THE EFFECTS OF TEST ORDER AND NODAL DISTANCE ON THE EMERGENCE AND STABILITY OF DERIVED DISCRIMINATIVE STIMULUS FUNCTIONS

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1 The Psychlgical Recrd, 2005, 55, THE EFFECTS OF TEST ORDER AND NODAL DISTANCE ON THE EMERGENCE AND STABILITY OF DERIVED DISCRIMINATIVE STIMULUS FUNCTIONS RUTH ANNE REHFELDT Suthern Illinis University SIMON DYMOND APU. Cambridge The present study examined the effects f equivalence test rder and ndal distance n the emergence and stability f derived discriminative stimulus functins. Participants in 1 grup were expsed t a transfer f functins test fllvi/ing a symmetry and equivalence test, anther grup f participants cmpleted a symmetry and equivalence test fllvwing a transfer test, and a final grup f participants received a symmetry test nly if they failed t demnstrate immediate transfer, after which time they were retested. At least 1 mnth fllwing their initial labratry experience, all participants wh had demnstrated the transfer f functins were cntacted and asked t return t the labratry fr a fllw-up transfer test. Results shwed that a prir equivalence test was nt necessary fr the transfer f functins, althugh a symmetry test may have facilitated transfer fr sme participants, A ndal distance effect fr the stability f the derived stimulus functins was bserved during the fllw-up transfer test. Research n derived stimulus relatins has cnsistently shwn that when peple are expsed t a series f interrelated cnditinal discriminatins, the stimuli can becme related t each ther in indirect and ften cmplex ways. The main finding is as fllws: Suppse, fr instance, reinfrcement is delivered fr selectin f stimulus B in the presence f stimulus A, and fr selectin f stimulus C in the presence f stimulus B, respectively. Mst participants will nw readily reverse these explicitly reinfrced cnditinal discriminatins in the absence f further training. That is, they will nw select A given B and B given C in accrdance with derived symmetrical, r mutually entailed, stimulus relatins. Furthermre, participants will nw als select C given A and A given C in accrdance with derived transitive and equivalence, r We thank Erik Arntzen and Lanny Fields fr helpful suggestins n an earlier versin. We als thank Kim ZImke tr assistane with subject running and Eamn Strain fr statistical advice. Address crrespndence t Ruth Anne Rehfeldt, Ph,D,, Rehabilitatin Services Prgram, Rehabilitatin Institute, Suthern Illinis University, Carbndale, IL , ( rehfeldt@siu,edu).

2 180 REHFELDTAND OYMOND cmbinatrially entailed, stimulus relatins withut further training. Fllwing such derived perfrmances, the stimuli are said t participate in an equivalence class (Sidman, 1994) r a relatinal frame f equivalence (Barnes, 1994; Hayes, Barnes-Hlmes, & Rche, 2001). Perhaps ne f the mst interesting features f derived stimulus relatins is the transfer r transfrmatin^ f functins, which has generated cnsiderable interest due in part t the implicatins it has fr understanding a wide range f cmplex behavir. The transfer r transfrmatin f functins ccurs when the functin f ne stimulus in a derived relatin alters the functins f anther stimulus accrding t the derived relatin between the stimuli, withut additinal training (Dymnd & Rehfeldt, 2000). Fr instance, Dymnd and Barnes (1994) first trained participants in six match-t-sample tasks (i.e., A1-B1, A2-B2, A3-B3, A1- C1, A2-C2, A3-C3) and then tested fr the emergence f three equivalence relatins (i.e., B1 -C1, B2-C2, B3-C3). Fllwing a successful equivalence test, participants were trained in tw self-discriminatin respnses n a schedule f reinfrcement task; if participants did nt emit an perant respnse n this task, chsing B1 was reinfrced, and if they emitted ne r mre respnses, chsing B2 was reinfrced. Finally, participants were tested fr a transfer f these self-discriminatin respnse functins thrugh equivalence relatins (i.e., 0 respnses = chse C1; >1 respnses = chse C2). T date, the transfer f functins thrugh equivalence relatins has been shwn with discriminative and self-discriminative functins (e.g., Barnes, Brwne, Smeets, & Rche, 1995; Barnes & Keenan, 1993; Dugher, Perkins, Greenway, Kns, & Chiassn, 2002; Dymnd & Barnes, 1994, 1998; Gatch & Osbrne, 1989; Khlenberg, Hayes, & Hayes, 1991; Rehfeldt & Hayes, 1998; Wulfert & Hayes, 1988), cnsequential functins (Greenway, Dugher, & Wulfert, 1996; Hayes, Khlenberg, & Hayes, 1991), and respndent eliciting and extinctin functins (e.g., Dugher, Augustsn, Markham, Greenway, & Wulfert, 1994; Rche & Barnes, 1997). A key issue in transfer f functin research cncerns the rle played by expsure t a prir test fr equivalence relatins in facilitating the subsequent derived transfer. In a typical transfer f functins study, a series f cnditinal discriminatins are first trained, and participants are then tested fr derived equivalence relatins. Next, a particular behaviral functin is directly trained t at least ne member f the relatin, and then sme r all f the remaining stimuli are tested t see if they have acquired the functin withut additinal training. Previus studies have shwn that discriminative (Barnes & Keenan, 1993; Rehfeldt & Hayes, 1998; Wulfert & Hayes, 1988), self-discriminative (Dymnd & Barnes, 1998), and cnsequential functins (Hayes et al., 1991) may transfer in accrdance with equivalence relatins withut a prir equivalence test fr such relatins. Occasinally, hwever, researchers laithugh 'Iransfrmatin" is preferable t 'Iransfer." the iatter term is apprpriate when deaiing with derived utcmes in accrdance with equivalence relatins and will be used thrughut the present article (see Dymnd & Rehfeldt, 2000, pp ).

