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A simpler route to stimulus equivalence? A replication and further exploration of a "Simple Discrimination Training Procedure" Canovas, Debert and Pilgrim 2014).

The formation of stimulus equivalence classes (Sidman 2000) has been demonstrated following a variety of training procedures. Prototypical are variants of the so-called matching-to-sample (MTS) procedure, where trained relations are established between stimuli in pairs by having one stimulus, the sample, followed by a choice of other stimuli, the comparisons, one of which the participant is taught to choose consistently. A variant of MTS is the single comparison, alternative response procedure, or "Go/No Go" procedure, in which the comparison may be correct or incorrect, and the participant is reinforced for indicating one or the other. A third procedure is respondent-type training in which each sample is followed by its correct comparison in unreinforced pairings, though the demonstration of the resultant emergent equivalence relations requires an MTS test procedure. To what extent are the behavioural manifestations of stimulus equivalence (Sidman and Tailby 1982) indifferent to such varied methods by means of which they may be engendered? Also the yield of these procedures--the proportion of participants thus trained who form stimulus equivalence classes--is often less than all. Can any simpler ways be found that at least as reliably have the same outcome?

Canovas, Debert and Pilgrim (2014) reported two experiments in which functional equivalence classes were established by two different procedures that they described as "simple discrimination training". The first experiment used repeated reversal learning, in which in one reversal each stimulus in one group of three (A1, B1, and C1) served as S+ for a given response, and those in the other group (A2, B2, and C2) as S-, with these roles being swapped in the next reversal. In due course, the appropriate switch in discriminative control was acquired by all the stimuli as soon as just one stimulus had changed its role at the beginning of a new reversal. The second experiment, of which the present paper is a replication and extension, trained participants to respond on one key to any stimulus from A1, B1, and C1, and on another key for any stimulus from A2, B2, and C2. When this had been established, new key responses were trained to A1 and A2 only, and then unreinforced test trials demonstrated transfer-of-function to B1 and C1, and B2 and C2. In both experiments, all participants were therefore deemed to have formed two functional equivalence classes. Tests were then conducted for emergent conditional relations between the stimuli using a Go/No-Go procedure with compound stimuli, either within-class or between-class pairs, respectively. Three out of the four participants in Experiment 1 and all four in Experiment 2 generated emergent stimulus relations taken to indicate equivalence class formation.

However, in Experiment 1, performance on these compound tests, as the authors make clear, "... could have been based on directly reinforced sequences or conditional discriminations during the repeated reversal training." (op. cit. p. 6). This was deemed not to apply to the "simple discrimination training procedure" in Experiment 2 [seemingly a three-term discrimination, rather than the four-term conditional discrimination in "matching-to-sample" (MTS) procedures].

The straightforwardness and effectiveness of the three stages of this second experiment--initial discrimination training, rapid transfer of this training to new key responses, and the near perfect performances on the compound test of equivalence relations--seemed to offer a simpler way of establishing stimulus equivalence classes, perhaps more adaptable to younger human participants, and even non-human species, as the authors imply in their conclusions. To explore this procedure further, and relate it to more conventional procedures, the first requirement was to attempt a replication with closely similar methods. A similar set of shape stimuli was therefore assembled, and the author's program used in previous studies was adapted to the discrimination, generalization, and compound Go/No-Go programs closely similar to those used by Canovas et al. Details are given below. If this replication were successful, various aspects would then be modified in further experiments.

Experiment 1: Replication of Canovas et al.'s Experiment 2

Method

Participants Six undergraduate students aged 19-21 years were recruited through the Department of Psychology "Experimental Participation Recruitment Scheme", in which all first-year undergraduate students have to serve as participants, as a course requirement, for a specified total number of hours in a choice of experiments.

Location This and the following experiments were conducted in an experimental room in the Psychology Department by the author, who remained present while one participant at a time carried out the computer-based tests and responded to the experimenter's questions in the debriefing.

Equipment The tests were conducted on a large-screen Macintosh iMac computer, and a digital voice recorder (Olympus WS-812) was used to record verbal responses and debriefing conversations.

Software A general puipose stimulus equivalence program constructed by Mr. Phil Jimmieson of the University of Liverpool Department of Computer Science was adapted by the author to deliver the experiments. Instructions screens could be read and moved on from in the participant's own time, and these alternated with blocks of paced trials as described below.

Stimuli Six shape stimuli (Fig. 1), similar to those used by Canovas et al. were used for participants Cl-3 (Fig. 1a for participants C1 and C2, Fig. 1b for C3). Participants C4 6 were given the same shapes as those used by Canovas et al. (Fig. 2).

Discrimination Training On each trial in a block of 12 trials, one of the shape stimuli was presented for 2 s on the left of the screen, after the participant was instructed as follows:

"DISCRIMINATION LEARNING 1 Here is a repeating series of stimuli. Press either the K key or the M key for each, and you will then see a "K" or an "M" to show you which you should have chosen. Blocks of these trials will be repeated until your performance is perfect."

After stimuli A1, B1, or C1, the K key was correct, and after stimuli A2, B2, or C2, the M key was correct. Irrespective of which key was actually selected (or after 2 s with no response), after 1 s either the letter M or the letter K, whichever would have been the correct response to that shape stimulus, was presented for a further 2 s, to provide informational feedback. An intertrial interval of 1 s followed. All six discriminative shape stimuli were presented in random order, occurring twice in each 12-trial test block. Blocks were presented until the participant scored 12/12 correct for two successive blocks.

Training of new key Responses to two of the Stimuli When the training criterion had been reached, participants were then given a similar re-training program, to the same criterion, but using only stimuli Al and A2, to which two new key responses were now required, B and G, respectively.

