![Reactive transport of trace elements and isotopes in …webhome.auburn.edu/~leeming/lee-pub5.pdf[1] We integrate groundwater geochemistry, mineralogy, and numerical modeling techniques](https://static.fdocuments.net/doc/165x107/5fab3e56a69c6e545b4947f4/reactive-transport-of-trace-elements-and-isotopes-in-leeminglee-pub5pdf-1-we.jpg)
pub5.pdf
6
The fan effect refers to an increase in response time and/or error rates on a memory test with an increase in the number of competing associations to that memory probe. The associations to a concept were assumed to “fan” out of the concept node, hence the name. Since its first demon- stration by Anderson (1974), the fan effect has been repli- cated in many different experimental paradigms with dif- ferent types of stimuli (Lewis & Anderson, 1976; Reder & Ross, 1983; Zbrodoff, 1995). The assumptions underlying the account of the fan effect specify how and why retrieval processes interact with memory representations. Specifi- cally, multiple facts linked to a concept in the probe will interfere with each other during retrieval because of lim- ited cognitive resources allocated to the probe. As more as- sociations are attached to the probe, the amount of activa- tion that spreads down any path from the probe is reduced, requiring more time for a particular fact to be retrieved. Alternatively, however, there has emerged a competing view that emphasizes a representational account based on situ- ation models (e.g., Radvansky & Zacks, 1991). In the pres- ent study, we seek to incorporate the different views of the fan effect and to test the predictions of these accounts. In the fan paradigm, participants learn arbitrary associ- ations between concepts (e.g., “Hippie–Park”). In the pres- ent study, participants memorized a set of 28 facts about people in locations. Figure 1 shows a basic network repre- sentation of some facts and their associated concepts. These facts are constructed so that one, two, or three facts are studied about each person and location. After com- mitting these facts to memory, participants are tested on their ability to recognize person–location pairs previously studied (targets), and to reject novel combinations of the same people and locations (foils). The fan of a probe is the number of facts associated with the person and the loca- tion, and the reaction latency increases with the fan. The fan effect holds for both targets and foils, although some- times the effect size varies (Anderson, 1976). The present study is concerned with better understand- ing why the size of the fan effect for different dimensions of the stimuli (e.g., person vs. location) sometimes varies and what influences that variation. In some studies, the size of the fan effect is comparable for both dimensions (Anderson, 1974). However, some types of material have produced different size fan effects for different dimensions (Radvansky & Zacks, 1991), the phenomenon known as the differential fan effect. First, we will describe the mental- model theory that was initially proposed to explain the dif- ferential fan effect. Second, we will describe the ACT-R theory, and how it differs from the mental-model theory. According to mental-model theory, facts are organized into mental models when the material is studied. For ex- ample, when object–location pairs are studied (e.g., “The potted plant is in the hotel”), these associations should be or- ganized into location-based mental models because a loca- tion can have many items in it, but an object can be in only one place at a time. Therefore, a location contains all the as- sociated objects in its own mental model, whereas an object may appear in multiple location-based mental models. In this example, locations organize the mental models, serving as the organizing dimension. According to Radvansky and Zacks (1991), there is only a fan effect of the nonorganizing dimension, since this will result in more mental models and it takes time to search through these: The fan of the organiz- ing dimension will have no effect because the objects within a mental model can be accessed quickly with little effect of the number of objects. In accordance with the hypothesis, the results showed that the location fan effect was smaller than the object fan effect (Radvansky & Zacks, 1991). 729 Copyright 2004 Psychonomic Society, Inc. This research was supported by National Science Foundation Grant BCS-9975220. We thank Mike Rinck, Ed O’Brien, and Gabe Radvan- sky for their helpful comments on an earlier version of this article. Cor- respondence should be addressed to M.-H. Sohn, Department of Psy- chology, 2125 G. St. NW, 313A Bldg GG, George Washington University, Washington, DC 20052 (e-mail: [email protected]). Differential fan effect and attentional focus MYEONG-HO SOHN, JOHN R. ANDERSON, LYNNE M. REDER, and ADAM GOODE Carnegie Mellon University, Pittsburgh, Pennsylvania As people study more facts about a concept, it takes longer to retrieve a particular fact about that concept. This fan effect (Anderson, 1974) has been attributed to competition among associations to a concept. Alternatively, the mental-model theory (Radvansky & Zacks, 1991) suggests that the fan effect disappears when the related concepts are organized into a single mental model. In the present study, attentional focus was manipulated to affect the mental model to be constructed. One group of partici- pants focused on the person dimension of person–location pairs, whereas the other group focused on the location dimension. The result showed that the fan effect with the focused dimension was greater than the fan effect with the nonfocused dimension, which is contrary to the mental-model theory. The number of associations with a concept is indeed crucial during retrieval, and the importance of the in- formation seems to be accentuated with attentional focus. Psychonomic Bulletin & Review 2004, 11 (4), 729–734
-
Upload
flori-andrei -
Category
Documents
-
view
214 -
download
0
Transcript of pub5.pdf
The fan effect refers to an increase in response timeandor error rates on a memory test with an increase in thenumber of competing associations to that memory probeThe associations to a concept were assumed to ldquofanrdquo out ofthe concept node hence the name Since its first demon-stration by Anderson (1974) the fan effect has been repli-cated in many different experimental paradigms with dif-ferent types of stimuli (Lewis amp Anderson 1976 Reder ampRoss 1983 Zbrodoff 1995) The assumptions underlyingthe account of the fan effect specify how and why retrievalprocesses interact with memory representations Specifi-cally multiple facts linked to a concept in the probe willinterfere with each other during retrieval because of lim-ited cognitive resources allocated to the probe As more as-sociations are attached to the probe the amount of activa-tion that spreads down any path from the probe is reducedrequiring more time for a particular fact to be retrievedAlternatively however there has emerged a competing viewthat emphasizes a representational account based on situ-ation models (eg Radvansky amp Zacks 1991) In the pres-ent study we seek to incorporate the different views of thefan effect and to test the predictions of these accounts
In the fan paradigm participants learn arbitrary associ-ations between concepts (eg ldquoHippiendashParkrdquo) In the pres-ent study participants memorized a set of 28 facts aboutpeople in locations Figure 1 shows a basic network repre-sentation of some facts and their associated conceptsThese facts are constructed so that one two or three factsare studied about each person and location After com-mitting these facts to memory participants are tested ontheir ability to recognize personndashlocation pairs previously
studied (targets) and to reject novel combinations of thesame people and locations (foils) The fan of a probe is thenumber of facts associated with the person and the loca-tion and the reaction latency increases with the fan Thefan effect holds for both targets and foils although some-times the effect size varies (Anderson 1976)
The present study is concerned with better understand-ing why the size of the fan effect for different dimensionsof the stimuli (eg person vs location) sometimes variesand what influences that variation In some studies thesize of the fan effect is comparable for both dimensions(Anderson 1974) However some types of material haveproduced different size fan effects for different dimensions(Radvansky amp Zacks 1991) the phenomenon known as thedifferential fan effect First we will describe the mental-model theory that was initially proposed to explain the dif-ferential fan effect Second we will describe the ACT-Rtheory and how it differs from the mental-model theory
According to mental-model theory facts are organizedinto mental models when the material is studied For ex-ample when objectndashlocation pairs are studied (eg ldquoThepotted plant is in the hotelrdquo) these associations should be or-ganized into location-based mental models because a loca-tion can have many items in it but an object can be in onlyone place at a time Therefore a location contains all the as-sociated objects in its own mental model whereas an objectmay appear in multiple location-based mental models In thisexample locations organize the mental models serving asthe organizing dimension According to Radvansky andZacks (1991) there is only a fan effect of the nonorganizingdimension since this will result in more mental models andit takes time to search through these The fan of the organiz-ing dimension will have no effect because the objects withina mental model can be accessed quickly with little effect ofthe number of objects In accordance with the hypothesisthe results showed that the location fan effect was smallerthan the object fan effect (Radvansky amp Zacks 1991)
729 Copyright 2004 Psychonomic Society Inc
This research was supported by National Science Foundation GrantBCS-9975220 We thank Mike Rinck Ed OrsquoBrien and Gabe Radvan-sky for their helpful comments on an earlier version of this article Cor-respondence should be addressed to M-H Sohn Department of Psy-chology 2125 G St NW 313A Bldg GG George Washington UniversityWashington DC 20052 (e-mail mhsohngwuedu)
Differential fan effect and attentional focus
MYEONG-HO SOHN JOHN R ANDERSON LYNNE M REDER and ADAM GOODECarnegie Mellon University Pittsburgh Pennsylvania
As people study more facts about a concept it takes longer to retrieve a particular fact about thatconcept This fan effect (Anderson 1974) has been attributed to competition among associations to aconcept Alternatively the mental-model theory (Radvansky amp Zacks 1991) suggests that the fan effectdisappears when the related concepts are organized into a single mental model In the present studyattentional focus was manipulated to affect the mental model to be constructed One group of partici-pants focused on the person dimension of personndashlocation pairs whereas the other group focused onthe location dimension The result showed that the fan effect with the focused dimension was greaterthan the fan effect with the nonfocused dimension which is contrary to the mental-model theory Thenumber of associations with a concept is indeed crucial during retrieval and the importance of the in-formation seems to be accentuated with attentional focus
Psychonomic Bulletin amp Review2004 11 (4) 729ndash734
730 SOHN ANDERSON REDER AND GOODE
The mental-model theory has been generalized to othermaterials (Radvansky Spieler amp Zacks 1993 Radvan-sky Wyer Curiel amp Lutz 1997) Radvansky et al (1993)argued that personndashlocation pairs follow different orga-nizing principles depending on the relative size of loca-tions With relatively large locations (eg public libraryhotel) either type of mental model can be formed becausepeople go to many places and a place can contain manypeople With relatively small locations (eg telephonebooth tanning bed) person-based mental models are to beformed because these small places can only contain oneperson at a time whereas the same person can go to all ofthese places This analysis was used to explain why the per-son fan effect was smaller than the location fan effect withrelatively small locations whereas the differential fan ef-fect was not obtained with relatively large locations
In contrast ACT-R emphasizes the retrieval processesIn ACT-R activation spreads from presented terms to theconnected nodes that represent various facts (Figure 1) Thelatency to retrieve any fact from memory is determined byactivation level of that fact The activation Ai of a particu-lar fact i is determined by the following activation equation
