an information integration approach to phenomenal causality

Memory & Cognition1993, 21(6), 785-801

An information integration approachto phenomenal causality

ANNE SCHLOTI’MANNUniversity College, London, England

and

NORMAN H. ANDERSONUniversity of California, San Diego, California

Phenomenal causality was studied by using Michotte’s launch event, in which successive mo-tion of two objects evokes an immediate perception that the first motioncauses thesecond. Infor-mation integration theory was used toaddress the complementary issuesof invariant perceptualstructure and individual differences inphenomenal causality. Three informational cues were variedconjointly: temporal and spatial contiguity ofthe two motions, and the ratio of their speeds. Thedependent measure was a judgment of degree of causality or naturalness. The results showedthat individual differences were related to these instruction conditions; the subjects showed fivedistinctive response patterns. Two were the modal patterns elicited by the instructions, and theothers fell in between. The averaging model gave a good account of the data, with meaningfulparameter estimates. Individual differences were localized in cueevaluation, whereas their integrationinto a unifiedjudgment followed an invariant averaging rule. The results allowsornereconeilia-tion between Michotte and his critics.

Everyday cognition relies heavily on our recognizingcausal relations among events. This article concerns phe-nomenal causality, as it was investigated by Albert Michotte(1946/1963). Michotte’s phenomenological approach hasevokedconsiderable criticism as well as conflicting resultsin subsequent work. Individual differences and their in-terpretation have been a central point of controversy.

The present study applies an information-integration ap-proach to phenomenal causality. The basic concern istwofold—with the invariant structure of phenomenalcausality, and with the individual difference controversy.These two concerns are complementary: Individual dif-ferences cannot be understood at a merely descriptivelevel; a theoretical model of the process in which theyfunction is required as well. Accordingly, this study isfocused on a fine-grained parametric analysis of multipleperceptual cues and on a quantitative model for the wayin which these cues are integrated into a unitary causalimpression. This model then provides a tool for analyz-ing individual differences in some depth.

Michotte’s ClaimsMichotte exploredconditions in which people say they

see one event causing or producing anotherevent. A prime

This work was supported by Grant PHS HD22932 from the NationalInstitute of Child Health and Development. We thank John Kruschke,Alan Leslie, and Peter White for valuable comments on a previous ver-sion, and Bill Gayer for programming support and discussion. Addresscorrespondenceto A. Schlottmannat the Department ofPsychology, Uni-versity College London, Gower Street, London WC1E 6BT, England.

example is his well-known launch event, illustrated in themotion sequence of Figure 1. Most people see the firstobject, A, pushing (launching) the secondobject, B, thusproducing its movement.

Michotte studied extensively the determinants of phe-nomenal causality, such as temporal and spatial contiguityat the point of impact, and speed of the objects A and B.The optimal conditions for the causal impression, as Mi-chotte stressed, depend on the particular configuration ofstimulus parameters. At higher speeds, for example, largerdisruptions in spatiotemporal contiguity are necessary ifthe causal impression is tobe destroyed. Given a suitablebalance in motion parameters, observers are said to im-mediately experience one event causing another (also seeMichotte & Thinès, 1963/1991).

Michotte considered such phenomenal causality to ariseas a Gestalt property of specific motion sequences. Sucha perceptual organization for causality could account forthe ease that people seem to have in recognizing somecausal relations. Indeed, even infants appear to react tothe specifically causal structure of launch events (Leslie,1982, 1984; Leslie & Keeble, 1987; Oakes & Cohen,1990; also see White, 1988).

Michotte’s claim had two aspects, one empirical, theother theoretical. The empirical claim was a demonstra-tion of phenomenal causality in visual scenes devoid ofactual causality. This is akin to Duncker’s (1935/1945)famous example of a light going on at one end of a hall-way at the moment a door is shut at the other end, whichyields a causal illusion that runs counter to factual knowl-edge. Phenomenal causality may thus be considered a per-

785 Copyright 1993 Psychonomic Society, Inc.

786 SCHLOTTMANN AND ANDERSON

A B —~

U ~I ~U

Figure 1. Prototypical launch event. Object A moves toward objectB, which is stationary. Immediately after collision, objectA is sta-tionary and object B moves away from it.

ceptual illusion, analogous to apparent movement. Itshould not be confused with the perceptual correlate ofphysical causation (see Runeson, 1977).

The main objection to this empirical claim is that noteveryone experiences the Michotte effect (Beasley, 1968;Boyle, 1960; Gemelli & Cappellini, 1958). Under sup-posedly optimal conditions, at least 10% of subjects re-port no causal perception, and many subjects shift betweencausal and noncausal reports. This matter was known toMichotte and was reported by Boyle (1960, 1972, 1973)and by Crabbé (1967, as cited by Boyle, 1973, and byThinès, Costall, & Butterworth, 1991), who had workeddirectly under Michotte. Why some people do not ex-perience phenomenal causality, or do not experience itall of the time, is unclear. The effect is real for most peo-ple, however, as has been shown by independent replica-tions (Gordon, Day, & Stecher, 1990; Millar, 1977;Schlottmann, 1987; Schlottmann & Shanks, 1992; White,Corballis, & Corballis, 1986, as cited in White, 1988;also see Johansson, von Hofsten, & Jansson, 1980).

Michotte’s theoretical claim was that this perception ofcausality was direct, unmediated by inference. He linkedthis claim with the further claim that it was not derivedfrom experience, but innately determined. Michotte’sview of the natureof perception is akin to that of Gibson(1967; seep. 142), who notes that he was “in strikinglynear agreement” with Michotte (for discussion of theseissues, see Costall, 1991).

The objections to Michotte’s theoretical claim also reston individual differences—especially on results suggest-ing that subjects’ reports are influenced by prior knowl-edge (Gemelli & Cappellini, 1958; Natsoulas, 1961). Butexperimental demonstrations of such experiential effectshave been scarce (Gruber, Fink, & Damm, 1957; Powes-land, 1959) and can be explained as sensory adaptation,which would not trouble Michotte. Nevertheless, thesefindings are sometimes interpreted to mean that phenom-enal causality is based on learning and inference (e.g.,Bruce& Green, 1990; Weir, 1978), a conclusion that goesfurther than the data.

Michotte himself did recognize that there could be ex-periential influences on phenomenal causality (e.g.,p. 256). He did not consider, however, how experientialand perceptual factors would interact. Indeed, Michotte

generally played down the role of experiential factors asmuch as possible.

Limits of Previous MethodologyElimination strategy. Michôtte conducted two basic

types of investigations, both intended to eliminate or min-imize the influence of prior experience. To demonstratethe generality of phenomenalcausality, he presented sin-gle launch events to large numbers of naive observers.His more quantitative investigations involved only a fewexperienced observers, generally including members ofhis laboratory. Michotte presumed that naive observerslacked the opportunity to develop attitudes towardlaunchevents, and that highly experienced observers would becapable of separating beliefs and perceptions.

The elimination strategy was not very successful, as issuggested by the individual differences in phenomenalcausality noted above. Indeed, Michoue’s procedures didnot escape the acid criticism of Joynson (1971), who sug-gested that his results may have been heavily influencedby subjects’ knowledge of the hypothesis and/or by theimplicit suggestions in such questions as, “could you bea little more precise?”

An alternative approach is adopted here. It may not bepossible to exclude experiential effects, but they can bemanipulated. This may provide some opportunity to dis-entangle the relative contributionsof experiential and per-ceptual factors.

Choice methodology. The inconsistent results citedabove may be amplified by ambiguities inherent in theuse of categorical choice data. Nearly all investigatorshave adopted Michotte’s procedures of categorical re-sponse. They have either obtained choices among pre-scribed response categories or have collected free verbalreports to be categorized by the experimenter.