Their instructions were:

"DISCRIMINATION 2 In this new stage, some of the same stimuli will again be presented. Now you should press either the G key or the B key for each, and you will then see a "G" or a "B" to show you which you should have chosen. Again, blocks of these trials will be repeated until your performance is perfect."

[FIGURE 1 OMITTED]

Transfer-of-Function Test When the new responses had been established to stimuli A1 and A2, the third program was presented in which only the remaining stimuli B1, B2, C1 and C2, were used. No informational feedback was given on this program, however, which constituted a test of the transfer of B and G responses to B1 and C1, and B2 and C2, respectively. The instructions were:

"TESTING WITHOUT FEEDBACK In this phase, you should continue to respond using the "G" and "B" keys. Try to respond according to what you learned in previous phases. You will not be shown whether or not you responded correctly on a trial because the correct key letters will not be shown."

[FIGURE 2 OMITTED]

The same criterion of mastery was again applied. If this was not attained, participants were returned to the original training program and the same stages were repeated as above. Once mastery had been established on the transfer-of-function test, the following test was given.

Compound Stimuli and the Go/No-Go Test This test Canovas et al. described as an "emergent relations test", using a "Go/No-Go procedure with compound stimuli". Here, "compound" simply meant two stimuli simultaneously present on the screen, one on the left and the other on the right, for 2 s. In the first test, these compounds comprised A1 or A2 on the left with either B1 or B2 on the right, and B1 or B2 on the left followed by either C1 or C2 on the right. These eight combinations were presented twice each in random order on each of four 16-trial test blocks. The instruction screen preceding each test block read as follows:

"COMBINATION TESTS In the following series of tests, your task will be modified. You should respond on the C key to stimulus pairs you think are correct and respond on the N key to the stimulus pairs you think are not correct. Try to respond according to what you learned in the previous phases. You will get no feedback on these trials."

Note that here, unlike Canovas et al., who only required a response to compounds the participant deemed "correct", an alternative key response was required for "not correct" combinations. Response latencies were also recorded. There was a 400-ms inter-trial interval.

Three such sets of tests were given in succession, the first with the AB and BC combinations described above, the second with BA and CB combinations, and the third with AC and CA combinations. (1)

Staged-Desynchronization Test

Since participants' performance was followed individually as the experiment progressed, it was noted that C4 had not transferred from reasonable performance on the compound tests to mastery of the final MTS test, unlike C1 and C2. In the spirit of Saunders and Green's (1999) analysis of the effects of the kinds of discrimination involved in tests of stimulus equivalence formation in different training structures, it was felt that a gradual transition between the compound test and the matching-to-sample (MTS) test (described below) would maximize the chances of demonstrating stimulus equivalence relations in these two mutually confirmatory ways. The staged-desynchronization test was therefore added for the remaining two participants in this experiment (C5 and C6), and for all participants in Experiments 2 and 3.

The staged-desynchronization test was a modification of the compound test in which, over the four test blocks, the onset of the right hand stimulus was made to occur at increasing intervals of 500 ms, 1000 ms, 1500 ms, and 2000 ms after the onset of the left hand stimulus, so that on the last test block the left stimulus ended as the right began, a 'zero-delay' procedure. The instructions were as follows:

"SEPARATING STIMULI TEST Just as before, you should respond on the C key to pairs of stimuli you think are correct and respond on the N key to pairs you think are not correct. Now however, on successive blocks of trials, the onset of the two stimuli will be staggered, until the first one on the left terminates before the second one on the right comes on. Respond in the presence of the second stimulus."

Two-Choice Matching-to-Sample Test A conventional MTS test was finally given in which the single left hand "sample" stimulus was followed after a zero delay by a choice between two comparison stimuli, one on the left and one on the right of the screen. The instructions were:

"In this test, on each trial, you will first be shown a single stimulus, followed by a choice of two stimuli. You should choose one of these two by pressing the C key for the one on the left or the M key for the one on the right. There is no feedback in this test. Please carry on over a series of test blocks."

Debriefing After the key-pressing tests, participants were given an individual debriefing, including a drawing test of the free recall of the stimuli and their associated keys, together with a report on their performance, including their interpretations of instructions and hypotheses. These conversations were all voice recorded and a few items from the conversations that seemingly throw light on participants' objective behaviour are described below.

Results

All six participants (C1-6) in initial training (column 2 of Table 1) reached the criterion of perfect performance on two successive blocks of 12 trials, which required a total number of 12-trial blocks varying from 6 to 13. The number of trials correct for successive blocks are listed with the total number of blocks in brackets.

Column 3 in Table 1 similarly indicates (some details not available for C1 and C22) progress in learning the new responses to A1 and A2, and column 4 shows the course of the unreinforced progress to criterion on the transfer-of-function of these new responses to the remaining stimuli.

Five out of six participants (C1, C2, C4, C5, and C6) passed the transfer-of-function test, though C5 and C6 failed this the first time round and were required to restart with the initial discrimination training.

C3 transferred imperfectly (last two blocks 10/12 and 9/12 correct), and failed compound tests and MTS. He should have been run to perfection on transfer-of-function or restarted (despite having learned the initial discrimination quickly first time around).

C4, although he transferred successfully on his first eight 12-trial blocks, was erroneously given 14 further blocks in which performance fell off dramatically to chance or below. Although he performed well on the compound tests, he failed the MTS test, probably explained by his adoption of a strange algorithm during this test, as described below.

