MATCHING COMPOUND SAMPLES WITH UNITARY COMPARISONS: DERIVED STIMULUS RELATIONS IN ADULTS AND CHILDREN.
Studies on stimulus equivalence typically use arbitrary match-to-sample tasks with single-element stimuli (e.g., Greek letters) as samples and as comparisons. For ease of exposition, these stimuli are commonly denoted by alphanumeric codes (Al, B2, etc.) with the numerals indicating class membership. In general, these studies show that after being trained on multiple interrelated match-to-sample tasks (e.g., A1-B1, A2-B2; B1-C1, B2-C2), most verbal humans (normal adults and children, persons with developmental disabilities) relate all same-class stimuli conditionally to one another: B1-A1, B2-A2, C1-B1, C2-B2 (symmetry); A1-C1, A2-C2 (transitivity); C1-A1, C2-A2 (symmetric transitivity); and Al-Al, A2-A2, B1-B1, B2-B2, C1-C1, C2-C2 (reflexivity). When these matching phenomena occur, equivalence classes are said to be formed (A1-B1-C1 and A2-B2-C2) because each member of the class is treated equivalently (Barnes, 1994; Saunders, Saunders, Kirby, & Spradlin, 1988; Sidman & Tailby, 1982; Wilson & Hayes, 1996).
Similar studies have been conducted with complex (i.e., multielement) stimuli as samples or as comparisons. In some of these studies, also conducted with adults, children, and persons with developmental delays (Maguire, Stromer, Mackay, & Demis, 1994; Schenk, 1993; Smeets, Schenk, & Barnes, 1995; Stromer & Stromer, 1990), the complex stimuli permitted each element independently to control comparison selections. Taken collectively, these studies showed that trained conditional relations between the complex and single-element stimuli (e.g., A1B1-C1, A2B2-C2) produce conditional relations between each element of the complex stimulus and the related single-element stimulus (A1-C1, A2-C2; B1-C1, B2-C2) and, perhaps as a result thereof, also between the elements of the complex stimulus (A1-B1, A2-B2).
Other studies used complex stimuli that functioned as compounds (Bush, Sidman, & de Rose, 1989; Gatch & Osborne, 1989; Kennedy & Laitinen, 1988; Lynch & Green, 1991; Markham & Dougher, 1993; Perez-Gonzalez, 1994; Serna, 1991). Compounds are stimuli that control behavior only when all elements are present (e.g., A1B1-C1, A2B2-C1, A1B2-C2, A2B1-C2) (Bush et al., 1989; Sidman, 1986). Some of these studies (e.g., Markham & Dougher, 1993; Perez-Gonzalez, 1994; Serna, 1991) have received considerable attention, not in the least because some of the emergent relations are difficult to reconcile with stimulus equivalence (Dougher & Markham, 1994; Markham & Dougher, 1993; Sidman, 1986; Stromer, McIlvane, & Serna, 1993) and with the traditional definitions of compounds (Berryman, Cumming, Cohen, & Johnson, 1965; Carter & Werner, 1978; Cumming & Berryman, 1965). For example, in the Markham and Dougher study (1993), adults were initially trained on match-to-sample tasks with nine AB compounds as samples and three single-e lement C stimuli as comparisons (AB-C). The subjects were trained to select C1 when given A1B1, A2B3, or A3B2, to select C2 when given A1B3, A2B2, or A3B1, and to select C3 when given A1B2, A2B1, or A3B3. Then they received (a) AC-B and BC-A probes, (b) C-AB probes (symmetry), or C-D training and AB-D probes (transitivity), or (c) C-D training and D-AB (equivalence), AD-B and BD-A probes. All subjects responded accurately on the rearranged baseline tasks (AC-B, BC-A), almost all of them also on the symmetry (C-AB) and transitivity probes (AB-D), and the majority of them also on the standard and rearranged equivalence probes (D-BA, AD-B, BD-A). These findings indicated that the compounds functioned as unitary stimuli during tests measuring equivalence (C-AB, AB-D, D-AB) but not in other tests (e.g., AC-B, AD-B).
Apart from the conceptual issues (see Discussion section), questions may be raised as to whether the emergence of such a multitude of complex relations is typical for, or perhaps restricted to, advanced human subjects. Existing equivalence research with compounds typically involves adults and, occasionally, a few (pre)adolescents. Unfortunately, there have been no studies with much younger populations. This omission might be related to problems with the training of the baseline relations that were reported in some studies (Gatch & Osborne, 1989; Kennedy & Laitinen, 1988) or, once the baseline relations are established, to problems in obtaining the designated emergent relations in at least some of the adult subjects (e.g., Bush et al., 1989; Lynch & Green, 1991; Markham & Dougher, 1993; Perez-Gonzalez, 1994).
