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The Psychological Record, 2010, 60, 437462The effects of different training structuresin the establishment of conditionaldiscriminations and subsequent performanceon tests for stimulus equivalenceErik Arntzen, Terje Grondahl, and Christoffer EilifsenAkershus University College

Previous studies comparing groups of subjects have indicated differentialprobabilities of stimulus equivalence outcome as a function of trainingstructures.One-to-Many (OTM) and Many-to-One (MTO) training structures seem toproduce positive outcomes on tests for stimulus equivalence more oftenthan

a Linear Series (LS) training structure does. One of the predictions from thediscrimination analysis of R. R. Saunders and Green (1999) is that thedifferencesin outcome between training structures should increase with number ofclass members. The purpose of the present experiment was to replicateandexpand earlier findings on the effect of training structures and the stimulusequivalence outcome in a single-subject design. We wanted to comparethe stimulus

equivalence outcome in three 3-member classes to the outcome in three4-member classes. In addition, we included all trial types in the tests andalsochanged the density of feedback before testing. The results from thecurrentstudy replicated some earlier findings and showed that OTM gave a slightlybetter outcome on the stimulus equivalence test than MTO, and that bothgavebetter outcome than LS. Thus, we did not find that MTO was superior toOTM

with increasing number of members in each class. Reaction time data alsoreplicatedearlier findings that showed an increase from baseline to testing, anda more pronounced increase in reaction time on equivalence thansymmetrytrials. Differential procedural issues and some contingencies that could beimportant


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in understanding the results are discussed.Key words: stimulus equivalence, matching to sample, protocols, trainingstructuresStimulus equivalence is defined as the interchangeability of stimuliwithin a class (Green & Saunders, 1998). The defining characteristic ofstimulusequivalence is responding in accord with reflexivity, symmetry, andtransitivity (e.g., Sidman & Tailby, 1982). Stable baseline responding, aprerequisitefor testing for emergent relations, is established through variousThe second author is now affiliated with Ostfold University College.Some of the data from the current study were presented as a paper at theinternational ABAconference in Sydney, Australia, in 2007. The study is a part of the second

authors master degree.Thanks to two anonymous reviewers and Carl Hughes for suggestions andcomments onearlier drafts.Correspondence concerning this manuscript should be addressed to ErikArntzen, Departmentof Behavioral Science, Akershus University College, PO Box 423, 2001Lillestrom, Norway. E-mail:[email protected] Arntzen et al.training protocols and training structures. The training structures andprotocolsseem to have dissimilar effects on responding in the subsequent stimulusequivalence tests. A training protocol defines the sequence of trainingand type of tests. Imam (2006) has given an account of three differenttrainingprotocols: simple-to-complex, simultaneous, and complex-to-simple.The term training structurehas been used to refer to the sequence ofconditional

discriminations and the arrangements that link stimuli in baselinetraining (R. R. Saunders & Green, 1999). The training structures have beenlabeled Linear Series (LS), Many-to-One (MTO) or Comparison-as-Node(CaN),and One-to-Many (OTM) or Sample-as-Node (SaN) (see K. J. Saunders,Saunders,


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Williams, & Spradlin, 1993, for an overview). A node can be defined as astimulusthat is connected to at least two other stimuli. However, the effects ofthe number of nodes can only be studied when using a linear seriestrainingstructure, because increasing the number of members in each class doesnotinfluence the number of nodes in MTO or OTM. A number of studies havefound nodal effects, i.e., stimulus equivalence outcome decrease andreactiontime increase, to be a function of the number of nodes (e.g., Arntzen &Holth,2000b; Bentall, Jones, & Dickins, 1999; Fields, Landon-Jimenez,Buffington, &

Adams, 1995; Kennedy, 1991). On the other hand, some other findingscontradictthis when the number of trials is equal per nodal number (Imam, 2006).Dymond and Rehfeldt (2001) have seen reaction time as an importantsupplementarymeasure in research on derived relations. A number of studies haveshown a characteristic pattern of reaction time to comparison stimuli, thatis,an increase from the last training trials to the first test trials and a decreaseduring testing (e.g., Arntzen, 2004), and a substantially greater increase forequivalence trials compared to symmetry trials (e.g., Wulfert & Hayes,1988).There are two main reasons for the interest in investigating respondingin accordance with stimulus equivalence as a function of different trainingstructures. First, in the original analyses of stimulus equivalence, thethree training structures were expected to lead to the same outcome ontestfor stimulus equivalence. Second, a number of experiments have shownthat responding in accord with stimulus equivalence varies as a function

of different training structures (e.g., Arntzen, 2007). Some studies havefound that MTO is the most effective training structure (Barnes, as cited inBarnes, 1994; Hove, 2003; K. J. Saunders et al., 1993; R. R. Saunders,Chaney,& Marquis, 2005; R. R. Saunders, Drake, & Spradlin, 1999; R. R. Saunders&McEntee, 2004), while others have found results in favor of OTM (Arntzen,


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2004; Arntzen & Holth, 1997, 2000a). Although there is at present no clearevidence of the differential effectiveness of MTO and OTM structures, theLS training structure has consistently been shown to be the least effectiveinproducing stimulus equivalence with a simultaneous protocol.However, most of the studies that have shown the superiority of theMTO training structure have used a two-choice procedure (see, e.g.,Barnes,1992; K. J. Saunders et al., 1993; R. R. Saunders et al., 1999; R. R.Saunders,Wachter, & Spradlin, 1988; Spradlin & Saunders, 1986). It is therefore apossibilitythat the S-control could explain the differences in stimulus equivalenceoutcome between the studies. Negative contextual control can be

reduced by using three or four choices in the matching-to-sample training(Carrigan & Sidman, 1992; Johnson & Sidman, 1993; Sidman, 1994).Some procedural factors could be responsible for the differences in thestudies that have compared the effects of different training structures. ForTraining Structures and Stimulus Equivalence 439example, the differences could have been due to the types of test trialsincludedin the testing, as argued by R.R. Saunders et al. (2005), and possiblyalso to fading of consequences before testing. In a recent experiment, wefound that for most of the participants, the baseline performance was intactduring testing even if the participant did not respond in accord with stimulusequivalence (Eilifsen & Arntzen, 2009).R. R. Saunders and Green (1999) put forward a discrimination analysis oftraining structures and the effect of using different training structures onstimulus equivalence outcomes. According to this discrimination analysis,for the performance to meet the criteria for acquisition of trained baselinerelations as well as the criteria for positive outcomes on all tests forstimulusequivalence, each stimulus must be discriminated from every other

stimulus in the experiment. Thus, different training structures can lead todifferences in the probability of a successful outcome on tests of stimulusequivalence because the numbers of necessary simple discriminationsdifferacross the training structures. According to the discrimination analysis, oneexplanation for the difference between the outcomes of following differenttraining structures is that during MTO training, every simple discrimination


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ParticipantsTwelve participants were recruited during lectures and via personalcontacts.Eight of the participants, four males and four females, were students(19 to 29 years old). The other four participants, two males and twofemales,were two adults (25 and 27 years old) and two children (#1351 and #1359,10.8 and 13.6 years old). All participants were unfamiliar with the stimulusequivalence paradigm and had never participated in such experiments.Each participant read and signed a consent form and in addition to beinggiven a written information sheet, were informed they could withdraw fromthe experiment at any time. All participants were debriefed on the purposeof the experiment and stimulus equivalence after they had completed theexperiment.