Three problems, notmutually exclusive, arisewith suchcategorical data. First, individual differences may existamong subjects evaluating the different cues; optimal con-ditions for one subject may be suboptimal for another,as already noted by Michotte (e.g., p. 111). Second, dif-ferent subjects may employ different decision criteria forassigning cases to the causal or noncausal categories.These are likely tobe affected by experimental procedureand instruction. Third, categoricaldata are not very sen-

PHENOMENAL CAUSALITY 787

sitive. With categorical data, it is difficult to determineoptimal conditions, especially across different apparatus.Forall these reasons, Michotte’s account of what consti-tutes an optimal launch event, on which subsequentworkers have focused, may lack generality.

Information Integration TheoryThe concepts of information integration theory (Ander-

son, 1974, 1981, 1982, 1991) introduce a new researchfocus to the study of phenomenal causality. This focusis on multiple determination, on how different cues arecombined into a unified impression. Michotte had alreadystressed that phenomenal causality depended on the par-ticular configurationof variables, but he typically studiedtheir effects one at a time. The present approach over-comes this limitation.

The integration approach does not entail any commit-ment about the experiential as opposed to the perceptualbasis of phenomenal causality. Both aspects must contrib-ute to adults’ reports of perceptual experience, and theintegration frameworkallows the study of their joint oper-ation in producing an impression of phenomenal causality.

Continuous response. In the present approach, we em-ployed a continuous response measure. This was appropri-ate, since Michotte had already pointed out that observersexperienced graded differences ingoodness of the causalimpression (e.g., p. 95). Continuous measures are moreinformative and powerful than the choice measures usedin previous work on phenomenal causality. They alsoavoid the cited difficulties stemming from the operationof the decision criterion. Accordingly, subjects were askedto judge goodness of the causal impression on a continu-ous scale.

A continuous measure may seem odd, for, in naivecausality, event A is or is not the cause of event B. How-ever, continuousjudgments of causality make sense in twoways. First, people can be more or less confident that Ahas caused B, even with all-or-none causation. Second,rarely is A a necessary and sufficient cause of B—eventsnormally have multiple causes, in which case A can havemore or less causaleffect on B. Preliminary work (Schlott-mann, 1987) showed that subjects considered both typesof judgment meaningful.

Parametric variation. In the present study, we inves-tigated how three variables conjointly influence the causalimpression: temporal delay and spatial gap at the pointof impact, and the ratio of the two objects’ speeds. Thestimulus values on these dimensions were chosen to coverthe transition range between definite causality and definitenoncausality. Only in this transition region will gradeddifferences in goodness of the causal impression be found.This selection followed Michotte’ s own specificationsfairly closely, supported by the preliminary work.

Each subject is exposed to multiple launch events cov-ering the range of stimulus values. The pattern of judg-ments for this set of events provides an overall pictureof how the goodness ofthe causal impressiondepends on

the three stimulus dimensions. With this procedure, thejudgment of any particular configuration can be seen inrelation to the overall integration pattern and optimallaunch events can be determined individually.

Model-based analysis. From the information integra-tion perspective, the conjoint action of multiple cues is boththe focus of empirical analysis and a base for theory. Inprevious studies, concern was with the consistency of somestimulus configuration to elicit a causal response across in-dividuals. The present concern, in contrast, is with the pro-cesses by which each individual arrives at this response.

The integration framework distinguishes three broadstages of processing. In the valuation stage, the informa-tion value of each stimulus variable is assessed indepen-dently, and the physical cues are transformed into sub-jective, task-specific representations. In the integrationstage, these separate representations are combined to formthe causal perception. Finally, the perceptual experienceis translated into a judgment response. The parametervalues for the separate stimulus variables as well as therule governing their integration can be determined fromthe overall pattern of judgments by virtue of functionalmeasurement methodology (Anderson, 1974, 1981).

Individual differences. Individual differences may belocated in the valuation or integration stage of the pro-cess. Different subjects may employ different rules to inte-grate the informational cues, a result that would raiseproblems for Michotte’s position. Alternatively, the in-tegration rule may be invariant, but the information valueof a given cue may differ across subjects.

The working hypothesis, on the basis of an initial study(Schlottmann, 1987), is that the integration of gap anddelay will obey an invariant averaging rule. Individualdifferences will have their locus in the valuation of theseparate cues. This hypothesis is compatible with Mi-chotte’s ideas of an invariant perceptual structure.

To allow for individual differences, single subject de-sign is employed with a large group of subjects. Thus,response patterns that vary across but are stable withinindividuals can be distinguished from mere responsevari-ability. In addition, the degree to which responsepatternsare consistent between individuals can be assessed.

Some individual differences may stem from differentattitudes toward causality. With multiple stimulus presen-tations, as was well known to Michotte, the question ofhow the task is interpreted is very important. The pre-dispositions brought to the experiment by naive observerscannot be known, but manipulating instructions may helpcontrol interpretation of the task. Accordingly, two in-struction conditions were used in the present study, onefor the customary judgments of causality, the other forjudgments of naturalness.

METHOD

General DesignSubjects saw launching scenes like that of Figure 1 in which three

factors were manipulated: the size of the spatial gap, the temporal

788 SCHLO~TMANNAND ANDFRS~)N

delay at the point o~impact, and ftc A:B speed ratio I tfc Thj ‘cEach subject was exposed to a 4 Ig p) x 4 dela~ 4 ~specd -a(10) factortal design that yielded 64 different scenes

Two instruction conditions were used In one, the ,uhectsjud4 ctheir confidence that A’s movement did r did not cause B’s movement. ti the other the subjects juugcd the naturalness of the c ll~~ion sequence. The confidence judgment was taken to representMichotte’~phenomenal causality Tne naturalness Judgrsent wasexpected to be influenced more by the physical reality of the visua

t

events

MaterialStits ulus scenes weregencreted on a Macintosh SE ~omputer with

the VideoWorks II Animation software. Playback was controlledby the VideoWorks II HyperCard driver. During playback. thescreen was updated every 17 msec. With this updcting fceuuency.an appearance of smooth, continuous motion was achieved.

Each scene consisted of the following sequence of events: A gray5 x 5 mm square (A) faded in on the left together with a blacksquare (B) of the same size in the middle of the screen. 6.~5cm

get of A. Th~ quarcs rested in (tier ~tar ~ngP0 iUo~tsfo.2 sec Then the left square moved at the constant velocity of

49 cm sec toward the middle, stopping 2.1, 1 4 0.7, or 0 mm beft cc square B. (This range was smaller than indicated by Michotteoccause he had used bjects much lar4er ifan use” I for the studic’manipulating spatial contiguity.) Square B started to move 6cr 170.119 68 or 17 msec, with a constant velocity of 49. 2-+.5 12,2,or 6.1 cmisec for 6.75 cm. These velocity combinations yieldedA:Bspeedratiosofl’l,2:I,4:1 and8:1. Bothsquarestl-enstayed‘,t Vest for I sec and “aded out. A scene therefrre Ia ed ~.oiut 2.53 6 ~ee

Each subject judged six sequences of the comolete set of64 scenesThe orders for three sequences were randomly generated for eachsubject The reverse sequences were used to counterbalance anyeffects of practice or oraer.

The experiment had two supplc’rentcr, coiditiens Befor~theomit task each subject was exposed ~oiou, ~ep i~a005 lone o’he three 4 x 4 subdesigns with the lesel of the th d factor fixedeta speed ratio of 4:’ a gap ofO ~ni, ~r a delay ci 68 tiSs... respec-tively. These data were collected for the modet estimation proce-dure, but were not used (see the Appendix). Type of subdesign wasrialanced across instruction conditions in the main task. This factorhad no substantial effect on juagments ard ~snot considered further.