The number of responses correct out of 16 in each of the four test blocks in the three compound tests are shown in Table 1, columns 5, 6, and 7. Participants C1, C2, C5 and C6 reached an accuracy of 16/16 and C4 15/16 by the end of these tests. Column 8 shows the near-perfect scores obtained by C5 and C6, the only participants given the extra staged-desynchronization test.

Column 9 shows the number of responses correct /12 for successive matching-to-sample test blocks, which were given until a criterion of 12/12 correct was reached (participants C1, C2, C5, and C6) or showed no prospect of being reached (C3 and C4). Debriefing, however, revealed that C2 had used a confounding shape difference, "rounded" versus "angular", between the two sets of stimuli (see Fig. 1a) as the basis for her MTS performance. This is why the A1 and A2 stimuli were interchanged (Fig. 1b) for participant C3, who ironically deployed the same binary shape discrimination, thus incorrectly interchanging these two stimuli. This was why the original stimuli used by Canovas et al. (Fig. 2) were adopted for the remaining three participants in Experiment 1. Even then, shape resemblances had an influence: C4, in debriefing, allocated the stimuli to three rather than two groups: A1 and A2, B1 and B2, and C1 and C2.

Debriefings

Different accounts were given by participants of the transfer-of-function test. C1 was fully aware of the transfer of keys from M to G and from K to B, implying a rule to apply in this test, but C2 seemed unaware of how she did this, though both participants showed virtually perfect and immediate transfer. C6 on her second time round, on the basis of the shapes of the stimuli (Fig. 2), conceptualized the lower row as "pattern shapes" and the upper row as "plain shapes", which informed her transfer-of-function performance as well as that on subsequent tests.

On the compound test, participants C1, C4, and probably C5 similarly used "same" keys versus "different" keys as the basis for "correct" and "incorrect" pairs, in line with the experimenters' expectations. However, the other participants were more concerned with stimulus shapes. C2 divided the stimuli into "angular" versus "round", which by inspection of Fig la can be seen to be confounded with the experimenter's allocations. Her use of this meant that her apparent equivalence performances may be seen instead as systematic shape discriminations. This confound was rectified by interchanging A1 and A2 so that the next participant, C3, was given the allocations in Fig. 1b. He, ironically, used the same shape dichotomy as C2, which in the compound trials would make all tests systematically wrong, except for BC and CB pairings, which meshed exactly with his perfonnance on the first two compound tests, and in the MTS test. For participants C4-C6, the shape stimuli in Fig. 2, identical with those used by Canovas et al., were substituted for those in Fig. 1. In Fig. 2, the reader may agree, any inherent resemblances are between the pairs of stimuli in each of the columns, which are orthogonal to the putative equivalence groupings (the rows). The further irony was that this was exactly how C4 reported he grouped the stimuli on post-experimental recall of the shapes, despite correctly assigning their associated key presses. Seemingly, he used key responses successfully in the first eight blocks of transfer-of-function trials, but as by then he was not informed that he had passed this test or moved on to the next test, he seemingly switched to a different hypothesis to guide his subsequent choices. He reported that for MTS, this was the seemingly unparsimonious rule, entirely at odds with equivalence, that if the pair of stimuli on the present trial was a repeat of the previous trial respond C, but if they were different, respond M. The record shows that most of his rare C responses were consistent with this infrequent contingency.

A final point of interest was the account participant C1 gave of her objectively faultless performance on the MTS test. She reported that she attended only to the stimuli on the left of the screen, first the sample, and then the comparison on the left. If these had both been allocated the same keys, she responded "same", otherwise "different". Given only two comparisons, she was able to transfer this parsimonious rule from the compound test to the MTS test.

All six participants correctly drew the shape stimuli they had been given from memory. These were grouped correctly and were given the correct key allocations by participants C1, C5, and C6. They were grouped in three rows C2B2, B1C1, and A1B1 and without labels by participant C2, and in two rows corresponding to Fig. 1a by C3, who had been trained on Fig. 1b, displaying the dominance of shape resemblances. C3 also allocated the stimuli to three disparate combinations of keys: 2 MB, 2 KG, and 2 KB. Participant C4 allocated keys correctly, but grouped the stimuli into three pairs, C2C1, B2B1, and A2A1.

Discussion

Only four or marginally five out of the six participants achieved equivalence as assessed by the compound tests, and only four of these fulfilled the technical criteria of equivalence in the additional MTS test, at least one of whom probably achieved this by the application of a rule not attributable to equivalence relations, but to adventitious similarities between the stimuli. Nevertheless, it was felt that the positive results of Canovas et al. had been sufficiently well replicated to proceed with the two following experiments, which incorporated a number of procedural changes.

From here on, in place of shape stimuli, phonologically correct non-words (hereinafter 'words'), as shown in Fig. 3, were used as sample stimuli, and, in place of the key-press responses to the samples, further words were used, which the participants were required to learn to say aloud before they subsequently appeared on the screen as informational feedback. If, and only if, the correct word had been said in advance, the participant was required to self score a correct response (which could be retrospectively checked from voice recordings).

Experiment 2

Participants Four more psychology undergraduate participants, C7-10, aged 18-19 years, from the same source as those in Experiment 1.

Stimuli Ten 4-letter phonologically correct non-words, as shown in Fig. 3a.

Discrimination Training This was given in the same way as in Experiment 1, except that the word stimuli A1, B1, C1 and A2, B2, C2 were given instead of shapes, and saying words X1 and X2 aloud were the required responses instead of key presses, with feedback showing the written correct X1 or X2 word after the vocal anticipatory response had been made.