Apparatus and StimuliThe experiments were conducted in two different labs. The collegestudentssat in a small room with two tables and some chairs, and the otherparticipants sat in a small room with two tables, a chair, a bookcase, and abed. One Dell Latitude D510 and two Compaq nc6320 portable personalcomputers,each with a two-button mouse and a 15-inch monitor, were used. Theexperimental software was made by Psych Fusion Ltd in collaboration withthe first author. This matching-to-sample software controlled all stimuluspresentations and the recording of the responses.ProcedureGeneral overview. We started training with three 3-member classesfollowedby three 4-member classes for all three training structures, i.e., LinearSeries, Many-to-One, and One-to-Many. Each structure had its ownspecificset of stimulus material, which was presented to each group of participantsin a random order unique to that group, i.e., the LS training structure with

three 3-member classes always had the same stimulus material and so on.The presentation of training trials was arranged in a variant of asimultaneousprotocol. In the current experiment, all trial types were presented fromthe beginning, that is, on concurrent basis, but starting with only the correctsample-comparison pair. This was followed by a gradual increase in the


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number of comparisons. The training was divided into two phases. InPhase1, the number of comparisons increased from 1 to 2. In Phase 2, allcomparisonswere presented and the feedback was gradually decreased from 100% to0%. Phase 3, the test phase, was designed to test for emergent relations.Stimulus material. Visual, abstract stimuli that were arbitrarily relatedwere presented on the screen, with the sample stimulus always presentedinthe middle of the screen and three comparison stimuli randomly presentedin three corners, leaving the fourth corner blank. Each training structure(see Figure 1) involved a different set of stimuli. The stimulus materialswereGreek, Cyrillic, Japanese, Hebrew, and Arabic letters. Figure 1 shows the

stimulus sets used for each condition.Training Structures and Stimulus Equivalence 441LS training structureThree 3-member classesLS training structureThree 4-member classes1 2 3 1 2 3A AB BC CDOTM training structureThree 3-member classesOTM training structureThree 4-member classesA AB BC CD

MTO training structureThree 3-member classesMTO training structureThree 4-member classesA AB BC C


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DFigure 1. Stimuli used with the 3-member and 4-member classes.Thestimulus set in thefirst panel includes the stimuli used with the LS training structure, in thesecond panelthe stimulus set used with the OTM training structure is depicted, and in thethird rowthe stimuli set used with the MTO training structure is shown.All participants were tested in individual sessions. The order of presentationof the training structures is shown in Table 1. Four participantsstarted with the LS training structure, followed by OTM and MTO trainingstructures, first with 3-member classes and then with 4-member classes(indicatedat the top of Table 1). The next four participants started with the

MTO training structure, followed by OTM and then LS training structures,first with 3-member classes and then with 4-member classes (indicatedin the middle of Table 1). The last four participants started with the OTMtraining structure, followed by LS and MTO training structures, first with3-member classes and then with 4-member classes (indicated at thebottomof Table 1).442 Arntzen et al.Table 1

The Order of Training Structures For Each ParticipantParticipant 3-member classes 4-member classesLS training structure first1351 LS OTM MTO LS OTM MTO1353 LS OTM MTO LS OTM MTO1354 LS OTM MTO LS OTM MTO1355 LS OTM MTO LS OTM MTOMTO training structure first1356 MTO OTM LS MTO OTM LS1357 MTO OTM LS MTO OTM LS

1358 MTO OTM LS MTO OTM LS1359 MTO OTM LS MTO OTM LSOTM training structure first1581 OTM LS MTO OTM LS MTO1582 OTM LS MTO OTM LS MTO1583 OTM LS MTO OTM LS MTO1585 OTM LS MTO OTM LS MTO


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Note: Participants experienced training structures in chronological order,with the first training structure each participant was exposed to shown inthefar left column and the last in the far right column.General information given to the participants. When the participantsagreed to participate in the experiment, they were told that the study wasan investigation in the field of behavior analysis involving some tasks beingpresented on a computer screen. They were told that the task involvedchoosingstimuli on the screen by using a computer mouse, and that no additionalcomputer skills were necessary. Furthermore, the participants were toldthatthe experiment would be conducted over 2 days and that it would last forapproximately

2 hours each day (a total of 4 hours), depending on how rapidlyand correctly they responded. The participants were also informed that theywould get one lottery ticket (Flax ticket) for each day of participation inthe experiment. The value of the lottery ticket was 25 Norwegian kroner,approximately4 U.S. dollars. Eight of the 12 participants completed the currentexperiment in two sessions, and the last 4 participants completed in threesessions.Instructions. When a participant was ready to start the experiment, thefollowing text came up on the screen:In a moment a stimulus will appear in the middle of the screen.A mouse click on the letter will make another symbol appear. Inthe first trials only one symbol will appear on the screen. Aftersome trials you have to choose one of the symbols in a corner ofthe screen by clicking on it with the mouse. The computer willtell you if your choices are correct or wrong. During some stagesof the experiment the computer will NOT tell you if your choicesare correct or wrong. However, based on what you have learnedso far, you can get all of the tasks correct. Please do your best to

get everything right. Thank you and good luck!Training Structures and Stimulus Equivalence 443Table 2Relations, Minimum Number of Training Trials, and Percentage ofFeedback In Each Phase For Training Structures with Three 3-MemberClassesTraining


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structuresPhases Trial types Minimum no. of trials/block FeedbackLS 1. Acquisition A1B1, A2B2, A3B3, B1C1, B2C2, B3C3 2 X 24 trials100%2. Maintenance Mixing of A-B and B-C trials in five blocks 120 trials Fadingfrom 100% to 0%3. Testing Sym: B1A1A2A3, B2A1A2A3, B3A1A2A3, B1C1C2C3,B2C1C2C3, B3C1C2C3 24 trials 0%Trans: A1C1C2C3, A2C1C2C3, A3C1C2C3Eq: C1A1A2A3, C2A1A2A3, C3A1A2A3 24 trials 0%OTM 1. Acquisition A1B1, A2B2, A3B3, A1C1, A2C2, A3C3 2 X 24 trials100%2. Maintenance Mixing of A-B and AC trials in five blocks 120 trials Fadingfrom 100% to 0%

3. Testing Sym: B1A1A2A3, B2A1A2A3, B3A1A2A3, C1A1A2A3,C2A1A2A3, C3A1A2A3 24 trials 0%Eq: B1C1C2C3,B2C1C2C3,B3C1C2C3,C1B1B2B3,C2B1B2B3,C3B1B2B324 trials 0%MTO 1. Acquisition A1C1, A2C2, A3C3, B1C1, B2C2, B3C3 2 X 24 trials100%2. Maintenance Mixing of AC and BC trials in five blocks 120 trials Fadingfrom 100% to 0%3. Testing Sym: C1A1A2A3, C2A1A2A3, C3A1A2A3, C1B1B2B3,C2B1B2B3, C3B1B2B3 24 trials 0%Eq: A1B1B2B3, A2B1B2B3, A3B1B2B3, B1A1A2A3, B2A1A2A3,B3A1A2A3 24 trials 0%Note: In Phase 1, trials are trained separately; first only one and then twocomparisons (the trial types with one comparison are shown in the table).Sym. = symmetry. Trans. = transitivity. Eq. = equivalence. In Phase 2, allthree comparisons are presented and all trials are trained simultaneously.The underlined comparison is the correct response.444 Arntzen et al.Table 3