Following the main task, each subject judged the subjective sizef gap and delay for three replications each of the 4 x 4 (gap x

delay) subdesign with the speed ratio fixed at 4. 1. i nese compo-nent ratings were collected to check for configural effects on cuealues, as noted later in the discussion of the 17-msec condition.

ProcedureThe subjects were tested individually in one session of about 2 h.

T icy v crc free to take short breaks throughout. They sat aboutI.e ro f-out the mon’tor (12 x 18 cm’ in the dimly lit experimert-

tal room They were told to focus on the area around the impactp silt and to keep a c Jnstant distance from the screen. The subjects

,aje th or judgments by moving a mouse along ar l i-cm un-rarkcd graphic rating scaledisplayed in the lower part of the screen.This scale had a resolution of 300 points. The instructions, displayf stimulus scenes and on-line collection of ratings were self-pacedr a H perCard ,nvironment.

Thy n txictions for the causality and na..uralness judgments wered rticall’, pnrased. except whet’ the task’ th v “s ~s ‘crc con--crned. rise ‘uNects were first showr foer intermemete c’amples—that is scenes with m ‘derate gaps. delays, and velocity ratios. Aftereach scene, they were asked. “Did it look like B moved becauseA hit it) Was B’s movement produced by A?—Or d d B take offon its owrC” or Did the collision between A and B look naturalto iou? Could it happen this way?—Or did the collision look im-

e and artifcial “‘ The instructions stressed that the subjectsw~rvwatching animation sequences in which “anything was pos‘, p, “and that no “real’ collision was ever involved. This instruc

r s s ueveloped t focus them on phenomenal causality ratherpresentation of concrete physical events,

e ~ating cisk vas introduced thu5. “Your task in this exper’-

me it will be to ,judee just how confident you are that A caused ordid “o’ cause B” or ‘just how natural a collision tooks “ The nstructioris included four anchor stimuli, to set up a frame of refer-ence for the rating scale. The high anchors had no gap and no delay; the low anchors had the largest gap and largest delay. Thesubjects were told that, in the experimenter’s judgment. these sceneswere among the most and least causal (or natural) scenes that thc~would see, althougo they need not agree with her opinion at allThen subjects practiced using the rating scale without feedback (10tr’als in the main task, 16 in the preliminary subdesign). Practiceand end anchors helped equate the response rang~.across sub~ectsthereby facilitating the pooling of individuals with similar integra-tion strategies. Anchor stimuli were repeated after the practice, andadditional clanfica~ionsand practice were given on demand. Numercu c~perimentsha is w n this rat ng orocedure with end ancfloto be effectise in e iminating nonlinear oiases in the resporse scale(Anderson, 1982, chap. 1).

SubjectsSixty UCSD undergraduates participated in the experiment to ful

fill a course requirement. Gender was balanced acrossconditi ns.All subjects claimed to have normal or corrected to normal vision

RESULTS AND DISCUSSION

The overall results can be summarized simply. The tn-tegration of the three cues followed an in”ariant averag-ing rule. The valuation of each cue, in contrast, showedI~r~eindividual differences. Th~se individual differenceshowever, exhibited a small number of distinct patterns.

A key to the analysis lay in the interaction between thetwo judgment conditions and individual differences Thetwo judgment conditions produced different responsepat-terns, as was expected. Individual differences were cxpected as well, and each subject served in six replicationsto enable reliable individual analyses. Inspection of theseindividual analyses showed that subjects differed widelyin the effect of speed ratio, which led to five distinctiveresponse patterns. These grouped themselves meaning-fully when considered together with the experimental ef-fects of the two instruction conditions: Two of the indi-vidual difference groups mapped onto the modal responsepatterns elicited by the two instructions’ the other threeformed an orderly spectrum between these poles It ap-peared that subjects had preexperimental predispGsitionsfor one or the other of the two kinds of judgments, andthese predispositions interacted with the experimental in -

structions to produce the five response patterns.

Initial Analysis: Integration Patternsfor Instruction Conditions

The mean results for the causality judgments are showrin the top row of Figure 2. Each panel shows the integra-tion pattern for the listed pair of variables. The top leftpanel, for example, shows the integration pattern for gapand delay. Smaller gaps produced markedly better im-


is

aBa

‘00a

aa00

0

Figure 2. Mean judgments of causality/naturalness for two instruction conditions. The three panels in each row give the three two-factor views of the three-factor integration (see text).

pressions of causality, as is shown by the upward sweepof the curves. Shorter delays generally produced bettercausal impressions, as is shown by the vertical separa-tion among the curves. Speed ratio (curve parameter inthe middle and right panels) had only small effects, al-though larger speed ratios produced somewhat bettercausal impressions.

The naturalness judgments, in the bottom row of Fig-ure 2, show a different pattern. This group exhibits largereffects of speed ratio, as is shown by the larger separa-tion among the curves in the bottom rightpanel, and largeeffects of delay, as is shown by the upward sweep of thecurves. In contrast, gap had small effects, as is shownby the small horizontal extent ofthe curves in the bottomleft and center panels (see the Appendix for statisticaldetails).

An unusual mode of graphing was employed in Fig-ure 2. Consider the two center panels. The four curvesrepresent the four speed ratios for each instruction con-dition; the horizontal extent of the curves in each panelrepresents the effect of gap. This horizontal spacing isbased on the marginal means of the gap factor in the de-sign. In this way, the gap effect can be read off the hori-zontal axis, whereas slope is normalized. This mode ofgraphing was found tobe more meaningful than the stan-dard factorial graph in which multiple slopes were hardto assess.

Integration Patterns for IndividualDifference Groupings

More finely grained analysis was achieved through in-spection of the individual subjects’ data. The individualsubjects were found to differ widely in preferred speedratio. The group differences seen in Figure 2 alreadypointed to speed ratio as a source of variation in judg-ment, but the group means oversimplified the results. Ac-cordingly, the subjects were classed in five groupings onthe basis of which speed ratio yieldedthe highest response.In Figure 3, each layerof the graph shows the results forone of these five groupings. The optimal speed ratio foreach group is indicated by the arrows in the right columnof Figure 3.

The patterns found in the top and bottom rows of panelsin Figure 3 are strikingly similar to those found for themean instruction conditions in Figure 2. Group 1 (top),with a large gap and negligible speed effect, exhibits themodal pattern of causality judgments. All but 1 of the 13subjects in Group 1 were from the causality instructioncondition. Group 5 (bottom) shows the modal pattern fornaturalness judgments, with a small gap and large speedeffect. All but 3 of the 14 subjects in this group receivedthe naturalness instructions.

The remaining three groups show intermediate patterns.This grouping revealed the top-to-bottom trends visible inFigure 3; gap decreases ineffect, whereas delay and speed

delay x speed

causalityinstruction

2.1 0.7 mm gap 2.1 0.7 mmmi gap 170 119 68 17 ms delay1.40 1.40


delay x speed

50

250

5,55,5

5-,

515

0‘I0eli

CeI-

CeI.)

250

50gap gap delay

Figure 3. Mean judgments of causality/naturalne.ss for five groups of subjects. Each row of the graph represents one group, classifiedaccording to which speed ratio yielded the highest judgments (see arrow in rightmost panels).


Table 1Distribution of Subjects from Causality and Naturalness Conditions in Five Groups

Group

ratio increase. The grouping is reliable, since it is basedon 6 replications of the 64 scenes for each individual.