The present research attempted to replicate and extend the findings reported by Markham and Dougher (1993) with subjects of various age groups. Adults were used in Experiment 1, and 6- to 11-year-old normal children in Experiment 2. Would the children perform like the adults, and if not, would age-related performance discrepancies emerge during training (AB-C and C-D) and testing (C-AB, BC-A, AC-B, D-AB, AD-B, BD-A)?
All subjects received the same training and test sequence: training of AB-C, testing C-AB and BC-A or AC-B, training C-D, testing D-C, D-AB, and AD-B or BD-A. The program was similar to the one used by Markham and Dougher (1993) except that a number of modifications were made. These modifications were designed to facilitate the training of the baseline relations and the emergence of novel class-consistent relations, and to maintain on-task behavior, particularly in the youngest subjects. These modifications involved table-top rather than computer-controlled presentations. Second, four rather than nine AB-C relations were trained: A1B1-C1, A2B2-C1, A1B2-C2, A2B1-C2. These relations were trained in a stepwise fashion rather than all at once. Third, all subjects received symmetry tests (C-AB) and equivalence tests (D-AB) rather than one or the other. In accordance with the simple-to-complex protocol (Adams, Fields, & Verhave, 1993; Fields, Adams, Newman, & Verhave, 1992), the symmetry tests were presented befor e the equivalence tests. Finally, each test measuring stimulus substitutability involved only one type of trial (e.g., AD-B trials only or BD-A trials only) rather than multiple-type trials (AD-B and BD-A).
This experiment was a modified replication of the Markham and Dougher study (1993) with normal adults.
Four psychology students, 3 females and 1 male (23-27 years), of Leiden University served as subjects. None of them were familiar with match-to-sample tasks or stimulus equivalence. The subjects were recruited through bulletin board announcement and were paid for their participation. After completing the experiment, the subjects were fully debriefed.
Setting, Sessions, and Observers
The experiment was conducted in a quiet room of the Psychology Department. Sessions were conducted individually and lasted 105 to 180 mm (M = 140 min) with a break of 5 min. All subjects completed the training and testing program in one session.
Two adult males participated, one as experimenter, the other as reliability observer. The experimenter and subject were seated at the same table facing one another. The experimenter had received extensive training on the correct execution of the test and training procedures, with special emphasis on the prevention of any cues (facial expression, eye darting) that could influence the subjects' responses. During the training trials, the experimenter looked at the, subject's face when giving instructions and delivering programmed consequences. During the remainder of these trials (i.e., when presenting stimulus materials and while the subject responded), the experimenter gazed at the center of the stimulus board. Precautions were taken to prevent the subjects from observing the experimenter's recordings on the data sheets. The reliability observer was present in the same room but was situated such that he could clearly observe the subjects' responses, but not the experimenter's data sheet.
Tasks, Stimuli, and Materials
Two-choice match-to-sample tasks were used. The stimuli were eight (3 x 3 cm) black forms, see Figure 1. For convenient reference, the stimuli are identified by alphanumeric codes (A1, B2, etc.). The subjects never saw these codes. The forms were shown on laminated white cards (15 x 21 cm) and were presented as unitary stimuli (e.g., A1 or B1) or as compounds (e.g., A1B2). The compounds were pairs of stimuli presented side by side. Each card showed three stimuli, two horizontally aligned comparisons and a sample centered below.
Trials, Responses, and Contingencies
Each trial started with the experimenter presenting a stimulus card. On training trials, the responses were recorded correct, incorrect, or invalid. Invalid responses, which seldom occurred, were recorded when a subject pointed without looking at the stimuli or pointed to both comparisons. Correct responses were followed by positive feedback ("good," "correct") and incorrect responses by negative feedback ("wrong"). Invalid responses were followed by a correction procedure (e.g., "You can point to only one picture.").
On test trials, the recording was the same except that responses consistent and inconsistent with the discrimination training were recorded as correct and incorrect, respectively. The test responses were followed by no programmed consequences other than the presentation of the next trial.
