Training and Testing Parameters In Formation of Stimulus ... - CiteSeerX

2012, 13, 123–135

EUROPEAN JOURNAL OF BEHAVIOR ANALYSIS

NUMBER 1 (SUMMER 2012) 123

Training and Testing Parameters In Formation of Stimulus Equivalence: Methodological Issues Erik Arntzen

Oslo and Akershus University College

Research on stimulus equivalence has been prominent for more than 40 years in behavior analysis. The present article will focus on issues related to methodological considerations in stimulus equivalence research. An introduction to stimulus equivalence is provided, followed by a discussion of parameters in training conditional discriminations and testing for the emergence of equivalence classes. Some issues related to different training structures, the use of instructions, simultaneous versus delayed matching to sample, the role of familiar stimuli, response requirements for the sample stimulus, and criteria for (a) defining responding in accordance with equivalence and (b) establishing conditional discrimination are discussed in more detail. Key words: conditional discrimination, stimulus equivalence, parameters, instructions, training structures, delayed matching-to-sample

Since Sidman’s first article on stimulus equivalence early in the seventies (Sidman, 1971), interest in stimulus equivalence among researchers has been substantial. Over the last 40 years, there have been a great number of publications on the subject; a search in PsycInfo (June 19, 2012) gave 434 and 288 hits for the terms stimulus equivalence and functional equivalence, respectively. Stimulus equivalence is defined as responding in accordance with the features of reflexivity, symmetry, and transitivity (Sidman, 2000; Sidman & Tailby, 1982). Stimulus equivalence has been demonstrated as a relatively robust phenomenon. Most of the published studies have been Author Note: The author would like to thank three anonymous reviewers and Iver Iversen for their constructive comments and suggestions on an earlier version of the manuscript. Correspondence concerning this manuscript should be addressed to Erik Arntzen, Oslo and Akershus University College, Department for Behavioral Science, PO Box 4 St. Olavs Plass, 0130 Oslo, Norway. E-Mail: erik. [email protected]

concerned with basic research questions (Sidman, 1994), while others have been within the area of applied behavior analysis (e.g., Arntzen, Halstadtro, Bjerke, & Halstadtro, 2010; LeBlanc, Miguel, Cummings, Goldsmith, & Carr, 2003). Furthermore, some of the studies have been concerned with what has lately been characterized as translational research (McIllvane, 2010). However, Sidman was discouraged by the lack of interest in applications: “Puzzled and disillusioned, we soon turned our attention almost exclusively away from applications. Instead, we concentrated our efforts on studying some of the more basic and systematic ramifications of the fascinating phenomenon we had happened upon” (Sidman, 1994, p. 66). In both basic and applied research on stimulus equivalence formation, the following questions seem to be pertinent: (1) Under what conditions will adult humans not respond in accordance with stimulus equivalence?

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(2) What are the most effective parameters for establishing stimulus equivalence? (3) Will the most effective parameters differ across age and participant characteristics? My interest in stimulus equivalence is fourfold: (1) the emergence of new relations — not directly trained, (2) variables that can influence the emergence of equivalence relations, (3) whether complex repertoires (e.g., concepts, problem solving, language formation) are amenable to behavior analysis, and (4) the impact of research on stimulus equivalence on the arrangement of effective conditional discrimination procedures in behavioral programs. The present article will not go into all of these areas but instead emphasize on one of the most fascinating areas is the emergence of new equivalence relations. Trained relations may be expressed as C x (M-1), and emergent relations could be expressed as C x (M-1)2, where C is the number of classes and M is the number of members. For example, if training potentially three 4-member classes—A1B1C1D1, A2B2C2D2, and A3B3C3D3—there are nine trained relations (A1B1, A2B2, A3B3, B1C1, B2C2 B3C3, C1D1, C2D2, and C3D3) and 27 emergent relations (B1A1, B2A2, B3A3, C1B1, C2B2, C3B3, D1B1, D2B2, D3B3, A1C1, A2C2, A3C3, C1A1, C2A2, C3A3, B1D1, B2D2, B3D3, D1B1, D2B2, D3B3, A1D1, A2D2, A3D3, D1A1, D2A2, and D3A3; see Table 1). The high 1. number of Table emergent relations when only

training a few relations have studied for example by Sidman and colleagues (Sidman, Kirk, & Willson-Morris, 1985). Much of the research in the area of stimulus equivalence has focused on what happens during testing. As shown in Table 2, a number of variables have been shown to influence successful outcome following conditional discrimination training. It seems that the different results can be attributed to differences in how the training and testing procedures have been arranged. The purpose of the present article is to discuss some of the variables that influence the outcome of responding in accordance with equivalence (see Table 2). The variables discussed herein are the effects of different training structures, the use of instructions, simultaneous versus delayed matching to sample, the role of familiar stimuli, response requirements for the sample stimulus, and criteria for (a) defining responding in accordance with stimulus equivalence and (b) establishing conditional discrimination. It is important to determine how to produce formation of equivalence classes in the most parsimonious way. Such knowledge will have great importance for arranging an effective technology for teaching. Related to differences in the findings, Sidman (1960) earlier suggested that one should “… inquire experimentally into the reasons for the differences” (p.78). The present article will support this notion and encourage

