by Frames ii and iv. The interval between "first ffset" and "last nset," within which all f the manipulated stimulus infrmatin was presented, was a cnstant ISO msec, Bth A, and Az assumed values f -SO, O. and +s msec with equal frequency, and values f the tw variables were cmbined factrially t define nine different stimulus patterns. Each bserver was seated in a testing chamber (Industrial Acustics Crpratin) and viewed the display unit thrugh a viewing tunnel external t the windw f the chamber. Viewing distance was abut 30 in. Observers were asked t judge the"nset rder", f the tw test stimuli, indicating their respnse n each trial by pressing ne f tw buttns (designated "left first," an R 1 respnse, and "right first," an Rz respnse). Trials were run in blcks f 135, with shrt rest intervals between blcks. Within each blck, the sequence f trials was randm, with the cnstraint that each f the nine stimulus patterns ccurred exactly 15 times. Typically, three r fur blcks cnstituted ne daily sessin fr each bserver. Three practice blcks and 11 data blcks were cllected. giving 165 bservatins per stimulus pattern per bserver. Finally, all three bservers were run in a "simple" tempral rder task, with n inducing stimuli: that is, lights A and B in Figure la were never illuminated. The design and prcedure f this simple cnditin, in which Al was the nly independent variable. were cmparable t the IAE cnditin, in which bth Al and Az were manipulated. A, assumed values ranging frm -SO msec t +s msec, in steps f 10 msec, randmly frm trial t trial. The sequence f events within a trial was as fllws: a fixatin pint lcated midway between the tw test stimulus psitins (crrespnding t psitins C and D in Figure l a), was illuminated fr 1,000 msec, fllwed by the illuminatin f the tw test nsets with asynchrny AI' The duratin f the stimulus illuminated secnd was 500 msec. The duratins f the respnse interval (2,000 msec) and the intertrial interval (l,ooo msec) were the same as in the IAE cnditin. Within each 165-trial blck, each f the 11 values f Al ccurred 15 times. Three practice and nine data blcks were cllected, giving 135 bservatins per stimulus pattern per bserver. Results Fr the IAE cnditin, the prprtins f "right-first" respnses cnditinal n each cmbinatin f A, and Az values are entered in Table 2 fr each bserver. Bth independent variables exert prnunced effects n respnse tendency. The directin f the effect due t manipulating Az is cnsistent with the results f Experiment I. Fr the simple cnditin, the prprtins f "right-first" respnses cnditinal n each value f A are entered in Table 3 fr each bserver. Theretical analysis. Cnsidering first the IAE cnditin, Figure 2 shws fr each bserver a plt f Z(R z I A l ), with Az as parameter. Fr each value f Az, a linear psychmetric functin has been fit t the data. These three functins differ in lcatin but nt in slpe fr each bserver, and appear t cnfrm reasnably well with the pattern f data.z The predicted respnse prbabilities are given in Table 2. A chi-square cmparisn f bserved and predicted respnse frequencies fr the pled data f all three bservers yielded a value f 3.53, which des nt apprach significance (p >.05, df = 5). By cntrast, functins which differ in slpe but nt in lcatin are clearly nt apprpriate, while functins which differ
INDUCED ASYNCHRONY EFFECT 51 Table 2 Observed P(R, IA,), Predicted P(R, IA,) in Parentheses, and Estimates f am, fr Each Value f A" and f ax, fr Each Observer, in the IAE Cnditin: Experiment II Observer C.C. R.H. J.W. A, = -50 msec A, = -50.01 (.0 I).08 (.07).33 (.29) A, = 0.04 (.05).14 (.12).37 <.