Test and Training Sequence
The test and training sequence consisted of seven phases. Four versions were used: A, B, C, and D (see Table 1). All subjects (Versions A, B, C, D) received AB-C training (A1B1-C1, A2B2-C1, AlB2-C2, A2B1-C2) in Phase 1, and AB-C and C-AB (symmetry) tests in Phase 2. Then they received rearranged symmetry probes in Phase 3: BC-A tests (Versions A and B) or AC-B tests (Versions C and D). At that point, all subjects (Versions A, B, C, D) received C-D training (C1-D1, C2-D2) in Phase 4, C-D and D-C (symmetry) tests in Phase 5, and D-AB (equivalence) tests in Phase 6. Finally, they received rearranged equivalence probes in Phase 7: AD-B tests (Versions A and C) or BD-A tests (Versions B and D). Subjects 1, 2, 3, and 4 received Version A, B, C, and D, respectively.
Phase 1: Training AB-C. This phase consisted of five steps. The A1B1-C1, A1B2-C2, and A2B1-C2 relations were trained in Steps 1-3, the A2B2-C1, A1B2-C2, and A2B1-C2 relations in Step 4, and all four AB-C relations in Step 5. Each step was a prerequisite for going to the next. Blocks of 12 trials were used. Criterion was set at 12 trials correct (100%) in one block, or 11 trials correct (92%) in each of two successive blocks.
In Step 1, the subjects were trained to point to C1 when given A1B1, and to C2 when given A2B1 or A1B2 (A1B1-C1, A1B2-C2, A2B1-C2). The locations of the C stimuli were fixed over trials: C1 left and C2 right (Smeets & Striefle, 1994). Each block consisted of 6 A1B1-C1 trials, 3 A2B1-C2 trials, and 3 A1B2-C2 trials. Each block was preceded by three demonstration trials, one on each task. Each demonstration trial started with the experimenter (a) presenting a stimulus card, (b) pointing to the sample while saying "Look here," (c) pointing to the correct comparison while saying "Point to this.", and (d) inviting the subject to point to the designated comparison, "Now you point."
Step 2 was the same as Step 1 except that (a) the locations of the comparisons, C1 and C2, were reversed (C2 always left and C1 always right), and (b) no demonstration trials were used.
Step 3 was the same as Step 2, except that the left-right locations of the C stimuli varied quasirandomly over trials with the constraints that (a) each C stimulus occurred equally often at each location, and (b) the correct comparison did not appear at the same location for more than three consecutive trials.
Step 4 was the same as Step 3, except that the A1B1-C1 trials were replaced by A2B2-C1 trials. Each block consisted of 6 A2B2-C1 trials mixed with three A1B2-C2 trials and three A2B1-C2 trials.
Step 5 was the same as Step 4, except that all four relations were trained: A1B1-C1, A2B2-C1, A1B2-C2, and A2B1-C2, each three trials per block. Criterion was reached if a subject responded correctly on 11 of 12 trials of each of two consecutive blocks.
Phase 2: Testing AB-C and C-AB. The trained AB-C relations and C-AB relations (symmetry) were tested. Four trial blocks were used: two blocks of 12 test trials (Blocks 1 and 3) and two blocks of 8 AB-C training trials (Blocks 2 and 4). Thus, each test block was followed by a block of training trials. The AB-C relations were tested in Block 1 and the C-AB relations in Block 3 (Block 1: Testing AB-C, Block 2: Training AB-C, Block 3: Testing C-AB, Block 4: Training AB-C). Immediately before each test block the experimenter said, "I will no longer say whether you are right or wrong. Do your best." From that moment on, the experimenter refrained from any communication and silently presented the stimulus cards, one after another. Immediately before each training block, the experimenter said, "Now I will say again whether you are right or wrong!' Criterion was reached if a subject responded correctly (a) on 11 of 12 trials (92%) in each test block and (b) on 15 of 16 training trials (94%).
Phase 3: Testing BC-A or AC-B. Same as Phase 2, except that each test block consisted of 12 BC-A trials (Versions A and B), or AC-B trials (Versions C and D). All subjects received this phase three times in succession.
Phase 4: Training C-D. The subjects were trained on new matching tasks with the C stimuli as samples and D stimuli as comparisons (C1-D1, C2-D2). The locations (left-right) of the comparisons changed randomly over trials. Blocks of 12 trials were used. Each block was preceded by two demonstration trials (see Phase 1). Criterion performance was set at 12 trials correct in one block or 11/12 trials correct in each of two consecutive blocks.