3 TRANSFER OF FUNCTIONS have fund it necessary t expse participants t either symmetry r partial equivalence tests in rder fr derived transfer t ccur {see Hayes et al., 1991). Thus, the relatinship between tests fr equivalence and transfer f functins is nt yet fully understd. Anther cmmn bservatin f the majrity f transfer f functins research is that nce derived stimulus functins have been measured, they are nt usually retested at a later date. That is, n published study has examined the lng-term stability f derived transfer. The stability f derived stimulus relatins, hwever, has been investigated by a handful f studies. Fr instance. Saunders. Wachter, and Spradlin, (1988; see als Spradlin. Saunders. & Saunders. 1992) shwed that participants with develpmental disabilities perfrmed with at least 90% accuracy n derived relatins tests cnducted 2 t 5 mnths fllwing their cmpletin f the riginal experiment. Likewise, Rehfeldt and Hayes (2000) and Rehfeldt and Rt (2004) demnstrated the maintenance f generalized equivalence relatins fr up t three mnths by participants with and withut develpmental disabilities. T date, n published study has investigated the lng-term stability f derived transfer f functins. Frm a practical perspective, understanding the lngevity f derived stimulus cntrl is critical in determining the utility f this apprach in teaching new behavir and in ascertaining the type and extent f any necessary retraining {Dymnd & Rehfeldt. 2000). The present experiment explred the lng-term stability f derived discfiminative stimulus functins. A discriminative functin was first trained t ne f the "B" stimuli, and transfer t the "A" and "C" stimuli was then tested. Next, participants were trained n a ne-t-many cnditinal discriminatin training prcedure (i.e., A-B and A-C). This training structure is cmmnly emplyed in transfer f functin research (e.g., Dymnd & Barnes, 1994) and allws fr the study f pssible ndal distance effects n the stability f derived transfer (see Arntzen & Hlth, 2000; Fields, Landn-Jimenez. Buffingtn, & Adams, 1995; Saunders & Green, 1999). Sme participants were expsed t the transfer test fllwing the symmetry and equivalence test, anther grup f participants cmpleted the symmetry and equivalence test fllwing the transfer test, and a final grup f participants received a symmetry test nly if they failed t demnstrate immediate transfer f functins, after which time they were retested. At least 1 mnth fllwing their initial labratry experience, all participants in each grup wh had demnstrated transfer f functins were cntacted and asked t return t the labratry fr a fllw-up stability test. Methd Participants Twenty-fur adults enrlled in a variety f undergraduate curses in a vahety f departments served as participants and were cmpensated with curse credit fr ding s. Participants were recnjited thrugh In-class