Classes, Sets of Stimuli, Members, Trained and Emergent Relations. Table 1. Classes, Sets of Stimuli, Members, Trained and Emergent Relations Classes

Sets of stimuli Labels

No 3

A B C D

Members No Labels 4 A1A2A3 B1B2B3 C1C2C3 D1D2D3

Trained Relations C x (M-1) = 3 x (4-1) =9

Emergent Relations

C x (M-1)2 BA/CB/AC/CA/DC = 3 x (4-1)2 /DB/BD/AD/DA =27 Training trials: Test trials: A1B1 A2B2 A3B3 B1A1 B2A2 B3A3 B1C1 B2C2 B3C3 C1B1 C2B2 C3B3 C1D1 C2D2 C3D3 D1C1 D2C2 D3C3 A1C1 A2C2 A3C3 C1A1 C2A2 C3A3 B1D1 B2D2 B3D3 D1B1 D2B2 D3B3 A1D1 A2D2 A3D3 D1A1 D2A2 D3A3 AB/BC/CD

Note. No=number, C=classes, and M=members. Note. No=number, C=classes, and M=members. In the overview of training and test trials, the to incorrect comparisons for each of the trials are not shown.

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Training and Testing Parameters

Table 2. Important Procedural Variables Variables and Parameters Variables and Parameters Details Variables Variables and Variables and Parameters Parameters Details andVariables Parameters Effects and Parameters Details Details Effects DetailsVariables Details and Effects Effects Parameters Effects Training protocols

Effects Details

Training protocols SIM, STC, and Training CTS SIM, protocols Training STC, and protocols TheCTS protocols TrainingSIM, protocols haveSTC, shown TheSIM, and protocols toCTS STC, and have SIM, CTS shown STC, The toand CTS Thehave protocols shown have to protocols shown tohave shown to Training protocols SIM, STC, and CTS Training The protocols protocols have shownThe toSIM, STC, and CTS different outcomes. have different outcomes. have different outcomes. have have outcomes. different have outcomes. have different different outcomes.

Effects

The protocols have shown t have different outcomes.

Training structures Training structures LS, MTO, and Training OTM LS, structures Training MTO, and structures TheOTM training TrainingLS, structures structures MTO, The have and LS, training OTM MTO, andLS, OTM MTO, have The training OTM The structures traininghave structures TheLS, training havestructures Training structures LS, MTO, and OTM structures Training Theand structures training structures have MTO, and OTMhave different different effects on the different effects on the different different on effects on the effects on the different effects effects on the the emergence of equivalence emergence of equivalence emergence of equivalenceemergence of of equivalence emergenceemergence of equivalence equivalence classes. classes. classes. classes. classes. classes.

The training structures have different effects on the emergence of equivalence classes.

Number of classes and/or Specialand/or case Number is two vs.Special of Itisclasses istwo not clear and/or how ancase case isSpecial two vs.It Itvs.ishow notan clear how an Number of classes of classes case and/or Number vs. Special of classes It isSpecial and/or is not clear vs. anNumber case not isclasses two clear It isSpecial not clear how an vs. Number ofNumber classes and/or Special case is two two vs.how It is isof not clear how and/or an case is two members etc. members increasing of increasing members three/four choices, etc.increasing increasing number of members members three/four choices, three/four choices, etc. three/four choices, number etc. increasing number of members members three/four choices, members etc. number number ofmembers members of members three/four choices, etc. increasing number of members members three/four choices, etc. number of classes and/or number of classes and/or number of classes and/or number of classesand/or of and/or number number of classes classes and/or the influences the emergence of influences the influences emergence of emergence of influences the emergenceinfluences of the of influences the emergence emergence of equivalence classes depending equivalence classes depending classes depending equivalence classes depending equivalence classes equivalenceequivalence classes depending depending on training structures. on training structures.on training structures. on training structures. structures. on training trainingon structures.

It is not clear how an increasing number of memb and/or number of classes influences the emergence of equivalence classes dependi on training structures.

Requirement of responseRequirement to of to of least response to effect atRequirement an effect least This on an on effect at least on This on has an leastThis on has Requirement of response to Requirement ThisofRequirement has an effect to at hasat effect least Requirement of response response toresponse This hasof anThis response effect atan to least on athas sample stimulus or not sample number of trials to or not sample stimulus or not number of trials number of trials sample to the sample stimulus or not sample the number or not of trials tothe number trials to sample stimulus stimulus orstimulus not thestimulus numberthe or of not trials to to of the criterion. criterion. criterion. criterion. criterion. criterion.

This has an effect at least on the number of trials to criterion.