where Bi is the base-level activation of the fact reflectingits recency and frequency of study The summation is overthe fact concepts j which are the activation sources whenthe probe is presented for recognition In the present studythese sources are person location and the preposition inThe multiplier Wj is the amount of attention given to a di-mension to which a particular source j belongs In ACT-Rthe fan effect depends on the associative strength Sji which is the relative associative strength of the fact i to agiven concept j As more facts are associated with a con-cept the associative strength of a particular fact is weak-ened because of competition for limited resources If thereis no factor biasing toward person or location the source
activation is assumed to be divided equally between theperson and the location dimensions This is reflected inequal values for Wj However if for some reason either di-mension is emphasized more than the other during learn-ing that dimension may get a higher attentional weight(Anderson amp Reder 1999) Consequently as implied inthe activation equation the dimension with higher atten-tional weight will produce a greater fan effect than the di-mension with lower weight
In summary the mental-model and ACT-R theories offerrather different conceptions of what produces the differ-ential fan effect According to ACT-R the dimension thatgets emphasized has a higher attentional weighting andshould have the greater fan effect So for example whenthere is a larger fan effect of the object dimension than thelocation dimension (eg Radvansky amp Zacks 1991) it isnot because the location is the organizing dimension asthe mental-model theory would argue Rather it is be-cause the object is the emphasized dimension Thus thetwo theories attribute the same effect to special processingof different dimensions
The problem with past research is that there has been noexplicit manipulation to influence which dimension re-ceives special processing Past research has typically taughtparticipants the material with a dropout procedure in whichthey have to produce the correct response to probes of theform ldquoWho is in this locationrdquo or ldquoWhere is this personrdquoThis paradigm ensures that participants receive questionsanchored on both location and person with the intentionof emphasizing both dimensions equally Despite probingfrom both terms during study participants sometimesseem to organize the information around just one term(eg Radvansky amp Zacks 1991) It was inferred that thiswas due to how participants would organize the materialbut this choice was not directly manipulated
The present study manipulated the way participants or-ganize the personndashlocation material during the study phaseParticipants in the person-focus condition received onlyperson-anchored questions with the explicit instruction toorganize material into person models These models in-volve each person visiting multiple locations (eg ldquoThelawyer was in the airport the stadium and the classroomrdquo)Conversely participants in the location-focus conditionreceived only location-anchored questions and were in-structed to organize the material into location models Inthis case the model involves locations that contain multi-ple people (eg ldquoIn the stadium there was the lawyer thesenator and the grandmardquo) Both groups received thesame personndashlocation pairsmdashonly the manner in whichthe material was studied differed Presenting one type ofcued recall question during learning was necessary to ma-nipulate the dimension that would be the focus of atten-tion or the organizing dimension for mental models Themental-model account predicts that the fan effect of the or-ganizing dimension should be smaller than that of the non-focused dimension However the ACT-R theory makes theopposite prediction
A B W Si i j jij
= + sum
Figure 1 An illustration of network representation of facts andtheir associated concepts
DIFFERENTIAL FAN EFFECT 731
METHOD
ParticipantsThere were two groups of participants one assigned to the person-
focus condition (19 participants) and another to the location-focuscondition (17 participants) Participants were undergraduate stu-dents at Carnegie Mellon University They participated in return formonetary reward
ProcedureIn the study phase participants were presented with 28 sentences
regarding a person in a location To accentuate the representationaldifference we used photographs in the person-focus condition anda spatial layout in the location-focus condition In the person-focuscondition participants viewed 25 photographs of individuals theydid not know (graduate students and staff members of the psychol-ogy departments of Carnegie Mellon University and the Universityof Pittsburgh 12 Caucasian male and 13 Caucasian female age range20ndash30) For each participant 17 of these pictures were randomly as-signed to occupation names such as lawyer and senator A personndashlocation sentence (eg ldquoThe lawyer is in the parkrdquo) was presented withthe picture of the corresponding person Occupation names andplaces are presented in the Appendix After reading the sentenceswith the pictures participants went through a two-tiered question-answering phase First they were presented with 25 faces in a 5 5grid and were asked to identify the correct face (eg ldquoClick on thelawyerrdquo) If a wrong face was identified the participant was promptedwith the correct face After identifying the person correctly partici-pants were asked to type in all the places associated with that personWrong answers were corrected To prevent participants from using alocation-based strategy each time a new question was asked the 25faces were presented in a new random configuration of the 5 5 grid
In the location-focus condition participants were presented witha 5 5 grid From the 25 possible positions in the grid 17 were ran-domly selected for each participant and were assigned locationnames such as park and church A sentence was presented in the gridcell that was assigned to the corresponding location Participantswere instructed to memorize which location was at which grid posi-tion and who were the occupants In the question-answering phasethe participants were also presented with two-fold questions Firstthey were asked to identify a certain location among 25 grids (egldquoClick on the parkrdquo) When the location was correctly identifiedthey were asked to type all the people associated with the location
Participantsrsquo memory for the associations was strengthened witha two-pass dropout cued recall procedure In each pass participantsreceived two-fold questions as described above in a random order ofall possible questions If they could not answer correctly the ques-tion was repeated after all the other questions had been asked Thiscontinued until all questions had been answered correctly twice
During the recognition test participants judged 168 targets and168 foils in the form of a personndashlocation pair (ldquolawyerndashparkrdquo) Theorder of the person and location within the probe was randomizedTo create foils we swapped personndashlocation pairs from the same fancondition The probes were presented in 6 blocks of 56 trials Onevery trial a fixation was presented for 500 msec The probe waspresented immediately and remained on the screen until the partici-pantrsquos response was made The feedback on accuracy and speed waspresented for 3 sec
RESULTS
A four-way analysis of variance was conducted for la-tency and accuracy with attentional focus (person or loca-tion) focused dimension (three fans) nonfocused dimen-sion (three fans) and trial type (target and foil) as variablesThe attentional focus was a between-groups factor
For the latency analysis only correct trials with latencyshorter than 3 sec were included Less than 7 of trialswere eliminated because of excessively long responsesMean accuracy and latency presented in Table 1 werenegatively correlated across the various conditions de-fined by the combinations of the variables (r 56 p 01) indicating that conditions with poor performance byone measure had poor performance by the other Table 2presents a detailed report of the significant effects involv-ing accuracy and latency One may notice a couple of sig-nificant interactions involving nonfocused dimension andtrial type In accuracy the interaction between nonfocusedfan and trial type was significant The nonfocused fan ef-fect was significant for targets [F(270) 3608 MSe 002 p 0001] but not for foils ( p 70) Also in la-tency a three-way interaction was significant involvingattentional focus nonfocused fan and trial type In theperson-focus condition the interaction between nonfo-cused fan and trial type was not significant ( p 20) Inthe location-focus condition the nonfocused fan effectwas significant for targets [F(216) 3291 MSe 6723p 0001] but not for foils (p 20) It is not clear at thispoint why the nonfocus fan effect differs depending ontrial type Below we report the main result of this studythe differential fan effect in latency
The latency of each condition is plotted in Figure 2There was a significant fan effect both for the emphasized
Table 1Mean Latency (RT in Milliseconds) and Accuracy
Focused Dimension
Target Foil
Nonfocused Fan 1 Fan 2 Fan 3 Fan 1 Fan 2 Fan 3
Dimension RT Acc RT Acc RT Acc RT Acc RT Acc RT Acc
Person-Focus ConditionFan 1 1110 96 1184 97 1298 94 1273 96 1358 96 1479 93Fan 2 1226 95 1280 91 1424 86 1418 93 1467 88 1542 88Fan 3 1186 95 1364 87 1508 79 1384 91 1500 87 1517 83
Location-Focus Condition
Fan 1 1057 94 1174 91 1208 86 1243 91 1307 91 1443 94Fan 2 1064 95 1294 92 1414 84 1239 97 1399 83 1505 93Fan 3 1181 96 1458 88 1448 85 1303 96 1409 96 1572 92
732 SOHN ANDERSON REDER AND GOODE
or organizing dimension and for the nonfocused dimen-sion The critical issue is the relative size of the fan effectfor these dimensions The mental-model theory predicts asmaller fan effect for the focused dimension than for thenonfocused dimension while the ACT-R theory predictsthe opposite To test this the fan slope was calculated forthe focused and the nonfocused conditions The slope wasdefined as the mean latency increase when there is an in-crease of the fan for a particular dimension In the person-focus condition the fan effect of the focused dimension(person dimension 98 msec) was greater than that of thenonfocused dimension [location dimension 63 msect (18) 259 p 05] In the location-focus conditionthe fan effect of the focused dimension (location dimen-sion 118 msec) was greater than that of the nonfocuseddimension [person dimension 73 msec t(16) 280 p 05] The differential fan effect (ie the difference betweenthe fan effects of the two dimensions) in each conditiondid not differ from each other (p 50) The fan effect ofthe focused dimension is comparable to those obtained inother studies using similar materials and designs (egAnderson Bothell amp Douglass 2004) As ACT-R sug-gests regardless of the type of mental model that was sup-posed to be constructed following the instruction the fo-cused dimension resulted in a greater fan effect than did
the nonfocused dimension This result supports ACT-R inthat the focused dimension received higher attentionalweight than the nonfocused dimension
MODELING
Previously developed ACT-R models for the fan effect(Anderson amp Lebiere 1998 Anderson amp Reder 1999) wereused to simulate the differential fan effects obtained in thepresent study These models assume that a participant be-gins by encoding the person and the location terms into theproblem representation then retrieves the relevant personndashlocation fact compares the retrieved result with the prob-lem representation and finally executes the response Thetiming of the encoding comparison and motor executionare considered as intercepts and the current modeling ef-fort concentrates on the retrieval time In ACT-R the ac-tivation level of information determines the retrieval timeaccording to the following latency equation
where F is the scale factor which is to be estimated In theactivation equation given earlier the total activation is asum of base level activation (B) and the sum of weightedassociative strengths (Wj Sji) The associative strength (Sji)
T Fe A= minus
Table 2 Summary of Significant Results
Conditions Statistics
AccuracyFocused fan F(268) 2176 MSe 01 p 0001Nonfocused fan F(268) 1046 MSe 007 p 0001Attentional focus focused fan F(268) 499 MSe 01 p 01Focused fan nonfocused fan F(4136) 333 MSe 008 p 05Nonfocused fan trial type F(268) 1338 MSe 008 p 0001
Latency
Focused fan F(268) 5680 MSe 47356 p 0001Nonfocused fan F(268) 3091 MSe 36066 p 0001Trial type F(268) 9429 MSe 36066 p 0001Nonfocused fan trial type F(268) 564 MSe 19105 p 01Attentional focus focused fan trial type F(268) 418 MSe 18128 p 05
Nonfocused 1Nonfocused 2Nonfocused 3Prediction
1600
1500
1400
1300
1200
1100
1000Focused 1 Focused 2 Focused 3 Focused 1 Focused 2 Focused 3
Person-focus condition Location-focus condition
Lat
ency
(m
sec)