Speed ratio, it seems, is a rather different perceptualcue from the delay and gap variables. For delay and gap,values closer to zero are more causal, and subjects uni-formly agreed on that. All speed ratios presented are pos-sible, however, for this is determined by the relativemasses of the objects and the elasticity of the collision(ignoring friction). The effectof speed ratio is only looselyconstrained by physical considerations, and more depen-dent on individual predisposition and preference. The oc-currence of individual subgroupings on this factor is thusnot entirely surprising, although not foreseen on the ba-sis of Michotte’s reports.

Causality, Naturalness, and Individual DifferencesThe present analysis indicates that individual differences

were related to the experimental instruction conditions.The two conditions elicit different information process-ing, as illustrated in Figure 2, and these differences reap-pear even more clearly in the individual difference group-ing of Figure 3: Two groups reflect pure effects of theexperimental manipulation, and the other three are inter-mediate in terms of the data patterns. They are also in-termediate in terms of the distribution of subjects. Thenumber of subjects judging causality decreases fromGroups 1 through 5, while the number judging natural-ness increases. These trends are shown in Table 1.

Instructions thus appear to have interacted with indi-vidual differences. The subjects seem to have had pre-dispositions toward one or the other of the two instruc-tion sets. A predisposition for causal judgments, forexample, would be enhanced by causality instructions anddepressed by naturalness instructions. Thus, causality in-structions enhanced the role of spatial contiguity anddepressed the role of the relative speeds; naturalness hadthe reverse’ effect (see Figure 2). Nonetheless, some sub-jects in the causality condition, but predisposed towardnaturalness, would have considered speed ratio. Con-versely, some subjects in the naturalness condition, butpredisposed toward causality, would have considered gap(see Figure 3). Hence, the effect of each stimulus cue de-pends partly on the instructions and partly on each sub-ject’s predisposition.

The meaningful coherence of individual differences andexperimental instruction conditions supports the group-ing in Figure 3. The present interpretation of individualdifferences in terms of predispositions, of course, can-not be checked in the present experiment; it would re-

quire some initial measurement of predisposition. Themain point here, however, is that the grouping adjoinsindividual differences to the experimental conditions. Amore detailed analysis thus becomes possible, as will ap-pear in the parameter estimates of Table 2 below.

Integration and ValuationThe hypothesis of an invariant integration rule is con-

sistent with the taper patterns visible in Figure 3. In nearlyevery panel, the curves are wider in the middle, with aconvergence toward one end or the other. In a few cases,the taper is bilateral, most notably in the upper left andlower right panels. This taper does not seem attributableto floor—ceiling effects, because the effective responserange occurs only over the inner two thirds of the 300-point response scale. Instead, this taper suggests that theinformation is integrated by an averaging rule in everygroup (see the preliminary study below).

Under this hypothesis, the large differences in surfaceresponse pattern, so obvious in Figure 3, arise at the stageof cue valuation—that is, in the processing of each sepa-rate stimulus variable for its information content. Suchdifferences invaluation are clear in the sharp differencesin effect of gap and speed ratio across groups in Figure 3.Once evaluated, the cues are integrated by the same ruleacross all groups. Quantitative analysis to buttress this in-terpretation will be given in the section on model analy-sis below.

Continuous CausalityContinuous perception of causality was obtained by

varying each stin-sulus dimension over the transition rangebetween definite phenomenal causality and definite non-causality. Unambiguous scenes outside this transitionrange, with larger delays, for example, would have com-pletely destroyed any impression of causality and wipedout all instruction and individual differences (Schlottmann& Shanks, 1992).

The use of continuousjudgments agrees with Michotte’sobservation of graded differences in goodness of causalimpression. It is consistent with the use of psychophysicalmethods to determine a “threshold” for causal percep-tion. A continuous response, actually a rating method, wasalso used by Gordon et al. (1990). The usefulness of thisprocedure, as already noted, rested in the selection ofstimulus levels over the causal—noncausal transitionranges.

It is still desirable to check that individual subjects didindeed make continuousjudgments. Group frequency dis-

2 3 4 5

Condition No. % No. % No. % No. % No. % Total

Causality 12 92 10 56 3 38 2 29 3 21 30Naturalness 1 8 8 44 5 63 5 71 11 79 30

Total 13 100 18 100 8 100 7 100 14 100 60


tributions are shown in Figure 4, which exhibits mildbipolarity for both instruction conditions. The group data,however, could mask bipolar, yes-no responding for in-dividual subjects. Since each subject had judged each ofthe 64 scenes six times, a frequency distribution basedon the 384 responseswas available for each subject. Mildbipolarity was seen in about halfthe causality subjects andabout a thirdof the naturalness subjects. All subjects, how-ever, made responses more or less uniformly over thewhole response range.

Two CrossoversTwo peculiarities of Figure 3 deserve mention. First,

in the top left panel, the 17-msec delay curve is relativelyflat, being the highest at the left, but almost the lowestat the right. This very short delay thus improves the causalimpression for large gaps, but makes it worse for smallgaps. Other panels in the first colunm show a similar, ifsmaller, effect. This agrees with Michotte’s observationthat a small temporal delay may improve phenomenalcausality under certain conditions (p. 94), a finding thatemphasizes that phenomenal causality is not physicalcausality.

This flattening of the 17-msec curve is reliable (alsosee Figure 5 for the preliminary study below). It appearsas a significant gap x delay interaction ina statistical com-parison of the 17- and 68-msec delay curves across allfive groups [F(3, 177) = 15.13]. Visual inspection showsthat this interaction takes crossover form mainly inGroups 1-3.

This flattening and crossover of the 1 7-mseccurve mayresult from a physical stimulus interaction. The gap is

600.

properly visible only during the delay, and the length ofthe delay accordingly limits the information physicallyavailable about the gap. Full apprehension of the gap maynot be possible within 17 msec, and this would lead toa reduced influence of gap on the overall judgment. Infact, such reduced effect would correspond to the rela-tively shallow slope of the 17-msec curves in the upperleft panels of Figure 3.

This interpretation in terms of a physical interaction issupported by the supplementary data on directjudgmentsof the size of the gap. These gap judgments ranged from110 to 195 in the 17-msec delay condition. The cor-responding ranges in the longer 68-, 119-, and 170-msecconditions were 86-256, 54-268, and 45-274, respec-tively. Discrimination was mainly reduced at the short-est delay, with a gap effect half or less in size than thatfound at the longer delays. The crossover of the 17-mseccurve in the left panels of Figure 3 thus appears to stemfrom a physical interaction of gap and delay informationavailable in the stimulus event.

The secondcrossover appears in the lower right panel,in which the 8:1 speed ratio curve is highest at the left,but next to lowest at the right. A high speed ratio thusimproves the causal impression for long delays, butdepresses it for short delays. A post hoc test between the8:1 and 4:1 curves for this group yielded a highly signif-icant speed ratio x delay interaction [F(3,39) = 24.00].Visual inspection shows similar flattening of the 8:1 curvefor Groups 3 and 4.

This statistical interaction corresponds toa reduced ef-fect of delay at the 8:1 speed ratio, but there is no reasonto suspect physical interaction. First, information aboutthe length of the delay is equally available at all speedratios. Second, not all groups show this interaction. Thecrossover ofthe 8:1 curve in Group 5 is thus consideredto arise at a later stage of processing. This interpretationagrees with the averaging rule of cue integration.

Preliminary StudyThe present study replicates and extends a preliminary

experiment (Schlottmann, 1987). Both obtained similarpatterns, as can be seen by comparing Figure 3 with Fig-ure 5, which presents the gap—delay integration data ofthe preliminary study. Of special importance is the taper

pattern, found in all six panels. This pattern led to thepresent hypothesis of an invariant integration process.

The six panels of Figure 5 are for three instruction con-ditions in which subjects estimated (1) confidence that Acaused B; (2) the magnitude of A’s effect on B; and (3) therealism or naturalness of the movement sequence. Eachsubject judged two sets of scenes in balanced order: SetA, in which A went faster than B, and Set B, in whichA went slower than B.