Arrangement trainingintroduction trials Arrangement (a)Arrangement Gradual introduction Arrangement of (a) Gradual of training introduction use of trials (a), introduction (b), of (a)or Gradual (c) The will use (b), of or (c) The use of will (a), introduction (b), or (c) will Arrangement of training trials (a)ofGradual ofof The trials of use training of (a), trials orThe (c)(a) will Gradual ofintroduction The use of (a), (b), orGradual (c) Arrangement of training training trials (a)(b), Gradual introduction of Arrangement training trials (a) of The use of of (a), (a), (b), or (c) will will or training trialsan or effect nothaveon an fast effect onor how or not have an effect onor how have fast training trials or not training trials have an effecttraining on howtrials fast training notfast effect on training how training trials or not nottrials have an effect onanhow how fasthave trials notfast conditional discriminations are conditional conditional are discriminations are conditional discriminations are discriminations conditional discriminations are conditional discriminations are (b) Serialized presentation (b) (b) of Serialized of (b) Serialized presentation of (b) Serialized presentation ofpresentation (b)ofSerialized Serialized presentation of (b)have Serialized presentation established. have an of established. Could have an established. Could an established. Could have an presentation established. anCould established. Could have haveCould an trials effect on the establishment trials trialseffect trials trials trialseffect of trials effect the of establishment of on the establishment of on establishment of effect on the establishment effect on the the establishment of on equivalence classes. equivalence classes. equivalence classes. equivalence classes. equivalenceequivalence classes. classes. (c) Concurrent presentation (c) Concurrent presentation (c) of Concurrentofpresentation of (c) Concurrent presentation of (c) Concurrent presentation (c) of Concurrent presentation of (c) Concurrent presentation of trials trials trials trials trials trials trials

The use of (a), (b), or (c) wi have an effect on how fast conditional discriminations established. Could have an effect on the establishment o equivalence classes.

Arrangement(a)ofTest test blocks trialsArrangement Test of blocks trials vs. Arrangement test (a) Test ofisblocks Data test show vs. thattrials this (a) Test probably Data blocks vs. that this is Data that thisvs. is test probably Arrangement of test trials vs. test(a)trials Arrangement of show test trials trials that probably (a)trials Test blocks vs.is test trialsshow Data show that this isTest probably Arrangement of test test Data trials (a)this Test blocks vs. test test trials Arrangement oftest testtrials trials (a)show blocks trials Data show that this is probably probably in in test not blocks critical. interspersednot in test blocksinterspersed notinterspersed critical. not interspersed in test blocks ininterspersed test blocks critical. critical. notinterspersed interspersed in test test blocks blocks in test blocks not critical. critical.

Data show that this is proba not critical.

(b) Equivalence trials (b)trials Equivalence (b) Equivalence trials(b) Equivalence Equivalence (b) clarified. Equivalence trials (b) Equivalence trials issue is not clarified. The(b)issue is not clarified. The is not clarified. The trials issue is not is notThe clarified. The issue issuetrials isThe notissue clarified. presented before symmetry presented symmetry presented before symmetry presented before symmetry presented before symmetry presented before before symmetry presented before symmetry trials trials trials trials trials trials trials could a difference. But It could make a difference. But make ItIt could aa difference. But It could make a difference. But It could make aIt difference. could make difference. But makeBut (c) Symmetry andand equivalence (c) Symmetry and equivalence (c) Symmetry andwhat equivalence (c) Symmetry and equivalence (c)and Symmetry andof equivalence (c)kind Symmetry andwhat equivalence (c)and Symmetry andofequivalence what kind kind how, how, what ofhow, how,kind andof whathow, kind of how, and and what kind of teststests or onlydifference? equivalence tests equivalence tests equivalence tests difference? tests or only equivalence tests or only equivalence tests tests or or only only equivalence tests or only tests or only equivalence tests difference? difference? difference? difference?

The issue is not clarified.

It could make a difference. B how, and what kind of difference?

SMTS vs. DMTS

SMTS vs. DMTS

SMTS SMTS vs. DMTS Different processes going Different processes are going Different going SMTS vs.Different DMTS processes are going processes are Differentare processes are going SMTS vs. vs. DMTS DMTS SMTS Different vs. DMTS processes are going on with SMTS and DMTS. on and DMTS. on with SMTS and DMTS. on with SMTS and DMTS. on with and DMTS. on with with SMTS SMTS and SMTS DMTS.

Different processes are goin on with SMTS and DMTS.

Intertrial interval

Intertrial interval

Intertrial Intertrial interval The issue not clarified. issue is not clarified. The issue is not clarified. Intertrial interval The issue is not clarified. is notThe clarified. Intertrial interval interval Intertrial The interval issue is isThe notissue clarified.

The issue is not clarified.

Response option

Response option Response Mouse option Response Mouse option show that this Mouse is probably Data show that is Data show that this is probably Mouse ResponseData option Mouse show that this isData probably show that this is probably Response option Mouse Response Mouse Data option show Data that this this is probably probably Touch Keyboard criticalKeyboard Touch click Keyboard Touchclick notclick criticalKeyboard not click Keyboard Touch not critical not critical notclick click Keyboard Keyboard Touch clickTouch not critical criticalTouch screen screen screen screen screen screen screen