Figure 2 Latency as a function of focused fan nonfocused fan and trial type in each attentional focuscondition
DIFFERENTIAL FAN EFFECT 733
depends on the total associative strength (S) and the num-ber of associations from the concept and is expressed asS ndash ln(n) where n is the number of associations and S isestimated The attentional weight whose total amount isfixed at 1 is the critical parameter because ACT-R pre-dicts that the dimension with a higher attentional weightshould result in a greater fan effect In previous ACT-Rmodels with no emphasis on a particular dimension it wasassumed that the total amount of W is divided equallyamong three termsmdashtwo dimensions of facts and the prepo-sition Therefore 667 is the amount of activation to bedistributed between the person and location dimensions inthis experiment and we estimate what amount of this isgiven to the organizing dimension In sum five param-eters were estimated including the three parameters com-mon to both conditions scale factor (F ) associativestrength (S) and attentional weight for the organizing di-mension (Wf ) Note that the activation and the latencyequation predict only retrieval times of fan facts To per-form a task other processes are also necessary such as en-coding a stimulus and producing a response These times areconsidered as intercepts Different intercepts (I) were es-timated for each condition to reflect the differences betweengroups These five parameters were estimated while min-imizing the χ2 deviation of the fit to the data defined as
which is the ratio of the actual deviation (sum of the squareddeviations of the predicted means from the actual means)to the estimated means (squared standard errors obtainedfrom the participant-by-condition interaction) Thereforea significant χ2 deviation indicates a poor fit of the modelto data This is a statistic whose degrees of freedom is thenumber of observations (36 in total) minus the number ofparameters (5) These predictions are displayed along withthe data in Figure 2 and the parameter values are presentedin Table 3 This intercepts are different between differentattentional focus conditions reflecting the between-groupsdifference The ACT-R model fits the data quite well esti-mating the same parameters for both attentional focusconditions [χ2(31) 3878 p 1] Moreover the esti-mated Wf (398) is greater than the attentional weight ofthe nonfocused dimension (Wn 269) Alternatively wefit the data with an equal amount of W for both dimen-sions (334) which produced a significant deviation fromthe data [χ2(32) 4878 p 05] This strongly supportsthe view that attentional focus can shift the amount of ac-
tivation that is sent from one dimension or another andthe dimension with greater emphasis produces a greaterfan effect
DISCUSSION
The purpose of the present study was to examine the ef-fect of memory representation on memory retrieval Weessentially forced participants into using one of two rep-resentations by requiring them to answer questions an-chored on only one of the dimensions (location or person)The fan effect of the focused dimension was significantlygreater which is inconsistent with the mental-model the-ory How then are we to understand the results that havebeen regarded as supporting the mental-model theory ofthe differential fan effects (eg Radvansky amp Zacks 1991)With object-location pairs for example a substantial faneffect of the object dimension was obtained but no fan ef-fect of the location dimension was obtained This resultwas interpreted as participants forming location-basedmental models Given the results of the present studyhowever it would seem that the object dimension not thelocation dimension served as an organizing dimensionwhen the fan effect was greater for the object dimension
One difference between our study and those of Rad-vansky and his colleagues is that we manipulated the focusof attention to bias which dimension should be selected asthe organizing dimension In their studies the organizingdimension was assumed to have emerged naturally on thebasis of the semantic information implied by the materi-als One might wonder whether attending to a certain di-mension is sufficient to allow organization of informationaround that dimension Zwaan Radvansky Hilliard andCuriel (1998) varied whether spatially organized infor-mation was emphasized or not They found that readingtimes increased when the relevant locations shifted withintext only when spatial information was emphasized How-ever this effect disappeared when the spatial informationwas not emphasized This result seems consistent with ourassumption that the attended dimension may serve as anorganizing dimension
The mental-model class of theories has been quite suc-cessful and influential in many cognitive domains such asreasoning (Johnson-Laird 1983) spatial thinking (Tayloramp Tversky 1996) text comprehension (Bower amp Rinck2001) complex problem solving (Kintsch 1988) and soforth The present study is concerned with a particular ap-plication of the mental-model view on memory retrieval
i ii
xX X sˆ minus( )sum2 2
Table 3Parameter Values and the Result of the
Best-Fitting ACT-R Model
Parameters Model Fit
I F Wf S χ2 df
Person-focus condition 689 msec911 msec 0398 125 3878 31
Location-focus condition 650 msec
NotemdashI intercept
734 SOHN ANDERSON REDER AND GOODE
proposed by Radvansky and his colleagues (Radvansky ampZacks 1991 Radvansky et al 1993 Radvansky et al1997) Therefore implications of the present study for themental-model view are limited However it is noteworthythat the memory representation which lies in the core ofthe mental-model view in general can be successfully in-corporated into an information-processing model that em-phasizes retrieval processes As Radvansky (1999) pointedout memory representation may be incorporated into theACT-R framework as part of declarative knowledge whichis the long-term memory for ACT-R We would add thatthe organization of declarative knowledge reflects the at-tentional focus given to different aspects of information
In conclusion two implications of ACT-R for memoryretrieval have been supported First the strength of the as-sociation between a concept and a fact in memory is ad-justed to reflect fan Second it is possible to vary the weight-ing given to various types of concepts by emphasizing oneof the concepts The ACT-R theory predicts larger fan ef-fects for concepts that receive greater attention empiricaldata and computational modeling of these data have sup-ported this prediction
REFERENCES
Anderson J R (1974) Retrieval of propositional information fromlong-term memory Cognitive Psychology 5 451-474
Anderson J R (1976) Language memory and thought Hillsdale NJErlbaum
Anderson J R Bothell D amp Douglass S (2004) Eye move-ments do not reflect retrieval processes Limits of the eyendashmind hy-pothesis Psychological Science 15 225-231
Anderson J R amp Lebiere C (Eds) (1998) The atomic componentsof thought Mahwah NJ Erlbaum
Anderson J R amp Reder L M (1999) The fan effect New resultsand new theories Journal of Experimental Psychology General 128186-197
Bower G H amp Rinck M (2001) Selecting one among many refer-ents in spatial situation models Journal of Experimental PsychologyLearning Memory amp Cognition 27 81-98
Johnson-Laird P N (1983) Mental models Cambridge CambridgeUniversity Press
Kintsch W (1988) The role of knowledge in discourse comprehensionA constructionndashintegration model Psychological Review 95 163-182
Lewis C H amp Anderson J R (1976) Inferences with real worldknowledge Cognitive Psychology 8 311-335
Radvansky G A (1999) The fan effect A tale of two theories Jour-nal of Experimental Psychology General 128 198-206
Radvansky G A Spieler D H amp Zacks R T (1993) Mentalmodel organization Journal of Experimental Psychology LearningMemory amp Cognition 19 95-114
Radvansky G A Wyer R S Jr Curiel J M amp Lutz M F(1997) Situation models and abstract ownership relations Journal ofExperimental Psychology Learning Memory amp Cognition 23 1233-1246
Radvansky G A amp Zacks R T (1991) Mental models and the faneffect Journal of Experimental Psychology Learning Memory ampCognition 17 940-953
Reder L M amp Ross B H (1983) Integrated knowledge in differenttasks The role of retrieval strategy on fan effects Journal of Experi-mental Psychology Learning Memory amp Cognition 9 55-72
Taylor H A amp Tversky B (1996) Perspective in spatial descrip-tions Journal of Memory amp Language 35 371-391
Zbrodoff N J (1995) Why is 9 7 harder than 2 3 Strength andinterference as explanations of the problem-size effect Memory ampCognition 23 689-700
Zwaan R A Radvansky G A Hilliard A E amp Curiel J M(1998) Constructing multidimensional situation models during read-ing Scientific Studies of Reading 2 199-220
APPENDIXConcepts Used in the Study
Person Location
banker beggar bishop cowboy cyclist airport capitol college desert factorydancer grandma grocer hippie infant kitchen library museum prison resortmaiden mermaid prince prowler rocket stable stadium subway tavern senator soldier speaker surgeon taxicab theater trailer tunnel valleytourist typist vandal writer village winery
NotemdashFor each participant 17 concepts were selected from each category to make upthe fan materials
(Manuscript received May 20 2003revision accepted for publication August 13 2003)
730 SOHN ANDERSON REDER AND GOODE
The mental-model theory has been generalized to othermaterials (Radvansky Spieler amp Zacks 1993 Radvan-sky Wyer Curiel amp Lutz 1997) Radvansky et al (1993)argued that personndashlocation pairs follow different orga-nizing principles depending on the relative size of loca-tions With relatively large locations (eg public libraryhotel) either type of mental model can be formed becausepeople go to many places and a place can contain manypeople With relatively small locations (eg telephonebooth tanning bed) person-based mental models are to beformed because these small places can only contain oneperson at a time whereas the same person can go to all ofthese places This analysis was used to explain why the per-son fan effect was smaller than the location fan effect withrelatively small locations whereas the differential fan ef-fect was not obtained with relatively large locations
In contrast ACT-R emphasizes the retrieval processesIn ACT-R activation spreads from presented terms to theconnected nodes that represent various facts (Figure 1) Thelatency to retrieve any fact from memory is determined byactivation level of that fact The activation Ai of a particu-lar fact i is determined by the following activation equation
where Bi is the base-level activation of the fact reflectingits recency and frequency of study The summation is overthe fact concepts j which are the activation sources whenthe probe is presented for recognition In the present studythese sources are person location and the preposition inThe multiplier Wj is the amount of attention given to a di-mension to which a particular source j belongs In ACT-Rthe fan effect depends on the associative strength Sji which is the relative associative strength of the fact i to agiven concept j As more facts are associated with a con-cept the associative strength of a particular fact is weak-ened because of competition for limited resources If thereis no factor biasing toward person or location the source
activation is assumed to be divided equally between theperson and the location dimensions This is reflected inequal values for Wj However if for some reason either di-mension is emphasized more than the other during learn-ing that dimension may get a higher attentional weight(Anderson amp Reder 1999) Consequently as implied inthe activation equation the dimension with higher atten-tional weight will produce a greater fan effect than the di-mension with lower weight
In summary the mental-model and ACT-R theories offerrather different conceptions of what produces the differ-ential fan effect According to ACT-R the dimension thatgets emphasized has a higher attentional weighting andshould have the greater fan effect So for example whenthere is a larger fan effect of the object dimension than thelocation dimension (eg Radvansky amp Zacks 1991) it isnot because the location is the organizing dimension asthe mental-model theory would argue Rather it is be-cause the object is the emphasized dimension Thus thetwo theories attribute the same effect to special processingof different dimensions
The problem with past research is that there has been noexplicit manipulation to influence which dimension re-ceives special processing Past research has typically taughtparticipants the material with a dropout procedure in whichthey have to produce the correct response to probes of theform ldquoWho is in this locationrdquo or ldquoWhere is this personrdquoThis paradigm ensures that participants receive questionsanchored on both location and person with the intentionof emphasizing both dimensions equally Despite probingfrom both terms during study participants sometimesseem to organize the information around just one term(eg Radvansky amp Zacks 1991) It was inferred that thiswas due to how participants would organize the materialbut this choice was not directly manipulated
