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

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1 The Psychological Record, 2005, 55, THE EFFECTS OF TEST ORDER AND NODAL DISTANCE ON THE EMERGENCE AND STABILITY OF DERIVED DISCRIMINATIVE STIMULUS FUNCTIONS RUTH ANNE REHFELDT Southern Illinois University SIMON DYMOND APU, Cambridge The present study examined the effects of equivalence test order and nodal distance on the emergence and stability of derived discriminative stimulus functions. Participants in 1 group were exposed to a transfer of functions test foillowing a symmetry and equivalence test, another group of participants completed a symmetry and equivalence test following a transfer test, and a final group of participants received a symmetry test only if they failed to demonstrate immediate transfer, after which time they were retested. At least 1 month following their initial laboratory experience, all participants who had demonstrated the transfer of functions were contacted and asked to return to the laboratory for a follow-up transfer test. Results showed that a prior equivalence test was not necessary for the transfer of functions, although a symmetry test may have facilitated transfer for some participants. A nodal distance effect for the stability of the derived stimulus functions was observed during the follow-up transfer test. Research on derived stimulus relations has consistently shown that when people are exposed to a series of interrelated conditional discriminations, the stimuli can become related to each other in indirect and often complex ways. The main finding is as follows: Suppose, for instance, reinforcement is delivered for selection of stimulus B in the presence of stimulus A, and for selection of stimulus C in the presence of stimulus B, respectively. Most participants will now readily reverse these explicitly reinforced conditional discriminations in the absence of further training. That is, they will now select A given Band B given C in accordance with derived symmetrical, or mutually entailed, stimulus relations. Furthermore, participants will now also select C given A and A given C in accordance with derived transitive and equivalence, or We thank Erik Arntzen and Lanny Fields for helpful suggestions on an earlier version. We also thank Kim Zlomke for assistance with subject running and Eamon Strain for statistical advice. Address correspondence to Ruth Anne Rehfeldt, PhD., Rehabilitation Services Program, Rehabilitation Institute, Southern Illinois University, Carbondale, IL (

2 180 REHFELDT AND DYMOND combinatorially entailed, stimulus relations without further training. Following such derived performances, the stimuli are said to participate in an equivalence class (Sidman, 1994) or a relational frame of equivalence (Barnes, 1994; Hayes, Barnes-Holmes, & Roche, 2001). Perhaps one of the most interesting features of derived stimulus relations is the transfer or transformation 1 of functions, which has generated considerable interest due in part to the implications it has for understanding a wide range of complex behavior. The transfer or transformation of functions occurs when the function of one stimulus in a derived relation alters the functions of another stimulus according to the derived relation between the stimuli, without additional training (Dymond & Rehfeldt, 2000). For instance, Dymond and Barnes (1994) first trained participants in six match-to-sample tasks (i.e., A 1-B1, A2-B2, A3-B3, A 1- C1, A2-C2, A3-C3) and then tested for the emergence of three equivalence relations (i.e., B1-C1, B2-C2, B3-C3). Following a successful equivalence test, participants were trained in two self-discrimination responses on a schedule of reinforcement task; if participants did not emit an operant response on this task, choosing B1 was reinforced, and if they emitted one or more responses, choosing B2 was reinforced. Finally, participants were tested for a transfer of these self-discrimination response functions through equivalence relations (i.e., 0 responses = choose C1 ; > 1 responses = choose C2). To date, the transfer of functions through equivalence relations has been shown with discriminative and self-discriminative functions (e.g., Barnes, Browne, Smeets, & Roche, 1995; Barnes & Keenan, 1993; Dougher, Perkins, Greenway, Koons, & Chiasson, 2002; Dymond & Barnes, 1994, 1998; Gatch & Osborne, 1989; Kohlenberg, Hayes, & Hayes, 1991; Rehfeldt & Hayes, 1998; Wulfert & Hayes, 1988), consequential functions (Greenway, Dougher, & Wulfert, 1996; Hayes, Kohlenberg, & Hayes, 1991), and respondent eliciting and extinction functions (e.g., Dougher, Augustson, Markham, Greenway, & Wulfert, 1994; Roche & Barnes, 1997). A key issue in transfer of function research concerns the role played by exposure to a prior test for equivalence relations in facilitating the subsequent derived transfer. In a typical transfer of functions study, a series of conditional discriminations are first trained, and participants are then tested for derived equivalence relations. Next, a particular behavioral function is directly trained to at least one member of the relation, and then some or all of the remaining stimuli are tested to see if they have acquired the function without additional training. Previous studies have shown that discriminative (Barnes & Keenan, 1993; Rehfeldt & Hayes, 1998; Wulfert & Hayes, 1988), self-discriminative (Dymond & Barnes, 1998), and consequential functions (Hayes et ai., 1991) may transfer in accordance with equivalence relations without a prior equivalence test for such relations. Occasionally, however, researchers 1 Although "transformation" is preferable to "transfer," the latter term is appropriate when dealing with derived outcomes in accordance with equivalence relations and will be used throughout the present article (see Dymond & Rehfeldt, 2000, pp ).