Data show that this is proba not critical

Stimuli used

Stimuli usedAbstract stimuli Stimuli Abstract Stimuli used Research stimuli has shown Abstract that Research stimuli shown Research shown that Stimulistimuli used Abstract stimuli Research hasAbstract shown that Research has thathasstimuli Stimuli used used Abstract stimuli Stimuli Research used has has shown that thatshown Abstract Non-figurative stimuli Non-figurative stimuli different stimuli could have stimulistimuli different stimuli could have stimuli could have Non-figurative stimuliNon-figurative Non-figurative stimuli different coulddifferent have different stimuli could have Non-figurative stimuli Non-figurative stimuli different stimuli could have Nonsense syllabus Pictures Nonsense syllabus Pictures different on the Pictures Nonsense syllabus different effects on the Pictures different effects on Nonsense syllabus Pictures Nonsense syllabus differentPictures effects on the different effects on the effects Nonsense syllabus Pictures different effects on the the Nonsense syllabus outcome of equivalence outcome of equivalence outcome equivalence outcome of equivalence of equivalence outcome of ofoutcome equivalence classes. classes. classes. classes. classes. classes.

Research has shown that different stimuli could have different effects on the outcome of equivalence classes.

Detailedorstart-up Detailed or Such start-up as “belong instruction Detailed or start-up This instruction seems together”, to orbe Such a critical as This “belong seems together”, to be aa critical This seems to be a critical Detailed start-up instruction Such instruction as “belong together”, Detailed start-up This together”, seems instruction be aas critical or“belong Such as “belong together”, This toorbe a critical Detailed start-up instruction or toSuch Such as “belong together”, Detailed This start-up seems to instruction beseems critical Such as “belong together”, not “are etc. thevariable. same”, etc.variable. variable. not etc. not variable. not “are the same”, notthe same”, variable. “are the etc. notetc. “are “are the the same”, same”, etc.same”,“are not variable. “are the same”, etc.

This seems to be a critical variable.

criterion Criterion Afor relatively mastery huge criterion Criterion variation; A relatively mastery It will huge criterion have variation; an effect A relatively not It only huge variation; effect not Iteffect will have an effect not only relatively huge variation; will have an effect not Aonly relatively huge variation; Itan will have anonly not only Criterion for mastery Criterion criterion forAmastery Criterion for mastery criterion Afor relatively huge variation; It will will have an effect not only A relatively huge variation; Criterion for masteryIt criterion Criterion forhave mastery criterion of conditional discriminations 83%–100% 83%–100% on 83%–100% how of 83%–100% discriminations of conditional discriminations on 83%–100% how the classes are on classes are 83%–100% on how the classes are on how the are the classes are of conditional discriminations of conditional discriminations 83%–100% on how how the the classes are classes of conditional conditional discriminations of conditional discriminations categorizing responding as in established butisalso on what is categorizing responding as categorizing in responding established but also categorizing on what established is responding but on what is established also what isas in established but also categorizing responding as in categorizing responding in on established but also alsoas onin what is on what categorizing responding as in but as accordance with stimulusaccordance with accordance withdefined stimulus as responding in defined as in defined as responding in defined in responding in accordance with stimulus with stimulus definedwith as responding responding in defined as accordanceaccordance with stimulus stimulus accordance stimulusas responding accordance equivalence or or not accordance with stimulus accordance with accordance with stimulus with stimulus equivalence or not equivalence or not orequivalence not with stimulus accordance with stimulus stimulus equivalenceequivalence or not not accordance equivalence or not or not — an equivalence or equivalence or not —equivalence an not — an or not — an equivalenceequivalence or not not — — an anorequivalence arbitrary boundary. arbitrary arbitrary boundary. arbitrary boundary. arbitrary boundary. arbitrary boundary. boundary.

It will have an effect not on on how the classes are established but also on wha defined as responding in accordance with stimulus equivalence or not — an arbitrary boundary.

A phase withEither changing A Either with changing no phase A phase reduction beEither with important, changing no phase could with reduction important, Either no This phase could with be bereduction important, important, This couldnobephase important, Thiswith could This could be important, A phase with changing no phase with reduction A phase with changing Either nobephase with reduction This could A phase phase with changing Either noThis phase with reduction A phase with changing Either with reduction before of of reinforcement especially if theisarrangement reinforcement of reinforcement density especially before reinforcement density if the arrangement density especially before isdensity if the arrangement especially especially is density ifif especially the the arrangement arrangement if the arrangement isreinforcement reinforcement densityreinforcement before of density reinforcement density before of reinforcement density reinforcement density before of reinforcement reinforcement density reinforcement density before ofis density is testing the or aa phase before with the or aset phase with set up without any or reduction testing before the tests set up ortesting awithout phasebefore with any reduction settests up without ofthe any reduction set settests up up of without without up any anywithout reduction reduction anybefore of of reduction of testing before the tests or a phase testing with before tests or a phase with testing before the tests or phase with testing the tests a phase of with reduction probability aprobability (i.e., reduction of probability (i.e.,testing. reinforcement testing. (i.e., a reduction reinforcement probabilityaa(i.e., before reinforcement testing. before testing. reinforcement reinforcement reinforcement before before testing. before testing. before a reduction of probability (i.e., of aof reduction of (i.e., reduction of probability (i.e., a reduction of probability 25%, 0%) 75%,0%) (50%), 25%, 0%) 75%, (50%), 25%, 0%) 75%, 75%, (50%), 25%, 0%) 75%, (50%), 75%, (50%), (50%), 25%, 0%) 25%, 75%, (50%), 25%, 0%)