The present study manipulated the way participants or-ganize the personndashlocation material during the study phaseParticipants in the person-focus condition received onlyperson-anchored questions with the explicit instruction toorganize material into person models These models in-volve each person visiting multiple locations (eg ldquoThelawyer was in the airport the stadium and the classroomrdquo)Conversely participants in the location-focus conditionreceived only location-anchored questions and were in-structed to organize the material into location models Inthis case the model involves locations that contain multi-ple people (eg ldquoIn the stadium there was the lawyer thesenator and the grandmardquo) Both groups received thesame personndashlocation pairsmdashonly the manner in whichthe material was studied differed Presenting one type ofcued recall question during learning was necessary to ma-nipulate the dimension that would be the focus of atten-tion or the organizing dimension for mental models Themental-model account predicts that the fan effect of the or-ganizing dimension should be smaller than that of the non-focused dimension However the ACT-R theory makes theopposite prediction
A B W Si i j jij
= + sum
Figure 1 An illustration of network representation of facts andtheir associated concepts
DIFFERENTIAL FAN EFFECT 731
METHOD
ParticipantsThere were two groups of participants one assigned to the person-
focus condition (19 participants) and another to the location-focuscondition (17 participants) Participants were undergraduate stu-dents at Carnegie Mellon University They participated in return formonetary reward
ProcedureIn the study phase participants were presented with 28 sentences
regarding a person in a location To accentuate the representationaldifference we used photographs in the person-focus condition anda spatial layout in the location-focus condition In the person-focuscondition participants viewed 25 photographs of individuals theydid not know (graduate students and staff members of the psychol-ogy departments of Carnegie Mellon University and the Universityof Pittsburgh 12 Caucasian male and 13 Caucasian female age range20ndash30) For each participant 17 of these pictures were randomly as-signed to occupation names such as lawyer and senator A personndashlocation sentence (eg ldquoThe lawyer is in the parkrdquo) was presented withthe picture of the corresponding person Occupation names andplaces are presented in the Appendix After reading the sentenceswith the pictures participants went through a two-tiered question-answering phase First they were presented with 25 faces in a 5 5grid and were asked to identify the correct face (eg ldquoClick on thelawyerrdquo) If a wrong face was identified the participant was promptedwith the correct face After identifying the person correctly partici-pants were asked to type in all the places associated with that personWrong answers were corrected To prevent participants from using alocation-based strategy each time a new question was asked the 25faces were presented in a new random configuration of the 5 5 grid
In the location-focus condition participants were presented witha 5 5 grid From the 25 possible positions in the grid 17 were ran-domly selected for each participant and were assigned locationnames such as park and church A sentence was presented in the gridcell that was assigned to the corresponding location Participantswere instructed to memorize which location was at which grid posi-tion and who were the occupants In the question-answering phasethe participants were also presented with two-fold questions Firstthey were asked to identify a certain location among 25 grids (egldquoClick on the parkrdquo) When the location was correctly identifiedthey were asked to type all the people associated with the location
Participantsrsquo memory for the associations was strengthened witha two-pass dropout cued recall procedure In each pass participantsreceived two-fold questions as described above in a random order ofall possible questions If they could not answer correctly the ques-tion was repeated after all the other questions had been asked Thiscontinued until all questions had been answered correctly twice
During the recognition test participants judged 168 targets and168 foils in the form of a personndashlocation pair (ldquolawyerndashparkrdquo) Theorder of the person and location within the probe was randomizedTo create foils we swapped personndashlocation pairs from the same fancondition The probes were presented in 6 blocks of 56 trials Onevery trial a fixation was presented for 500 msec The probe waspresented immediately and remained on the screen until the partici-pantrsquos response was made The feedback on accuracy and speed waspresented for 3 sec
RESULTS
A four-way analysis of variance was conducted for la-tency and accuracy with attentional focus (person or loca-tion) focused dimension (three fans) nonfocused dimen-sion (three fans) and trial type (target and foil) as variablesThe attentional focus was a between-groups factor
For the latency analysis only correct trials with latencyshorter than 3 sec were included Less than 7 of trialswere eliminated because of excessively long responsesMean accuracy and latency presented in Table 1 werenegatively correlated across the various conditions de-fined by the combinations of the variables (r 56 p 01) indicating that conditions with poor performance byone measure had poor performance by the other Table 2presents a detailed report of the significant effects involv-ing accuracy and latency One may notice a couple of sig-nificant interactions involving nonfocused dimension andtrial type In accuracy the interaction between nonfocusedfan and trial type was significant The nonfocused fan ef-fect was significant for targets [F(270) 3608 MSe 002 p 0001] but not for foils ( p 70) Also in la-tency a three-way interaction was significant involvingattentional focus nonfocused fan and trial type In theperson-focus condition the interaction between nonfo-cused fan and trial type was not significant ( p 20) Inthe location-focus condition the nonfocused fan effectwas significant for targets [F(216) 3291 MSe 6723p 0001] but not for foils (p 20) It is not clear at thispoint why the nonfocus fan effect differs depending ontrial type Below we report the main result of this studythe differential fan effect in latency
The latency of each condition is plotted in Figure 2There was a significant fan effect both for the emphasized
Table 1Mean Latency (RT in Milliseconds) and Accuracy
Focused Dimension
Target Foil
Nonfocused Fan 1 Fan 2 Fan 3 Fan 1 Fan 2 Fan 3
Dimension RT Acc RT Acc RT Acc RT Acc RT Acc RT Acc
Person-Focus ConditionFan 1 1110 96 1184 97 1298 94 1273 96 1358 96 1479 93Fan 2 1226 95 1280 91 1424 86 1418 93 1467 88 1542 88Fan 3 1186 95 1364 87 1508 79 1384 91 1500 87 1517 83
Location-Focus Condition
Fan 1 1057 94 1174 91 1208 86 1243 91 1307 91 1443 94Fan 2 1064 95 1294 92 1414 84 1239 97 1399 83 1505 93Fan 3 1181 96 1458 88 1448 85 1303 96 1409 96 1572 92
732 SOHN ANDERSON REDER AND GOODE
or organizing dimension and for the nonfocused dimen-sion The critical issue is the relative size of the fan effectfor these dimensions The mental-model theory predicts asmaller fan effect for the focused dimension than for thenonfocused dimension while the ACT-R theory predictsthe opposite To test this the fan slope was calculated forthe focused and the nonfocused conditions The slope wasdefined as the mean latency increase when there is an in-crease of the fan for a particular dimension In the person-focus condition the fan effect of the focused dimension(person dimension 98 msec) was greater than that of thenonfocused dimension [location dimension 63 msect (18) 259 p 05] In the location-focus conditionthe fan effect of the focused dimension (location dimen-sion 118 msec) was greater than that of the nonfocuseddimension [person dimension 73 msec t(16) 280 p 05] The differential fan effect (ie the difference betweenthe fan effects of the two dimensions) in each conditiondid not differ from each other (p 50) The fan effect ofthe focused dimension is comparable to those obtained inother studies using similar materials and designs (egAnderson Bothell amp Douglass 2004) As ACT-R sug-gests regardless of the type of mental model that was sup-posed to be constructed following the instruction the fo-cused dimension resulted in a greater fan effect than did
the nonfocused dimension This result supports ACT-R inthat the focused dimension received higher attentionalweight than the nonfocused dimension
MODELING
Previously developed ACT-R models for the fan effect(Anderson amp Lebiere 1998 Anderson amp Reder 1999) wereused to simulate the differential fan effects obtained in thepresent study These models assume that a participant be-gins by encoding the person and the location terms into theproblem representation then retrieves the relevant personndashlocation fact compares the retrieved result with the prob-lem representation and finally executes the response Thetiming of the encoding comparison and motor executionare considered as intercepts and the current modeling ef-fort concentrates on the retrieval time In ACT-R the ac-tivation level of information determines the retrieval timeaccording to the following latency equation
where F is the scale factor which is to be estimated In theactivation equation given earlier the total activation is asum of base level activation (B) and the sum of weightedassociative strengths (Wj Sji) The associative strength (Sji)
T Fe A= minus
Table 2 Summary of Significant Results
Conditions Statistics
AccuracyFocused fan F(268) 2176 MSe 01 p 0001Nonfocused fan F(268) 1046 MSe 007 p 0001Attentional focus focused fan F(268) 499 MSe 01 p 01Focused fan nonfocused fan F(4136) 333 MSe 008 p 05Nonfocused fan trial type F(268) 1338 MSe 008 p 0001
Latency
Focused fan F(268) 5680 MSe 47356 p 0001Nonfocused fan F(268) 3091 MSe 36066 p 0001Trial type F(268) 9429 MSe 36066 p 0001Nonfocused fan trial type F(268) 564 MSe 19105 p 01Attentional focus focused fan trial type F(268) 418 MSe 18128 p 05
Nonfocused 1Nonfocused 2Nonfocused 3Prediction
1600
1500
1400
1300
1200
1100
1000Focused 1 Focused 2 Focused 3 Focused 1 Focused 2 Focused 3
Person-focus condition Location-focus condition
Lat
ency
(m
sec)
Figure 2 Latency as a function of focused fan nonfocused fan and trial type in each attentional focuscondition
DIFFERENTIAL FAN EFFECT 733
depends on the total associative strength (S) and the num-ber of associations from the concept and is expressed asS ndash ln(n) where n is the number of associations and S isestimated The attentional weight whose total amount isfixed at 1 is the critical parameter because ACT-R pre-dicts that the dimension with a higher attentional weightshould result in a greater fan effect In previous ACT-Rmodels with no emphasis on a particular dimension it wasassumed that the total amount of W is divided equallyamong three termsmdashtwo dimensions of facts and the prepo-sition Therefore 667 is the amount of activation to bedistributed between the person and location dimensions inthis experiment and we estimate what amount of this isgiven to the organizing dimension In sum five param-eters were estimated including the three parameters com-mon to both conditions scale factor (F ) associativestrength (S) and attentional weight for the organizing di-mension (Wf ) Note that the activation and the latencyequation predict only retrieval times of fan facts To per-form a task other processes are also necessary such as en-coding a stimulus and producing a response These times areconsidered as intercepts Different intercepts (I) were es-timated for each condition to reflect the differences betweengroups These five parameters were estimated while min-imizing the χ2 deviation of the fit to the data defined as
which is the ratio of the actual deviation (sum of the squareddeviations of the predicted means from the actual means)to the estimated means (squared standard errors obtainedfrom the participant-by-condition interaction) Thereforea significant χ2 deviation indicates a poor fit of the modelto data This is a statistic whose degrees of freedom is thenumber of observations (36 in total) minus the number ofparameters (5) These predictions are displayed along withthe data in Figure 2 and the parameter values are presentedin Table 3 This intercepts are different between differentattentional focus conditions reflecting the between-groupsdifference The ACT-R model fits the data quite well esti-mating the same parameters for both attentional focusconditions [χ2(31) 3878 p 1] Moreover the esti-mated Wf (398) is greater than the attentional weight ofthe nonfocused dimension (Wn 269) Alternatively wefit the data with an equal amount of W for both dimen-sions (334) which produced a significant deviation fromthe data [χ2(32) 4878 p 05] This strongly supportsthe view that attentional focus can shift the amount of ac-