New Response Training and Transfer-of-Function Testing For participants C7, C8, and C9, the new responses of saying aloud stimuli Y1 and Y2, with similar feedback, were substituted for saying X1 or X2 to stimuli A1 and A2, and transfer-of-training training to B1, C1 and B2, C2 was given in the same way as in Experiment 1; that is, in the absence of visual feedback. For participant C10, these retraining and transfer-of-training phases were omitted.

Compound Tests Three blocks each of 16 trials were given as in Experiment 1, followed in all cases by a staged-desynchronization test.

Matching-to-Sample Test This was given to all participants as in Experiment 1 with repeated trial blocks until the criterion of 12/12 trials correct was reached, except in the case of participant C9, who was only given eight blocks of trials since she showed no signs of above chance responding.

Debriefing Participants were questioned after the final MTS test in the same way as in Experiment 1, and were also given a recognition and sorting test in which participants were confronted by an empty table of five columns and seven rows, surrounded by a random array of the ten words used in the experiment plus eight other words that had not been used. They were instructed to click on and drag the words that they remembered had been used into separate cells in the table, putting them into some kind of order. Figure 4 shows participant C7's response to this, as an example.

[FIGURE 4 OMITTED]

Results

All four participants (C7-10) in initial training (column 2 of Table 2) reached the 24/24 correct criterion (perfect performance on four successive blocks of six trials), which required a total number of blocks varying from 29 to 52. The number of trials correct for successive blocks are listed with the total number of blocks in brackets. A less rigorous criterion of (say) 11/12 correct would have required far fewer blocks to have been achieved in most cases.

Training to two new vocalized words was only initially given to participants C7 and C8, which they learned for two stimuli (column 3) and transferred successfully to the other four stimuli (column 4). These two participants then performed rather poorly on the four compound stimulus tests (columns 5-8), with only C7 reaching perfect 16/16 correct performance on the last block of the fourth (staged-desynchronization) test. Both, however, reached the criterion of 12/12 correct on the final MTS test (column 9).

Participant C9 was initially not given the new response and transfer-of-function tests, and was taken straight to the first three compound tests. Performance on these did not transcend chance, and deteriorated so far that she was returned [row (b)] to initial training, followed by training to new vocal responses. Transfer-of-function of these was less than perfect, and her subsequent performance on the repeated compound tests was at first much improved, but deteriorated to chance levels on the last three blocks of test 3 and all four blocks of the staged-desynchronization test. On the final MTS test, C9's performance was at chance level over the eight test blocks she was given.

For participant C10, transfer-of-function training was also omitted, and in his case there was progressive improvement on the compound tests. He attained the criterion of 12/12 correct on MTS on the eighth test block.

Debriefing The three participants who performed above chance on the compound tests and satisfied the criterion on MTS were able to give a clear account of the basis of their choices, the grouping together of words that had been linked to the same "pair words" or "ending words", that is, the vocalized 'comparison' words. Only participant C8 was able to recall the stimuli verbally, but all three distinguished them from the unused words and grouped them correctly in the sorting test.

Participant C9 described a different principle which had guided her choices in the compound and MTS tests, of some kind of "opposition in sound of the words", which was hard to understand and was evidently unrelated to the formation of linkages compatible with stimulus equivalence.

Discussion

Substitution of words for both visual stimuli and vocalized responses seemed to have made initial learning harder and performance on the compound tests less accurate if the two small groups of participants in Experiments 1 and 2 are compared. Initially omitting the training to new responses and the transfer-of-function tests may have made the compound tests harder for participant C9, though she performed poorly on the transfer-of-function tests when retrained, and did little better on the compound tests, failing the MTS tests completely. A similar by-passing of the stages for setting up functional equivalence classes had less discernible effect on participant C10's performance on the compound tests, which improved, especially on the last staged-desynchronization test, and he attained the criterion of equivalence class formation on the MTS test.

It was tentatively concluded that the "simple discrimination training" procedure alone might well be sufficient to establish stimulus equivalence relations in most participants. This conjecture was tested further in Experiment 3, which included the additional demand of a third potential equivalence class, using non-words again as stimuli.

Experiment 3

Participants Five more psychology undergraduate participants, C11-15, from the same source as those in Experiments 1 and 2, aged 18-20 years.

Stimuli Twelve 4-letter phonologically correct non-words, as shown in Fig. 3(b).

Discrimination Training The number of discriminative stimuli (Fig. 3(b) columns A, B, and C) was increased to nine, with three vocal response stimuli (column X), giving three potential three-member equivalence classes. There was no training to a second set of vocal responses, nor a transfer-of-training phase.

Compound Tests Participant C11 was only given a single compound test before the final MTS test, but the remaining participants (C12-15) were given three compound tests, each of which included a balanced mixture of AB, BA, AC, CA, BC and CB dyads, all of which can be taken as tests of equivalence, followed by a similar fourth test incorporating a phased desynchronization of the stimuli.

MTS Tests All participants were given a final series of MTS tests. Finally, debriefings and sorting tests were conducted as in Experiment 2.

Results (see Table 3)

Participant C11 only received one compound test, on which he performed no better than chance, but he nevertheless reached the criterion of equivalence with a strong performance over seven test blocks.

Participants C12-15 were given three compound tests, over which they showed increasing accuracy, and all attained the criterion score of 12/12 correct responses on the MTS test of equivalence.

Debriefing Participant C11 well understood that it was the presence or absence of a shared "key word"--correctly recalled as "yecn, zurl, twip" that determined his choices in the brief compound test and the MTS, and though he only imperfectly recalled four or five of the other stimulus words, he grouped the stimuli perfectly in the sorting test. C12 fully understood the principle of shared or unshared comparison stimuli, and was able to recall all the stimuli and their interrelations verbally, except for one stimulus word, and performed perfectly on the sorting test. She reported forming compounds of the non-words and their resemblance to real words such as "dowf-yeen" = "downstream", "frob-yeen" = "throbbing", "brez-zurl" = "brazil".