This could be important, especially if the arrangemen set up without any reduction reinforcement before testing

Characteristics of participants Characteristics Characteristics Children of of participants participants Characteristics Children ofIt participants seems like thereChildren are Characteristics ItIt seems seems like like of participants there are are It seems Children Characteristics of participants Children Characteristics It seems of participants like Children there are Children It there seems like there are like there are and age Adults Adults and and age age Adults and agedepending Adults differences andonage differences differencesdifferences depending depending on ondifferences Adults and age Adults and age differences onAdults depending depending on depending on Children with autism with autism different training structures. autism training Children different with autism training structures. different different training training structures. structures. Children with autism Children with autism Children with different structures. Children with Children autism different training structures. Dementia Dementia patients Dementia patients patients Dementia patients Dementia patients Dementia patients Dementia patients Elderly Elderly participants Elderly participants participants Elderly participants Elderly participants Elderly participants Elderly participants

It seems like there are differences depending on different training structures.

Note. Different relevant variables and parameters in addition to some details, in the procedures, are shown in the first two columns. Some of the effects are commented on in the far right column. SIM=simultaneous, STC=simple-to-complex, CTS=complex-to-simple, LS=linear series, MTO=manyto-one, and OTM=one-to-many.

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Figure 1. Solid arrows indicate trained relations, dashed-line arrows indicate tests for responding in accord, symmetry, transitivity and equivalence. In this example it is only three members indicating by the letters A, B, and C.

researchers to continue to explore the variables that influence equivalence class formation. Training Structures Three training structures have been used in establishing conditional discriminations necessary for testing of emergent relations: linear series (LS), many-to-one (MTO), and one-to-many (OTM) (e.g., K. J. Saunders, Saunders, Williams, & Spradlin, 1993). In potential three 3-member classes, LS involves training of AB and BC relations before testing of emergent relations. MTO involves training of AC and BC relations, and OTM involves training of AB and AC relations (see Figure 1). In the earliest publications on stimulus equivalence, it was assumed, depending on the training structures used to establish the conditional discriminations, that there should not be any differences in equivalence formation among LS, MTO, and OTM training structures (e.g., Sidman, 1994; Sidman & Tailby, 1982). It is difficult to compare equivalence yields across different labs and different studies because the parameters differ. Some studies have found that MTO is the most effective training structure (Fields, Hobbie-Reeve, Adams, & Reeve, 1999; 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; R. R. Saunders, Wachter, & Spradlin, 1988; Spradlin & Saunders, 1986), while others have found results in favor of OTM (Arntzen & Holth, 1997, 2000). Furthermore, some studies have found very little difference between MTO and OTM (Arntzen, Grondahl, & Eilifsen, 2010; Arntzen & Hansen, 2011; Arntzen & Nikolaisen, 2011; Arntzen & Vaidya, 2008; Smeets & Barnes-Holmes, 2005). However, the existing results indicate that LS is the least effective training structure in the formation of equivalence classes, at least with a simultaneous protocol, which means that all relations are trained and tested simultaneously (see Imam, 2006, for an extensive description of different protocols). Furthermore, it is important to note that almost all studies that have shown superiority of the MTO training structure have used two classes only. It is therefore a possibility that S-control can explain the differences in stimulus-equivalence outcomes between the studies. Negative contextual control can be reduced by using three or four choices in matching-to-sample training (Carrigan & Sidman, 1992; Johnson & Sidman, 1993; Sidman, 1994). Some other procedural variables that may be responsible for differences


in outcomes across studies include the types of test trials (e.g., global equivalence trials only) included in testing (R. R. Saunders et al., 2005), thinning of the probability of programmed consequences, and whether baseline performance was intact during testing (Eilifsen & Arntzen, 2009). R. R. Saunders and Green (1999) discussed how outcomes on equivalence tests could be related to the number of trained discriminations, and proposed a discrimination analysis that highlighted important differences between the three training structures. Saunders and Green argued that for the participant to respond in accordance with stimulus equivalence, each stimulus must be discriminated from every other stimulus in the experiment. Therefore, outcomes may differ on tests for stimulus equivalence because the number of necessary simple discriminations differ across the training structures. For MTO, every simple discrimination is established, which is not the case for OTM and LS. For example, OTM (e.g., AB and AC) does not require the participant to discriminate between B and C stimuli during baseline training because both are presented as comparisons and, thus, are never presented together. However, during the test phases, participants are required to discriminate between BC and CB stimuli. In a potential three 3-member class after training of AC and BC using MTO, then there will be three discriminations among the C1, C2, and C3 stimuli. Furthermore, C1 will be discriminated from A1, A2, A3, B1, B2, and B3, which will give six discriminations. C2 will be discriminated from A1, A2, A3, B1, B2, and B3, which will give six discriminations. C3 will be discriminated from A1, A2, A3, B1, B2, and B3, which will also give six discriminations. The two samples, A and B, also have to be discriminated because they are mixed in test trials, yielding 15 discriminations (A1A2, A1A3, A2A3, B1B2, B1B3, B2B3, A1B1, A1B2, A1B3, A2B1, A2B2, A2B3, A3B1, A3B2, and A3B3). The total will be 36 discriminations (i.e., 3+6+6+6+15=36).