4 182 REHFELDT AND DYMOND annuncements. Befre the experiment, all participants signed a statement f infrmed cnsent and were infrmed that they culd withdraw frm the experiment at any time, althugh nne chse t d s. Upn cmpletin f the study, participants were thrughly debriefed. Participants were assigned t ne f three grups based n the rder in which they signed up fr the experiment: The first 8 participants t cmplete the experiment were assigned t Grup 1; the secnd 8 participants t cmplete the experiment were assigned t Grup 2; and the third 8 participants t cmplete the experiment were assigned t Grup 3. Apparatus and Stimuli Stimulus presentatin and data cllectin were cmputer cntrlled. The experiment was cntrlled by an IBM-cmpatible persnal cmputer, equipped with a clr mnitr and a tw-buttn muse. The cmputer was centered n a 2-ft x 2-ft table. Experimental sessins were cnducted in a 10-ft x 10-ft rm cntaining a table and chair. The experiment was prgrammed in Micrsft Visual Basic^*^ (Versin 6.0; see Dixn & MacLin, 2003) by the first authr. As shwn in Figure 1, stimuli cnsisted f nine arbitrarily cnfigured symbls. 6 t 7 cm in diameter. The figures were arbitrarily divided int three stimulus classes. During the discriminatin training and transfer test phases, stimuli were individually presented in the tp center f the screen. During the cnditinal discriminatin training and symmetry and equivalence test phases, sample stimuli appeared in the tp center f screen and cmparisn stimuli were displayed evenly spaced acrss the bttm f A B 1 Ih Figure 1. Experimental stimuli.

5 TRANSFER OF FUNCTIONS 1B3 the screen. The lcatins f cmparisn stimuli varied randmly acrss trials. Sample stimuli were identical in all phases, except in the symmetry and equivalence test phases, during which the sample stimuli were stimuli that had previusly been presented as cmparisn stimuli during cnditinal discriminatin training. Prcedure The experiment cnsisted f up t six phases, as illustrated in Figure 2. Participants in all three grups cmpleted discriminatin and c; it r I: DiKrimliialhifl Trst \i-it2, \i.m. I VI.BI.AMi;. V<-(U, Mtl, A3-C:, V.VU»i i Hymnttry A EqahilMKt In< (111- \ HH;, HI, V> t'l-a.(-2-v; IJ-U B1-C B:-Ci BJ-Cl, CI-HI.C1-B2,CVB»1 TnuMfrr r Fmnlaai T«) n.i \\. \: \.i II. ficii I nnifrr r FHKMIW TrM llllll i T FBKIIOIU TtM (»1-.\I.B3-A3,H.V,\.' tl-m;c:-,\j,o-.m f IrualTTuI id ay Tmaimif FB Tnarfrraf t'hcttb Ti Figure 2. Schemalic representatin f the training and testing rder fr the three grups f participants. cnditinal discriminatin training phases first. Participants in Grup 1 cmpleted the transfer test fllwing their cmpletin f the symmetry and equivalence test, while participants in Grup 2 cmpleted the symmetry and equivalence test fllwing their cmpletin f the transfer test. Participants in Grup 3 cmpleted the transfer test fllwing their cmpletin f cnditinal discriminatin training, and then cmpleted a symmetry test nly if they failed t demnstrate transfer f functins during the transfer test, after which time they were retested fr transfer f functins. At least 1 mnth fllwing their initial labratry experience, al) participants in each grup wh had demnstrated transfer f functins were cntacted and asked t return t the labratry fr a fllw-up test, but nly sme f the participants in each grup were able t d s, During discriminatin and cnditinal discriminatin training phases, all crrect respnses were reinfrced. Reinfrcement cnsisted f the delivery f ne pint accmpanied by an auditry beep, and the

6 184 REHFELDT AND DYMOND Statement "Gd! 1 pint!" Pint ttals were displayed at ail times in the lwer left crner f the cmputer screen. Sessins lasted up t 1 hur fr all participants. Discriminatin Training Participants were given the fllwing instructins; Yur jb in this experiment is t perfrm yur best. Yu must pay careful attentin and try t get as many pints as yu can. First, yur task is t place the image at the tp f the screen in ne f the three bxes belw it. T mve the image t the bx f yur chice, simply ciick the muse n the image and drag t the bx f yur chice. Yu will receive a pint when yu have respnded crrectly. D yur best- During this phase, discriminative functins were established t stimuli B1, B2, and B3, which wuld subsequently be presented as cmparisn stimuli during cnditinal discriminatin training. Specifically, participants POINTS: GOON Figure 3. Example f n-screen stimulus array during discriminatin training.