tivation that is sent from one dimension or another andthe dimension with greater emphasis produces a greaterfan effect
DISCUSSION
The purpose of the present study was to examine the ef-fect of memory representation on memory retrieval Weessentially forced participants into using one of two rep-resentations by requiring them to answer questions an-chored on only one of the dimensions (location or person)The fan effect of the focused dimension was significantlygreater which is inconsistent with the mental-model the-ory How then are we to understand the results that havebeen regarded as supporting the mental-model theory ofthe differential fan effects (eg Radvansky amp Zacks 1991)With object-location pairs for example a substantial faneffect of the object dimension was obtained but no fan ef-fect of the location dimension was obtained This resultwas interpreted as participants forming location-basedmental models Given the results of the present studyhowever it would seem that the object dimension not thelocation dimension served as an organizing dimensionwhen the fan effect was greater for the object dimension
One difference between our study and those of Rad-vansky and his colleagues is that we manipulated the focusof attention to bias which dimension should be selected asthe organizing dimension In their studies the organizingdimension was assumed to have emerged naturally on thebasis of the semantic information implied by the materi-als One might wonder whether attending to a certain di-mension is sufficient to allow organization of informationaround that dimension Zwaan Radvansky Hilliard andCuriel (1998) varied whether spatially organized infor-mation was emphasized or not They found that readingtimes increased when the relevant locations shifted withintext only when spatial information was emphasized How-ever this effect disappeared when the spatial informationwas not emphasized This result seems consistent with ourassumption that the attended dimension may serve as anorganizing dimension
The mental-model class of theories has been quite suc-cessful and influential in many cognitive domains such asreasoning (Johnson-Laird 1983) spatial thinking (Tayloramp Tversky 1996) text comprehension (Bower amp Rinck2001) complex problem solving (Kintsch 1988) and soforth The present study is concerned with a particular ap-plication of the mental-model view on memory retrieval
i ii
xX X sˆ minus( )sum2 2
Table 3Parameter Values and the Result of the
Best-Fitting ACT-R Model
Parameters Model Fit
I F Wf S χ2 df
Person-focus condition 689 msec911 msec 0398 125 3878 31
Location-focus condition 650 msec
NotemdashI intercept
734 SOHN ANDERSON REDER AND GOODE
proposed by Radvansky and his colleagues (Radvansky ampZacks 1991 Radvansky et al 1993 Radvansky et al1997) Therefore implications of the present study for themental-model view are limited However it is noteworthythat the memory representation which lies in the core ofthe mental-model view in general can be successfully in-corporated into an information-processing model that em-phasizes retrieval processes As Radvansky (1999) pointedout memory representation may be incorporated into theACT-R framework as part of declarative knowledge whichis the long-term memory for ACT-R We would add thatthe organization of declarative knowledge reflects the at-tentional focus given to different aspects of information
In conclusion two implications of ACT-R for memoryretrieval have been supported First the strength of the as-sociation between a concept and a fact in memory is ad-justed to reflect fan Second it is possible to vary the weight-ing given to various types of concepts by emphasizing oneof the concepts The ACT-R theory predicts larger fan ef-fects for concepts that receive greater attention empiricaldata and computational modeling of these data have sup-ported this prediction
REFERENCES
Anderson J R (1974) Retrieval of propositional information fromlong-term memory Cognitive Psychology 5 451-474
Anderson J R (1976) Language memory and thought Hillsdale NJErlbaum
Anderson J R Bothell D amp Douglass S (2004) Eye move-ments do not reflect retrieval processes Limits of the eyendashmind hy-pothesis Psychological Science 15 225-231
Anderson J R amp Lebiere C (Eds) (1998) The atomic componentsof thought Mahwah NJ Erlbaum
Anderson J R amp Reder L M (1999) The fan effect New resultsand new theories Journal of Experimental Psychology General 128186-197
Bower G H amp Rinck M (2001) Selecting one among many refer-ents in spatial situation models Journal of Experimental PsychologyLearning Memory amp Cognition 27 81-98
Johnson-Laird P N (1983) Mental models Cambridge CambridgeUniversity Press
Kintsch W (1988) The role of knowledge in discourse comprehensionA constructionndashintegration model Psychological Review 95 163-182
Lewis C H amp Anderson J R (1976) Inferences with real worldknowledge Cognitive Psychology 8 311-335
Radvansky G A (1999) The fan effect A tale of two theories Jour-nal of Experimental Psychology General 128 198-206
Radvansky G A Spieler D H amp Zacks R T (1993) Mentalmodel organization Journal of Experimental Psychology LearningMemory amp Cognition 19 95-114
Radvansky G A Wyer R S Jr Curiel J M amp Lutz M F(1997) Situation models and abstract ownership relations Journal ofExperimental Psychology Learning Memory amp Cognition 23 1233-1246
Radvansky G A amp Zacks R T (1991) Mental models and the faneffect Journal of Experimental Psychology Learning Memory ampCognition 17 940-953
Reder L M amp Ross B H (1983) Integrated knowledge in differenttasks The role of retrieval strategy on fan effects Journal of Experi-mental Psychology Learning Memory amp Cognition 9 55-72
Taylor H A amp Tversky B (1996) Perspective in spatial descrip-tions Journal of Memory amp Language 35 371-391
Zbrodoff N J (1995) Why is 9 7 harder than 2 3 Strength andinterference as explanations of the problem-size effect Memory ampCognition 23 689-700
Zwaan R A Radvansky G A Hilliard A E amp Curiel J M(1998) Constructing multidimensional situation models during read-ing Scientific Studies of Reading 2 199-220
APPENDIXConcepts Used in the Study
Person Location
banker beggar bishop cowboy cyclist airport capitol college desert factorydancer grandma grocer hippie infant kitchen library museum prison resortmaiden mermaid prince prowler rocket stable stadium subway tavern senator soldier speaker surgeon taxicab theater trailer tunnel valleytourist typist vandal writer village winery
NotemdashFor each participant 17 concepts were selected from each category to make upthe fan materials
(Manuscript received May 20 2003revision accepted for publication August 13 2003)
DIFFERENTIAL FAN EFFECT 731
METHOD
ParticipantsThere were two groups of participants one assigned to the person-
focus condition (19 participants) and another to the location-focuscondition (17 participants) Participants were undergraduate stu-dents at Carnegie Mellon University They participated in return formonetary reward
ProcedureIn the study phase participants were presented with 28 sentences
regarding a person in a location To accentuate the representationaldifference we used photographs in the person-focus condition anda spatial layout in the location-focus condition In the person-focuscondition participants viewed 25 photographs of individuals theydid not know (graduate students and staff members of the psychol-ogy departments of Carnegie Mellon University and the Universityof Pittsburgh 12 Caucasian male and 13 Caucasian female age range20ndash30) For each participant 17 of these pictures were randomly as-signed to occupation names such as lawyer and senator A personndashlocation sentence (eg ldquoThe lawyer is in the parkrdquo) was presented withthe picture of the corresponding person Occupation names andplaces are presented in the Appendix After reading the sentenceswith the pictures participants went through a two-tiered question-answering phase First they were presented with 25 faces in a 5 5grid and were asked to identify the correct face (eg ldquoClick on thelawyerrdquo) If a wrong face was identified the participant was promptedwith the correct face After identifying the person correctly partici-pants were asked to type in all the places associated with that personWrong answers were corrected To prevent participants from using alocation-based strategy each time a new question was asked the 25faces were presented in a new random configuration of the 5 5 grid
In the location-focus condition participants were presented witha 5 5 grid From the 25 possible positions in the grid 17 were ran-domly selected for each participant and were assigned locationnames such as park and church A sentence was presented in the gridcell that was assigned to the corresponding location Participantswere instructed to memorize which location was at which grid posi-tion and who were the occupants In the question-answering phasethe participants were also presented with two-fold questions Firstthey were asked to identify a certain location among 25 grids (egldquoClick on the parkrdquo) When the location was correctly identifiedthey were asked to type all the people associated with the location
Participantsrsquo memory for the associations was strengthened witha two-pass dropout cued recall procedure In each pass participantsreceived two-fold questions as described above in a random order ofall possible questions If they could not answer correctly the ques-tion was repeated after all the other questions had been asked Thiscontinued until all questions had been answered correctly twice
During the recognition test participants judged 168 targets and168 foils in the form of a personndashlocation pair (ldquolawyerndashparkrdquo) Theorder of the person and location within the probe was randomizedTo create foils we swapped personndashlocation pairs from the same fancondition The probes were presented in 6 blocks of 56 trials Onevery trial a fixation was presented for 500 msec The probe waspresented immediately and remained on the screen until the partici-pantrsquos response was made The feedback on accuracy and speed waspresented for 3 sec
RESULTS
A four-way analysis of variance was conducted for la-tency and accuracy with attentional focus (person or loca-tion) focused dimension (three fans) nonfocused dimen-sion (three fans) and trial type (target and foil) as variablesThe attentional focus was a between-groups factor
For the latency analysis only correct trials with latencyshorter than 3 sec were included Less than 7 of trialswere eliminated because of excessively long responsesMean accuracy and latency presented in Table 1 werenegatively correlated across the various conditions de-fined by the combinations of the variables (r 56 p 01) indicating that conditions with poor performance byone measure had poor performance by the other Table 2presents a detailed report of the significant effects involv-ing accuracy and latency One may notice a couple of sig-nificant interactions involving nonfocused dimension andtrial type In accuracy the interaction between nonfocusedfan and trial type was significant The nonfocused fan ef-fect was significant for targets [F(270) 3608 MSe 002 p 0001] but not for foils ( p 70) Also in la-tency a three-way interaction was significant involvingattentional focus nonfocused fan and trial type In theperson-focus condition the interaction between nonfo-cused fan and trial type was not significant ( p 20) Inthe location-focus condition the nonfocused fan effectwas significant for targets [F(216) 3291 MSe 6723p 0001] but not for foils (p 20) It is not clear at thispoint why the nonfocus fan effect differs depending ontrial type Below we report the main result of this studythe differential fan effect in latency
The latency of each condition is plotted in Figure 2There was a significant fan effect both for the emphasized
Table 1Mean Latency (RT in Milliseconds) and Accuracy
Focused Dimension
Target Foil
Nonfocused Fan 1 Fan 2 Fan 3 Fan 1 Fan 2 Fan 3
Dimension RT Acc RT Acc RT Acc RT Acc RT Acc RT Acc
Person-Focus ConditionFan 1 1110 96 1184 97 1298 94 1273 96 1358 96 1479 93Fan 2 1226 95 1280 91 1424 86 1418 93 1467 88 1542 88Fan 3 1186 95 1364 87 1508 79 1384 91 1500 87 1517 83
Location-Focus Condition