The manipulation of instructions produced effects corn-~ parable to those found in the present study. The subjects’

judgments of confidence and of the magnitude of A’s ef-fect (top and middle panels of Figure 5, respectively) werequite similar to each other. In the present study, accord-ingly, only the confidence instruction was retained. Real-

causality

I

500.

400.

300

200

100.

0.

500.

400

300.

200

100.

0.

naturalness

tOO 200

Figure 4. Group frequency distributions for 30 subjects judgingcausality and 30 subjects judging naturalness. Each graph contains11,520 total observations.


SetA

2.1 1.4 0.7

(

Set B

confidenceinstruction

effectinstruction

realisminstruction

gap gap

Figure 5. Gap—delay integration patterns of the preliminary study. The three rows of the graph represent sub-jects in three instruction conditions; the two panels in each row correspond to two stimulus sets.

ism judgments (bottom panels), in contrast, showed a rela-tively small effect of gap, a result replicated in the presentstudy.

Speed ratio had small effects, but this seemed to reflecta less appropriate manipulation. In Set A, object B alwaysmoved at the same low speed, and A’s speed was scaledup to vary the ratio. Mean speed thus was less than half

down to manipulate the speed ratio, and this producedlarger effects of speed ratio. Both studies agree, however,that the effect of speed ratio is easily affected by contex-tual factors.

that in the present study, thereby reducing the effect ofthe speed ratio. In addition, the first object had variablespeedacross trials, which made comparisons of speedra-tios difficult. In the present study, accordingly, A alwaysmoved at the same high speed while B’s speedwas scaled data.

MODEL ANALYSIS

In this section, the data are analyzed in terms of theaveraging model of information integration theory. To il-luminate the issue, it may help to show first how two ad-ditive models are not helpful to an understanding of the

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.—

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E

2.1 1.4 0.7 0mm

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r=

r = i/Jg + ~1’d+ ~,

F’ = ~,t’g+ ~,l’d + ‘4s + Cgds.

(wg ~g + Wd ~l’d + W5

~ + Wo ~o)(Wg + Wd + Ws + Wo)

(2)

(3)

Integration Models A separate weight parameter is used for each cue level,Additive model. The simplest model would specify the because cues may differ not only in value, but also in in-

judgment, r, as an additive integration of the three infor- formativeness or diagnosticity, and this is represented inmational cues: the weight. A small gap, for example, may be more di-

(1)

where 1~/g, i~j, and t~i~are the information values for gap,delay, and speed ratio, respectively. Despite its simplic-ity, this model is fairly powerful because the ~ values aretreated as subjective parameters, with no fixed relationto the physical cues. This is important, because these ~‘

values may thus embody individual differences in the pro-cessing of the physical cues. Hence the model may be ap-plied separately to the five groups already discussed inFigure 3. It captures the main effects in the data.

The additive model, however, makes strong predictionsat variance with the data. First, it predicts no crossovers,contrary to the lower right panel of Figure 3. Second, onthe assumption that the response scale is linear, whichseems reasonable in light of previous work on functionalmeasurement, the additive model predicts parallelism,whereas most panels in Figure 3 show marked taperpatterns,

To account for the nonparalleldata, the additive modelcould incorporate a configural parameter, denoted by Cgds,

which is added to the main effects of the three cues:

agnostic than an intermediate gap, because it points moredefinitely toward causality. A large gap, on the otherhand, may also be more diagnostic than an intermediategap, because it points definitely toward noncausality. Ifdifferent cue levels carry different amounts of informa-tion, weights may notbe equal or stand in a simple mono-tonic relation to value. In general, extreme cue levels areoften more informative than intermediate levels. Hence,extremity weighting would be expected, with higherweights for both high and low than for intermediate cuelevels.

This two-parameter, w-~, representation of the physi-cal cues corresponds to two psychologically distinct as-pects of processing. The value parameter reflects aspectsof the psychophysical stimulus dimension; the weight pa-rameter, w, reflects attentional or decisional aspects. Thistwo-parameter representation makes the averaging modelqualitatively different from an additive model, in whichweight parameters are not generally identifiable.

Configurality in the averaging model. Configuralityarises in the averaging model when different levels of astimulus variable have different weights. In this case, thesum of the weights in the denominator of Equation 3 be-

Here the effects of the informational cues differ accord-ing to the particular informational configurations inwhichthe cues are presented. For example, a long delay mightappear even less causal in the context of an unfavorablespeed ratio than in the context of a favorable speed ratio,

This configural model, unfortunately, is not testable,because it can always fit the data perfectly. Mathemati-cally, there is a free parameter, Cgds, for each combina-tion of cues. There are other ways to incorporate con-figural processing into strict adding models, of course,especially if one considers pairwise configurality amongthe three cues. Psychologically, however, thereis no ob-vious way to specify the form of the configural process-ing so as to restrict the number of free parameters.

Averaging model. A more useful account of the datacan be obtained with the averaging model of informationintegration theory, which has been used successfully ina number of areas of psychology (Anderson, 1981, 1982,1991). The averaging model incorporates configurality,

comes variable for different configurations of cues. Be-cause of this configural property, the averaging model canaccount for certain patterns of nonparallelism.

This configurality is conceptually and mathematicallyconstrained, however. Mathematically, each level of agiven cue must have the same fixed weight across all con-figurations. The weight for each level of delay, for ex-ample, is the same across all 4 x 4 cells of the gap xspeed ratio design. This limits the number of free param-eters and makes the model testable. Unlike the configuraladditive model, therefore, the averaging model cannot ac-count for all patterns of nonparallelism.

Conceptually, the configural process is localized in theintegration stage of processing. This constrains the ap-plicabiity ofthe model. The averaging model may be usedtoaccount for nonparallelism produced by psychologicalinteraction. Physical interaction, however, requires amodel that allows for configurality at the prior valuationstage of processing. This is not allowed in the present ver-sion of the model.

together with an adding-type integration. Formally, theoverall judgment is a weighted average of the three in-formational cues:

Averaging with extremity weighting predicts taper pat-terns as seen throughout Figure 3. To illustrate, considera medium-weight cue combined either with a nondiag-nostic, low-weight cue or with a diagnostic, high-weightcue. The denominator of Equation 3 is smaller in theformer than in the latter case. Hence, the medium-weight

Each stimulus level has its own scale value, ~‘, and its cuecontributes more to the overall judgment in the formerown weight, w. Thus, ~g denotes the value of. each level than in the latter case. In this way, the averaging processof the gap variable on the response dimension, and so automatically deemphasizes nondiagnostic cues and em-forth. The symbols Wo and ~o represent an initial expec- phasizes diagnostic cues.tancy that is standard in averaging theory, although not While the taper suggests invariant averaging integra-a present concern. lion, the individual difference in the curve patterns of Fig-


ure 3 are taken to arise during valuation processing. Sub-jects may differ, in other words, in the weight-valuerepresentation for the stimulus cues. The particular pa-rameter structure for each of the five groups can be clar-ified through model estimation, described in the follow-ing section.

Averaging Theory AnalysisModel fitting. The parameters of the averaging model

were estimated with the use of the AVERAGE program(Zalinski & Anderson, 1986, 1991). Since the averagingmodel does not apply to physical interaction, as notedabove, the data for the l7-msec delay were omitted in themodel analysis. This left 48 data points for the estima-tion. With the present design, weight parameters for eachinformational dimension are mathematically identifiableup to a linear transformation (Anderson, 1982, Section2.3.2).