7 TRANSFER OF FUNCTIONS 185 were taught t mve each stimulus t ne f three specific bxes n the screen. The nset f each trial was marked by the presentatin f ne f the three stimuli in the tp center f the screen, fllwed by the presentatin f three vertically aligned bxes in the center f the screen, psitined directly belw the first stimulus. The bxes were utlined in black with a frame f apprximately 4 mm, as shwn in Figure 3, In rder t drag the stimulus t a bx, participants were required t click the muse using the left muse buttn upn the stimulus, hld the buttn dwn, and drag the muse until the stimulus was placed in the bx f the participant's chice. Once the stimulus was psitined in a bx, the remaining bxes disappeared s that participants culd nt mve a stimulus t a different bx nce it was already placed. After participants had respnded, they were required t click the muse n a buttn placed at the bttm f the screen that read, "Dne," Reinfrcement was prvided cntingent upn placing stimulus B1 in the bx at the tp f the screen, stimulus B2 in the bx in the center f the screen, and stimulus B3 in the bx at the bttm f the screen. Incrrect respnses were fllwed by the presentatin f the next trial. Training was presented in 15-trlal blcks, with each f the three stimuli presented five times per blck. The rder f stimulus presentatins was randmly determined. The phase ended when a participant had respnded crrectly n 14/15 trials (93% crrect per blck). Cnditinal Discriminatin Training The next phase cnsisted f the cnditinal discriminatin training f six relatins (A1-B1, A2-B2, A3-B3, A1-C1, A2-C2, and A3-C3). Participants were given the fllwing instructins: Remember that yur jb is t perfrm yur best. Yu must try t get as many pints as yu can. A figure will appear in the center f the screen. Next, 3 figures will appear belw the first figure. It is yur jb t chse ne f the three figures. T chse ne f the 3 figures, click the muse nce n the figure that is yur chice. The A-B relatins were trained first. Every trial began when a sample stimulus was presented in the center f the screen. Participants were required t select ne f three cmparisn stimuli (B1, B2, r B3) in the presence f ne f three sample stimuli {A1, A2, r A3). When participants respnded crrectly, the sample stimulus and its matching cmparisn were utlined in black fr 1.5 s, after which crrect respnses were reinfrced. All trials were separated by a 1-s intertrial interval. The rder f the sample stimulus presentatins was determined randmly, but each sample stimulus culd be presented n mre than five times per 15-trial blck. After participants had achieved a mastery criterin f 14/15 crrect respnses, r 93% crrect per blck fr the A-B relatins, the A-C relatins were trained. The prcedure fr training these relatins was identical t that used t train the A-B relatins, except that C1, C2, and C3 were presented as cmparisn stimuli. After participants had