Relations, Minimum Number of Training Trials, and Percentage ofFeedback In Each Phase For Training Structures with Three 4-MemberClassesTraining structures Phases Trial types No. of trials FeedbackLS 1. Acquisition A1B1, A2B2, A3B3, B1C1, B2C2, B3C3, C1D1, C2D2,C3D3 2 X 36 trials 100%


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2. Maintenance Mixing of AB, BC, and CD trials in five blocks 180 trialsFading from 100% to 0%3. Testing Sym: B1A1A2A3, B2A1A2A3, B3A1A2A3, C1B1B2B3,C2B1B2B3, C3B1B2B3,D1C1C2C3, D2C1C2C3, D3C1C2C336 trials 0%Trans: A1C1C2C3, A2C1C2C3, A3C1C2C3, B1D1D2D3, B2D1D2D3,B3D1D2D3, A1D1D2D3, A2D1D2D3, A3D1D2D3Eq: C1A1A2A3, C2A1A2A3, C3A1A2A3, D1A1A2A3, D2A1A2A3,D3A1A2A3,D1B1B2B3, D2B1B2B3, D3B1B2B372 trials 0%OTM 1. Acquisition A1B1, A2B2, A3B3, A1C1, A2C2, A3C3, A1D1, A2D2,A3D3 2 X 36 trials 100%

2. Maintenance Mixing of AB, AC, and AD trials in five blocks 180 trialsFading from 100% to 0%3. Testing Sym: B1A1A2A3, B2A1A2A3, B3A1A2A3, C1A1A2A3,C2A1A2A3, C3A1A2A3,D1A1A2A3, D2A1A2A3, D3A1A2A336 trials 0%Eq: B1C1C2C3, B2C1C2C3, B3C1C2C3, C1B1B2B3, C2B1B2B3,C3B1B2B3, C1D1D2D3,C2D1D2D3, C3D1D2D3, D1C1C2C3, D2C1C2C3, D3C1C2C3,B1D1D2D3, B2D1D2D3,B3D1D2D3, D1B1B2B3, D2B1B2B3, D3B1B2B372 trials 0%MTO 1. Acquisition A1D1, A2D2, A3D3, B1D1, B2D2, B3D3, C1D1, C2D2,C3D3 2 X 36 trials 100%2. Maintenance Mixing of AD, BD, and CD trials in five blocks 180 trialsFading from 100% to 0%3. Testing Sym: D1A1A2A3, D2A1A2A3, D3A1A2A3, D1B1B2B3,D2B1B2B3, D3B1B2B3,D1C1C2C3, D2C1C2C3, D3C1C2C3

36 trials 0%Eq: A1B1B2B3, A2B1B2B3, A3B1B2B3, B1A1A2A3, B2A1A2A3,B3A1A2A3, A1C1C2C3,A2C1C2C3, A3C1C2C3, C1A1A2A3, C2A1A2A3, C3A1A2A3, B1C1C2C3,B2C1C2C3,B3C1C2C3, C1B1B2B3, C2B1B2B3, C3B1B2B372 trials 0%


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Note: In Phase 1, trials are trained separately; first only one and then twocomparisons (the trial types with one comparison are shown in the table).Sym. = symmetry. Trans. = transitivity. Eq. = equivalence. In Phase 2, alltrials are trained simultaneously. The underlined comparison is the correctresponse.Training Structures and Stimulus Equivalence 445The last instruction on the screen was, Press here when you are ready to start.Training and testing. Each trial started with the presentation of a samplestimulus. The sample stimulus always appeared in the middle of thescreen. Comparison stimuli were presented when the participant clickedon the sample stimulus. The comparison stimuli were presented randomlyper trial in the corners of the screen. The sample stimulus remained on thescreen until the participant clicked on a comparison stimulus. A correct

choice was followed by feedback consisting of written text, such as Correct,Super, and Awesome. An incorrect choice was followed by the written textWrong. The duration of the feedback was 1,000 milliseconds. Allcomparisonstimuli disappeared after any choice response, and after an intertrialintervalof 1,000 milliseconds a new sample stimulus was presented (i.e., startof the next trial). At the start of each trial, the position of the mouse wasautomatically reset to the middle of the screen near the sample stimulus.For the training structures with three 3-member classes, all trainingblocks consisted of 24 trials, with 4 trials of each trial type randomlypresentedin each block. A minimum of 22 correct trials out of 24 trials wasrequired to proceed to the next block or phase. For the training with three4-member classes, the number of trials in each block was 36, and thecriterionwas a minimum of 33 correct trials out of 36 trials. The phases, numberof trials to criterion, feedback, and trial types included in the trainingstructures

are shown in Tables 2 and 3, respectively, for both the three 3-memberclasses and the three 4-member classes.Phase 1Acquisition. The Acquisition phase consisted of two blocks inwhich the comparisons were gradually increased (errorless training). In thefirst block, a response to the sample stimulus was followed by only thecorrectcomparison (S+) being presented on the screen. However, all trial types


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were presented separately, and each trial type was presented four times ina random order before the next block was introduced. Examples of the trialtypes are described below (only for the LS training structure; see Tables 2and 3 for details concerning the other training structures). For the three3-member classes (see Table 2), the trial types were A1B1, A2B2, A3B3,B1C1,B2C2, and B3C3 (the underlined comaprison is the correct response). Inthethree 4-member classes (see Table 3), the trial types were A1B1, A2B2,A3B3,B1C1, B2C2, B3C3, C1D1, C2D2, and C3D3.In the next block, two comparisons were presented on the screen (S+ andS) after a response to the sample stimulus, and again all trial types werepresented randomly. For the three 3-member classes the trials were

A1B1B2,A1B1B3, A2B1B2, A2B2B3, A3B1B3, A3B2B3, B1C1C2, B1C1C3,B2C1C2, B2C2C3,B3C1C3, and B3C2C3. For the three 4-member classes they wereA1B1B2,A1B1B3, A2B1B2, A2B2B3, A3B1B3, A3B2B3, B1C1C2, B1C1C3,B2C1C2, B2C2C3,B3C1C3, B3C2C3, C1D1D2, C1D1D3, C2D1D2, C2D2D3, C3D1D3, andC3D2D3.Phase 2Maintenance. This training phase consisted of five blocks. Allcomparisons were randomly presented in each trial. For the three 3-memberclasses, the trial types were A1B1B2B3, A2B1B2B3, A3B1B2B3,B1C1C2C3,B2C1C2C3, and B3C1C2C3. For the three 4-member classes, the trialtypeswere A1B1B2B3, A2B1B2B3, A3B1B2B3, B1C1C2C3, B2C1C2C3,B3C1C2C3,C1D1D2D3, C2D1D2D3, and C3D1D2D3. In the first of the five blocks, the

feedback was 100%. The next four blocks were identical to that describedabove, except that the feedback was reduced in four steps from 75% to50% to25%, and finally to 0% probability.446 Arntzen et al.Phase 3Testing. Phase 2 training was followed by a test phase with a