(7) A, = +50.15 (.09).20 (.20).50 (.51 ) A, =0 msec A, = -50.19 (.16).23 (.23).36 (041) A, = 0 042 (.37).32 (.34) 047 (.50) A, = +50.51 (049).39 (AS).61 (.63) A, =+50 msec A, = -50.68 (.63) A8 (.50).54 (.54) A, = 0.84 (.83).63 (.63).64 (.62) A, = +50.84 (.90).79 (.74).77 (.75) amla, = -50 37.8 50.2 3504 amla2 = 0 12.7 27.7 2.0 amla 2 = +50.7 7.9-52.8 ax 38.6 67.1 153.8 Prprtin*.983.982.960 "Prprtin f variance accunted fr. in slpe as well as lcatin seemed nt t imprve the lit f the mdel enugh t warrant the estimatin f six, rather than fur, theretical parameters fr each bserver. Hence, in terms f the mdel, it is reasnable tu attribute the effect f A z in this experiment. slely t changes in the value f am. The value f ax and three values f am (ne fr each value f A 2 ) are entered in Table 2 fr each bserver, tgether with the prprtiun uf data variance accunted fr by the mdel. Nte that the present data are nt sufficient t determine the relative cntributins f Up and Ue t the IAE. Regarding the simple cnditin. predicted respnse prbabilities were btained.trm the linear functin which best tit the values f Z(R 2 I At) fr each bserver. These predictins. tgether with the prprtins f data variance accunted fr by the mdel, and estimates f am and ax fr each bserver, are included in Table 3. The fit f the mdel is adequate fr bservers c.c. and R.H.. but relatively pr fr bserver 1. W.. whse data depart frm mntnicity as well as frm linearity fr psitive values f At. 3 The validity f parameter estimates based n the latter set f data is therefre questinable. Hwever. if anything. it seems that the linear functin tit t bserver 1.S.'s data prvides an underestimatin f his sensitivity. since he des appreciably better n negative values f At. Thus ne can argue in general that all three bservers shwed higher discriminatin in the simple cnditin than in the 1AE cnditin. The lwer slpes (higher values f ux) in the IAE cnditin suggest that additinal "nise" is present when the inducing stimuli are added t the stimulus pattern. One interpretatin f this result is that the inducing stimuli in the IAE cnditin prduce lateral masking. which degrades the sensry registratin f the test nsets. Anther interpretatin is that bservers respnd, t sme extent, n the basis f A 2, and. t that extent. independently f At. Tw versins f this secnd hypthesis are: (i) that n sme prprtin f trials the bserver's respnse is "cued" r determined slely by the ffset rder f the inducing stimuli; and (ii) that the bserver respnds n the basis f a weighted cmbinatin f internal effects assciated with bth At and A 2 n erery trial. Bth versins f this hypthesis predict thilt: (i) the slpe f the psychmetric functin will be lwer in the IAE cnditin than in the simple cnditin; and (ii) that the slpe f the psychmetric functin wiii nt be independent f A 2 if sme values f A 2 exert mre cntrl ver the bserver's respnse than ther values. The lwer slpes (higher values f ax) in the IAE cnditin are cnsistent with the first predictin. Fr mst f the data. slpes that are independent f A 2 give a gd accunt f the experimental results." This is anther way f saying that the effects f At and A 2 are additive; hence. ne can draw the imprtant cnclusin that bservers utilize the infrmatin available abut A 1 t abut the same extent ver all values f A 2 Fr example, bservers d nt appear t base their respnses n the strnger f the tw internal effects assciated with A 1 and A 2 n each trial. It is interesting t nte that the results f Experiment II are incnsistent with the hypthesis that the bserver bases his respnse n the relative duratins f the intervals between inducing stimulus ffset and test stimulus nset n each side f the display. Since the duratin f the interstimulus interval between right ffset and nset is a decreasing functin f At. ne strategy available t the bserver is Table 3 Observed P(R, IA,), Predicted P(R 2 IA,) in Parentheses, and Parameter Estimates fr Each Observer in the Simple Cnditin: Experiment II Observer e.e. R.H. J.W. A msec -50.01 (.01 ).10 (.05).13 (.24) -40.02 (.03).07 (.09).25 (.29) -30.05 (.06).13 (.14).39 (.35) -20.08 (.12).19 (.22) A6 (AO) -10.26 (.21 ).28 (.31).54 (046) 0.40 (.34).38 ( 042).67. (.52) 10.55 (A8) 046 (.54).59 (.58) 20.59 (.64).62 (.65).70 (.64) 30.79 (.77).75 (.75).61 (.69) 40.86 (.87 ).89 (.83).68 (.74) 50.90 (.93).91 (.89).74 (.79) ax 26.3 34.5 66.7 am +10.9 +7.0-3.2 Prprtin*.986.982.835 "Prprtin f variance accunted fr.