Fan 1 1057 94 1174 91 1208 86 1243 91 1307 91 1443 94Fan 2 1064 95 1294 92 1414 84 1239 97 1399 83 1505 93Fan 3 1181 96 1458 88 1448 85 1303 96 1409 96 1572 92
732 SOHN ANDERSON REDER AND GOODE
or organizing dimension and for the nonfocused dimen-sion The critical issue is the relative size of the fan effectfor these dimensions The mental-model theory predicts asmaller fan effect for the focused dimension than for thenonfocused dimension while the ACT-R theory predictsthe opposite To test this the fan slope was calculated forthe focused and the nonfocused conditions The slope wasdefined as the mean latency increase when there is an in-crease of the fan for a particular dimension In the person-focus condition the fan effect of the focused dimension(person dimension 98 msec) was greater than that of thenonfocused dimension [location dimension 63 msect (18) 259 p 05] In the location-focus conditionthe fan effect of the focused dimension (location dimen-sion 118 msec) was greater than that of the nonfocuseddimension [person dimension 73 msec t(16) 280 p 05] The differential fan effect (ie the difference betweenthe fan effects of the two dimensions) in each conditiondid not differ from each other (p 50) The fan effect ofthe focused dimension is comparable to those obtained inother studies using similar materials and designs (egAnderson Bothell amp Douglass 2004) As ACT-R sug-gests regardless of the type of mental model that was sup-posed to be constructed following the instruction the fo-cused dimension resulted in a greater fan effect than did
the nonfocused dimension This result supports ACT-R inthat the focused dimension received higher attentionalweight than the nonfocused dimension
MODELING
Previously developed ACT-R models for the fan effect(Anderson amp Lebiere 1998 Anderson amp Reder 1999) wereused to simulate the differential fan effects obtained in thepresent study These models assume that a participant be-gins by encoding the person and the location terms into theproblem representation then retrieves the relevant personndashlocation fact compares the retrieved result with the prob-lem representation and finally executes the response Thetiming of the encoding comparison and motor executionare considered as intercepts and the current modeling ef-fort concentrates on the retrieval time In ACT-R the ac-tivation level of information determines the retrieval timeaccording to the following latency equation
where F is the scale factor which is to be estimated In theactivation equation given earlier the total activation is asum of base level activation (B) and the sum of weightedassociative strengths (Wj Sji) The associative strength (Sji)
T Fe A= minus
Table 2 Summary of Significant Results
Conditions Statistics
AccuracyFocused fan F(268) 2176 MSe 01 p 0001Nonfocused fan F(268) 1046 MSe 007 p 0001Attentional focus focused fan F(268) 499 MSe 01 p 01Focused fan nonfocused fan F(4136) 333 MSe 008 p 05Nonfocused fan trial type F(268) 1338 MSe 008 p 0001
Latency
Focused fan F(268) 5680 MSe 47356 p 0001Nonfocused fan F(268) 3091 MSe 36066 p 0001Trial type F(268) 9429 MSe 36066 p 0001Nonfocused fan trial type F(268) 564 MSe 19105 p 01Attentional focus focused fan trial type F(268) 418 MSe 18128 p 05
Nonfocused 1Nonfocused 2Nonfocused 3Prediction
1600
1500
1400
1300
1200
1100
1000Focused 1 Focused 2 Focused 3 Focused 1 Focused 2 Focused 3
Person-focus condition Location-focus condition
Lat
ency
(m
sec)
Figure 2 Latency as a function of focused fan nonfocused fan and trial type in each attentional focuscondition
DIFFERENTIAL FAN EFFECT 733
depends on the total associative strength (S) and the num-ber of associations from the concept and is expressed asS ndash ln(n) where n is the number of associations and S isestimated The attentional weight whose total amount isfixed at 1 is the critical parameter because ACT-R pre-dicts that the dimension with a higher attentional weightshould result in a greater fan effect In previous ACT-Rmodels with no emphasis on a particular dimension it wasassumed that the total amount of W is divided equallyamong three termsmdashtwo dimensions of facts and the prepo-sition Therefore 667 is the amount of activation to bedistributed between the person and location dimensions inthis experiment and we estimate what amount of this isgiven to the organizing dimension In sum five param-eters were estimated including the three parameters com-mon to both conditions scale factor (F ) associativestrength (S) and attentional weight for the organizing di-mension (Wf ) Note that the activation and the latencyequation predict only retrieval times of fan facts To per-form a task other processes are also necessary such as en-coding a stimulus and producing a response These times areconsidered as intercepts Different intercepts (I) were es-timated for each condition to reflect the differences betweengroups These five parameters were estimated while min-imizing the χ2 deviation of the fit to the data defined as
which is the ratio of the actual deviation (sum of the squareddeviations of the predicted means from the actual means)to the estimated means (squared standard errors obtainedfrom the participant-by-condition interaction) Thereforea significant χ2 deviation indicates a poor fit of the modelto data This is a statistic whose degrees of freedom is thenumber of observations (36 in total) minus the number ofparameters (5) These predictions are displayed along withthe data in Figure 2 and the parameter values are presentedin Table 3 This intercepts are different between differentattentional focus conditions reflecting the between-groupsdifference The ACT-R model fits the data quite well esti-mating the same parameters for both attentional focusconditions [χ2(31) 3878 p 1] Moreover the esti-mated Wf (398) is greater than the attentional weight ofthe nonfocused dimension (Wn 269) Alternatively wefit the data with an equal amount of W for both dimen-sions (334) which produced a significant deviation fromthe data [χ2(32) 4878 p 05] This strongly supportsthe view that attentional focus can shift the amount of ac-
tivation that is sent from one dimension or another andthe dimension with greater emphasis produces a greaterfan effect
DISCUSSION
The purpose of the present study was to examine the ef-fect of memory representation on memory retrieval Weessentially forced participants into using one of two rep-resentations by requiring them to answer questions an-chored on only one of the dimensions (location or person)The fan effect of the focused dimension was significantlygreater which is inconsistent with the mental-model the-ory How then are we to understand the results that havebeen regarded as supporting the mental-model theory ofthe differential fan effects (eg Radvansky amp Zacks 1991)With object-location pairs for example a substantial faneffect of the object dimension was obtained but no fan ef-fect of the location dimension was obtained This resultwas interpreted as participants forming location-basedmental models Given the results of the present studyhowever it would seem that the object dimension not thelocation dimension served as an organizing dimensionwhen the fan effect was greater for the object dimension
One difference between our study and those of Rad-vansky and his colleagues is that we manipulated the focusof attention to bias which dimension should be selected asthe organizing dimension In their studies the organizingdimension was assumed to have emerged naturally on thebasis of the semantic information implied by the materi-als One might wonder whether attending to a certain di-mension is sufficient to allow organization of informationaround that dimension Zwaan Radvansky Hilliard andCuriel (1998) varied whether spatially organized infor-mation was emphasized or not They found that readingtimes increased when the relevant locations shifted withintext only when spatial information was emphasized How-ever this effect disappeared when the spatial informationwas not emphasized This result seems consistent with ourassumption that the attended dimension may serve as anorganizing dimension
The mental-model class of theories has been quite suc-cessful and influential in many cognitive domains such asreasoning (Johnson-Laird 1983) spatial thinking (Tayloramp Tversky 1996) text comprehension (Bower amp Rinck2001) complex problem solving (Kintsch 1988) and soforth The present study is concerned with a particular ap-plication of the mental-model view on memory retrieval
i ii
xX X sˆ minus( )sum2 2
Table 3Parameter Values and the Result of the
Best-Fitting ACT-R Model
Parameters Model Fit
I F Wf S χ2 df
Person-focus condition 689 msec911 msec 0398 125 3878 31
Location-focus condition 650 msec
NotemdashI intercept
734 SOHN ANDERSON REDER AND GOODE
proposed by Radvansky and his colleagues (Radvansky ampZacks 1991 Radvansky et al 1993 Radvansky et al1997) Therefore implications of the present study for themental-model view are limited However it is noteworthythat the memory representation which lies in the core ofthe mental-model view in general can be successfully in-corporated into an information-processing model that em-phasizes retrieval processes As Radvansky (1999) pointedout memory representation may be incorporated into theACT-R framework as part of declarative knowledge whichis the long-term memory for ACT-R We would add thatthe organization of declarative knowledge reflects the at-tentional focus given to different aspects of information
In conclusion two implications of ACT-R for memoryretrieval have been supported First the strength of the as-sociation between a concept and a fact in memory is ad-justed to reflect fan Second it is possible to vary the weight-ing given to various types of concepts by emphasizing oneof the concepts The ACT-R theory predicts larger fan ef-fects for concepts that receive greater attention empiricaldata and computational modeling of these data have sup-ported this prediction
REFERENCES
Anderson J R (1974) Retrieval of propositional information fromlong-term memory Cognitive Psychology 5 451-474
Anderson J R (1976) Language memory and thought Hillsdale NJErlbaum
Anderson J R Bothell D amp Douglass S (2004) Eye move-ments do not reflect retrieval processes Limits of the eyendashmind hy-pothesis Psychological Science 15 225-231
Anderson J R amp Lebiere C (Eds) (1998) The atomic componentsof thought Mahwah NJ Erlbaum
Anderson J R amp Reder L M (1999) The fan effect New resultsand new theories Journal of Experimental Psychology General 128186-197
Bower G H amp Rinck M (2001) Selecting one among many refer-ents in spatial situation models Journal of Experimental PsychologyLearning Memory amp Cognition 27 81-98
Johnson-Laird P N (1983) Mental models Cambridge CambridgeUniversity Press
Kintsch W (1988) The role of knowledge in discourse comprehensionA constructionndashintegration model Psychological Review 95 163-182
Lewis C H amp Anderson J R (1976) Inferences with real worldknowledge Cognitive Psychology 8 311-335
Radvansky G A (1999) The fan effect A tale of two theories Jour-nal of Experimental Psychology General 128 198-206
Radvansky G A Spieler D H amp Zacks R T (1993) Mentalmodel organization Journal of Experimental Psychology LearningMemory amp Cognition 19 95-114
Radvansky G A Wyer R S Jr Curiel J M amp Lutz M F(1997) Situation models and abstract ownership relations Journal ofExperimental Psychology Learning Memory amp Cognition 23 1233-1246
Radvansky G A amp Zacks R T (1991) Mental models and the faneffect Journal of Experimental Psychology Learning Memory ampCognition 17 940-953
Reder L M amp Ross B H (1983) Integrated knowledge in differenttasks The role of retrieval strategy on fan effects Journal of Experi-mental Psychology Learning Memory amp Cognition 9 55-72
Taylor H A amp Tversky B (1996) Perspective in spatial descrip-tions Journal of Memory amp Language 35 371-391
Zbrodoff N J (1995) Why is 9 7 harder than 2 3 Strength andinterference as explanations of the problem-size effect Memory ampCognition 23 689-700
Zwaan R A Radvansky G A Hilliard A E amp Curiel J M(1998) Constructing multidimensional situation models during read-ing Scientific Studies of Reading 2 199-220
APPENDIXConcepts Used in the Study
Person Location
banker beggar bishop cowboy cyclist airport capitol college desert factorydancer grandma grocer hippie infant kitchen library museum prison resortmaiden mermaid prince prowler rocket stable stadium subway tavern senator soldier speaker surgeon taxicab theater trailer tunnel valleytourist typist vandal writer village winery
NotemdashFor each participant 17 concepts were selected from each category to make upthe fan materials
(Manuscript received May 20 2003revision accepted for publication August 13 2003)
732 SOHN ANDERSON REDER AND GOODE