8 186 REHFELDT AND DYMOND respnded crrectly n 14/15 trials, r 93% crrect per blck, the A-B and A-C relatins were trained tgether. The prcedure fr training these relatins was identical t that used t train the A-B and A-C relatins separately, except that n a given trial B1, B2, and B3, r C1, C2, and C3 culd be presented as cmparisn stimuli. The rder f the sample stimulus presentatins was determined randmly. Cnditinal discriminatin training ended when participants had respnded crrectly n 28/30 trials, r 93% crrect per blck f the mixed A-B and A-C trials. Transfer f Functins Test The test fr transfer f functin evaluated the transfer f discriminative functins frm stimulus B1 t stimuli A1 and C1; stimulus B2 t stimuli A2 and C2; and stimulus B3 t stimuli A3 and C3. The test was presented In 27-trial blcks, in which test prbe trials were inserted int reinfrced baseline trials. Participants were presented with the fllwing instructins befre the transfer test: Yu will receive pints fr putting SOME f the figures in bxes, but there are sme figures that yu WONT receive a pint fr putting in the crrect bx. Hwever, there is ALWAYS A CORRECT RESPONSE s respnd in a way yu believe is CORRECT fr EVERY FIGURE. Reinfrced baseline trials cnsisted f the presentatin f stimuli B1, B2, r B3, while test prbe trials cnsisted f the presentatin f stimuli A1, A2, A3, C1, C2, r C3. Each f the nine stimuli was presented three times, with their presentatin ccurring in a randm rder. Crrect baseline trials were reinfrced, but incrrect baseline and all test trials were never reinfrced and were fllwed by the next trial. A test trial was recrded as crrect if a participant placed stimuli A1 r C1 in the same bx in which they had been taught t place stimulus B1, if a participant placed stimuli A2 r C2 in the same bx in which they had been taught t place stimulus B2, and if the participant placed stimuli A3 r C3 in the same bx in which they had been taught t place stimulus B3. The transfer test ended after a participant respnded crrectly n at least 24/27 trials (89% crrect per blck), r after five blcks, whichever came first. Test fr Symmetry and Equivalence Relatins The emergence f six symmetry relatins (B1-A1, B2-A2, B3-A3, C1- A1, C2-A2, and C3-A3) and six equivalence relatins (B1-C1, B2-C2, B3- C3, C1-B1, C2-B2, and C3-B3) was assessed fr participants in Grups 1 and 2, Prir t the symmetry and equivalence test participants were tld: Althugh yu will n lnger receive pints n the screen, the cmputer is still keeping track f yur crrect and incrrect respnses. Please cntinue t d yu best.

9 TRANSFER OF FUNCTIONS 187 Participants received n feedback fr crrect r incrrect respnses. The test cnsisted f 36 trials. Each f the six symmetry and six equivalence relatins was assessed three times each. Participants in Grup 3 cmpleted symmetry test trials nly, and did s nly if they failed t demnstrate criterin perfrmance during the transfer test. Fr these participants, the test cnsisted f 18 trials, in which each f the six symmetry relatins was examined three times each. Fllw-up Transfer f Functins Test All participants wh demnstrated transfer f functins were asked t return t the labratry at least 1 mnth fllwing their initial labratry experience. All thse wh were able t return fr a fllw-up test cmpleted the transfer test a secnd time. Participants were nt given any instructins prir t ding s. The fllw-up test was identical t the first transfer test. Results Grup 1 Discriminatin training. Discriminative cntrl was established by stimuli B1, B2, and B3 fr all 8 participants, in anywhere frm ne t six trial blcks. Cnditinal discriminatin training. All 8 participants mastered the A- B, A-C, and mixed A-B and A-C cnditinal discriminatins in anywhere frm ne t five trial blcks. Symmetry and equivalence test. The criterin fr inferring the emergence f symmetry relatins was 16/18 (89%) crrect respnses. The same criterin was used t infer the emergence f equivalence relatins. As shwn in Figure 4, 7 f the 8 participants (JM, CH, YS, SF, AB, KL, and MS) demnstrated the emergence f symmetry relatins, the exceptin being JeM. Figure 4 als shws that 6 f the 8 participants (JM, CH, YS, AB, KL, and MS) demnstrated the emergence f equivalence relatins, the exceptins being SF and JeM. Transfer f functins test. The functins f the "B" stimuli were held t have transferred t the "A" stimuli if the "A" stimuli ccasined at least eight f nine (89%) crrect respnses, and t the "C" stimuli if the "C" stimuli ccasined at least eight f nine (89%) crrect respnses. Figure 4 shws that 4 f the 8 participants (JM, CH, YS, and JeM) demnstrated transfer f functins t bth the "A" and "C" stimuli, while SF demnstrated transfer f functins t the "A" stimuli; AB demnstrated transfer f functins t the "C" stimuli, and KL demnstrated transfer f functins t the "A" stimuli. MS failed t demnstrate the transfer f functins t either the "A" r "C" stimuli. Of the 7 participants wh demnstrated transfer f functins, all but 1 had demnstrated the emergence f symmetry relatins during the prir symmetry and equivalence test JeM demnstrated transfer f functins despite failing t shw the emergence f symmetry relatins. Likewise, all

10 188 REHFELDT AND DYMOND GROUP 1 Symm Equiv Transfer Taal Fllw-up Tesi JM c Q. " I ' i_ O " " ' c.2 0. p Jli a- -A- -c- -B- -A- -c- SF JEM AB CH YS B- -A" 'C- MS Figure 4. Prprtin f crrect respnses n symmetry, equivalence, and transfer f functins test trials fr participants in Grup 1. Prprtin f crrect respnses is shwn separately fr the "A," "B," and "C" stimuli during the transfer f functins test and the filw-up test.