52 COLLYER 9 JW.8 7 6 P.5 0 Z.4.3.2.1 A 2 ms 05 +50 0-50 t::. -I +1 +2-50 0 +50-50 0 +50-50 0 +50 Al ms Flgure 2. Results f Experiment B, fr three bllerver;s. Data pints reprellent ebserved prprtins f "right-nset-first" respnses. LInear functins shw the mdel's predicted pattern f results. The rdinate Is a Gaussian-transfrmed prbablllty scale (prblt scale). t respnd "right first" (R:J when the right ffset-nset interval appears shrter in duratin than the left interval, and t respnd "left first" (R t) therwise. The directin f the effect f A z is incnsistent with the hypthesis that bservers use such a strategy. This is s because the duratin f the right interstimulus interval is an increasing functin f Az Thus, under the duratin strategy hypthesis, the prprtin f Rz respnses is predicted t be a decreasing functin f Az. The data shw that the prprtin f Rzrespnses is an increasing functin f Az. Therefre, the hypthesis predicts that the directin f the effect f Az shuld be the ppsite f the directin bserved. A similar argument rules ut the hypthesis that bservers base their judgments n the relative velcities f apparent mtin n each side f the display. T summarize, Experiment II, tgether with the freging analysis, (i) prvides a demnstratin f the IAE; (ii) shws that the mdel gives ne reasnable and simple accunt f the pattern f data, in which the effects f At and A z are, t a clse apprximatin, additive with respect t a Gaussian transfrmatin; (iii) shws that the slpe f the psychmetric functins in the IAE cnditin differs systematically frm the slpe f the cmparable functin fr simple tempral rder discriminatin; (iv) advances tw types f explanatin fr this difference; and (v) shws that tw plausible hyptheses cncerning the basis f the bservers' judgments are incnsistent with the directin f the effect f Az. DISCUSSION In develping the mdel in its present frm, it was emphasized that changes in the lcatin f the psychmetric functin are prblematic, because Uc and Up cannt be separately estimated frm tempral rder data alne. The IAE is an example f this prblem. Further research will be necessary -in.rder t partial ut the relative cntributins f perceptual errr and respnse bias t the value f am. One can speculate abut the ptential theretical reslutins f this prblem in the case f the IAE. Perhaps the mst exciting pssibility is that the variable A z cntrls rapid shifts in the distributin f attentin ver the visual field. If, as several investigatrs (e.g., Sternberg & Knll, 1973) maintain, the arrival latency f attended stimuli is shrter than that f nnattended stimuli, then, under the attentin hypthesis, the IAE wuld be a "prir entry" effect under very gd stimulus cntrl. Furthermre, perfrmance in infrmatin-prcessing tasks ther than tempral rder might be influenced by similar inductin manipulatins. It wuld be interesting t knw, fr example, whether Az influences the accuracy f recgnitin f letters presented briefly in the spatial vicinity f the inducing stimuli. A secnd pssibility is that Az influences the value f Up, nt as a cnsequence f shifts in attentin, but mre directly, and withut effects n ther kinds f prcessing. Third, the IAE may be "simply" a
5 A c B D A c ~ 1 0 10'--+ B ~---- 2 ----0+ 020' ) (a) T,, INDUCED ASYNCHRONY EFFECT 53 An induced asynchrny effect can be btained using the cnfiguratin f stimulus psitins shwn in Figure 3a. The time curse f their presentatin is again illustrated by Figure lb. As befre, the nset f that test stimulus clsest t the first preceding stimulus t be extinguished tends t be judged earlier than the ther test nset. Figure 3b is a "space-time diagram" representing this dynamic stimulus pattern. In this diagram, the rdinate represents spatial psitins alng the hrizntal dimensin f the stimulus array; the abscissa is time. Thus, tke velcity f apparent mtin between, fr example, psitins A and C is represented by the slpe f the dashed line cnnecting the ffset at A and the nset at C. Nte that the IAE, which in the example f Figure lb is a tendency t judge the nset at C t be earlier than the nset at D, wuld have the effect f frcing the velcities f apparent mtin tward