The model was fitted separately for each of the fivegroups. Since the speed effect was very small in Group 1,an additional constraint was imposed; namely, weightsfor all levels of speed ratio were fixed at 1. For Groups 4and 5, similarly, weights for gap were fixed at 1 (see theAppendix).

Theoretical predictions from the averaging model aregiven inFigure 6, which has the same format as does Fig-ure 3. The curves show the predictions, the points showthe observed data. The overall fit is good: The meanmag-nitude deviations between predicted and observed are 5.0,4.7, 5.0, 6.5, and 4.4 on the 300-point scale range inGroups 1-5, respectively. The qualitative trends are cap-tured well. In particular, each set of predicted curvesshows the same taper patternas do the data. Notably, themodel also accounts for the crossover in the lower rightpanel.

Value estimates. Value estimates are found in thecolumns headed ~ inTable 2. A ~ value around the mid-point of 150 may be regarded as neutral; larger valuesrepresent favorable or good values on the dimension ofjudgment; smaller values represent unfavorable or badvalues.

Value estimates for delay are shown in the middle layerof Table 2. These show a uniform trend across all groups:high values for short delays and low values for long de-lays, in line withphenomenology. Value estimates for gapare shown in the bottom layer of Table 2. These also showa uniform trend across groups: high values for small gapsand low values for large gaps, also in line with phenome-nology. This trend (with one minor inversion) appearseven in Groups 4 and 5, where the overall effect of gapwas small. These values thus provide a quantitative rep-resentationof the psychophysical effects of the delay andgap variables.

Value estimates for speed ratio are shown in the toplayer of Table 2. In Group 1, these estimates are all near150, the neutral point of the response scale, which reflectsthe virtually complete lack of speed effect in this group.For each remaining group, the highest value correspondsto the highest speed ratio curve, indicated by the arrowin Figure 3, whereas the lowest value corresponds to thelowest curve. For this perceptual dimension, therefore,the subjective values show different ordinal dependenceon the physical speed ratio in different groups. Groups 2and 3 actually show opposite ordering.

Weight estimates. Estimates of the weights, whichmeasure diagnostic power, have primary theoretical in-terest. These estimates point to a general “good-bad”strategy: Subjects used one informational dimension todefine “good” launch events, another to define “bad”launch events.

This good-bad strategy can be illustrated with theweight estimates for Group 1, leftmost in Table 2.Weights for the gap dimension are found in the bottomlayer. These range from a high of 9.2 for the largestgapto a low of 2.6 for no gap. Since large gaps have lowscale values, the high weight means that the gap is primar-ily used to diagnose bad causal events. But there is nocorresponding tendency to use small gaps to diagnosegood causal events, because the weights show no cor-responding increase for small gaps.

Group 1 shows an opposite good-bad strategy for thedelay dimension in the middle layer. The weight of 3.8

Table 2Weight and Value Estimates for Three- Cues from Averaging Model

Cue Group

speed 1 2 3 4 5

Ratio Delay Gap w w w w w

1:1 1 151 7.9 87 3.5 186 5.6 158 6.9 1262:1 1 145 4.7 122 3.9 177 5.5 180 5.5 1654:1 1 154 3.7 166 5.0 146 5.8 170 5.6 1888:1 1 167 3.9 189 7.2 108 5.9 136 8.4 160

68 7.4 167 2.9 240 1.6 206 2.9 180 4.1 235119 4.6 124 1.7 107 2.5 97 5.5 120 2.4 99170 3.8 100 2.2 19 5.7 66 7.1 79 4.5 48

00.71.42.1

2.64.56.49.2

24015111386

4.5 1992.7 1583.0 1223.2 97

5.7 2362.4 1781.8 1331.6 96

1111

187192152112

1111

20219213586

Note—Delay is giyen in milliseconds; gap, in millimeters.


delay x speed

2.1 0.71.4 0 mm gap

2.1 0.71.4 0 mmgap

Figure 6. Comparison between predictions of the averaging model (curves) and the observed data (points). Thisgraph has a format and data pointsidentical to those in Figure 3, except for the omission of data for the 17-nasec delay.

PHENOMENAL C ~LSALITY

for large delays is smallest, and weigr~sincrease withshorter delays. Group I thus uses the delay dimension todefine goodness of an event

Here, as elsewhere, it should be rec go red th~.the de-sign only allows a linear scale for wetghts s~the kp-pendix). Weights may thus not be comparable across di-mensions, but differences between weights within eachdimension are meaningful. The logic of the present “good-bad” interpretation rests on the weight trends within eachcue dimension for each group.

A different strategy can be seen in the rightmost columnfor Group 5, which judged naturalness and ignored gap.Weight estimates for delay are found in the middle layerof the right column. Here, both extremes have receivednigher weights, 4.1 and 4.5, whereas intermedtate delayhas a smaller weight of 2.4. Group 5 thus used the delaydimension to select both good and bad events.

Weight estimates for speed ratio for Group 5 are in thetop layer From Figure 2, Group 5 co ~sidereda speedratio of 4.1 most natural, 1:1 east natural. Since 1:1received a higher weight than 4: I, spe.~dratio was usedto define bad events Note hat 8:1 received the highestweight on the speed dimension, which reflects the flat-ness and crossover of tne 8’ 1 curve in Figure 2. This isnotan extremity effect, however, since 8. 1 does not havea high scale value as well

Indications of similar good-bad strateg’es can be seenin the weight estimates for the other groups. A glance overall groups hot’ eser, wiP show that the selection of goodand bad dimensions differs across groups.

One important implication of these different good-badstrategies is hat the saluat on process~. that extrgct thecue information have a cognitive component. Purely per-ceptual considerations would imply pattern of weight-ing tied to the pattern of r~s alues—that is, higher weightsfor both higher and lower stimulus let els, and lowerweights for the less diagnostic intermediate levels. In con-trast, in the present good—bad strategies, the diagnosticfunction of the stimulus variables does not reflect theirpsychophysical content.

These parameter estimates reveal aspects of processingthat could notbe understood from the data patterns them-selves. The model application is tentative, but the resultssuggest the potential of the approach. The taper patternsin the judgmcnt data suggested differential weighting, butdid not localize it; that required the model anal;sis

CONCLUSIONS

The averaging model of information integration theorygives a good account of Michotte’s phenomenal causal-ity. The model provides a clear distinction between twoprocessing stages, valuation and integration. Al hough in-disidual d1fferen-e were large, they Lould I localizedin the valuation operation that constructs the paraw ~Jersof the integration model. Thus, different subjects extractedquite different informational content from the same stim-ulus variable, but all integrated the information by a uni-form averaging rule.

The present ‘ascount allows some reconciliation betweenMichotte and nis critics The averaging integrat on modelmay correspond to the invariant perceptual structure ofphenomenal causality as proposed by Michotte The sale-ation operation. -n the ither hand can accommodate in-dividual differences that may have experient ~i1compo-nents, as suggested by his critics.

Good ‘-Bad StrategyCharacteristic of the valuation operation was a “good—

bad” strategy in cue weighting. For the most part, sub-jects treated each stimulus dimension either as ‘good.giving higher weights to stimulus levels considered moreindicative of a causal relation, or as “bad,” gis ing higherweights to stimulus levels more indicative of a noncacsa~relation. Detection of this good-bad strategy dependedon the model parameter analysis. which cue separate theweight parameter prom toe scale clue C singular capa-bility of the averaging mode’

The good—bad strategy points to acognitive lcvJ c t ru-cessing inphenomenal causality, Ps~chophvsicaIconsider-ations in line with phenornenoIog~ can acco nt o- thepattern of d’ values. But the weighting pattern of the good’-bad strategy was nor tied to this pattern of the values Thu.,the weighting structure in ‘olves additional operaticn’~presumably reflecting the experience of the onservers.