3 TRANSFER OF FUNCTIONS 181 have found it necessary to expose participants to either symmetry or partial equivalence tests in order for derived transfer to occur (see Hayes et ai., 1991). Thus, the relationship between tests for equivalence and transfer of functions is not yet fully understood. Another common observation of the majority of transfer of functions research is that once derived stimulus functions have been measured, they are not usually retested at a later date. That is, no published study has examined the long-term stability of derived transfer. The stability of derived stimulus relations, however, has been investigated by a handful of studies. For instance, Saunders, Wachter, and Spradlin, (1988; see also Spradlin, Saunders, & Saunders, 1992) showed that participants with developmental disabilities performed with at least 90% accuracy on derived relations tests conducted 2 to 5 months following their completion of the original experiment. Likewise, Rehfeldt and Hayes (2000) and Rehfeldt and Root (2004) demonstrated the maintenance of generalized equivalence relations for up to three months by participants with and without developmental disabilities. To date, no published study has investigated the long-term stability of derived transfer of functions. From a practical perspective, understanding the longevity of derived stimulus control is critical in determining the utility of this approach in teaching new behavior and in ascertaining the type and extent of any necessary retraining (Dymond & Rehfeldt, 2000). The present experiment explored the long-term stability of derived discriminative stimulus functions. A discriminative function was first trained to one of the "B" stimuli, and transfer to thb "A" and "C" stimuli was then tested. Next, participants were trained on a one-to-many conditional discrimination training procedure (i.e., A-B and A-C). This training structure is commonly employed in transfer of function research (e.g., Dymond & Barnes, 1994) and allows for the study of possible nodal distance effects on the stability of derived transfm (see Arntzen & Holth, 2000; Fields, Landon-Jimenez, Buffington, & Adams, 1995; Saunders & Green, 1999). Some participants were exposbd to the transfer test following the symmetry and equivalence teist, another group of participants completed the symmetry and equivalence test following the transfer test, and a final group of participants received a symmetry test only if they failed to demonstrate immediate transfer of functions, after which time they were retested. At least 1 month following their initial laboratory experience, all participants in EIach group who had demonstrated transfer of functions were contacted and asked to return to the laboratory for a follow-up stability test. Method Participants Twenty-four adults enrolled in a variety of undergraduate courses in a variety of departments served as participants and were compensated with course credit for doing so. Participants were recruited through in-class

4 182 REHFELDT AND DYMOND announcements. Before the experiment, all participants signed a statement of informed consent and were informed that they could withdraw from the experiment at any time, although none chose to do so. Upon completion of the study, participants were thoroughly debriefed. Participants were assigned to one of three groups based on the order in which they signed up for the experiment: The first 8 participants to complete the experiment were assigned to Group 1; the second 8 participants to complete the experiment were assigned to Group 2; and the third 8 participants to complete the experiment were assigned to Group 3. Apparatus and Stimuli Stimulus presentation and data collection were computer controlled. The experiment was controlled by an IBM-compatible personal computer, equipped with a color monitor and a two-button mouse. The computer was centered on a 2-ft x 2-ft table. Experimental sessions were conducted in a 10-ft x 10-ft room containing a table and chair. The experiment was programmed in Microsoft Visual Basic (Version 6.0; see Dixon & Maclin, 2003) by the first author. As shown in Figure 1, stimuli consisted of nine arbitrarily configured symbols, 6 to 7 cm in diameter. The figures were arbitrarily divided into three stimulus classes. During the discrimination training and transfer test phases, stimuli were individually presented in the top center of the screen. During the conditional discrimination training and symmetry and equivalence test phases, sample stimuli appeared in the top center of screen and comparison stimuli were displayed evenly spaced across the bottom of A B C 1 II- AA mj 2 e II 3 S Figure 1. Experimental stimuli.