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However, with training of AB and AC (OTM), the number of discriminations among samples will be three. Between comparisons, there will be six discriminations. Furthermore, discriminations between the samples and comparisons will be A1B1, A1B2, A1B3, A2B1, A2B2, A2B3, A3B1, A3B2, A3B3, A1C1, A1C2, A1C3, A2C1, A2C2, A2C3, A3C1, A3C2, and A3C3 (18 discriminations). Thus, OTM entails 27 discriminations (i.e., 3+6+6+18=27). In the LS training structure with three members and three classes, there will be three discriminations between samples and six discriminations between comparisons, along with A1B1, A1B2, A1B3, A2B1, A2B2, A2B3, A3B1, A3B2, A3B3, B1C1, B1C2, B1C3, B2C1, B2C2, B2C3, B3C1, B3C2, and A3B3 (18 discriminations). Thus, LS entails 27 discriminations (i.e., 3+6+18=27). In summary, with three 3-member classes, the number of discriminations required in MTO is 36, versus 27 in OTM and LS. So there are nine discriminations that are not presented in OTM and LS. This difference will increase with the number of members in a class and/or the number of classes. Relatively few experiments, however, have been conducted to test whether the difference in the outcomes on equivalence tests following different training structures changes as a function of increasing class members and/ or number of classes (Arntzen, Grondahl, et al., 2010; Arntzen & Hansen, 2011; Fields et al., 1999; R. R. Saunders et al., 2005). For example, in Arntzen and Hansen’s study, in which potentially three 6-member equivalence classes were trained, there were only small differences in formation of stimulus equivalence after OTM and MTO training. This could indicate that other variables are as important as the number of simple discriminations during training. One other possibility that could account for the different outcomes between MTO, LS, and OTM is related to the number of successive and simultaneous discriminations (Arntzen, 2011; Sidman, 2011).

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In the following an example with three members and only one class is used for illustration purposes only. Because many samples (A1 and B1) are trained to one comparison (C1) in MTO, while one sample (A1) is trained to many comparisons (B1 and C1) in OTM, there is a difference between the number of successive discriminations of sample stimuli (two times higher in MTO than in OTM) and simultaneous discriminations of comparison stimuli (two times higher in OTM than in MTO), depending on the training structure. In addition, in the test for emergent relations for MTO, some of the stimuli that have served as samples in training will serve as comparisons in the test because the participants have discriminate every sample successively and the comparisons simultaneously. For OTM, some of the stimuli that have served as comparisons during training will serve as samples during testing. For LS (AB and BC) there will be a special case in which the B’s will serve as both comparisons and samples. Further research needs to be done to elaborate the effects of the change from successive to simultaneous discriminations and, inversely, the change from simultaneous to successive discriminations. In addition, the effects of stimuli serving both as samples and comparisons seem to be an interesting research question. Instructions Sidman (1992) pointed out that one should be careful about instructions in experiments on stimulus equivalence: “Until we have answered the question of whether rules give rise to equivalence, or equivalence makes rules possible, we are going to have to be careful about our experimental procedures in investigations of equivalence. If we tell our subjects that stimuli ‘go with’ each other (or that they ‘match each other,’ ‘belong together,’ ‘are the same,’ ‘go first’ or ‘go second,’ etc.), the data may then tell more about the subject’s verbal history than about the effects of current experimental operations” (pp. 21–22). A number of studies have shown that

instructions can play an important role in the development of conditional discriminations (Devany, Hayes, & Nelson, 1986; Pilgrim, Jackson, & Galizio, 2000; Schilmoeller, Schilmoeller, Etzel, & LeBlanc, 1979; Zygmont, Lazar, Dube, & McIlvane, 1992). Hence, it seems important to ask questions about the role of instructions in the formation of equivalence classes. Pilgrim et al. (2000) found that instructions or instructions plus sample naming increased the establishment of arbitrary conditional discriminations in 3- to 6-year-old children. Arntzen, Vaidya, and Halstadtro (2008) raised a number of questions about the effectiveness of the instructions. One issue is timing: It could be that instructions given after participants have failed to respond correctly could be more effective than instructions given at the very beginning of training. “For example, instructions presented at the beginning, when the participant is unfamiliar with many aspects of the task, may be less effective than instructions delivered after the participant has become familiar with the basic requirements of the task, such as orienting to stimuli, scanning the stimulus array, using a mouse or another device to select and respond to a stimulus, and so forth” (Arntzen et al., 2008, p. 29). Another variable is the content of the instruction. It could be that more general instructions like “belong together” are more effective in establishing a rule that ensures that the participant will respond more effectively with novel exemplars. Therefore, Arntzen et al. wanted to study the effects of general instructions presented by the experimenter after the participants did not pass the training criterion for the first conditional discrimination (AB). The participants had approximately 580 trials without any progress in the establishment of the conditional discriminations. The results showed that the instruction “belong together” was effective in establishing conditional discrimination performance of the AB relations. Furthermore, additional relations were