or organizing dimension and for the nonfocused dimen-sion The critical issue is the relative size of the fan effectfor these dimensions The mental-model theory predicts asmaller fan effect for the focused dimension than for thenonfocused dimension while the ACT-R theory predictsthe opposite To test this the fan slope was calculated forthe focused and the nonfocused conditions The slope wasdefined as the mean latency increase when there is an in-crease of the fan for a particular dimension In the person-focus condition the fan effect of the focused dimension(person dimension 98 msec) was greater than that of thenonfocused dimension [location dimension 63 msect (18) 259 p 05] In the location-focus conditionthe fan effect of the focused dimension (location dimen-sion 118 msec) was greater than that of the nonfocuseddimension [person dimension 73 msec t(16) 280 p 05] The differential fan effect (ie the difference betweenthe fan effects of the two dimensions) in each conditiondid not differ from each other (p 50) The fan effect ofthe focused dimension is comparable to those obtained inother studies using similar materials and designs (egAnderson Bothell amp Douglass 2004) As ACT-R sug-gests regardless of the type of mental model that was sup-posed to be constructed following the instruction the fo-cused dimension resulted in a greater fan effect than did
the nonfocused dimension This result supports ACT-R inthat the focused dimension received higher attentionalweight than the nonfocused dimension
MODELING
Previously developed ACT-R models for the fan effect(Anderson amp Lebiere 1998 Anderson amp Reder 1999) wereused to simulate the differential fan effects obtained in thepresent study These models assume that a participant be-gins by encoding the person and the location terms into theproblem representation then retrieves the relevant personndashlocation fact compares the retrieved result with the prob-lem representation and finally executes the response Thetiming of the encoding comparison and motor executionare considered as intercepts and the current modeling ef-fort concentrates on the retrieval time In ACT-R the ac-tivation level of information determines the retrieval timeaccording to the following latency equation
where F is the scale factor which is to be estimated In theactivation equation given earlier the total activation is asum of base level activation (B) and the sum of weightedassociative strengths (Wj Sji) The associative strength (Sji)
T Fe A= minus
Table 2 Summary of Significant Results
Conditions Statistics
AccuracyFocused fan F(268) 2176 MSe 01 p 0001Nonfocused fan F(268) 1046 MSe 007 p 0001Attentional focus focused fan F(268) 499 MSe 01 p 01Focused fan nonfocused fan F(4136) 333 MSe 008 p 05Nonfocused fan trial type F(268) 1338 MSe 008 p 0001
Latency
Focused fan F(268) 5680 MSe 47356 p 0001Nonfocused fan F(268) 3091 MSe 36066 p 0001Trial type F(268) 9429 MSe 36066 p 0001Nonfocused fan trial type F(268) 564 MSe 19105 p 01Attentional focus focused fan trial type F(268) 418 MSe 18128 p 05
Nonfocused 1Nonfocused 2Nonfocused 3Prediction
1600
1500
1400
1300
1200
1100
1000Focused 1 Focused 2 Focused 3 Focused 1 Focused 2 Focused 3
Person-focus condition Location-focus condition
Lat
ency
(m
sec)
Figure 2 Latency as a function of focused fan nonfocused fan and trial type in each attentional focuscondition
DIFFERENTIAL FAN EFFECT 733
depends on the total associative strength (S) and the num-ber of associations from the concept and is expressed asS ndash ln(n) where n is the number of associations and S isestimated The attentional weight whose total amount isfixed at 1 is the critical parameter because ACT-R pre-dicts that the dimension with a higher attentional weightshould result in a greater fan effect In previous ACT-Rmodels with no emphasis on a particular dimension it wasassumed that the total amount of W is divided equallyamong three termsmdashtwo dimensions of facts and the prepo-sition Therefore 667 is the amount of activation to bedistributed between the person and location dimensions inthis experiment and we estimate what amount of this isgiven to the organizing dimension In sum five param-eters were estimated including the three parameters com-mon to both conditions scale factor (F ) associativestrength (S) and attentional weight for the organizing di-mension (Wf ) Note that the activation and the latencyequation predict only retrieval times of fan facts To per-form a task other processes are also necessary such as en-coding a stimulus and producing a response These times areconsidered as intercepts Different intercepts (I) were es-timated for each condition to reflect the differences betweengroups These five parameters were estimated while min-imizing the χ2 deviation of the fit to the data defined as
which is the ratio of the actual deviation (sum of the squareddeviations of the predicted means from the actual means)to the estimated means (squared standard errors obtainedfrom the participant-by-condition interaction) Thereforea significant χ2 deviation indicates a poor fit of the modelto data This is a statistic whose degrees of freedom is thenumber of observations (36 in total) minus the number ofparameters (5) These predictions are displayed along withthe data in Figure 2 and the parameter values are presentedin Table 3 This intercepts are different between differentattentional focus conditions reflecting the between-groupsdifference The ACT-R model fits the data quite well esti-mating the same parameters for both attentional focusconditions [χ2(31) 3878 p 1] Moreover the esti-mated Wf (398) is greater than the attentional weight ofthe nonfocused dimension (Wn 269) Alternatively wefit the data with an equal amount of W for both dimen-sions (334) which produced a significant deviation fromthe data [χ2(32) 4878 p 05] This strongly supportsthe view that attentional focus can shift the amount of ac-
tivation that is sent from one dimension or another andthe dimension with greater emphasis produces a greaterfan effect
DISCUSSION
The purpose of the present study was to examine the ef-fect of memory representation on memory retrieval Weessentially forced participants into using one of two rep-resentations by requiring them to answer questions an-chored on only one of the dimensions (location or person)The fan effect of the focused dimension was significantlygreater which is inconsistent with the mental-model the-ory How then are we to understand the results that havebeen regarded as supporting the mental-model theory ofthe differential fan effects (eg Radvansky amp Zacks 1991)With object-location pairs for example a substantial faneffect of the object dimension was obtained but no fan ef-fect of the location dimension was obtained This resultwas interpreted as participants forming location-basedmental models Given the results of the present studyhowever it would seem that the object dimension not thelocation dimension served as an organizing dimensionwhen the fan effect was greater for the object dimension
One difference between our study and those of Rad-vansky and his colleagues is that we manipulated the focusof attention to bias which dimension should be selected asthe organizing dimension In their studies the organizingdimension was assumed to have emerged naturally on thebasis of the semantic information implied by the materi-als One might wonder whether attending to a certain di-mension is sufficient to allow organization of informationaround that dimension Zwaan Radvansky Hilliard andCuriel (1998) varied whether spatially organized infor-mation was emphasized or not They found that readingtimes increased when the relevant locations shifted withintext only when spatial information was emphasized How-ever this effect disappeared when the spatial informationwas not emphasized This result seems consistent with ourassumption that the attended dimension may serve as anorganizing dimension
The mental-model class of theories has been quite suc-cessful and influential in many cognitive domains such asreasoning (Johnson-Laird 1983) spatial thinking (Tayloramp Tversky 1996) text comprehension (Bower amp Rinck2001) complex problem solving (Kintsch 1988) and soforth The present study is concerned with a particular ap-plication of the mental-model view on memory retrieval
i ii
xX X sˆ minus( )sum2 2
Table 3Parameter Values and the Result of the
Best-Fitting ACT-R Model
Parameters Model Fit
I F Wf S χ2 df
Person-focus condition 689 msec911 msec 0398 125 3878 31
Location-focus condition 650 msec
NotemdashI intercept
734 SOHN ANDERSON REDER AND GOODE
proposed by Radvansky and his colleagues (Radvansky ampZacks 1991 Radvansky et al 1993 Radvansky et al1997) Therefore implications of the present study for themental-model view are limited However it is noteworthythat the memory representation which lies in the core ofthe mental-model view in general can be successfully in-corporated into an information-processing model that em-phasizes retrieval processes As Radvansky (1999) pointedout memory representation may be incorporated into theACT-R framework as part of declarative knowledge whichis the long-term memory for ACT-R We would add thatthe organization of declarative knowledge reflects the at-tentional focus given to different aspects of information
In conclusion two implications of ACT-R for memoryretrieval have been supported First the strength of the as-sociation between a concept and a fact in memory is ad-justed to reflect fan Second it is possible to vary the weight-ing given to various types of concepts by emphasizing oneof the concepts The ACT-R theory predicts larger fan ef-fects for concepts that receive greater attention empiricaldata and computational modeling of these data have sup-ported this prediction
REFERENCES
Anderson J R (1974) Retrieval of propositional information fromlong-term memory Cognitive Psychology 5 451-474
Anderson J R (1976) Language memory and thought Hillsdale NJErlbaum
Anderson J R Bothell D amp Douglass S (2004) Eye move-ments do not reflect retrieval processes Limits of the eyendashmind hy-pothesis Psychological Science 15 225-231
Anderson J R amp Lebiere C (Eds) (1998) The atomic componentsof thought Mahwah NJ Erlbaum
Anderson J R amp Reder L M (1999) The fan effect New resultsand new theories Journal of Experimental Psychology General 128186-197
Bower G H amp Rinck M (2001) Selecting one among many refer-ents in spatial situation models Journal of Experimental PsychologyLearning Memory amp Cognition 27 81-98
Johnson-Laird P N (1983) Mental models Cambridge CambridgeUniversity Press
Kintsch W (1988) The role of knowledge in discourse comprehensionA constructionndashintegration model Psychological Review 95 163-182
Lewis C H amp Anderson J R (1976) Inferences with real worldknowledge Cognitive Psychology 8 311-335
Radvansky G A (1999) The fan effect A tale of two theories Jour-nal of Experimental Psychology General 128 198-206
Radvansky G A Spieler D H amp Zacks R T (1993) Mentalmodel organization Journal of Experimental Psychology LearningMemory amp Cognition 19 95-114
Radvansky G A Wyer R S Jr Curiel J M amp Lutz M F(1997) Situation models and abstract ownership relations Journal ofExperimental Psychology Learning Memory amp Cognition 23 1233-1246
Radvansky G A amp Zacks R T (1991) Mental models and the faneffect Journal of Experimental Psychology Learning Memory ampCognition 17 940-953
Reder L M amp Ross B H (1983) Integrated knowledge in differenttasks The role of retrieval strategy on fan effects Journal of Experi-mental Psychology Learning Memory amp Cognition 9 55-72
Taylor H A amp Tversky B (1996) Perspective in spatial descrip-tions Journal of Memory amp Language 35 371-391
Zbrodoff N J (1995) Why is 9 7 harder than 2 3 Strength andinterference as explanations of the problem-size effect Memory ampCognition 23 689-700
Zwaan R A Radvansky G A Hilliard A E amp Curiel J M(1998) Constructing multidimensional situation models during read-ing Scientific Studies of Reading 2 199-220
APPENDIXConcepts Used in the Study
Person Location
banker beggar bishop cowboy cyclist airport capitol college desert factorydancer grandma grocer hippie infant kitchen library museum prison resortmaiden mermaid prince prowler rocket stable stadium subway tavern senator soldier speaker surgeon taxicab theater trailer tunnel valleytourist typist vandal writer village winery
NotemdashFor each participant 17 concepts were selected from each category to make upthe fan materials
(Manuscript received May 20 2003revision accepted for publication August 13 2003)
DIFFERENTIAL FAN EFFECT 733