5 TRANSFER OF FUNCTIONS 183 the screen. The locations of comparison stimuli varied randomly across 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 previously been presented as comparison stimuli during conditional discrimination training. Procedure The experiment consisted of up to six phases, as illustrated in Figure 2. PartiCipants in all three groups completed discrimination and GROUl)3: Discrim ination T raining (to B I, B2, B3) l)jscrimination Tmining (to B I, B2, B3) Discrimination Trainin g (to B I, B2, B3) COllditionru Discrimination Tnlillin (AI,Bl : A2,B2: A3,B3: AI,C I: A2,C2; A3,B3 Conditional Db cnminituon 'l'ruinin (AI'Bl ; A2,B2; A3,B3; AI,CI: A2,C2; A3,B3 Conditionnl Dix riminmion Trainin (AI,BI; A2,B2; A3,B3; AI,CI; A2,C2; A3,83) SYJ1 l1netl")' & Equivalence Test (B I,AI; B2,A2; B3,A3; CI,AI;C2,A2; C3,A3; B I,CI; B2,C2; B3,C3; CI,BI; C2,B2; C3,B3) Tra nsfer of Functions Test (to AI, A2, A3, C I, C2, C3) Transfer of Functions 'fest (to AI,.'12, A3, CI, C2, C3) Symmetry & Equivalence Test (B I,AI; B2' A2; 83,A3; C l -A I ; C2-A2; C3-A3; BI,CI ; B2,C2; B3,C3: C I, BI; C2,B2; C3,B3) Transfer of Functions T est. (to AI, A2, A3, CI, C2, C3) if ftl.i\: Sym met ry Test (BI,AI; B2,A2; B3,A3 C I,AI; C2,A2; C3,A3; if pass: ~ Follow-up Transfer' of Functions '1'('sl Follow-up Transfer of Funclioos Test Tnnsfcl' of FUJlctions Test (to AI, A2, A3, CI, C2, C3) Figure 2, Schematic representation of the training and testing order for the three groups of participants, conditional discrimination training phases first. PartiCipants in Group 1 completed the transfer test following their completion of the symmetry and equivalence test, while participants in Group 2 completed the symmetry and equivalence test following their completion of the transfer test. Participants in Group 3 completed the transfer test following their completion of conditional discrimination training, and then completed a symmetry test only if they failed to demonstrate transfer of functions during the transfer test, after which time they were retested for transfer of functions. At least 1 month following their initial laboratory experience, all participants in each group who had demonstrated transfer of functions were contacted and asked to return to the laboratory for a follow-up test, but only some of the participants in each group were able to do so. During discrimination and conditional discrimination training phases, all correct responses were reinforced. Reinforcement consisted of the delivery of one point accompanied by an auditory beep, and the

6 184 REHFELDT AND DYMOND statement "Good! 1 point!" Point totals were displayed at all times in the lower left corner of the computer screen. Sessions lasted up to 1 hour for all participants. Discrimination Training Participants were given the following instructions: Your job in this experiment is to perform your best. You must pay careful attention and try to get as many points as you can. First, your task is to place the image at the top of the screen in one of the three boxes below it. To move the image to the box of your choice, simply click the mouse on the image and drag to the box of your choice. You will receive a point when you have responded correctly. Do your best. During this phase, discriminative functions were established to stimuli B1, B2, and 83, which would subsequently be presented as comparison stimuli during conditional discrimination training. Specifically, participants ~ D D POINTS: D D GOON ' I Figure 3. Example of on-screen stimulus array during discrimination training.