Phase 5: Testing C-D and D-C. Same as Phase 2. Each test block consisted of 12 C-D trials (Block 1) or 12 D-C (symmetry) trials (Block 3). Each training block (Blocks 2 and 4) consisted of four AB-C trials mixed with four C-D trials (Block 1: Testing C-D, Block 2: Training AB-C and C-D, Block 3: Testing D-C, Block 4: Training AB-C and C-D).
Phase 6: Testing D-AB. Same as Phase 5, except that each test block consisted of 12 D-AB (equivalence) trials (Block 1: Testing D-AB, Block 2: Training AB-C and C-D, Block 3: Testing D-AB, Block 4: Training AB-C and C-D). Criterion was set at 21/24 (88%) test trials correct (i.e., 10/12 in Block 1 and 11/12 in Block 3), and 15/16 (94%) training trials correct in Blocks 2 and 4.
Phase 7: Testing AD-B or BD-A. Same as Phase 6, except that each test block (Blocks 1 and 3) consisted of 12 AD-B trials (Versions A and C) or BD-A trials (Versions B and D). All subjects received Phases 6 and 7 three times in succession (i.e., 6, 7, 6, 7, 6, 7).
The experiment consisted of 2591 trials, 578 (22.3%) of which were checked by a reliability observer. The experimenter and observer always agreed.
All subjects completed the experiment. Training required 126 to 312 trials (M = 192.8) to learn the AB-C tasks (Phase 1) and 12 trials to learn the C-D task (Phase 4). All subjects continued to respond accurately on these tasks during subsequent training and testing trials (Phases 2, 3, 5, 6, and 7).
Table 2 shows the tasks, number of trials in each test set, and percentages of correct responses for each test. All four subjects responded accurately during the AB-C (baseline), C-AB (symmetry), and BC-A or AC-B tests. Following the C-D training, all subjects responded accurately during the C-D and D-C tests and, though not always immediately (Subject 1), during the D-AB (equivalence) and AD-B or BD-A tests. These results are very similar to those reported by Markham and Dougher (1993) and Serna (1991).
This experiment examined whether the results of Experiment 1 could be replicated with 6- to 11-year-old children.
Twelve children served as subjects. Table 3 shows the sex and age for each subject. None of the children had served in experimental studies before.
The experiment was conducted in a quiet room of the subjects' school building. Three adults (1 male, 2 females) participated, one as experimenter, the others as reliability observers. The procedures (instructions, stimulus materials, tasks, and contingencies) were the same as in Experiment 1, except that an additional registration form was used during training. This form showed a string of 100 cells numbered 1 to 100 and was placed near the subject. Following each correct response, the experimenter provided positive verbal feedback ("Good") and made a mark in the following cell. After all cells had been marked, the subjects were given a picture card (animal, cartoon character, racing car) of his or her choice. Three subjects (1, 7, 10) received Version A, three (2, 6, 9) Version B, three (3, 5, 11) Version C, and three (4, 8, 12) Version D.
The 7- to 11-year-old subjects required 2 or 3 sessions, each lasting 60 to 90 mm over a time span of 2 to 8 days. The 6-year-old children required 6 to 8 sessions of 30 to 40 mm each over a time span of 8 to 11 days.
The experiment consisted of 8129 trials, 3398 (41.8 %) of which were checked by a reliability observer. The experimenter and observer disagreed on four test trials.
The results of the AB-C and C-D training were very similar to those of the adults in Experiment 1. Training of the AB-C tasks (Phase 1) required 138-357 trials (M = 204.0) and training of the C-D task (Phase 4) never more than 12 trials.
The test results are shown in Table 4. All subjects continued to respond accurately on the trained AB-C and C-D tasks, demonstrated symmetry (C-AB and D-C), responded accurately during the BC-A and AC-B probes and, except for Subject 8 (7 years), also during the D-AB (equivalence), AD-B and BD-A probes.
The present findings were very similar to those reported by Markham and Dougher (1993) and Serna (1991). Training of the AB-C match-to-sample tasks (A1 B1-C1, A2B2-C1, A1B2-C2, A2B1-C2) produced class-consistent C-AB and class-like AC-B or BC-A relations in all 16 subjects; and following C-D training, class-consistent D-AB, and class-like BD-A or AD-B relations in 15 subjects (94%), the exception being a 7-year-old child. Irrespective of how these relations are conceptualized (see below), these findings, together with those reported by Markham and Dougher (1993) and Serna (1991) indicate that we are dealing with a very robust phenomenon. These performances, notably those by the young children, were rather impressive given the multitude and complexity of the emergent relations, many of which were demonstrated immediately. In hindsight, however, the trained and tested relations may not be essentially different from, or more complex than, the combinatorial skills trained during reading or math activities. Consi der game-like reading activities requiring children to match correctly spelled words like OR (A1B1) and AS (A2B2) to a happy face (Cl), and incorrectly spelled words like OS (A1B2) and AR (A2B1) to a sad face (C2). Presumably, following this training, most reading children have no difficulties writing or pointing to the letter R when given the letter O next to a happy face (A1C1-B1); and writing or pointing to the letter S when given the letter O next to a sad face (A1C2-B2). Thus, future research should assess whether these relations also emerge in children with no or only rudimentary reading skills.