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block of test trials. In this test block, all test trial types were randomlyintermixed(i.e., symmetry trials and transitivity/equivalence trials). When testingfor three 3-member classes, the test block consisted of a block mixing24 symmetry and 24 transitivity/equivalence trials. In the three 3-memberclasses, the test trial types for LS were B1A1A2A3, B2A1A2A3,B3A1A2A3,B1C1C2C3, B2C1C2C3, and B3C1C2C3 (symmetry); A1C1C2C3,A2C1C2C3,and A3C1C2C3 (transitivity); and C1A1A2A3, C2A1A2A3, and C3A1A2A3(equivalence).In the test after training with three 4-member classes, a block of 36trials tested for symmetry and 72 trials tested for transitivity/equivalence.The test trial types for LS were B1A1A2A3, B2A1A2A3, B3A1A2A3,

C1B1B2B3, C2B1B2B3, C3B1B2B3, D1C1C2C3, D2C1C2C3, andD3C1C2C3 (symmetry);A1C1C2C3, A2C1C2C3, A3C1C2C3, B1D1D2D3, B2D1D2D3, B3D1D2D3,A1D1D2D3, A2D1D2D3, and A3D1D2D3 (transitivity); C1A1A2A3,C2A1A2A3,C3A1A2A3, D1A1A2A3, and D2A1A2A3, D3A1A2A3, D1B1B2B3,D2B1B2B3,and D3B1B2B3 (equivalence).No feedback was given during the test trials. We ended the experimentif the test was passed with a minimum of 90% correct responses. Thus, ifthe participants did not respond above 90% correct, new training wasintroduced,as described in Phase 2, followed by the final test for symmetry andtransitivity/equivalence.Definition of responding in accord with equivalence and symmetry.We defined responding in accord with symmetry and equivalence in three3-member classes as a participant response of 22/24 (correct/total) or moreon both tests, or a sum of both scores that were more than 90% correct.For

the training of 3 four-member classes, the numbers were 33/36 and 65/72ormore, or a more than 90% correct sum of scores.Reaction time. Reaction time was recorded for responses to comparisonstimuli. We calculated the median reaction time to comparison stimuli foreach participant for (1) the last five training trials, (2) the first five symmetrytrials, (3) the first five equivalence trials in the test block, (4) the last


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five symmetry trials, and (5) the last five equivalence trials in the test block.Means of reaction times for all the five types above were calculated for thefour participants in each group.ResultsNumber of ResponsesIndividual data for number of training trials, number of errors, andnumber of responses in accord with symmetry and transitivity/equivalenceare shown in Tables 4 through 9. The training structures with three 3-memberclasses are referred to as LS-3, MTO-3, and OTM-3 and the structureswith three 4-member classes are referred to as LS-4, MTO-4, and OTM-4.Thefirst column in each table shows the participant numbers, followed by thenumber of training trials the number of and errors and responding during

testing. The training has been divided into two parts, acquisition andmaintenance (the phases with fading of the feedback). The tables show thenumber of responses above the number of trials to criterion. In the columnswith symmetry, transitivity (for LS) and equivalence, successful respondingaccording to the criteria set has been marked in bold text.Training Structures and Stimulus Equivalence 447Table 4Three-Member Class Training Structure Scores for Participants WhoBegan With the LS Training StructureParticipantLS OTM MTOAcquisition Maintenance Testing Acquisition Maintenance TestingAcquisition Maintenance TestingTot. Err. Tot. Err. Sym. Eq. Tot. Err. Tot. Err. Sym. Eq. Tot. Err. Tot. Err.Sym. Eq.1351 96 31 0 0 24/24 17/24 0 0 0 0 24/24 24/24 48 14 0 0 24/24 22/240 0 0 2 24/24 24/241353 48 11 0 1 24/24 21/24 48 15 0 1 24/24 24/24 48 15 0 2 22/24 17/240 2 0 4 23/24 23/24

1354 72 20 0 0 20/24 11/24 24 5 0 0 24/24 24/24 48 10 0 0 23/24 24/240 0 0 0 24/24 14/241355 72 20 0 0 10/24 8/24 24 5 0 0 24/24 20/24 48 10 0 0 23/24 24/240 0 0 0 20/24 11/24Note. Tot. = total number of training trials above the minimum required; Err.= errors; Sym. = symmetry; Eq. = equivalence. Scores that aredefined as symmetry or equivalence are in bold text (i.e., 22 of 24 or more).


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448 Arntzen et al.Table 5Four-Member Class Training Structure Scores for Participants Who BeganWith the LS Training StructureParticipantLS OTM MTOAcquisition Maintenance Testing Acquisition Maintenance TestingAcquisition Maintenance TestingTot. Err. Tot. Err. Sym. Eq.1-nodeEq.2-nodeTot. Err. Tot. Err. Sym. Eq.1-node

Tot. Err. Tot. Err. Sym. Eq.1-node1351 36 7 0 1 36/36 47/48 23/24 0 0 0 3 35/36 72/72 72 12 0 4 34/36 69/721353 72 19 0 2 25/36 37/48 16/24 36 5 0 0 36/36 72/72 36 5 0 0 36/3672/7236 8 36 10 36/36 48/48 24/241354 108 26 36 6 36/36 43/48 22/24 0 0 0 0 36/36 71/72 72 21 0 0 35/3669/721355 108 26 36 6 36/36 47/48 21/24 0 0 0 0 36/36 71/72 72 21 0 0 35/3669/72Note. Tot. = total number of training trials above the minimum required; Err.= errors; Sym. = symmetry; Eq. = equivalence. Scores that are definedas symmetry or equivalence are in bold text (i.e., 33/36, 44/48, and 65/72or more).Training Structures and Stimulus Equivalence 449Table 6Three-Member Class Training Structure Scores for Participants WhoBegan With the MTO Training StructureParticipant

MTO OTM LSAcquisition Maintenance Testing Acquisition Maintenance TestingAcquisition Maintenance TestingTot. Err. Tot. Err. Sym. Eq. Tot. Err. Tot. Err. Sym. Eq. Tot. Err. Tot. Err.Sym. Eq.1356 120 39 0 0 24/24 24/24 0 0 0 0 24/24 24/24 0 0 0 0 24/24 24/241357 48 14 24 4 20/24 17/24 0 0 0 0 24/24 24/24 0 0 0 0 24/24 24/24


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0 0 0 2 24/24 24/241358 144 44 0 0 24/24 24/24 48 10 0 0 24/24 24/24 24 6 0 0 24/24 24/241359 72 16 0 2 21/24 23/24 0 0 0 1 24/24 24/24 0 4 0 3 22/24 22/24Note. Tot. = total number of training trials above the minimum required; Err.= errors; Sym. = symmetry; Eq. = equivalence. Scores that are definedas symmetry or equivalence are in bold text (i.e., 22 of 24 or more).Table 7Four-Member Class Training Structure Scores For Participants Who BeganWith the MTO Rraining StructureParticipantMTO OTM LSAcquisition Maintenance Testing Acquisition Maintenance TestingAcquisition Maintenance TestingTot. Err. Tot. Err. Sym. Eq.