7 TRANSFER OF FUNCTIONS 185 were taught to move each stimulus to one of thme specific boxes on the screen. The onset of each trial was marked by the presentation of one of the three stimuli in the top center of the screen, followed by the presentation of three vertically aligned boxes in Ule center of the screen, positioned directly below the first stimulus. The boxes were outlined in black with a frame of approximately 4 mm, as shown in Figure 3. In order to drag the stimulus to a box, participants were required to click the mouse using the left mouse button upon the stimulus, hold the button down, and drag the mouse until the stimulus was placed in the box of the participant's choice. Once the stimulus was positioned in a box, the remaining boxes disappeared so that participants could not move a stimulus to a different box once it was already placed. After participants had responded, they were required to click the mouse on a button placed at the bottom of the screen that read, "Done!." Reinforcement was provided contingent upon placing stimulus 81 in the box at the top of the screen, stimulus 82 in the box in the center of the screen, and stimulus 83 in the box at the bottom of the screen. Incorrect responses were followed by the presentation of the next trial. Training was presented in 15-trial blocks, with each of the three stimuli presented five times per block. The order of stimulus presentations was randomly determined. The phase ended when a participant had responded correctly on 14/15 trials (93% correct per block). Conditional Discrimination Training The next phase consisted of the conditional discrimination training of six relations (A 1-81, A2-82, A3-83, A 1-C1, A2-C2, and A3-C3). Participants were given the following instructions: Remember that your job is to perform your best. You must try to get as many points as you can: A figure will appear in the center of the screen. Next, 3 figures will appear below the first figure. It is your job to choose one of the three figures. To choose one of the 3 figures, click the mouse once on the figure that is your choice. The A-8 relations were trained first. Every trial began when a sample stimulus was presented in the center of the scmen. Participants were required to select one of three comparison stimuli (81, 82, or 83) in the presence of one of three sample stimuli (A 1, A2, or A3). When participants responded correctly, the sample stimulus and its matching comparison were outlined in black for 1.5 s, after which correct responses were reinforced. All trials were separated by a 1-s intertrial interval. The order of the sample stimulus presentations was determined randomly, but each sample stimulus could be presented no more than five times per 15- trial block. After participants had achieved a mastery criterion of 14/15 correct responses, or 93% correct per block for the A-8 relations, the A-C relations were trained. The procedure for training these relations was identical to that used to train the A-8 relations, except that C1, C2, and C3 were presented as comparison stimuli. After participants had

8 186 REHFELDT AND DYMOND responded correctly on 14/15 trials, or 93% correct per block, the A-B and A-C relations were trained together. The procedure for training these relations was identical to that used to train the A-B and A-C relations separately, except that on a given trial B1, B2, and B3, or C1, C2, and C3 could be presented as comparison stimuli. The order of the sample stimulus presentations was determined randomly. Conditional discrimination training ended when participants had responded correctly on 28/30 trials, or 93% correct per block of the mixed A-B and A-C trials. Transfer of Functions Test The test for transfer of function evaluated the transfer of discriminative functions from stimulus B1 to stimuli A 1 and C1; stimulus B2 to stimuli A2 and C2; and stimulus B3 to stimuli A3 and C3. The test was presented in 27-trial blocks, in which test probe trials were inserted into reinforced baseline trials. Participants were presented with the following instructions before the transfer test: You will receive points for putting SOME of the figures in boxes, but there are some figures that you WON'T receive a point for putting in the correct box. However, there is ALWAYS A CORRECT RESPONSE so respond in a way you believe is CORRECT for EVERY FIGURE. Reinforced baseline trials consisted of the presentation of stimuli B1, B2, or B3, while test probe trials consisted of the presentation of stimuli A 1, A2, A3, C1, C2, or C3. Each of the nine stimuli was presented three times, with their presentation occurring in a random order. Correct baseline trials were reinforced, but incorrect baseline and all test trials were never reinforced and were followed by the next trial. A test trial was recorded as correct if a participant placed stimuli A 1 or C1 in the same box in which they had been taught to place stimulus B1, if a participant placed stimuli A2 or C2 in the same box in which they had been taught to place stimulus B2, and if the participant placed stimuli A3 or C3 in the same box in which they had been taught to place stimulus B3. The transfer test ended after a participant responded correctly on at least 24/27 trials (89% correct per block), or after five blocks, whichever came first. Test for Symmetry and Equivalence Relations The emergence of six symmetry relations (B1-A1, B2-A2, B3-A3, C1- A 1, C2-A2, and C3-A3) and six equivalence relations (B 1-C1, B2-C2, B3- C3, C1-B1, C2-B2, and C3-B3) was assessed for participants in Groups 1 and 2. Prior to the symmetry and equivalence test participants were told: Although you will no longer receive points on the screen, the computer is still keeping track of your correct and incorrect responses. Please continue to do you best.