Individual Differences and Instruction ConditionsIndividual differences played a Unique rule ‘n the ‘mat-

ysis, a role actualized by the two instruction c nditionsAs expected, instructions to judge naturalness yielded adifferent r”~p~n~c pattern from ,~‘n~t!on¼to judgecausality. Study of the individual patterns re c’aled twocorresponding odal patterns, ore f

2r eausa~t’ ~rd ei~

for naturalness. Between these two modal patterns werefound three ‘ntevnediate patterns each characterized bya different optimal level of the speed ratio s unable.

Instead of the customary analysis at the level of the in-structton condit’ons, therefore, a more meaningful anal-ysis could he obtained at a finer evC of individual dif-ference groups. This revealed aspects of the responsepatterns that were obscured in the overall analys~o~’~hetwo instruction groups. It was this breakdown, Louptedwith the model analysis, that localized the indis idual d Cferences in the s luation operation, followed by the samintegrution ope ation across suhioct

The value or the two sets o instructions deserves em-phasis. Subjects appear to have pred~sposttionsto one fhetw~rep , ,~iu~ali~~rratc a ~ .

instructions were carefully deveioped in the preliminaiwwork, yet individual differences were found w ithin theseinstructioi con’~tlons Som~of the lncons~ten~as in 0vious w rk ‘nay reflect diG rence~in in~truct’~’as, wb, hiavc not pr~“ .. re a’ ~i ouch it’ - en tk thperinlental ‘na ipulation I n ueti os. .h s Inuldifference.. ~ar he oroke’ down meanine ully.

Th:s ‘~onjalt use of ir.strurt ons and inc’ idiot dtLer-ences may have vo e ge ie’ai applicabilit~a an naical tool. Indivoleal difference nave been noted by ~runy


experimental psychologists, and Underwood (1975) hassuggested that they should be a crucible for theory con-struction. Underwood’s argument is attractive, but it hasremained largely an aspiration. Too often, the criticism thatexperimental psychology consigns individual differencesto the error variability is justified. In the present study,individual differences are adjoined to experimental condi-tions. This technique illustrates a potentially general methodfor utilizing individual differences productively.

Phenomenal Causality and Individual DifferencesThe present results may provide at least some agree-

ment betweenMichotte and his critics. The model analy-sis indicates a uniform integration process, the same acrossdifferent individuals. This integration process leadsdirectly to the phenomenal experience, which is the in-tegrated resultant. Although Michotte did not pursue theissue of cue integration, he emphasized that the phenom-enal experience would dependon the combined action ofoperative cues. The averaging model gives precision tothis integration problem. It is not an additive model, butit captures one aspect of cue configurality through the rel-ative weights. Tentatively, therefore, it seems reasonableto relate Michotte ‘ s concept of a uniform perceptual struc-ture directly to the integration rule.

The large individual differences agreewith Michotte’scritics. Indeed, they provide more definite evidence thanhas previously been available, and they could be specifi-cally related to cue valuation processes. But the implica-tions of these individual differences for Michotte’s claimsneed to be reconsidered.

Individual differences in ~ values could be attributedin part to predispositions to judge causality or natural-ness. Perhaps this is not too surprising. Both ratings aremeaningful, and if philosophers cannot agree on how toview causality, one should not expect this from casualob-servers. Michotte had already observed an “analytic at-titude” in some subjects, but dismissed such subjects asdeviant. In theory, he recognized that “attitudes” couldaffect phenomenal causality (e.g., p. 333), but this wasnot relevant to his theoretical concerns; inpractice he con-sidered such effects negligible. This assumption can bedropped in the present approach, which allows a rangeof attitudes toward causality, as shown in the five-groupbreakdown of Figure 3.

The individual differences in cue weighting suggest agreater problem for Michotte’s view. The real problemis not that there are individual differences, but their pat-tern: They follow the “good-bad” strategies describedabove. Even the delay variable, which showed relativelysmall individual differences in ~lvalues, exhibited suchweighting strategies. These seem to involve a cognitivelevel of processing, in disagreement with Michotte.

A possible resolution is to separate Michotte’s twinclaims of direct perception and of innateness. Individualdifferences, as in the “good-bad” strategies, hardly seemconsistent with innate perception, but they neednot raise

a problem for direct perception. A similar separation hasbeen suggested by Costall (1991, p. 58) in an overviewof Michotte’s work. In this approach, the present resultscontribute to the explication of how experiential factorsinfluence perception, a point acknowledged but not pur-sued by Michotte.

Phenomenal Causality and Effects of ExperienceOne major alternative approach to phenomenal causal-

ity goes back at least to Hume (1739/1978), who proposedthat causal beliefs are acquired through repeated ex-perience of the constant conjunction of essentially indepen-dent events. Many contemporary studies have indeedshown that causality judgment is sensitive to the predic-tive relationships between events (for an overview, seeShanks, 1993; Wasserman, 1990).

This work, however, has little bearing on the percep-tual task chosen by Michotte to exhibit direct perceptionof causality. In the one attempt to manipulate predictiverelations within sequences of launch events, learning ef-fects on phenomenal causality were not found (Schlott-mann & Shanks, 1992).

A different approach to experiential modification of phe-nomenal causality in the launch event is suggested by thegood-bad strategies indicated by the present model analy-sis. These weighting strategies seem to havecognitive com-ponents and thus should be modifiable through experience.

One direct form of experiential modification could con-sist of preliminary training to influence these strategies.This might be done by holding a selected cue constantin an initial phase, while the other two were varied jointly.The present Group 1, for example, used the gap cue todefine bad causal events. With the gap held constant, how-ever, it could not be used as a basis for the bad strategy.Instead, strategies would have to have been based exclu-sively on the other two cues. Such effects might be main-tained when the gap variable was faded in during a sub-sequent test phase in which all three cues were varied.

A related test is suggested by Groups 4 and 5, who con-sidered the gap essentially irrelevant. By holding delayconstant in an initial phase, these subjects might be im-pelled to take the gap into account, for otherwise theywould have to rely entirely on the speed ratio. Alterna-tively, an initial three-cue phase like that in the presentstudy might be used to diagnose good-bad strategies, fol-lowed by directed two-cue training, with subsequent trans-fer back to the three-cue task. The averaging model maybe used to analyze the structure of any such learning ef-fects on phenomenal causality in terms of weight and valueparameters.

The Continued Relevance of Michotte’s IdeasMichotte pointed out a basic aspect of everyday phe-

nomenology—that certain instances of causality are intui-tively obvious. The very artificiality of the stimulus dis-plays for launch events strengthens this point. Michotte wasthe first to tackle the problem of phenomenal causality in


a systematic way, and his work is notable for the attemptto combine phenomenology and empirical quantification.

Subsequent workers have fixated on Michotte’s claimthat phenomenal causality is innate. Some have empha-sized the phenomenal immediacy of the effect and its in-dependence of physical reality; others have stressed theeffects of prior experience and individual differences. Theresults havebeen inconclusive. Little more has been addedto Michotte’s work than that individual differences exist.Michotte had already acknowledged this, but his invoca-tion of an “analytical attitude” was not a satisfactory con-ceptualization ofthe processes involved. The present ap-proach allows for more detailed study of phenomenalcausality at the individual level.

The integration approach returns to Michotte’s focuson the phenomenon, especially to his concern with para-metric variation along relevant stimulus dimensions.Through the incorporation of a continuous response mea-sure, the usefulness of Michotte’s task could be increased.It deserves reemphasis that the parameter specificationsreported in Michotte’s extensive studies were generallywell supported in the present work.