depends on the total associative strength (S) and the num-ber of associations from the concept and is expressed asS ndash ln(n) where n is the number of associations and S isestimated The attentional weight whose total amount isfixed at 1 is the critical parameter because ACT-R pre-dicts that the dimension with a higher attentional weightshould result in a greater fan effect In previous ACT-Rmodels with no emphasis on a particular dimension it wasassumed that the total amount of W is divided equallyamong three termsmdashtwo dimensions of facts and the prepo-sition Therefore 667 is the amount of activation to bedistributed between the person and location dimensions inthis experiment and we estimate what amount of this isgiven to the organizing dimension In sum five param-eters were estimated including the three parameters com-mon to both conditions scale factor (F ) associativestrength (S) and attentional weight for the organizing di-mension (Wf ) Note that the activation and the latencyequation predict only retrieval times of fan facts To per-form a task other processes are also necessary such as en-coding a stimulus and producing a response These times areconsidered as intercepts Different intercepts (I) were es-timated for each condition to reflect the differences betweengroups These five parameters were estimated while min-imizing the χ2 deviation of the fit to the data defined as
which is the ratio of the actual deviation (sum of the squareddeviations of the predicted means from the actual means)to the estimated means (squared standard errors obtainedfrom the participant-by-condition interaction) Thereforea significant χ2 deviation indicates a poor fit of the modelto data This is a statistic whose degrees of freedom is thenumber of observations (36 in total) minus the number ofparameters (5) These predictions are displayed along withthe data in Figure 2 and the parameter values are presentedin Table 3 This intercepts are different between differentattentional focus conditions reflecting the between-groupsdifference The ACT-R model fits the data quite well esti-mating the same parameters for both attentional focusconditions [χ2(31) 3878 p 1] Moreover the esti-mated Wf (398) is greater than the attentional weight ofthe nonfocused dimension (Wn 269) Alternatively wefit the data with an equal amount of W for both dimen-sions (334) which produced a significant deviation fromthe data [χ2(32) 4878 p 05] This strongly supportsthe view that attentional focus can shift the amount of ac-
tivation that is sent from one dimension or another andthe dimension with greater emphasis produces a greaterfan effect
DISCUSSION
The purpose of the present study was to examine the ef-fect of memory representation on memory retrieval Weessentially forced participants into using one of two rep-resentations by requiring them to answer questions an-chored on only one of the dimensions (location or person)The fan effect of the focused dimension was significantlygreater which is inconsistent with the mental-model the-ory How then are we to understand the results that havebeen regarded as supporting the mental-model theory ofthe differential fan effects (eg Radvansky amp Zacks 1991)With object-location pairs for example a substantial faneffect of the object dimension was obtained but no fan ef-fect of the location dimension was obtained This resultwas interpreted as participants forming location-basedmental models Given the results of the present studyhowever it would seem that the object dimension not thelocation dimension served as an organizing dimensionwhen the fan effect was greater for the object dimension
One difference between our study and those of Rad-vansky and his colleagues is that we manipulated the focusof attention to bias which dimension should be selected asthe organizing dimension In their studies the organizingdimension was assumed to have emerged naturally on thebasis of the semantic information implied by the materi-als One might wonder whether attending to a certain di-mension is sufficient to allow organization of informationaround that dimension Zwaan Radvansky Hilliard andCuriel (1998) varied whether spatially organized infor-mation was emphasized or not They found that readingtimes increased when the relevant locations shifted withintext only when spatial information was emphasized How-ever this effect disappeared when the spatial informationwas not emphasized This result seems consistent with ourassumption that the attended dimension may serve as anorganizing dimension
The mental-model class of theories has been quite suc-cessful and influential in many cognitive domains such asreasoning (Johnson-Laird 1983) spatial thinking (Tayloramp Tversky 1996) text comprehension (Bower amp Rinck2001) complex problem solving (Kintsch 1988) and soforth The present study is concerned with a particular ap-plication of the mental-model view on memory retrieval
i ii
xX X sˆ minus( )sum2 2
Table 3Parameter Values and the Result of the
Best-Fitting ACT-R Model
Parameters Model Fit
I F Wf S χ2 df
Person-focus condition 689 msec911 msec 0398 125 3878 31
Location-focus condition 650 msec
NotemdashI intercept
734 SOHN ANDERSON REDER AND GOODE
proposed by Radvansky and his colleagues (Radvansky ampZacks 1991 Radvansky et al 1993 Radvansky et al1997) Therefore implications of the present study for themental-model view are limited However it is noteworthythat the memory representation which lies in the core ofthe mental-model view in general can be successfully in-corporated into an information-processing model that em-phasizes retrieval processes As Radvansky (1999) pointedout memory representation may be incorporated into theACT-R framework as part of declarative knowledge whichis the long-term memory for ACT-R We would add thatthe organization of declarative knowledge reflects the at-tentional focus given to different aspects of information
In conclusion two implications of ACT-R for memoryretrieval have been supported First the strength of the as-sociation between a concept and a fact in memory is ad-justed to reflect fan Second it is possible to vary the weight-ing given to various types of concepts by emphasizing oneof the concepts The ACT-R theory predicts larger fan ef-fects for concepts that receive greater attention empiricaldata and computational modeling of these data have sup-ported this prediction
REFERENCES
Anderson J R (1974) Retrieval of propositional information fromlong-term memory Cognitive Psychology 5 451-474
Anderson J R (1976) Language memory and thought Hillsdale NJErlbaum
Anderson J R Bothell D amp Douglass S (2004) Eye move-ments do not reflect retrieval processes Limits of the eyendashmind hy-pothesis Psychological Science 15 225-231
Anderson J R amp Lebiere C (Eds) (1998) The atomic componentsof thought Mahwah NJ Erlbaum
Anderson J R amp Reder L M (1999) The fan effect New resultsand new theories Journal of Experimental Psychology General 128186-197
Bower G H amp Rinck M (2001) Selecting one among many refer-ents in spatial situation models Journal of Experimental PsychologyLearning Memory amp Cognition 27 81-98
Johnson-Laird P N (1983) Mental models Cambridge CambridgeUniversity Press
Kintsch W (1988) The role of knowledge in discourse comprehensionA constructionndashintegration model Psychological Review 95 163-182
Lewis C H amp Anderson J R (1976) Inferences with real worldknowledge Cognitive Psychology 8 311-335
Radvansky G A (1999) The fan effect A tale of two theories Jour-nal of Experimental Psychology General 128 198-206
Radvansky G A Spieler D H amp Zacks R T (1993) Mentalmodel organization Journal of Experimental Psychology LearningMemory amp Cognition 19 95-114
Radvansky G A Wyer R S Jr Curiel J M amp Lutz M F(1997) Situation models and abstract ownership relations Journal ofExperimental Psychology Learning Memory amp Cognition 23 1233-1246
Radvansky G A amp Zacks R T (1991) Mental models and the faneffect Journal of Experimental Psychology Learning Memory ampCognition 17 940-953
Reder L M amp Ross B H (1983) Integrated knowledge in differenttasks The role of retrieval strategy on fan effects Journal of Experi-mental Psychology Learning Memory amp Cognition 9 55-72
Taylor H A amp Tversky B (1996) Perspective in spatial descrip-tions Journal of Memory amp Language 35 371-391
Zbrodoff N J (1995) Why is 9 7 harder than 2 3 Strength andinterference as explanations of the problem-size effect Memory ampCognition 23 689-700
Zwaan R A Radvansky G A Hilliard A E amp Curiel J M(1998) Constructing multidimensional situation models during read-ing Scientific Studies of Reading 2 199-220
APPENDIXConcepts Used in the Study
Person Location
banker beggar bishop cowboy cyclist airport capitol college desert factorydancer grandma grocer hippie infant kitchen library museum prison resortmaiden mermaid prince prowler rocket stable stadium subway tavern senator soldier speaker surgeon taxicab theater trailer tunnel valleytourist typist vandal writer village winery
NotemdashFor each participant 17 concepts were selected from each category to make upthe fan materials
(Manuscript received May 20 2003revision accepted for publication August 13 2003)
734 SOHN ANDERSON REDER AND GOODE
proposed by Radvansky and his colleagues (Radvansky ampZacks 1991 Radvansky et al 1993 Radvansky et al1997) Therefore implications of the present study for themental-model view are limited However it is noteworthythat the memory representation which lies in the core ofthe mental-model view in general can be successfully in-corporated into an information-processing model that em-phasizes retrieval processes As Radvansky (1999) pointedout memory representation may be incorporated into theACT-R framework as part of declarative knowledge whichis the long-term memory for ACT-R We would add thatthe organization of declarative knowledge reflects the at-tentional focus given to different aspects of information
In conclusion two implications of ACT-R for memoryretrieval have been supported First the strength of the as-sociation between a concept and a fact in memory is ad-justed to reflect fan Second it is possible to vary the weight-ing given to various types of concepts by emphasizing oneof the concepts The ACT-R theory predicts larger fan ef-fects for concepts that receive greater attention empiricaldata and computational modeling of these data have sup-ported this prediction
REFERENCES
Anderson J R (1974) Retrieval of propositional information fromlong-term memory Cognitive Psychology 5 451-474
Anderson J R (1976) Language memory and thought Hillsdale NJErlbaum
Anderson J R Bothell D amp Douglass S (2004) Eye move-ments do not reflect retrieval processes Limits of the eyendashmind hy-pothesis Psychological Science 15 225-231
Anderson J R amp Lebiere C (Eds) (1998) The atomic componentsof thought Mahwah NJ Erlbaum
Anderson J R amp Reder L M (1999) The fan effect New resultsand new theories Journal of Experimental Psychology General 128186-197
Bower G H amp Rinck M (2001) Selecting one among many refer-ents in spatial situation models Journal of Experimental PsychologyLearning Memory amp Cognition 27 81-98
Johnson-Laird P N (1983) Mental models Cambridge CambridgeUniversity Press
Kintsch W (1988) The role of knowledge in discourse comprehensionA constructionndashintegration model Psychological Review 95 163-182
Lewis C H amp Anderson J R (1976) Inferences with real worldknowledge Cognitive Psychology 8 311-335
Radvansky G A (1999) The fan effect A tale of two theories Jour-nal of Experimental Psychology General 128 198-206
Radvansky G A Spieler D H amp Zacks R T (1993) Mentalmodel organization Journal of Experimental Psychology LearningMemory amp Cognition 19 95-114
Radvansky G A Wyer R S Jr Curiel J M amp Lutz M F(1997) Situation models and abstract ownership relations Journal ofExperimental Psychology Learning Memory amp Cognition 23 1233-1246
Radvansky G A amp Zacks R T (1991) Mental models and the faneffect Journal of Experimental Psychology Learning Memory ampCognition 17 940-953
Reder L M amp Ross B H (1983) Integrated knowledge in differenttasks The role of retrieval strategy on fan effects Journal of Experi-mental Psychology Learning Memory amp Cognition 9 55-72
Taylor H A amp Tversky B (1996) Perspective in spatial descrip-tions Journal of Memory amp Language 35 371-391
Zbrodoff N J (1995) Why is 9 7 harder than 2 3 Strength andinterference as explanations of the problem-size effect Memory ampCognition 23 689-700
Zwaan R A Radvansky G A Hilliard A E amp Curiel J M(1998) Constructing multidimensional situation models during read-ing Scientific Studies of Reading 2 199-220
APPENDIXConcepts Used in the Study
Person Location
banker beggar bishop cowboy cyclist airport capitol college desert factorydancer grandma grocer hippie infant kitchen library museum prison resortmaiden mermaid prince prowler rocket stable stadium subway tavern senator soldier speaker surgeon taxicab theater trailer tunnel valleytourist typist vandal writer village winery
NotemdashFor each participant 17 concepts were selected from each category to make upthe fan materials
(Manuscript received May 20 2003revision accepted for publication August 13 2003)