11 TRANSFER OF FUNCTIONS 189 but 2 f the 7 participants wh demnstrated transfer f functins had demnstrated the emergence f equivalence relatins, the exceptins being SF and JeM, bth f whm demnstrated transfer f functins despite failing t shw equivalence during the prir test. Fllw-up transfer f functins test. The same criterin fr inferring the transfer f functins was used t infer the stability f the derived stimulus functins. Three participants, JM, CH, and YS were able t return fr the fllw-up transfer f functins test. As shwn In Figure 4, nne f the participants demnstrated stability f the derived stimulus functins. The "A" stimuli ccasined crrect respnses n mre trials than the "C" stimuli fr all 3 participants. Grup 2 Discriminatin training. Discriminative cntrl was established by stimuli B1, B2, and B3 fr all 8 participants, in anywhere frm ne t seven trial blcks. Cnditinal discriminatin training. All 8 participants mastered the A- B, A-C, and mixed A-B and A-C cnditinal discriminatins in anywhere frm ne t fur trial blcks. Transfer f functins test. The same criterin that was used t infer the transfer f functins fr participants in Grup 1 was used fr participants in Grup 2. Figure 5 shws that 6 f the 8 participants (SH, MD, TG, BW, SR, and KZ) demnstrated transfer f functins t bth the "A" and "C" stimuli. AG and JM failed t demnstrate the transfer f functins t either the "A" r "C" stimuli. Symmetry and equivalence test. The criterin fr inferring the emergence f symmetry and equivalence relatins was the same as that utilized fr participants in Grup 1. As shwn in Figure 5, 7 f the 8 participants (SH, MD, TG, BW, SR, KZ, and JM) demnstrated the emergence f symmetry relatins, the exceptin being AG. Figure 5 als shws that the same 7 participants demnstrated the emergence f equivalence relatins. All f the participants wh had demnstrated the transfer f functins during the prir transfer f functins test als demnstrated the emergence f symmetry and equivalence relatins. Fllw-up transfer f functins test. Fur participants, SH, MD, TG, and BW, were able t return fr the fllw-up transfer f functins test. As shwn in Figure 5, 1 subject, TG, demnstrated the stability f derived stimulus functins. The "A" stimuli ccasined crrect respnses n mre trials than the "C" stimuli fr 2 f the 4 participants. Grup 3 Discriminatin training. Discriminative cntrl was established by stimuli B1, B2, and B3 fr all 8 participants, in anywhere frm ne t fur trial blcks. Cnditinal discriminatin training. All 8 participants mastered the A- B, A-C, and mixed A-B and A-C cnditinal discriminatins in anywhere frm ne t fur trial blcks.

12 190 REHFELDT AND DYMOND GROUP 2 TramlBr TBSI Symm Eqiirv FUmv-up Ts SH MD TG t CO c Q c O 0 O c O,,5 Q. O -r -A- -Csn KZ JOM I Figure 5. Prprtin f crrect respnses n symmetry, equivalence, and transfer f functins test trials fr participants in Grup 2. Prprtin f crrect respnses is shwn separately fr the "A," "B," and "C stimuli during the transfer f functins test and the fllw-up test.

13 TRANSFER OF FUNCTIONS 191 GROUP 3 1 st T'anster Tesl Sym r TasI Fnllpiv-up Tssi R B I I cw V) c CL W a: ^ > u I I LW O c g a. I D n MN YG I Figure 6. Prprtin f crrect respnses n symmetry, equivalence, and transfer f functins test trials fr participants in Grup 3, Prprtin f crrect respnses is shwn separately fr the "A." "B," and "C" stimuli during the first and secnd transfer f functins tests and the fllw-up test.