9 TRANSFER OF FUNCTIONS 187 Participants received no feedback for correct or incorrect responses. The test consisted of 36 trials. Each of the six symme!try and six equivalence relations was assessed three times each. Participants in Group 3 completed symmetry test trials only, and did SID only if they failed to demonstrate criterion performance during the transfer test. For these participants, the test consisted of 18 trials, in which each of the six symmetry relations was examined three times each. Follow-up Transfer of Functions Test All participants who demonstrated transfer of functions were asked to return to the laboratory at least 1 month following their initial laboratory experience. All those who were able to return for a follow-up test completed the transfer test a second time. Participants were not given any instructions prior to doing so. The follow-up test was identical to the first transfer test. Results Group 1 Discrimination training. Discriminative control was established by stimuli B1, B2, and B3 for all 8 participants, in anywhere from one to six trial blocks. Conditional discrimination training. All 8 participants mastered the A B, A-C, and mixed A-B and A-C conditional discriminations in anywhere from one to five trial blocks. Symmetry and equivalence test. The critl9rion for inferring the emergence of symmetry relations was 16/18 (8!3%) correct responses. The same criterion was used to infer the eme,rgence of equivalence relations. As shown in Figure 4, 7 of the 8 participants (JM, CH, YS, SF, AB, KL, and MS) demonstrated the emergence of symmetry relations, the exception being JeM. Figure 4 also shows that 6 of the 8 participants (JM, CH, YS, AB, KL, and MS) demonstrated the eml9rgence of equivalence relations, the exceptions being SF and JeM. Transfer of functions test. The functions of the "B" stimuli were held to have transferred to the "A" stimuli if the "A" stimuli occasioned at least eight of nine (89%) correct responses, and to the "C" stimuli if the "C" stimuli occasioned at least eight of nine (89%) correct responses. Figure 4 shows that 4 of the 8 participants (JM, CH, YS, and JeM) demonstrated transfer of functions to both the "A" and "C" stimuli, while SF demonstrated transfer of functions to the "A" stimuli; AB demonstrated transfer of functions to the "C" stimuli, and KL demonstrated transfer of functions to the "A" stimuli. MS failed to demonstrate the transfer of functions to either the "A" or "C" stimuli. Of the 7 participants who demonstrated transfer of functions, all but 1 had demonstrated the emergence of symmetry relations during the prior symmetry and equivalence test-jem demonstrated transfer of functions despite failing to show the emergence of symmetry relations. Likewise, all

10 188 REHFELDT AND DYMOND GROUP 1 Symm Equiv Transfer Test Follow-up Test ":IH H~ JM I ~ ~ "8" "AN "CO "B" "A" 'C' "8 " "A" "CO Figure 4. Proportion of correct responses on symmetry, equivalence, and transfer of functions test trials for participants in Group 1. Proportion of correct responses is shown separately for the "A," "8," and "C" stimuli during the transfer of functions test and the follow-up test.