equality. A simpler example is shwn in Figure 4a, which represents a three-stimulus array. The tempral pattern f illuminatin is as fllws: ne f the end lights (A) is presented briefly, fllwed after a brief dark interval by the simultaneus presentatin f the middle light (B) and the ther end light (C). Observers ( b) Figure 3. (a) Linear array versin f IAE display. (b) Representatin f an IAE trial using linear array. Slid lines dente the n perids f stimuli In spatial psitins given by rdinate; dashed llnes represent apparent mtin between successive stimuli. respnse bias effect, reflecting changes in the value f Uc alne. Finally, there may be sme cntributin t the effect frm bth perceptual errr and respnse bias. The existence f these diverse and interesting pssibilities shuld encuragethe develpment f new experiments and thery. Many prblems f current interest in perceptin (e.g.. tachistscpic letter recgnitin, visual masking, apparent mtin, tempral rder, and duratin discriminatin) are investigated by requiring bservers t extract frm a stimulus pattern, within a very brief interval f time, infrmatin which is sufficient t discriminate ne pattern frm anther. Kahneman (1968) has made a related bservatin in discussing varius limiting cases f visual masking paradigms. Investigatrs in a number f prblem areas, then, are interested in discvering general principles gverning the perceptin f rapidly changing visual displays. The IAE is a relatively simple dynamic phenmenn which may be useful in discvering such principles. Althugh a detailed parametric analysis has nt yet been carried ut, inspectin f a few variants f the effect has revealed interesting similarities between the IAE and three ther dynamic perceptual phenmena. The fllwing discussin develps these similarities and suggests ne way f cnceptualizing them. s 10J -: +. -. - -I,, //~- lei,,, +1 ~ Figure 4. Space-time diagrams representing fur dynamic perceptual "illusins": (a) simple frm f IAE, (b) tau effect, (c) kappa effect, (d) simple frm f rabbit effect. The paradigms are arranged In the figure as fllws: Tp rw, "even" spacing and "uneven" timing; bttm rw, "uneven" spacing and "even" timing; left clumn, tempral judgment tasks; right clumn, spatial judgment tasks. Arrws represent the directin f perceptual distrtin reprted fr each paradigm. The bserver may have a tendency t judge the spatial psitins r times f presentatin f the three stlmud in such a way as t preserve cnstant velcity f apparent mtin, which is represented by the dashed line. -I, /' ~ IbJ,.: Idl +1
54 COLLYER viewing this pattern tend t judge the nset f B t be earlier than the nset f C. (The phenmenal impressin is weaker than in the riginal IAE cnfiguratin; hwever, this simple pattern may be the IAE's minimal frm) Again, the effect is in the directin f minimizing the difference in slpe between the apparent mtins A-t-B and A-t-C. Three ther effects in the literature (which have been studied cutaneusly as well as visually) are als represented in Figure 4. The tau effect (Helsn & King, 1931) and the rabbit effect (Geldard & Sherrick, 1972) are spatial distrtins in the judged psitin f the secnd f three sti"1,uli. The kappa effect (Chen, Hansel, & Sylvester, 1955), like the IAE, is a tempral distrtin. The tau and Kappa effects have. at varius times, caught the imaginatin f wrkers in perceptin because these phenmena demnstrate interdependence between psychlgical space and time, the main dimensins f ur sensry experience. Althugh it has been recgnized (Chen, 1967)that the tau and kappa paradigms are, in a way, "mirrr images" f each ther, an attempt t classify spati-tempral "illusins" did nt appear t be cnceptually prmising until recently, with the discvery f the "rabbit," and nw the IAE. Figure 4 represents an attempt by the authr t rganize the essential similarities and differences amng these fur phenmena. The figure captin summarizes this rganizatin. The simple IAE and the tau effect have been bserved in stimulus patterns where the tw spatial intervals separating the three stimuli are equal, but the tempral intervals are unequal. The rabbit and kappa effects have been bserved