1-nodeTot. Err. Tot. Err. Sym. Eq.1-nodeTot. Err. Tot. Err. Sym. Eq.1-nodeEq.2-node1356 36 12 0 1 36/36 72/72 0 0 0 0 36/36 72/72 0 0 0 0 36/36 48/48 24/241357 0 1 0 0 34/36 71/72 0 0 0 0 36/36 72/72 0 0 0 2 36/36 47/48 23/241358 36 5 0 0 34/36 71/72 36 8 0 0 36/36 72/72 0 0 0 0 36/36 48/48 24/241359 72 16 0 6 34/36 69/72 0 1 0 3 35/36 66/72 36 12 0 3 35/36 48/4824/24Note. Tot. = total number of training trials above the minimum required; Err.= errors; Sym. = symmetry; Eq. = equivalence. Scores that aredefined as symmetry or equivalence are in bold text (i.e., 33/36, 44/48, and65/72 or more).450 Arntzen et al.Table 8Three-Member Class Training Structure Scores For Participants Who

Began With the OTM Training StructureParticipantOTM LS MTOAcquisition Maintenance Testing Acquisition Maintenance TestingAcquisition Maintenance TestingTot. Err. Tot. Err. Sym. Eq. Tot. Err. Tot. Err. Sym. Eq. Tot. Err. Tot. Err.Sym. Eq.1581 432 139 24 8 20/24 22/24 48 8 24 3 24/24 24/24 24 5 0 0 21/24 21/24


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0 1 24/24 24/24 0 0 24/24 24/241582 72 25 0 0 23/24 24/24 0 0 0 0 24/24 24/24 0 0 0 1 24/24 24/241583 48 14 144 38 17/24 23/24 72 15 96 24 18/24 14/24 48 9 0 3 20/2417/240 3 24/24 24/24 0 1 18/24 15/24 0 3 20/24 18/241585 48 19 0 2 24/24 24/24 0 0 0 2 23/24 23/24 0 1 0 2 24/24 24/24Note. Tot. = total number of training trials above the minimum required; Err.= errors; Sym. = symmetry; Eq. = equivalence. Scores that are definedas symmetry or equivalence are in bold text (i.e., 33/36, 44/48, and 65/72or more).Table 9Four-Member Class Training Structure Scores For Participants Who BeganWith the OTM Training StructureParticipant

OTM LS MTOAcquisition Maintenance Testing Acquisition Maintenance TestingAcquisition Maintenance TestingTot. Err. Tot. Err. Sym. Eq.1-nodeTot. Err. Tot. Err. Sym. Eq.1-nodeEq.2-nodeTot. Err. Tot. Err. Sym. Eq.1-node1581 72 22 0 0 36/36 72/72 36 5 0 1 36/36 47/48 21/24 0 2 0 7 36/36 70/720 0 36/36 48/48 24/241582 0 1 0 3 36/36 72/72 0 1 0 0 36/36 47/48 23/24 0 0 0 0 36/36 72/721583 0 3 0 2 36/36 71/72 0 3 72 21 31/36 33/48 12/24 0 2 0 4 36/36 71/7236 8 32/36 33/48 15/241585 36 8 0 1 36/36 72/72 0 0 0 0 36/36 48/48 24/24 0 1 0 0 36/36 72/72Note. Tot. = total number of training trials above the minimum required; Err.= errors; Sym. = symmetry; Eq. = equivalence. Scores that are defined

as symmetry or equivalence are in bold text (i.e., 33/36, 44/48, and 65/72or more).Training Structures and Stimulus Equivalence 451Participants starting with LS . As shown in Tables 4 and 5, Participants1351 and 1354 had the least number of responses in the OTM conditionscompared to other conditions, and not more responses than the criterion inthe OTM-4 condition. Participant 1353 had a high number of responses for


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all conditions. Participant 1355 had a large number of responses in the LS-3condition, but for the following conditions the responses were minimal, andnot more than the criterion for the four last conditions. The total numberof training trials with both 3 and 4 members is highest for the LS trainingstructures. All participants required more training trials during the MTOstructure than during the OTM structure, for both 3 and 4 members. Duringthe first part of training, the number of errors was highest for the LS-3 andMTO-4 training structures. Furthermore, during the second part of training,the number of errors was highest in the LS-4 training structure.Participants starting with MTO. Tables 6 and 7 show that, for allconditions except for the two MTO conditions, Participant 1356 did notrespond with more responses than the criterion. Participant 1357 neededa second training and test phase in MTO-3. In the rest of the conditions,

this participant did not respond with more responses than the criterion.Participant 1358 had more responses than the criterion for all conditionsexcept for LS-4. Participant 1359 had more responses than the criterionfor all conditions except the two OTM conditions and the LS-3 condition.Thus, the number of training trials was highest for the MTO trainingstructure with both 3 and 4 members. The number of training trials forboth the OTM and LS structures is substantially lower than for the MTO.As shown in Table 7, the pattern of number of errors is the same as fornumber of responses.Part icipants start ing with OTM. As shown in Tables 8 and 9,Participant 1581 had the most responses in all training structures, thatis, nearly 400 responses more than the other 3 participants in the firstcondition. Participant 1582 had more responses than criterion only in thefirst training condition, OTM-3. Participant 1583 had many responses inall training structures except for OTM-4 and MTO-4. Participant 1584 hadmore responses than criterion only in the OTM-3 and OTM-4 conditions.The total number of training trials in the first phase of training in thefirst condition, OTM-3, was 600 trials for all 4 participants. Furthermore,the number decreased as a function of the introduction of the new training

structures. The total number of trials in the second phase of trainingshowed a similar pattern except for the LS-4 training structure, in whichthe number of trials increased. The number of errors shows the samepatternacross training structures as the number of responses does.Stimulus Equivalence Class EstablishmentParticipants starting with LS . Participants 1351 and 1354 did not respond


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in accord with stimulus equivalence in the LS-3 condition in the firsttest, but did respond in accord with stimulus equivalence in the second testand in all the following conditions (see Tables 4 and 5). Participant 1353didnot respond in accord with stimulus equivalence in the first test in LS-3,MTO-3, and MTO-4, but did respond in accord with stimulus equivalence inthe second test in all 3-member conditions. The participant responded inaccordwith stimulus equivalence in the OTM-4 and MTO-4 conditions.452 Arntzen et al.Participants starting with MTO. Participants 1356 and 1358 responded inaccord with stimulus equivalence in all conditions, as shown in Tables 6and 7.Participant 1357 responded in accord with stimulus equivalence in the

secondtest in the MTO-3 condition, and responded in accord with stimulusequivalencein all of the other conditions. Participant 1359 did not respond in accordwithsymmetry in the MTO-3 condition, and did not receive a second trainingandtest phase due to programming error. Even so, the participant responded inaccordwith stimulus equivalence in all of the following conditions.Participants starting with OTM. As shown in Tables 8 and 9, all 4participantsresponded in accord with stimulus equivalence, but 2 of the participants(1581 and 1583) did not respond in accord with symmetry in the firsttest. In the LS-3 training structure, 3 of 4 participants responded in accordwith stimulus equivalence. Participant 1583, who did not respond in accordwith stimulus equivalence in the first test, did not do so in the second testeither. Two of 4 participants responded in accord with stimulus equivalencein the MTO-3 training structure. Participant 1581 did respond in accord with

stimulus equivalence in the second test, after retraining. Participant 1583didnot respond in accord with stimulus equivalence after the second test. IntheOTM-4 training structure, all participants responded in accord with stimulusequivalence. In the LS-4 training structure 2 of 4 participants respondedin accord with stimulus equivalence. One participant, 1581, did not respond