14 192 REHFELDT AND DYMOND First transfer f functins test. The same criterin that was used t infer the transfer f functins fr participants in Grups 1 and 2 was used fr participants in Grup 3. As shwn in Figure 6, 1 subject, CC, demnstrated transfer f functins during the first test. The remaining 7 subjects failed t demnstrate criterin perfrmance during the first transfer f functins test. Symmetry test. The criterin fr inferring the emergence f symmetry relatins was the same as that utilized fr participants in Grups 1 and 2. As shwn in Figure 6, 3 f the 7 participants {CW, LW, and YG) tested demnstrated the emergence f symmetry relatins. (CC was nt asked t cmplete the symmetry test because this participant had demnstrated transfer f functins withut expsure t symmetry test trials.) Secnd transfer f functins test. Figure 6 shws that 3 participants {MRB, CW, and PB) demnstrated transfer f functins t bth the "A" and "C" stimuli during the secnd transfer f functins test. LW, MN, and AL demnstrated transfer f functins t the "A" stimuli, and YG failed t demnstrate transfer f functins t either the "A" r "C" stimuli during the secnd test. Of the 6 participants wh demnstrated transfer f functins fllwing the symmetry test, 2 participants {CW and LW) had demnstrated the emergence f symmetry relatins during the prir symmetry test. The exceptins were MRB and PB (bth f whm wuld have demnstrated criterin perfrmance during the symmetry test had they made ne less errr). YG demnstrated transfer f functins yet failed t shw the emergence f symmetry relatins during the prir symmetry test. Fllw-up transfer f functins test. Tw participants, MRB and CW, were able t return fr the fllw-up transfer f functins test. As shwn in Figure 5, MRB demnstrated stability f the derived stimulus functins, as the "A" stimuli ccasined crrect respnding n 100% f the test trials. The "A" stimuli als ccasined crrect respnses n mre trials than the "C" stimuli fr CW. Ndal distance effect fr fllw-up transfer f functins test. During the fllw-up transfer f functins test, a higher prprtin f respnding was ccasined by the A stimuli {M ) than the C stimuli {M = 0.49) and this difference was shwn t be statistically significant, t{9) = 2.63, p <.03. This finding highlights a significant ndal distance effect fr the fllw-up transfer test. Discussin In this experiment, the transfer f discriminative stimulus functins was examined in 24 participants, 8 f whm cmpleted the transfer test after the test fr symmetry and equivalence, 8 f whm cmpleted the transfer test prir t the test fr symmetry and equivalence, and 8 f whm cmpleted a symmetry test nly if they failed t shw transfer f functins. The results suggest that a frmal demnstratin f derived stimulus relatins is nt necessary fr stimulus functins t transfer, thus

15 TRANSFER OF FUNCTIONS 193 cnverging with previusly reprted results (Barnes & Keenan, 1993; Dymnd & Barnes, 1998; Hayes et al., 1991; Rehfeldt & Hayes, 1998; Wulfert & Hayes, 1988). The perfrmances f the participants in Grup 2 in the present experiment mst clearly illustrate this pint, as 6 f the 8 participants in the grup demnstrated transfer f functins t bth the "A" and "C" stimuli in the absence f the symmetry and equivalence test. Hwever, it appears that a frmal test fr derived stimulus relatins may facilitate functin transfer. The perfrmances f participants in Grup 3 speak t this issue; Of the 7 participants wh failed t demnstrate transfer f functins withut a symmetry test, 3 demnstrated transfer t bth the "A" and "C" stimuli fllwing the symmetry test, while 3 thers demnstrated transfer f functins t the "A" stimuli nly fllwing the symmetry test. The simple repetitin f the transfer test may have als facilitated the transfer f functins fr participants in Grup 3. Future research evaluating the facilitative rle f symmetry testing n the transfer f functins shuld cntrl fr test repetitin. This study was als the first t evaluate the lng-term stability f derived stimulus functins. Surprisingly, the derived stimulus functins were nt shwn t be remarkably stable during the fllw-up transfer f functins test. These results d nt cincide with thse reprted by Saunders et al. (1988), Rehfeldt and Hayes (2000), r Rehfeldt and Rt (2004), all f whm reprted that derived stimulus relatins can be maintained several mnths fllwing participants' riginal labratry experience. These results are surprising given that the fllw-up test was cnducted n mre than 1 t 2 mnths fllwing the initial sessin, and that crrect respnses that ccurred in the presence f the "B" stimuli were reinfrced during the fllw-up test. A particularly interesting finding was that the "A" stimuli, which served as the ndal stimuli and were directly paired with the "B" stimuli during cnditinal discriminatin training, ccasined substantially mre crrect respnses during the fllw-up transfer test than did the "C" stimuli, which were separated frm the "B" stimuli by ne nde. This finding thus reflects the effects f ndal distance n the stability f derived stimulus functins (see Fields, Adams, & Verhave, 1993; Fields, Adams, Verhave, & Newman, 1990; Fields et al., 1995; Saunders & Green, 1999). Mre wrk is needed t determine the lngevity f derived stimulus functins. Everyday experience suggests that derived functins are extremely durable t the passage f time, as illustrated by the lifelng debilitating cnditins experienced by persns with clinical anxiety (see Dymnd & Rehfeldt, 2000; Friman, Hayes, & Wilsn, 1998). Further attempts t demnstrate this empirically are in rder. One pssible alternative interpretatin f the transfer effects bserved in this study is that during discriminatin training, the reinfrcement cntingencies established cnditinal discriminatins between the "B" stimuli and lcatinally defined cmparisn stimuli, in effect establishing B- D relatins. Participants' perfrmances during the transfer f functins test may have reflected the expansin f three-member t fur-member equivalence classes cnsisting f tw ndes (the "A" and "B" stimuli) (see als Fields, Newman, Adams, & Verhave, 1992).