Participant C13 gave a completely clear explanation of the principles of the tests, but was only able to recall five of the stimuli verbally. Her sort was perfect, however. Participant C14 similarly understood the principles and saw three groups. She promptly recalled 11/12 words and sorted them perfectly. She could visualize the two words as one in her head, noting certain patterns of letters, but without meaning. Participant C15 became convinced, after many MTS test blocks that he had performed perfectly (unless he had remembered one pairing incorrectly). From the behavioural record, it can be seen that this was indeed the case, but he eventually figured out which one this was, corrected it, and reached criterion (and exonerated the computer!). In a clear explanation of how he correctly used the sample-comparison links to guide his responses, he actually used the word "equivalent" and later revealed he was familiar with this concept in his mathematics and computer science education. He recalled 11/12 of the words in correct groupings and performed perfectly on the sorting test, he said his method of remembering connections between stimuli involved primarily phonetic properties of the words, not meanings.

Discussion

Judged by the criterion of correct responding on the MTS tests, all five participants formed three equivalence classes, but although the level of performance over the preceding compound test blocks only occasionally reached 17 or 18/18 correct for participants C12-15, one cannot be sure whether or not these prior tests prepared participants in some way for the multiple choice task. For participant C11, who only had one set of four 12-trial blocks of compound tests, on which he performed no better than chance, this can hardly be the case.

These results, however, confirm that the initial training, without further training to alternative vocalization responses or demonstration of functional equivalence relations between the sample stimuli, was sufficient to establish three 3-member equivalence classes in parallel in 5/5 participants.

General Discussion

In Canovas et al.'s study, the initial "simple discrimination" training (discussed below) was followed by a demonstration of the formation of functional equivalence classes before applying the compound test which gave evidence of stimulus equivalence relations between the stimuli within each class. All four of their participants performed almost perfectly on all tests.

There are a number of procedural differences between Canovas et al.'s (2014), Experiment 2 and Experiment 1 in the present study, largely due to the adaptation for the latter of software designed for other experiments (see e.g., Dickins and Ozolins 2011). The main one was the use of informational feedback--showing the correct key label (or printed nonsense word) that should have been selected--rather than awarding credit points or a similar reinforcer. Comparing performances of participants in the two laboratories: on initial training they were similar, though two of the present participants required fewer trials to reach the same criterion. Training a new key response to A1 and A2 took a similar number of trials to reach the same criterion. Transfer-of-function, which was near perfect for Canovas et al., was similarly quick for three participants (C1, C2 and C4), but two others required restarting from the beginning, one (C6) being quick the second time round, but the other (C5) taking 18 blocks of 12 trials to reach criterion. The remaining (sixth) participant (C3) should be discounted, since he was given 13 trial blocks but did not achieve the criterion and should have been retrained. (He was taken directly to the compound and the MTS tests, on both of which he performed well below chance.) C4, having reached criterion, was erroneously given further transfer-of-function trials on which performance dropped to below chance levels, and though he performed better than chance on the compound tests, he did not attain criterion on the MTS test. On the compound tests in the present study, four participants (C1, C2, C5, and C6) reached 16/16 correct after varying numbers of trial blocks, whereas all four of the Canovas et al.'s participants were perfect or near perfect from the start. Whether this is due to the addition of a definitive response for "incorrect" pairs as well as a different response for "correct" pairs cannot be determined. These detailed differences notwithstanding Experiment 1 may be seen to provide a fair, although not exact, replication of the findings of Canovas et al.

Did the transfer-of-function test given by Canovas et al. generate functional equivalence between the three stimuli in each class that subsequently supported the stimulus equivalence (SE) relations between them demonstrated by the compound tests? Or did the initial training itself generate SE relations that manifested themselves on both the tests of functional equivalence and of stimulus equivalence? Two of the four participants in Experiment 2, and all five participants in Experiment 3 were not given the transfer tests, but proceeded from initial training straight to the compound tests. All except one passed the final MTS tests. The exception was C9, who gave only chance performance on her first set of compound tests. She therefore received repeat initial training and this time was given the transfer tests, on which she repetitively ceilinged on 5/6 trials correct. Her performance on the compound tests was little better the second time around and she completely failed the subsequent MTS test.

In the remaining participants, successful establishment of functional classes was found not to be necessary for subsequent performance on the compound or MTS tests of equivalence. All six participants (C10-15) for whom this stage was omitted reached the 12/12 responses correct criterion on the MTS test, though their best performance on the compound tests varied (see Table 4). (Interestingly, one (C11) was only given a single set of four blocks of compound trials on which he performed at chance level, but he still passed the subsequent MTS test.) Whether prior exposure to the compound tests in general promoted the emergence of MTS equivalence responding cannot be determined in this study, especially since the phased-desynchronization test, given to all but the first four participants (C1-C4), was designed to scaffold transfer from a simultaneous to a successive discrimination.

An alternative way to look at the initial training of all participants on what Canovas et al. termed a "simple discrimination training procedure" is that this constituted a "many-to-one" (MTO) or "comparison-as-node" matching-to-sample procedure: each of the sample stimuli can be seen as a conditional stimulus governing a discrimination between two or three 'comparisons'. In the case of key pressing, these comparisons are the keys themselves, already present, and already specified in the instructions, which need to be visually and/or proprioceptively distinguished, before one is pressed. This can be seen as a simultaneous discrimination. In the case of the vocal responses in the present study, anticipation was required. Prior to the response, the words were not physically present, and had to be retrieved from a remembered array. This array is not specified in advance, but only starts to build when the early sample-comparison pairings are presented. Participants soon presumably discern that the number of words to be discriminated between is only two (in Experiment 2), or three (in Experiment 3). The subsequent appearance of the correct word, after the vocal response therefore served both as a determinant and a confirmation of the response, like the presentation of the correct letter after the key presses in the present study.