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correctly on the two-node test, but responded in accord with stimulusequivalenceon the second test. Participant 1583 did not respond in accord withstimulusequivalence after the second test. All participants responded in accordwith stimulus equivalence in the MTO-4 training structure.Comparing all conditions. Following the LS-3 structure, none of the4 participants responded in accord with stimulus equivalence, and 2 ofthe participants responded in accord with symmetry in the first test (seeTable 4). In the second attempt at LS-3 second test, the other 2participantsalso responded in accord with symmetry, and 1 of 4 participants respondedin accord with stimulus equivalence. When the number of members wasincreased

to 4, 3 of 4 participants responded in accord with stimulus equivalencewhen LS-4 was introduced as the fourth condition (see Table 5). WhenLS-3 was introduced after MTO-3 and OTM-3, 4 of 4 participantsrespondedin accord with stimulus equivalence (see Table 6), and 4 of 4 participantsresponded in accord with stimulus equivalence when LS-4 was introducedas the last condition (see Table 7). When they followed the OTM trainingstructure, both 3 and 4 members, and independent of the sequence, 4 of4 participants responded in accord with symmetry and equivalence. Whenfollowing the MTO training structure, either introduced first or at the end ofthe sequence, 3 of 4 participants responded in accord with stimulusequivalence.With 4 members in the MTO structure, 4 of 4 participants respondedin accord with symmetry and equivalence.Reaction timeIn Figures 2, 3, and 4, each bar represents median reaction time tocomparisonstimuli for all participants. In each panel in the figures, the whitebar is the median reaction time to comparison stimuli for the last five

trainingtrials, the gray bar is the median reaction time to comparison stimuliTraining Structures and Stimulus Equivalence 453for the first five test trials, and the black bar is the median reaction timeto comparison stimuli for the last five test trials. The upper panel in eachfigure shows median reaction time for the symmetry trials, while the lowerpanel is for the equivalence trials. The results show that for all participants,


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reaction times to comparison stimuli during the first five test trials werehigher than during the last five trials in training in both equivalence andsymmetry. Furthermore, reaction times to comparison stimuli during thefirst five trials in the equivalence test were higher than reaction times tocomparison stimuli during the first five trials in the symmetry test.As shown in the upper panel in Figure 2, for the participants startingwith LS-3, the increase from training to test was most pronounced for theLS training structures. For the equivalence trials (lower panel), the increasefrom baseline to testing was even more pronounced, especially for the LStraining structure, both in LS-3 and LS-4.0123

45LS-3 OTM-3 MTO-3 LS-4 OTM-4 MTO-4Median in Sec.Symmetry Trials Last 5 Training TrialsFirst 5 Test TrialsLast 5 Test Trials0246810LS-3 OTM-3 MTO-3 LS-4 OTM-4 MTO-4Median in Sec.Equivalence Trials Last 5 Training TrialsFirst 5 Test TrialsLast 5 Test TrialsFigure 2. Median reaction times to comparison stimuli for the participants

who startedwith LS-3. The white bars are the reaction times for last five training trials,the gray barsare the reaction time to the first five test trials, and the black bars are thereaction timesto the last five test trials. The upper panel is showing the reaction times forthe symmetry


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trials, while the lower panel is showing the reaction times for theequivalence trials.454 Arntzen et al.As shown in the upper panel in Figure 3, the part icipants whostarted with MTO-3 showed an increase from training to test that wasmost pronounced for the LS-3, LS-4, and MTO-4 training structures.For the equivalence trials (lower panel), the increase from baseline totesting was most pronounced for the LS training structure with fourmembers.01238

645MTO-3 OTM-3 LS-3 MTO-4 OTM-4 LS-4Median in Sec.Symmetry Trials Last 5 Training TrialsFirst 5 Test TrialsLast 5 Test Trials0241012MTO-3 OTM-3 LS-3 MTO-4 OTM-4 LS-4Median in Sec.Equivalence Trials Last 5 Training TrialsFirst 5 Test TrialsLast 5 Test TrialsFigure 3. Median reaction times to comparison stimuli for the participants

whostarted with MTO-3. The white bars are the reaction times for last fivetraining trials,the gray bars are the reaction time to the first five test trials, and the blackbars arethe reaction times to the last five test trials. The upper panel is showing thereaction


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times for the symmetry trials, while the lower panel is showing the reactiontimes forthe equivalence trials.For the participants who began with the OTM-3 training structure,the median reaction times for the symmetry trials were about the samefor all conditions (see Figure 4). The median reaction times for equivalencetrials were most pronounced in the LS-3 and the OTM-3 trainingconditions.Training Structures and Stimulus Equivalence 45501234

5012345OTM-3 LS-3 MTO-3 OTM-4 LS-4 MTO-4OTM-3 LS-3 MTO-3 OTM-4 LS-4 MTO-4Median in Sec.Symmetry Trials Last 5 Training TrialsFirst 5 Test TrialsLast 5 Test TrialsMedian in Sec.Equivalence Trials Last 5 Training TrialsFirst 5 Test TrialsLast 5 Test TrialsFigure 4. Median reaction times to comparison stimuli for the participantswho started with

OTM-3. The white bars are the reaction times for last five training trials, thegray bars arethe reaction time to the first five test trials, and the black bars are thereaction times to thelast five test trials. The upper panel is showing the reaction times for thesymmetry trials,


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while the lower panel is showing the reaction times for the equivalencetrials.DiscussionThe main purpose of the current experiment was to explore the stimulusequivalence outcome as a function of different training structures inmatching-to-sample tasks arranged in a within-subject design.Furthermore,we wanted to study (1) if there were any differences between the trainingstructures when the number of members in each class was increased and(2) if the order of training and testing was important. The main findingswere that (1) the LS training structure produced the lowest outcome on theequivalence tests, (2) the OTM training structure gave higher outcomesthanthe MTO training structure in testing for 3-member classes, and (3) in the

tests following the training of 4-member classes, there was no difference456 Arntzen et al.between the OTM and MTO training structures. When the MTO trainingstructure was introduced first, it actually gave lower outcomes than theOTM. Therefore, the differences in stimulus equivalence outcome betweenthe OTM and MTO training structures were not as predicted from the R. R.Saunders and Green (1999) hypothesis. The stimulus equivalenceoutcomefollowing the LS training structure was lower compared to both OTM andMTO, which is a replication of earlier findings (Arntzen & Holth, 1997,2000a;R. R. Saunders et al., 2005). Furthermore, the current study replicated thefindings from other studies with three choices in which OTM gave higheroutcome than MTO (Arntzen & Holth, 1997, 2000a).With respect to the number of training trials to criterion, we foundfewer training trials in the OTM training structure compared to the MTOtraining structure, with both 3- and 4-member classes. In addition, we foundthat the reaction time to comparison stimuli was longer in equivalence trialsthan symmetry trials. The participants in the current study showed

longer reaction time in the test for symmetry and equivalence trials thanin baseline trials, and this was more pronounced for the equivalence trials.These findings are in accordance with a number of other studies (Arntzen &Holth, 1997, 2000a; Arntzen & Lian, in press; Eilifsen & Arntzen, 2009;Holth& Arntzen, 1998, 2000; R. R. Saunders et al., 2005; Spencer & Chase,1996).