16 194 REHFELDT AND DYMOND In cnclusin, the present study supprts previus findings that have shwn that a prir equivalence test is nt necessary fr derived transfer t ccur, even thugh a symmetry test may facilitate subsequent transfer. Future research shuld cmpare the lng-term stability f derived versus directly trained stimulus functins. Fr instance, are directly trained functins maintained in the absence f further reinfrcement and if nt, hw much cntact with the riginal cntingencies is necessary fr perfrmance t stabilize? The stability f derived stimulus functins established using preparatins ther than matching-t-sampie, such as the respndent-type training prcedure (see Leader, Barnes, & Smeets, 1996), and f derived stimulus relatins ther than equivalence, such as same, different, mre than, and less than, are als questins wrthy f empirical investigatin. Indeed, understanding the lngevity f derived perfrmances established using prcedures that are analgus t the pairings f stimuli in the natural envirnment will extend the relevance f transfer f functins research t the study f cmplex human behavir. References ARNZTEN, E., & HOLTH. P. (1997). Prbability f stimulus equivalence as a functin f training design. The Psychlgical Recrd, 47, BARNES, D. (1994). Stimulus equivalence and relatinal frame thery. The Psychlgical Recrd, 44, BARNES, D., BROWNE, M., SMEETS, P, & ROCHE, B. (1995). A transfer f functins and a cnditinal transfer f functins thrugh equivalence relatins in three- t six-year-ld children. The Psychlgical Recrd, 45, BARNES, D., & KEENAN, M. (1993). A transfer f functins thrugh derived arbitrary and nn-arbitrary stimulus relatins. Jurnal f the Experimental Analysis f Behavir, 59, DIXON, M. R., & MACLIN, O. H. (2003). V isual basic fr behaviral psychlgists. Ren, NV: Cntext Press. DOUGHER, M. J., AUGUSTSON, E., MARKHAM, M. R., GREENWAY, D. E., & WULFERT, E. (1994). The transfer f respndent eliciting and extinctin functins thrugh stimulus equivalence classes. Jumal f the Experimental Analysis f Behavir, 62, DOUGHER, M., PERKINS, D. R., GREENWAY, D., KOONS, A., & CHIASSON, C. (2002). Cntextual cntrl f equivalence-based transfrmatin f functins. Jurnal f the Experimental Analysis f Behavir, 78, DYMOND, S., & BARNES, D. (1994). A transfer f self-discriminatin respnse functins thrugh equivalence relatins. Jurnal f the Experimental Analysis f Behavir, 62, DYMOND, S.,& BARNES, D. (1998). The effects f prir equivalence testing and detailed verbal instructins n derived self-discriminatin transfer: A fllwup study. The Psychlgical Recrd, 48, DYMOND, S., & REHFELDT R- A. (2000). Understanding cmplex behavir: The transfrmatin f stimulus functins. The Behavir Analyst, 23, FIELDS, L, ADAMS, B. J., & VERHAVE, T. (1993). The effects f equivalence class structure n test perfrmances. The Psychlgical Recrd, 43,

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