An interesting feature of these experiments is that, by being attached to their three-sample stimuli, the non-words seemingly fulfill the role of "names" in the theoretical account of equivalence class formation set out by Home and Lowe (1996). Now there is evidence that equivalence class formation may take place more quickly and readily with stimuli that are easy to name, such as icons representing familiar signs or objects, compared with "abstract" letter-like symbols taken from esoteric languages or that are just made up (Bentall et al. 1993). When these authors taught participants individual names for "abstract" stimuli, however, there was little improvement in equivalence class formation, whereas when a common name was taught to all members of each potential class of abstract stimuli, equivalence relations were rapidly established, and without the distinction normally found between nodal relations (transitivity or equivalence) and nonnodal relations (trained relations and symmetry) of lower accuracy and longer reaction times when nodes are involved (Bentall et al. 1993, 1999). One might expect in general an absence or attenuation of such differences following MTO compared with linear training structures: it is possible that any item fulfilling the role of common comparison in such structures, whether it is a vocalized "name", or just another visual stimulus, or a specific action, such as pressing a particular key, will have similar effects. Unfortunately, in the present study, there were no non-nodal relations that could be compared with the nodal ones in either the compound or the MTS tests.

These considerations bear on the key properties of "naming", which it has been proposed (Home and Lowe 1996, 1997) may be a necessary and not just a sufficient prerequisite for equivalence class formation. A naturally nameable stimulus is one that has meaning, in some sense of this complex concept. One behavioural analytic approach to meaning is exemplified in recent work by Fields et al. (2012) and Amtzen et al. (2014), which indicated that establishing one otherwise abstract stimulus as a discriminative stimulus, governing some other unrelated response, in each training class of five such stimuli made it much more likely that all five would form equivalence classes. This was in a context of linear training, and using the simultaneous protocol (all possible trained relations taught at the same time), in which the usual yield of equivalence class formation with all abstract stimuli was very low. Such discrimination training boosted this yield in the same direction--though to a lesser extent-- as did the use of a meaningful picture as one of the stimuli in each training class, along with four abstract items.

If it were found to be the case that an attachment to any operant, not only a vocalization, can help weld a bunch of arbitrary stimuli together into functional equivalence and stimulus equivalence classes, this would not necessarily undermine the intuitive resemblances that equivalence relations have with symbolic language (e.g. Place 1995; Dickins and Dickins 2001). Signing, demonstrable early in human ontogeny (though its developmental significance here is questionable (Kirk et al. 2013; Fitzpatrick et al. 2014), and often accorded an important speculative role in the phytogeny of language (Corballis 1992), may well be an example of just such an operant.

Ethical Statement This study, like all studies administered by the School of Psychology Research Participation Scheme, was scrutinized by and received the approval of the University of Liverpool Committee on Research Ethics.

DOI 10.1007/s40732-015-0134-3

Published online: 11 July 2015

References

Amtzen, E., Nartey, R. K., & Fields, L. (2014). Identity and delay functions of meaningful stimuli: Enhanced equivalence class formation. The Psychological Record, 64(3), 349-360. doi:10.1007/s40732014-0066-3.

Bentall, R. P., Dickins, D. W., & Fox, S. R. A. (1993). Naming and equivalence: Response latencies for emergent relations. Quarterly Journal of Experimental Psychology: Comparative and Physiological Psychology, 46B, 187-214. doi: 10.1080/14640749308401085.

Bentall, R. P, Jones, R. M., & Dickins, D. W. (1999). Control over emergent relations during the formation of equivalence classes: Response error and latency data for 5-member classes. The Psychological Record, 49, 93-116.

Canovas, D. d., Debert, P., & Pilgrim, C. (2015). Transfer-of-Function and Novel Emergent Relations Using Simple Discrimination Training Procedures. The Psychological Record, 65, 337-346. doi: 10.1007/s40732-014-0109-9.

Corballis, M. C. (1992). On the evolution of language and generativity. Cognition, 44, 197-226.

Dickins, T. E., & Dickins, D. W. (2001). Symbols, stimulus equivalence and the origins of language. Behavior and Philosophy, 29, 221-244.

Dickins, D. W., & Ozolins, A. (2011). Strengths and limitations of a single-comparison, alternate-response (SCAR) procedure for establishing uni- and multi-nodal stimulus equivalence classes. European Journal of Behavior Analysis, 12, 135-156.

Fields, L., Arntzen, E., Nartey, R. K., & Eilifsen, C. (2012). Effects of a meaningful, a discriminative, and a meaningless stimulus on equivalence class formation. Journal of the Experimental Analysis of Behavior, 97(2), 163-181. doi: 10.1901/jeab.2012.97-163.

Fitzpatrick, E. M., Thibert, J., Grandpierre, V., & Johnston, J. C. (2014). How HANDy are baby signs? A systematic review of the impact of gestural communication on typically developing, hearing infants under the age of 36 months. First Language, 34(6), 486-509. doi: 10.1177/0142723714562864.

Home, P. J., & Lowe, C. F. (1996). On the origins of naming and other symbolic behavior. Journal of the Experimental Analysis of Behavior, 65, 183-353. doi: 10.1901/jeab. 1996.65-185.