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The reaction time was longer with an increased number of nodes, that is,thereaction time was longer in the LS training structure with 4 members thanwith 3-members. This is in accordance with previous research (Arntzen &Holth, 2000b; Bentall, et al., 1999; Fields, Adams, Newman, & Verhave,1990),but not in accordance with Imam (2006).Procedural issues raised during this study include (1) fading of feedbackbefore the tests and (2) differing trial types during testing across studies,which could be related to the differential outcomes reported. With respecttothe first issue, in some studies, fading of consequences was instigated attheend of the training. In earlier studies in our lab we did not include a phase

with fading of consequences prior to testing. It could be argued that the lowrates in stimulus equivalence outcome in the earlier studies could berelatedto extinction. Therefore, in order to control for this in the current study, wegradually faded the feedback in the last part of training before weconductedtesting. Nonetheless, we still replicated earlier findings from our lab,suggestingto us that the feedback fading is not responsible for the differingoutcomes evidenced with the OTM and MTO training structures.In regard to the second issue, the trial types during testing, R. R.Saunders et al. (2005) have argued that conducting only a CA test (or aglobalequivalence test) could have influenced the results found by Arntzen andHolth (1997, 2000a). In order to control for this, in the current study, weinitiateda more comprehensive testing protocol that included all types of testtrials randomly mixed in a block. Again we replicated the earlier findingsfrom our lab, suggesting to us that the arrangement of only having included

the global equivalence test (i.e., CA only) does not explain the previousfindingscoming from our lab.How the training trials have been introduced in the training could beimportant when analyzing the difference in outcome on the tests, and couldhave implications for the differences in number of trials to criterion anderrors


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that have been reported. In some studies, the training trials have beenintroduced as errorless training, as in the current and other experimentsTraining Structures and Stimulus Equivalence 457(Arntzen & Holth, 1997, 2000a; Arntzen & Vaidya, 2008). However, in otherstudies the relations are presented simultaneously from the start of training(e.g., R. R. Saunders et al., 2005). In the current study, we sawsubstantiallyfewer errors in the OTM training structure compared to the MTO trainingstructure in the initial training and also in the maintenance part of training.Furthermore, we saw more errors in the LS-3 and MTO-3 training structurein both initial and mixed training, but no difference between OTM-4and MTO-4. These findings are partly in accord with other studies that haveshown that the number of trials to criterion is higher for the MTO than theOTM training structure (Arntzen & Holth, 1997, 2000a; Fields, Hobbie-

Reeve,Adams, & Reeve, 1999; R. R. Saunders et al., 1999). Because the trials inthecurrent experiment were introduced as errorless training and still theparticipantsmade some errors in the acquisition phase, it could be argued thatthey did not observe the different stimuli on the screen, but merely clickedon the comparison because only one was presented at a time. However,duringthe training with mixed trials, the number of training trials was aboutthe same as trials to criterion. R. R. Saunders et al. (1999) argued thatovertrainingin the OTM training structure is a reason for higher outcomescompared to the MTO training structure. However, in the findings reportedhere this could not be the case, because the OTM training structure did notrequire more training trials than the other structures.The current experiment was arranged in a within-subject design to see ifand how earlier training with different training structures influenced theperformance

on later training structures. As mentioned earlier, the LS trainingstructure gives the lowest yields of responding in accord with stimulusequivalence.In the current experiment, it is interesting that when the LS structurewas trained first (see Tables 4 and 5) or second, following OTM (seeTables 8


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and 9), test performances often did not show equivalence, even onretesting.On the other hand, when training began with MTO, symmetry andequivalenceresponding was nearly perfect in the LS training structure. As mentionedbefore, the participants must in the MTO structure discriminate everystimulus from every other and therefore this structure is the most difficultone to train. One interpretation could be that those participants have theopportunityduring testing to learn the importance of having acquired all thosediscriminations. Therefore, this can have an effect on what is happening inthe OTM and LS training structures that are introduced later. Actually, thereare very few extraneous training trials in either the OTM or LS structures.Furthermore, there are also near-perfect test performances in both

structures.As can be seen in Tables 8 and 9, when OTM is trained first, there is nosucheffect on the LS and MTO structures that follow. Therefore, it could bearguedthat the MTO training structure is a very effective structure in the sense thatit will give higher yields in the structures that follow, even in LS with three3-member and three 4-member classes. Further research should focus onthisand expand the number of members in each class.Another variable that could have influenced the outcome on theequivalencetests is the difference in number of sample comparison relations. Inthe OTM training structure, one sample is related to more than onecomparisonstimulus; while in MTO, one comparison stimulus is related tomore than one sample stimulus. In training in the MTO, the participantscould learn to predict correct comparison stimuli based on the choiceof sample stimulus. However, in the test it would not be possible to make

458 Arntzen et al.such predictions about comparison stimuli based on the sample stimulus(Arntzen & Holth, 2000a). Reaction time data could shed light on the shiftamong stimuli between sample and comparison when going from trainingto test. In the current study, we replicated earlier findings (Arntzen & Holth,1997, 2000a) in which the relative differences in reaction times increasesubstantially


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more from the baseline to the equivalence test in the MTO trainingstructure compared to the OTM training structure. The greater increase inreaction time in the MTO training structure supports the interpretation thatit is possible to predict the comparison stimuli in the MTO training. In thetest, the sample is suddenly related to more than one comparison stimulus,and the reaction time could then increase. For all training structures, theincrease in reaction time from baseline to the tests for responding in accordwith stimulus equivalence could indicate that stimulus equivalence emergesmore gradually and that reaction times indicate some problem-solvingbehavioror precurrent behavior (Arntzen & Holth, 1997, 2000b). It is importantto note that this precurrent response is not some sort of interveningvariable(Arntzen, 2004).

Results from the current study are in accordance with results fromother studies with college students from our lab (Arntzen & Holth, 1997,2000a). On the other hand, most of the studies that have shown thesuperiorityof MTO have used children or participants with mental disabilities(e.g., Arntzen & Vaidya, 2008; K. J. Saunders et al., 1993; R. R. Saunderset al.,1999; R. R. Saunders & McEntee, 2004) and elderly citizens (R. R.Saunders etal., 2005). Wilson and Milan (1995) found significant differences inrespondingin accord to stimulus equivalence between a group of adults 19 to 22years old and a group of adults between 62 and 81 years old. Theparticipantsin the last group responded to a lesser degree in accord with stimulusequivalence compared to the younger ones in the first group. Arntzen andVaidya (2008) argued that it is possible that the difference betweensimultaneousand successive discriminations is more pronounced in children

than in adults with a more comprehensive and complex behavioralrepertoire.However, such factors could be responsible for the differences in theoutcome of OTM and MTO training structures with children and adults asparticipants. More systematic studies with different age groups need to bedone to clarify the issue of age and outcome on equivalence tests.In summary, except for the study by R. R. Saunders et al. (2005), none