11 TRANSFER OF FUNCTIONS 189 but 2 of the 7 participants who demonstrated transfer of functions had demonstrated the emergence of equivalence reilations, the exceptions being SF and JeM, both of whom demonstrated transfer of functions despite failing to show equivalence during the prior test. Follow-up transfer of functions test. The same criterion for inferring the transfer of functions was used to infer the stability of the derived stimulus functions. Three participants, JM, CH, and YS were able to return for the follow-up transfer of functions test. As shown in Figure 4, none of the participants demonstrated stability of the derived stimulus functions. The "A" stimuli occasioned correct responses on more trials than the "C" stimuli for all 3 participants. Group 2 Discrimination training. Discriminative control was established by stimuli B1, B2, and B3 for all 8 participants, in anywhere from one to seven trial blocks. Conditional discrimination training. All 8 participants mastered the A B, A-C, and mixed A-B and A-C conditional discriminations in anywhere from one to four trial blocks. Transfer of functions test. The same criterion that was used to infer the transfer of functions for participants in Group 1 was used for participants in Group 2. Figure 5 shows that 6 of the 8 participants (SH, MD, TG, BW, SR, and KZ) demonstrated transfer of functions to both the "A" and "C" stimuli. AG and JoM failed to demonstrate the transfer of functions to either the "A" or "C" stimuli. Symmetry and equivalence test. The critl9rion for inferring the emergence of symmetry and equivalence relations was the same as that utilized for participants in Group 1. As shown in Figure 5, 7 of the 8 participants (SH, MD, TG, BW, SR, KZ, and J1oM) demonstrated the emergence of symmetry relations, the exception being AG. Figure 5 also shows that the same 7 participants demonstrated the emergence of equivalence relations. All of the participants who had demonstrated the transfer of functions during the prior transfer of functions test also demonstrated the emergence of symmetry and equivalence relations. Follow-up transfer of functions test. Four par1icipants, SH, MD, TG, and BW, were able to return for the follow-up transfer of functions test. As shown in Figure 5, 1 subject, TG, demonstrated the stability of derived stimulus functions. The "A" stimuli occasioned correct responses on more trials than the "C" stimuli for 2 of the 4 participants. Group 3 Discrimination training. Discriminative control was established by stimuli B1, B2, and B3 for all 8 participants, in anywhere from one to four trial blocks. Conditional discrimination training. All 8 participants mastered the A B, A-C, and mixed A-B and A-C conditional discriminations in anywhere from one to four trial blocks.

12 190 REHFELDT AND DYMOND GROUP 2 Transfer Test Symm Equiv Follow.upTest ~ lh ~ H h ~ ~ US" ~A ' "C "S" "AO "C' ':W_UJlo., "6" ~A" C" "6" "A" "C ~ liluwr i CL "S" "A" C "S" "A" C (/) ~WllW 'W o "8" "A" "C" t'llllilr o """ "'" "C" '"- ~ lllll ~ "S" "AO -Co AG JW_lj_ "S" "A" "C ':lj1c Figure 5. Proportion of correct responses on symmetry, equivalence, and transfer of functions test trials for participants in Group 2. Proportion of correct responses is shown separately for the "A," "8," and "C" stimuli during the transfer of functions test and the follow-up test.

13 TRANSFER OF FUNCTIONS 191 GROUP 3 l~im]lll'" "S" "AO C "S" "A" 'C' "8" "A" C o:llli_uj~ I L ' "B" "A" C "S" "A" "C "S" "A" "CO ~ o:lwi]_ ~ " C "8" "A" "C "B" "A" "C o ~ ': l lnill~ C. i l- s.- "S" "A" "C" "S" "A" C o ~ I I ~ n I I]_Q M' o "S" "A" C "8" "A" "CO CL Jllllullin AL T w ~ T W ~ YG ~~ "S" "A" "CO "S" "A" "CO JI~[ " "S" "A" "C" Figure 6. Proportion of correct responses on symmetry, equivalence, and transfer of functions test trials for participants in Group 3. Proportion of correct responses is shown separately for the "A," "6," and "C" stimuli during the first and second transfer of functions tests and the follow-up test.