under cnditins f equal time intervals but unequal spatial intervals. In all fur phenmena, the perceptual distrtin is in the directin that wuld be expected under the hypthesis that bservers have a tendency tward cnstant velcity in the perceptin f apparent mtin. Fr example, the tau effect in Figure 4b is a distrtin in the judged psitin f the middle stimulus, which tends t be displaced in psychlgical space tward the third stimulus, which is clsest t it in time. It may be prfitable fr future investigatrs t cnsider these fur paradigms tgether, and t generalize them; until nw, research effrts have tended t fcus n ne r anther f the effects. Sme unanswered questins, fr example, are: (i) Can all fur phenmena be btained ver the same ranges f space and time? (ii) What is their relatinship t ther infrmatin-prcessing prblems, such as masking? (iii) Is the bserver's task (time r space judgment) the nly difference between tau and kappa under cnditins in which bth the spacing. and the timing f the three stimuli are uneven? REFERENCES BARON. J. Tempral ROC curves and the psychlgical mment. Psychnmic Science, 1969, 15, 299-300. COHEN. J. Psychlgical time in health and disease, Springfield, Ill: Thmas. 1967. COHEN. J., HANSEL, C. E. M., & SYLVESTER, J. D. Interdependence in judgments f space, time and mvement. Acta Psychlgia, 1955, 11, 360-372. GELDARD, F. A., & SHERRICK, C. E. The cutaneus "rabbit": A perceptual illusin. Science, 1972, 178, 178-179. GIBBON. J.. & RUTSCHMANN, R. Tempral rder judgment and reactin time. Science, 1969, 165,413-415. HELSON, H.. & KING, S. M. The tau effect: An example f psychlgical relativity. Jurnal f Experimental Psychlgy, 1931. 14. 202-217. HIRSH, I. J. Auditry perceptin f tempral rder. Jurnal fthe Acustical Sciety famerica, 1959, 31, 759 767. KAHNEMAN. D. Methd, findings and thery in studies f visual masking. Psychlgical Bulletin, 1968,69,404-425. KOMDA. M. K., FESTINGER, L., PHILLIPS, L. J., DUCKMAN, R. H., & YOUNG, R A. Sme bservatins cncerning saccadic eye mvements. Visin Research. 1973, 13. 1009-1020. RUTSCHMANN, R. Perceptin f tempral rder and relative visual latency. Science. 1966. 152, 1099-1101. STERNBERG. S.. & KNOLL. R. L. The perceptin f tempral rder: Fundamental issues and a general mdel. In S. Krnblum (Ed'>, Attentin and perfrmance IV. Press. 1973. NOTES New Yrk: Academic 1. One bserver, J.W., had previusly been a subject in Experiment I, Grup II; his judgment f Sequence R was "left first," a reversal f the IAE. That this ne respnse des nt reflect a basic difference between J. W. and mst ther bservers is shwn by the results f Experiment II, in which all three bservers, ver many trials, displayed the IAE in a cnsistent way. 2. The slpe (frm which an estimate f X can be derived) was btained by applying simple regressin analysis t the.averages f the three Z values assciated with each value f At. The Z intercepts (frm which estimates f the crrespnding values f am can be derived) were btained by averaging the three Z values assciated with each value f Az 3. A chi-square cmparisn f bserved and predicted respnse frequencies in the simple cnditin yielded the fllwing results. Obtained values f 12.16 and 16.16 fr bservers c.c. and R.H., respectively. indicated n significant differences (p >.05. df = 9). An btained value f 40.52 fr bserver J.W. was significant (p <.005), indicating pr crrespndence with the mdel fr this set f data. 4. Chi-square cmparisns between bserved and predicted respnse frequencies were carried ut fr each bserver's data. The data f bservers RH. and J. W., with btained values f 5.70 and 4.65, respectively, shwed n significant departure frm the predictins f the mdel (p>.05, df = 5). Hwever, a value f 19.25 was btained fr C.C.'s data, which represents a significant difference. Mst (68"70) f this difference is attributable t the data fr A 1 = +50, which displays a slightly lwer slpe than predicted. As indicated in the text, ne interpretatin f such a slpe decrement is that there is a slightly higher tendency t respnd n the basis f Az fr this value f Az (Received fr publicatin May 7, 1975; revisin received September 23, 1975.)