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have actually tested the prediction made by R. R. Saunders and Green(1999)as we have directly addressed it in the current study. The results from thecurrent experiment did not fully support the predictions derived from thediscrimination analysis. The current experiment showed that (1) LS was theleast effective training structure, (2) the OTM training structure was slightlymore effective than MTO, and (3) this was especially the case when thenumber of classes increased. The finding that LS without any experimentalhistory is the least effective training structure is in accordance with otherstudies (e.g., Arntzen & Holth, 1997, 2000a; Saunders et al., 2005;Saunders& McEntee, 2004). The results for the participants starting with the MTOtraining structure showed that responding in accord with stimulusequivalence

in the LS training structure was considerably higher than when the LStraining structure or the OTM training structure were the first structurestrained. The participants showed longer reaction times to the first five testtrials compared to the last five training trials. In addition, we also foundTraining Structures and Stimulus Equivalence 459longer reaction times on equivalence trials compared to symmetry trials.There are relatively few studies that have found that OTM gives the highestoutcome on the equivalence test and that the difference between thetraining structures does not increase as a function of increasing numberof members. We have also discussed some variables in the training andtestprotocols that may be important in explaining different findings, andsuggestedimportant avenues for further study.ReferencesArnt zen , E. (2004). Probability of equivalence formation: Familiar stimuliand training sequence. The Psychological Record, 54, 275291.Arnt zen , E. (2007, March). Some procedural variables that might influenceequivalence class formation. Paper presented at the annual convention of

the Texas Association for Behavior Analysis, Dallas, TX.Arnt zen , E., & Holth , P. (1997). Probability of stimulus equivalence as afunction of training design. The Psychological Record, 47, 309320.Arnt zen , E., & Holth , P. (2000a). Differential probabilities of equivalenceoutcome in individual subjects as a function of training structure. ThePsychological Record, 50, 603628.


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Arnt zen , E., & Holth , P. (2000b). Probability of stimulus equivalence as afunctionof class size vs. number of classes. The Psychological Record, 50, 79104.Arnt zen , E., & Lian , T. (in press). Trained and derived relations withpictures as nodes. The Psychological Record.Arnt zen , E., & Vaid ya, M. (2008). The effect of baseline training structureon equivalence class formation in children. Experimental Analysis ofHuman Behavior Bulletin, 29, 18.Barnes , D. (1994). Stimulus equivalence and relational frame theory. ThePsychological Record, 44, 91124.Bentall , R. P., Jones , R. M., & Dickins , D. W. (1999). Errors and responselatencies as a function of nodal distance in 5member equivalenceclasses. The Psychological Record, 49, 93115.Carrigan , P. F., & Sidman , M. (1992). Conditional discrimination and

equivalence relations: A theoretical analysis of control by negativestimuli. Journal of the Experimental Analysis of Behavior, 58, 183204.Dymond , S., & Rehfeldt , R. A. (2001). Supplemental measures andderivedstimulus relations. Experimental Analysis of Human Behavior Bulletin, 19,812.Eilifsen , C., & Arnt zen , E. (2009). On the role of trial types in tests forstimulus equivalence. European Journal of Behavior Analysis, 10, 187202.Fields , L., Adams , B. J., Newman , S., & Verha ve, T. (1990). The effectsofnodality on the formation of equivalence classes. Journal of theExperimental Analysis of Behavior, 53, 345358.Fields , L., HobbieRee ve, S. A., Adams , B. J., & Ree ve, K. F. (1999).Effectsof training directionality and class size on equivalence class formationby adults. The Psychological Record, 49, 703724.Fields , L., LandonJimene z, D. V., Buffington , D. M., & Adams , B. J.(1995). Maintained nodaldistance effects in equivalence classes. Journal

of the Experimental Analysis of Behavior, 64, 129145.Green , G., & Saunders , R. R. (1998). Stimulus equivalence. In K. A. Lattal&M. Perone (Eds.), Handbook of research methods in human operantbehavior(pp. 229262). New York: Plenum Press.460 Arntzen et al.Holth , P., & Arnt zen , E. (1998). Stimulus familiarity and the delayed


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emergence of stimulus equivalence or consistent nonequivalence. ThePsychological Record, 48, 81110.Holth , P., & Arnt zen , E. (2000). Reaction times and the emergence ofclass consistent responding: A case for precurrent responding? ThePsychological Record, 50, 305338.Hove, O. (2003). Differential probability of equivalence class formationfollowing a onetomany versus a manytoone training structure. ThePsychological Record, 53(4), 617634.Imam , A. A. (2006). Experimental control of nodality via equalpresentationsof conditional discriminations in different equivalence protocols underspeed and nospeed conditions. Journal of the Experimental Analysis ofBehavior, 85, 107124.Johnson , C., & Sidman , M. (1993). Conditional discrimination and

equivalence relations: Control by negative stimuli. Journal of theExperimental Analysis of Behavior, 59, 333347.Kenned y, C. H. (1991). Equivalence class formation influenced by thenumber of nodes separating stimuli. Behavioural Processes, 24, 219245.Saunders , K. J., Saunders , R. R., Williams , D. C., & Spradlin , J. E.(1993).An interaction of instructions and training design on stimulus classformation: Extending the analysis of equivalence. The PsychologicalRecord, 43, 725744.Saunders , R. R., Chane y, L., & Mar quis , J. G. (2005). Equivalence classestablishment with two-, three-, and four-choice matching to sample bysenior citizens. The Psychological Record, 55, 539559.Saunders , R. R., Drake , K. M., & Spradlin , J. E. (1999). Equivalenceclassestablishment, expansion, and modification in preschool children.Journal of the Experimental Analysis of Behavior, 71, 195214.Saunders , R. R., & Green , G. (1999). A discrimination analysis oftrainingstructure effects on stimulus equivalence outcomes. Journal of the

Experimental Analysis of Behavior, 72, 117137.Saunders , R. R., & Mcentee , J. E. (2004). Increasing the probability ofstimulus equivalence with adults with mild mental retardation. ThePsychological Record, 54(3), 423435.Saunders , R. R., Wachter , J. A., & Spradlin , J. E. (1988). Establishingauditory stimulus control over an eightmember equivalence class viaconditional discrimination procedure. Journal of the Experimental


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Analysis of Behavior, 49, 95115.Sidman , M. (1994). Equivalence relations and behavior: A research story.Boston: Authors Cooperative.Sidman , M., & Tailb y, W. (1982). Conditional discrimination vs. matchingtosample: An expansion of the testing paradigm. Journal of theExperimental Analysis of Behavior, 37, 522.Spencer , T. J., & Chase , P. N. (1996). Speed analysis of stimulusequivalence.Journal of the Experimental Analysis of Behavior, 65, 643659.Spradlin , J. E., & Saunders , R. R. (1986). The development of stimulusclasses using matchtosample procedures: Sample classification versuscomparison classification. Analysis and Intervention in DevelopmentalDisabilities, 6, 4158.

Training Structures and Stimulus Equivalence 461Wilson , K. M., & Milan , M. A. (1995). Age differences in the formation ofequivalence classes. Journals of Gerontology Series B: PsychologicalSciences and Social Sciences, 50, 212218.Wulfert , E., & Hayes , S. C. (1988). Transfer of conditional orderingresponse through conditional equivalence classes. Journal of theExperimental Analysis of Behavior, 50, 125144.462

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