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established without any further training. All nine participants reached the mastery criterion for the conditional discrimination training. All participants passed the tests for symmetry, and two of nine passed for equivalence. There are some limitations with the Arntzen et al. (2008) study. For example, we cannot be sure that the presentation of instructions actually influenced the establishment of AB conditional discrimination. Some researchers have argued for a type of learning-set outcome in arbitrary matching that is based on the empirical observation that novel successive arbitrary matching relations are faster for the first relation compared to the next trained relations (K. J. Saunders & Spradlin, 1990, 1993). However, the number of trials for the establishment of AB conditional discriminations in the present study was about 8 times greater than the number of trials for the establishment of AC conditional discriminations, which were trained after the presentation of the instruction. Participants’ performance prior to the instruction was poorer than their performance following the instruction. Therefore, the data suggest that the instructions played an important role in establishing conditional discriminations in children in the present study. Future studies should more systematically investigate (1) how the content of the instructions could influence the outcome on equivalence tests and (2) younger participants with varying levels of verbal behavior.

the sample stimulus increased accuracy and they argued that requirement of a high number of responses to sample stimuli ensured exposure to the sample. In a study with college students as participants, Carlin, Wirth, and Chase (1998) compared conditions with and without a requirement of a response to the sample stimulus and they found that a response to sample stimulus increased accuracy. Most of the research involving conditional discrimination procedures has included a requirement of a response to the sample stimulus. The arrangement of conditional discriminations trials could differ as follows: (a) A sample is presented followed by one or more responses to the sample and subsequent presentation of a certain number of comparisons, (b) a sample and a certain number of comparison stimuli are presented at the same time, or (c) a sample is presented and a certain number of comparison stimuli are presented after an interval (usually 1–2 s). The author is not aware of any studies that have compared the effects of different procedural arrangements of sample–comparison presentation. However, in our lab, we have studied the effect of alternatives (a) and (b) (Arntzen, Braaten, Lian, & Eilifsen, 2011), and results showed a faster training for alternative (a) than for alternative (b). These findings could for the role of observing behavior. There is a need for a comparison of all three alternatives in future research.

Requirement of a Response to the Sample Stimulus

Several studies have shown that different types of stimuli may affect the formation of stimulus equivalence. Some types of stimuli may facilitate the formation of stimulus equivalence, while others may hinder equivalence class formation. For example, an increase in formation of stimulus equivalence has been shown with one or more sets of stimuli which have been nameable (Dickins, Bentall, & Smith, 1993), pictures (Arntzen, 2004; Arntzen & Lian, 2010; Arntzen & Nikolaisen, 2011; Holth & Arntzen, 1998), or acquired discriminative function

In the non-human literature a number of studies have been done regarding the importance of observing responses in conditional discrimination procedures (Eckerman, Lanson, & Cumming, 1968; Spetch & Treit, 1986). Eckerman et al. (1968) showed that accuracy increased with requirement of response to sample stimulus and Spetch and Treit (1986) found that number responses to

Pictures or Meaningful Stimuli

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(Fields, Arntzen, Nartey, & Eilifsen, 2012; Tyndall, Roche, & James, 2004). In other studies, it has been shown that some types of stimuli do not easily become part of an equivalence class (e.g., McGlinchey & Keenan, 1997). McGlinchey and Keenan trained potentially two 3-member classes in 28 primary school children randomly selected from one Catholic and one Protestant school, 2 older children, and 6 adults. They used an LS training structure in which A and C stimuli were Protestant or Catholic stimuli and B stimuli were arbitrary stimuli. In the presence of A1 (Protestant stimulus), selecting B1 (arbitrary stimulus) was correct, while in the presence of A2 (Catholic stimulus), B2 was correct. In addition, in the presence of B1, C1 (Catholic stimulus) was correct, and in the presence of B2, selecting C2 (Protestant stimulus) was correct. They also included arbitrary and nonarbitrary novel stimuli (Protestant and Catholic names) in the tests for emergent relations. They found that in 36% of the cases, the participants did not respond in accordance with stimulus equivalence. In training of potential classes, the position of the picture stimulus has been studied. The main findings are that familiar pictures or familiar presented as nodes give the highest equivalence yields (e.g., Arntzen & Lian, 2010). For example, if the conditional discriminations have been trained in an LS structure (with three potential 3-member classes; AB and BC relations), having the pictures as B-stimuli has been the most effective arrangement (Holth & Arntzen, 1998). Furthermore, to have the pictures as A stimuli is more effective than presenting them later in training as C stimuli (Arntzen, 2004). Most of the studies that use familiar stimuli have used conditional discrimination training on a serialized basis, which means that AB trials are trained first, followed by BC trials, then followed by mixing of AB and BC trials. Another way to arrange the training is training on a concurrent basis, presenting a mix