Home, P. J., & Lowe, C. F. (1997). Toward a theory of verbal behavior. Journal of the Experimental Analysis of Behavior, 68, 271-296. doi: 10.1901/jeab. 1997.68-271.

Kirk, E., Howlett, N., Pine, K. J., & Fletcher, B. C. (2013). To sign or not to sign? The impact of encouraging infants to gesture on infant language and maternal mind-mindedness. Child Development, 84(2), 574-590. doi:10.1111/j.1467-8624.2012.01874.x.

Place, U. T. (1995). Symbolic processes and stimulus equivalence. Behavior and Philosophy, 23, 13-30.

Saunders, R. R., & Green, G. (1999). A discrimination analysis of training-structure effects on stimulus equivalence outcomes. Journal of the Experimental Analysis of Behavior, 72(1), 117-137.

Sidman, M. (2000). Equivalence relations and the reinforcement contingency. Journal of the Experimental Analysis of Behavior, 74(1), 127-146.

Sidman, M., & Tailby, W. (1982). Conditional discrimination vs. matching to sample: An expansion of the testing paradigm. Journal of the Experimental Analysis of Behavior, 37, 5-52.

(1) Note that these different combinations do not correspond to trained relation, symmetry, and transitivity, respectively, but are all instances of a combination of transitivity-cum-equivalence as in many-to-one or comparison-as-node training structures

(2) A programming error prevented computer recording of these participants' choices, but they were also directly observed by the experimenter and clearly seen to master the new key responses to the A1 and A2 stimuli

David W. Dickins (1)

[mail] David W. Dickins

dickins@liverpool.ac.uk

(1) University of Liverpool, Liverpool, UK
Table 1 Correct responses per trial block in Experiment 1

     Train 1 /12            Train 2 /12            Transfer-of-function
                                                   /12

C1   4, 3, 8, 6, 5, 8, 8,   12, 12, ??             12, 12
     10, 10, 11,  12,
     12(12)

C2   9, 11, 10, 10, 10,     5 runs + 4 trials      11, 12, 12
     12, 12(7)

C3   6, 11, 10, 11, 12,     9, 12, 12              3, 2, 4, 5, 5, 5, 4,
     12(6)                                         3, 5, 6, 8, 10, 9

C4   5, 2, 9, 8, 9, 9,      6 runs + 1 trial       11, 11, 11, 12, 10,
     10, 10, 10,  11, 11,                          12, 11, 12, 2, 1,
     12, 12 (13)                                   3, 8, 2, 1, 6, 4, 1,
                                                   5, 3, 4, 0, 6

C5   (a) 5, 5, 4, 6, 9,     (a) 11, 8, 11, 12,     (a) 6, 9, 2, 8, 9,
     11, ?                  12                     8, 5, 4, 7, 5, 6
     (b) 7, 6, 6, 7, 9,     (b) 10, 11, 9, 10,     (b) 10, 9, 6, 0, 0,
     9, 6, 10, 12,          12, 12                 3, 4, 3, 3, 3, 5, 0,
     12(10)                                        0, 0, 12, 8, 11, 12

C6   (a) 6, 6, 11, 10, 7,   (a) 5, 6, 11, 10, 7,   (a) 5, 7, 6, 6, 5,
     12, 12(7)              12, 12                 8, 6, 6, 8, 9, 6, 6,
     (b) 9, 10, 11, 11,     (b) 12, 12             (b) 8, 12, 12
     12, 11, 12(7)

     Compound         Compound         Compound
     AB/BC /16        BA/CB /16        AC/CA/16

C1   8, 8, 15, 10,    14, 16, 16, 15   14, 14, 14, 16

C2   16, 16, 15, 14   16, 16, 15, 16   16, 16, 15, 16

C3   4, 8, 8, 7       8, 7, 8, 8       0, 1, 0, 3

C4   10, 8, 12, 13    14, 14, 10, 11   10, 15, 11, 15,

C5   6, 13, 7, 8      11, 9, 15, 12    13, 15, 9, 16

C6   11, 16, 13, 15   13, 15, 16, 15   12, 16, 16, 16

     Desync           MTS /12
     AC/CA /16

C1   Not given        5, 8, 12

C2   Not given        11, 12

C3   Not given        6, 5, 4, 4, 4, 4, 4, 5, 4, 4

C4   Not given        6, 5, 4, 5, 8, 8, 8, 5, 6

C5   15, 15, 15, 15   10, 11, 11, 12

C6   16, 16, 16, 14   11, 12

Table 2 Correct responses per trial block in Experiment 2

      Train 1 /6 criterion        Train 2 /6        Transfer-of-
      24/24 correct                                 function /6

C1    0, 2, 2, 6, 0, 2, 5, 6,     3, 6, 6, 6, 6     0, 4, 0, 4, 5,
      1, 4, 4, 4, 5, 6, 0, 3,                       4, 5, 1, 1, 0,
      4, 5, 6, 1, 6, 1, 5, 4,                       1, 0, 2, 6, 6,
      4, 6, 3, 5, 6, 3, 4, 5,                       6, 6
      6, 3, 6, 5, 5, 5, 6, 5,
      6, 6, 6, 5, 5, 6, 5, 6,
      6, 6, 6, 6 (52)

C8    0, 0, 0, 0, 0, 3, 5, 5,     2, 5, 6, 6, 5,    1, 6, 6, 6, 6
      3, 6, 5, 5, 6, 5, 6, 5,     6, 5, 6, 4, 6,
      5, 6, 6, 6, 5, 6, 5, 6,     5, 6, 6, 5, 6,
      6, 5, 5, 5, 6, 5, 6, 6,     6, 6, 6
      6, 6 (34)