The innate-versus-learned controversy is finessed in thepresent approach. This dichotomy has become increas-ingly simplistic in light of recent developmental work,which shows innate organization for causality in infants(e.g., Leslie, 1988). This does not preclude experientiallearning. Indeed, some consider such scaffolding a learn-ing device (e.g., Gelman, 1990; Leslie, 1988). In adultcognition, at any rate, the perceptual illusion of phenom-enal causality must function togetherwith acquired knowl-edge about causality in the physical world. Thus, waysare needed that can make effective progress on the innate-plus-learned question.

Information integration theory is one useful tool in thisendeavor. The complete pattern of individuals’ impres-sions can be obtained via continuous responses to para-metric variation of multiple cues over the causality—non-causality transition range. Analysis of these patternsprovided evidence for an invariant integration modelunderlying phenomenal causality. At the same time, thismodel-based approach enabled a more principled con-sideration of individual differences. Thus, the integrationframework provides the potential to study phenomenalcausality within everyday cognition.

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APPENDIX

Because the interpretation of the data centered on the five-group classification of Figure 3 and the model-based parame-ters, the standard statistical analyses had secondary interest.Thus, the two instruction conditions produced different usagesof the informational cues, as was seen in Figure 2, but an un-derstanding ofthe usage depended on overriding this experimen-tal variable with the individual differences classification. Somestatistical details that may be of interest are noted here.

Analysis for Two Instruction ConditionsTheoverall analysis yielded significant main effects for gap,

delay, and speed ratio [F(3,l44) = 49.50, 220.21, and 10.41,respectively]. (Results are reported at p < .05.) Only the gapeffect differed in the two instruction conditions [F(3, 144) =

15.71]. Interactions of gap x delay, gap x speed ratio, anddelay x speed ratio were found as well [F(9,432) = 17.68, 3.72,and 12.60, respectively]. The interactions of both gap x delayand speed ratio x delay differed in the two instruction condi-tions [F(9,432) = 7.57 and 2.82, respectively]. These inter-actions reflect the difference in group patterns seen in Figure 2.

This overall analysis was a 2 x 3 x 2 x 4 x 4 x 4 mixeddesign analysis of variance (ANOVA) conducted on all 60 sub-jects’ judgment data, with gender, type of prior subdesign, andinstruction asbetween-subjects factors, and gap, delay, and speedratio as within-subjects factors. Gender and type of subdesignentered into only one five-way interaction of marginal signifi-cance. Since there were 48 effects involving these two variables,this one significant effect may be a Type Ierror. Accordingly,these factors were not considered further.

Analyses for Individual Difference GroupsA 4 (gap) X 4 (delay) x 4 (speed ratio) ANOVA was run

for each subject, with 320 df for error. The means for the speedratio variable were used to classify individuals into groups, asalready noted. All but 2 subjects showed significant effects ofdelay, and all subjects except those in Group 1 showed signifi-cant effects of speed ratio. Twelve of 13 subjects in Group 1showed significant effects of gap, whereas 21 of the remaining47 subjects showed nonsignificant effects of gap, scatteredthrough the remaining four groups with a somewhat higher fre-quency in Group 5. Roughly half of the subjects showed sig-nificant gap X delay and speed ratio x delay interactions, butonly 10 of the 60 showed speed x gap interactions; only 5showed three-way interactions. The majority of the gap x de-lay interactions—l9 of29—were found in the causality instruc-tion condltlon; the majority of the speed x delay interactions—22of36—were found in the naturalness instruction condition. Theseinteractions reflect nonparallelism in the individual factorialgraphs, which has been interpreted in terms of the weightingstrategies associated with the averaging model.

Subjects were classified according to the speed ratio consid-ered most causal/natural, which resulted in the five groups ofFigure 3. A repeated-measures ANOVA was run for each groupof Figure 3, and these are presented in Table Al. These F ra-tios generally agree with the visual inspection of Figure 3. Thegap x delay interaction is significant for Groups 1-3, whichreflects the taperpatterns visible in the left column of Figure 3.The gap x speed interaction is nonsignificant for all groups,which reflects thenear parallelism in the centercolumns of Fig-ure 3. The delay x speed interaction is significant for all groups,which reflects the taperpatterns in the right column of Figure 3,except for Group 1, in which the interaction arises from a smallspeed effect at no delay for some subjects.

This five-group classification naturally includes some indi-viduals who did not fit exactly to the group pattern. Futureresearchers may find it useful to go into individual analysis inmore detail. The usefulness of individual analysis, however, de-pends heavily on the applicability ofthe averaging model, whichaccordingly needs to be studied more extensively.

Parameter EstimationThe averaging model with differential weighting was fitted

to the mean data for each of the five groups by applying theAVERAGE program (Zalinski & Anderson, 1986, 1991) to thethree-factor design. The program estimates 12 weights and 12scale values, 1 each for each stimulus level and the initial ex-pectation. The model requires the weights to sum to unity, so

Table AlSummary Analyses of Variance: F Ratios

Source

Group

1F MSe

2F MSe

3F MSe

4F MS,

5F MS~

GapDelaySpeed RatioGap )< delayGap X speed ratioDelay x speed ratioGap x delay x speed ratio

42.57*19.78*0.62

10.67*1.433.64*1.25

14,17612,005

8352,092

873713588

10.06*72.08*56.96*7,99*1.10

10.06*1.06

14,9937,5026,8371,141

619866357

6.75*27.86*20.45*5,44*1.03

11.36*0.87

16,11110,8997,1741,718

4861,001

656

1.3434.51*8.84*1.321.043.04*1.09

4,1179,4757,478

584426

1,227504

5.58*179.45*26.30*

1.291.32

11.91*1.09

3,5965,6126,395

709469972464

Note—MSes are for scores on 300-point scale; numerator dfs are 3, 9, and 27 for main effects, two-way, and three-way interactions,respectively; denominator df s depend on group size listed in Table 1. *p < .05.


there are only 23 free parameters. This was reduced to 19 forGroups 1, 4, and 5, as noted in the text. There were 48 datapoints, so the data:parameter ratio was slightly above 2:1. Withthis ratio, the AVERAGE program yields stable estimates withno problems of local minima, as shown in Monte Carlo studiesby Zalinski and Anderson (1991).

If the full design could have been supplemented with subde-signs that involved only one or two of the threecues, the modelcould yield weight estimates for all three variables on a com-mon ratio scale. Such subdesigns, unfortunately, may not berealizable in the present task; all threevariables are physicallyinherent in the launch event. A launch event always contains,for example, some spatial contiguity information. The level ofuniqueness of the weight estimates, accordingly, may be no morethan a linear scale for each separate variable. This allows com-parisons of differences between weight estimates within eachdimension, but comparisons across dimensions areproblemati-cal. Scale values suffer an associated bias, although the meaning-fulness of the estimates in Table 2 suggests that this bias wassmall.

The initial state variable, which may be conceptualizedas anexpectancy for the average launch event, yielded estimates of~o close to the neutral midpoint of 150 for each group and ofWE around —5 for each group. This negative estimate is not ananomaly. Similar negative values were obtained with MonteCarlo runs on perfectdata generatedfrom the averaging model,and reflect the indicated level of uniqueness. It results from theprogram, which leaves WE unbounded in the estimation.

In future work, it may be useful to seeksome additional vari-able that is not physically integral to the perception ofthe launchevent, one that will be ignored unless it is specifically made sa-lient. Relativesize, for example, would presumably have an ef-fect if manipulated over more than one level, but perhaps notif held constant at one value. If such variables can be established,they may provide a useful sharpening of uniqueness for theweight estimates. The AVERAGE program can be used to testfor uniqueness properties of a design before it is run.

(Manuscript received September 17, 1992;revision accepted for publication May 3, 1993.)

an information integration approach to phenomenal causality

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