of AB and BC trials from the beginning. In an arrangement with concurrent presentation of baseline trials, the order of presentation should not be important. Future research should focus not only on the importance of how the training trials are introduced in general but also on how the introduction of training trials may interact with familiar or unfamiliar stimuli. Simultaneous Matching to Sample Versus Delayed Matching to Sample Conditional discrimination procedures used in stimulus equivalence research have, for the most part, been arranged as simultaneous matching to sample (SMTS). In SMTS, a response to the sample is followed by the presentation of comparisons. Both sample and comparisons are presented on the screen until one of the comparisons is chosen. However, some studies have used delayed matching to sample (DMTS; (Arntzen, 2006; Arntzen, Galaen, & Halvorsen, 2007; Arntzen & Haugland, 2012; Bortoloti & De Rose, 2012; R. R. Saunders et al., 2005; Tomanari, Sidman, Rubio, & Dube, 2006; Vaidya & Smith, 2006). In DMTS, the offset of the sample is followed by a delay until the onset of the comparisons. In these delayed matching-to-sample experiments, either a 0-s delay or an n-s delay between the offset of the sample and onset of the comparisons has been used, as either one delay value or as a comparison of different delay values. In the studies that have compared different delay values, the main findings have been that longer values have resulted in high accuracy during training (DeFulio, 2002) and have resulted in high equivalence yields (Arntzen, 2006). It is reasonable to assume that different behavioral processes are going on in SMTS as compared with DMTS procedures. As Sidman (1969) has pointed out, some type of behavior needs to fill the gap between the sample offset and the comparison onset. Blough (1959) showed that for two of four

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pigeons some stereotyped behavior shown in the delay between the sample offset and the comparison onset could have function as a type of mediation behavior which controlled the choice behavior. Related to humans, the question is, what type of behavior could this be? Furthermore, what is the status of that type of behavior? Some research has found that when distracters are presented during testing, the number of participants responding in accordance with stimulus equivalence has been reduced (Arntzen, 2006). This could indicate that some rehearsal behavior is going on in the gap between the sample offset and the comparison onset, and that distracters may hinder the rehearsal behavior. Criterion for Correct Responding During Training and Test A low mastery criterion in training could be troublesome, especially when the conditional discrimination training is arranged to establish potentially only two classes of stimuli. Another issue is the number of training trials per block in conditional discrimination training. If the conditional discrimination training is arranged to establish three potential 3-member classes, each training block consists of 18 trials, and the mastery criterion is, for example, 88 %, then each trial type or sample–comparison is presented three times. In theory, it could be that for one trial type, two of three trials are incorrect and still the participant will respond in accordance with the mastery criterion if he or she has 16 of 18 trials correct. A recommendation would be to have a high mastery criterion for training; 95 % or higher. The criterion for defining responding in accordance with stimulus equivalence is arbitrary. The criterion used differs across experiments within stimulus equivalence research. However, customarily a criterion of responding in accordance with stimulus equivalence is at 90% or above. It could be that some of the differences in outcome on equivalence tests across laboratories are related

to differences in mastery criterion. We should be careful with the criterion for the definition of responding in accordance with stimulus equivalence, especially when using two classes. Conclusion The present article has focused on some methodological variables or parameters in stimulus equivalence research that could influence the outcome on the test for the emergence of equivalence classes. Some of these variables have been discussed. For example, the experiment with instructions is a demonstration of how a certain type of instruction can influence the establishment of conditional discrimination. Furthermore, the present article raises some more general questions, for example, can differences in stimulus equivalence outcome be related to the different instructions employed? Another issue that seems to be of substantial importance is the criteria used to document adequate training and the criteria used in test for categorizing responding in accordance with stimulus equivalence. For example, mastery criterion should be higher in training (e.g., 95–100%) than in testing (e.g., 90–100%). Finally, the evaluation of different variables will hopefully facilitate the development of an effective teaching of stimulus equivalence classes. References Arntzen, E. (2004). Probability of equivalence formation: Familiar stimuli and training sequence. The Psychological Record, 54, 275–291. Retrieved from http://thepsychologicalrecord.siuc.edu/ index.html. Arntzen, E. (2006). Delayed matching to sample and stimulus equivalence: Probability of responding in accord with equivalence as a function of different delays. The Psychological Record, 56, 135–167. Retrieved from http://thepsychologicalrecord.siuc.edu/index.html.

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10.1016/0270-4684(86)90005-4 Tomanari, G. Y., Sidman, M., Rubio, A. R., & Dube, W. V. (2006). Equivalence classes with requirements for short response latencies. Journal of the Experimental Analysis of Behavior, 85, 349–369. doi: 10.1901/jeab.2006.107-04 Tyndall, I. T., Roche, B., & James, J. E. (2004). The relation between stimulus function and equivalence class formation. Journal of the Experimental Analysis of Behavior, 81, 257–266. Retrieved from ISI:000223182300003 Vaidya, M., & Smith, K. N. (2006). Brief report: Delayed matching-to-sample training facilitates derived relational responding. Experimental Analysis of Human Behavior Bulletin, 24, 9–16. Retrieved from http://www.eahb.org/ NewSitePages/BulletinHomepage.htm. Zygmont, D., Lazar, R., Dube, W. V., & McIlvane, W. J. (1992). Teaching arbitrary matching via sample stimulus-control shaping to young children and mentally retarded individuals. Journal of the Experimental Analysis of Behavior, 57, 109–117. doi: 10.1901/jeab.1992.57-109