14 192 REHFELDT AND DYMOND First transfer of functions test. The same criterion that was used to infer the transfer of functions for participants in Groups 1 and 2 was used for participants in Group 3. As shown in Figure 6, 1 subject, CC, demonstrated transfer of functions during the first test. The remaining 7 subjects failed to demonstrate criterion performance during the first transfer of functions test. Symmetry test. The criterion for inferring the emergence of symmetry relations was the same as that utilized for participants in Groups 1 and 2. As shown in Figure 6, 3 of the 7 participants (CW, LW, and YG) tested demonstrated the emergence of symmetry relations. (CC was not asked to complete the symmetry test because this participant had demonstrated transfer of functions without exposure to symmetry test trials.) Second transfer of functions test. Figure 6 shows that 3 participants (MRB, CW, and PB) demonstrated transfer of functions to both the "A" and "c" stimuli during the second transfer of functions test. LW, MN, and AL demonstrated transfer of functions to the "A" stimuli, and YG failed to demonstrate transfer of functions to either the "A" or "c" stimuli during the second test. Of the 6 participants who demonstrated transfer of functions following the symmetry test, 2 participants (CW and LW) had demonstrated the emergence of symmetry relations during the prior symmetry test. The exceptions were MRB and PB (both of whom would have demonstrated criterion performance during the symmetry test had they made one less error). YG demonstrated transfer of functions yet failed to show the emergence of symmetry relations during the prior symmetry test. Follow-up transfer of functions test. Two participants, MRB and CW, were able to return for the follow-up transfer of functions test. As shown in Figure 5, MRB demonstrated stability of the derived stimulus functions, as the "A" stimuli occasioned correct responding on 100% of the test trials. The "A" stimuli also occasioned correct responses on more trials than the "c" stimuli for Cw. Nodal distance effect for follow-up transfer of functions test. During the follow-up transfer of functions test, a higher proportion of responding was occasioned by the A stimuli (M = 0.67) than the C stimuli (M = 0.49) and this difference was shown to be statistically significant, t(9) = 2.63, P <.03. This finding highlights a significant nodal distance effect for the follow-up transfer test. Discussion In this experiment, the transfer of discriminative stimulus functions was examined in 24 participants, 8 of whom completed the transfer test after the test for symmetry and equivalence, 8 of whom completed the transfer test prior to the test for symmetry and equivalence, and 8 of whom completed a symmetry test only if they failed to show transfer of functions. The results suggest that a formal demonstration of derived stimulus relations is not necessary for stimulus functions to transfer, thus

15 TRANSFER OF FUNCTIONS 193 converging with previously reported results (Barnes & Keenan, 1993; Dymond & Barnes, 1998; Hayes et ai., 1991; Flehfeldt & Hayes, 1998; Wulfert & Hayes, 1988). The performances of thh participants in Group 2 in the present experiment most clearly illustrate this point, as 6 of the 8 participants in the group demonstrated transfer of functions to both the "A" and "e" stimuli in the absence of the symmetry and equivalence test. However, it appears that a formal test for derived stimulus relations may facilitate function transfer. The performances of participants in Group 3 speak to this issue: Of the 7 participants who failed to demonstrate transfer of functions without a symmetry test, 3 demonstrated transfer to both the "A" and "e" stimuli following the symmetry test, while 3 others demonstrated transfer of functions to the "A" sitimuli only following the symmetry test. The simple repetition of the transfer test may have also facilitated the transfer of functions for participants in Group 3. Future research evaluating the facilitative role of symmetry testing on the transfer of functions should control for test repetition. This study was also the first to evaluate the long-term stability of derived stimulus functions. Surprisingly, the derived stimulus functions were not shown to be remarkably stable during the follow-up transfer of functions test. These results do not coincide with those reported by Saunders et al. (1988), Rehfeldt and Hayes (2000), or Rehfeldt and Root (2004), all of whom reported that derived stimulus relations can be maintained several months following participants' original laboratory experience. These results are surprising given that the follow-up test was conducted no more than 1 to 2 months following the initial session, and that correct responses that occurred in the presence of the "B" stimuli were reinforced during the follow-up test. A particularly interesting finding was that the "A" stimuli, which served as the nodal stimuli and were directly paired with the "B" stimuli during conditional discrimination training, occasioned substantially more correct responses during the follow-up transfer test than did the "e" stimuli, which were separated from the "B" stimuli by one node. This finding thus reflects the effects of nodal distance on the stability of derived stimulus functions (see Fields, Adams, & Verhave, 1993; Fields, Adams, Verhave, & Newman, 1990; Fields et ai., 1995; Saunders & Green, 1999). More work is needed to determine the longevity of derived stimulus functions. Everyday experience suggests that derived functions are extremely durable to the passage of time, as illustrated by the lifelong debilitating conditions experienced by persons with clinical anxiety (see Dymond & Rehfeldt, 2000; Friman, Hayes, & Wilson, 1998). Further attempts to demonstrate this empirically are in order. One possible alternative interpretation of the 1transfer effects observed in this study is that during discrimination training, the reinforcement contingencies established conditional discriminations between the "B" stimuli and locationally defined comparison stimuli, in effect establishing B D relations. Participants' performances during the transfer of functions test may have reflected the expansion of three-member to four-member equivalence classes consisting of two nodes (the "A" and "B" stimuli) (see also Fields, Newman, Adams, & Verhave, 1992).

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