C9    (a) 0, 0, 0, 0, 2, 3, 5,    (a) not given     (a) not given
      4, 3, 5, 5, 4, 3, 5, 6,
      3, 5, 5, 5, 4, 4, 5, 3,
      6, 5, 6, 6, 6, 6 (29)
      (b) 6, 6, 6, 5, 6, 6, 6,    (b) 1, 3, 4, 5,   (b) 1, 4, 3, 4,
      6 (8)                       6, 6, 6, 6        5, 4, 3, 5, 5,
                                                    4, 4, 4, 5, 5,
                                                    5, 5, 5, 5, 4

C10   0, 0, 2, 1, 3, 4, 3, 4,     omitted
      5, 4, 5, 4, 5, 6, 6, 4,
      2, 4, 6, 5, 5, 6, 6, 5,
      4, 5, 5, 5, 5, 5, 5, 6,
      6, 6, 6 (35)

      Compound         Compound            Compound
      AB/BC /16        BA/CB/16            AC/CA /16

C1    3, 4, 4, 6       7, 10, 13, 10       9, 11, 12, 10

C8    10, 8, 12, 13    13, 12, 15, 12      7, 7, 9, 14

C9    (a) 4, 3, 10,    (a) 7, 6, 5, 9      (a) 8, 6, 3, 1
      7
      (b) 8, 9, 8, 9   (b) 10, 9, 10, 10   (b) 12, 4, 5, 7

C10   8, 7, 9, 11      10, 10, 9, 8        7, 13, 9, 11

      Desynch           MTS /12
      AC/CA/16          criterion 12/12

C1    14, 14, 15, 16    10, 12

C8    14, 12, 12, 13    11, 8, 9, 8, 8, 4, 6, 11, 11,
                        10, 10, 7, 8, 9, 10, 11,
                        11, 10, 10, 12

C9    (a) not given
      (b) 6, 4, 4, 6    6, 3, 1, 8, 5, 3, 5, 6

C10   12, 14, 12, 14.   9, 9, 10, 9, 6, 9, 10, 12

Table 3 Correct responses per trial block in Experiment 3

      Train 1/9 criterion 25/27        Compound/12    All dyads/18
      correct

C11   1, 2, 2, 5, 2, 1, 0, 1, 4, 6,    8, 8, 3, 7
      4, 3, 4, 5, 4, 3, 6, 6, 5, 3,
      4, 6, 6, 6, 4, 6, 8, 7, 9, 6,
      7, 7, 7, 8, 8, 7, 8, 6,  9, 7,
      9, 6, 8, 8, 9, 9, 8 (47)

C12   1, 2, 5, 4, 4, 5, 5, 5, 7, 8,                   9, 5, 8, 9
      8, 9, 9, 8(14)

C13   0, 6, 1, 2, 3, 4, 3, 5, 6, 5,                   14, 14, 13, 9
      6, 5, 5, 6, 6, 5, 7, 5, 7, 7,
      6, 6, 9, 8,  7, 9, 9, 7 (28)

C14   0, 0, 3, 3, 2, 2, 4, 1, 3, 4,                   9, 8, 11, 10
      3, 2, 6, 7, 3, 5, 4, 4, 5, 4,
      7, 8, 6, 7, 7,  6, 6, 9, 8, 8,
      9, 5, 7, 8, 8, 8,  9, 8, 9, 9,
      8 (41)

C15   0, 4, 4, 2, 3, 4, 5, 6, 4, 5,                   6, 7, 11, 13
      4, 6, 4, 5, 7, 7, 7, 7, 8, 8,
      9, 9, 8 (23)

      All dyads/18     All dyads        MTS/12
                       desynch./18

C11                                     8, 10, 7, 11, 11, 11, 12

C12   13, 17, 16, 13   17, 18, 18, 17   12 rpt: 12

C13   13, 12, 13, 12   11, 12, 13, 12   9, 10, 10, 11, 10, 10, 11, 8,
                                        9, 12

C14   11, 12, 13, 13   14, 17, 14, 17   10, 12 rpt: 11, 11, 11, 12

C15   10, 16, 12, 11   15, 14, 16, 14   10, 9, 9, 9, 9, 7, 9, 7, 9,
                                        9, 9, 10, 9, 9, 10, 9, 12

Table 4 Participants'
performances on the three tests

Participant   Generalization test:      Compound    MTS
              Passed [check],           test:Best   test:Best
              failed X, Not given --    score       score

C1            [check]                   16/16       12
C2            [check]                   16/16       12
C3            X                         8/16        6
C4            [check] [right arrow] X   15/16       8
C5            X [right arrow] [check]   16/16       12
C6            X [right arrow] [check]   16/16       12
Cl            [check]                   16/16       12
C8            [check]                   15/16       12
C9            -- [right arrow] [check]  12/16       8
C10           --                        14/16       12
C11           --                        8/18        12
C12           --                        18/18       12
C13           --                        14/18       12
C14           --                        17/18       12
C15           --                        16/18       12

Fig. 3 Phonologically correct non-words used as printed
sample stimuli (columns A, B, and C) and as spoken responses
(columbus X and Y), (a) in Experiment 2. and (b) in Experiment 3

(a)
      A      B      C      X      Y

1     yolf   vuzz   rerb   twip   kose
2     mrm    brez   slif   zurl   stec

(b)

      A      B      C      X

1     yolf   vuzz   rerb   twip
2     ning   brez   slif   zurl
3     dowf   frob   tibe   yeen
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Title Annotation:ORIGINAL ARTICLE
Author:Dickins, David W.
Publication:The Psychological Record
Article Type:Clinical report
Date:Dec 1, 2015
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