As has been pointed out by others (Dougher & Markham, 1994; Markham & Dougher, 1993; Stromer et al., 1993), the emergence of class-consistent (C-AB, D-AB) and class-like performances (AC-B, BC-A, BD-A, AD-B) raise questions about the controlling properties of the compounds. These performances could be seen as demonstrations of contextually controlled equivalence relations (e.g., Bush et al., 1989; Gatch & Osborne, 1989; Lynch & Green, 1991). For example, when training AB-C, Al could have functioned as a contextual stimulus controlling B1-C1 and B2-C2, and A2 as a contextual stimulus controlling B1-C2 and B2-C1. Conversely, B1 could have functioned as a contextual stimulus controlling Al-Cl and A2-C2, and B2 as a contextual stimulus controlling A2-C1 and A1-C2. This account, however, leaves the question as to which compound element functioned as a contextual stimulus and which as a conditional stimulus, unanswered (Dougher & Markham, 1994; Markham & Dougher, 1993). Moreover, present findings are inconsistent with Sidman's hierarchical account involving contextual control over matching to sample (Sidman, 1986). This account implies that contextual stimuli can not function as members over stimulus classes over which they exert discriminative control. If they did, all stimuli would be expected to collapse into one large class (Dougher & Markham, 1994; Stromer et al., 1993).
As an alternative, the AB samples could have functioned as compounds that, in combination with the C comparisons, led to the formation of ABC compounds. This position, however, is also not tenable, because, as traditionally defined, compounds are inseparable units that do not tolerate alterations without performance deterioration (Berryman et al., 1965; Cumming & Berryman, 1965).
To resolve this dilemma, Stromer et al. (1993) proposed a separable compound account of equivalence. This account implies that the AB-C training does not establish nor require conditional relations between AB samples and C comparisons (Sidman, 1986), but produces simple discriminations of ABC compounds. In contrast to traditional views of compounds, however, Stromer et al. (1993) see compounds as separable in that substitution of stimuli may occur without deterioration of stimulus control the joint presence of the elements A1, B1, and C1 occasions a response to whichever element of the compound is displayed as a comparison stimulus. Moreover, any stimulus that is shown to be equivalent to A1, B1, or C1 could be substituted without disrupting performance (Stromer et al., 1993, p. 593).
Thus, stimulus equivalence is not defined by the hierarchical relationships among A, B, and C stimuli, but by the separability and substitutability of compound elements.
Although the parsimony of this account is quite obvious, several questions remain. First, is it really necessary to abandon Sidman's hierarchical account? Given that match-to-sample training leads to transfer of functions between conditional stimuli (samples) and discriminative stimuli (comparisons), why should there not also be transfer of contextual control? Suppose that A1 functioned as a contextual stimulus, B1 as a conditional stimulus, and C1 as a discriminative stimulus during AB-C training (A1B1-C1). Why could the contextual control from A1 not transfer to B1, the conditional control from B1 to C1, and the discriminative control from C1 not transfer to A1 (BC-A test)? Thus conceptualized, each stimulus of a triad could function as contextual, conditional, or as a discriminative stimulus, depending upon the configuration of the stimulus array. This formulation comes very close to the one used by Stromer et al. (1993, p. 593):
certain stimulus elements of separable compounds may serve different functions ...; those functions may also transfer to the other elements within the separable compound.
If these functions imply contextual, conditional, and discriminative control, there is no need for a novel account. It would be sufficient to change Sidman's unidirectional hierarchical account into a bidirectional account of hierarchical functions.
Second, how can the separable compound account be empirically validated? Surely other accounts are possible. The separable compound account requires that the subjects learned four compound discriminations in the present study (A1B1C1, A2B2C1, A1B2C2, A2B1C2) and nine in the Markham and Dougher study (1993) (A1B1C1, A2B3C1, A3B2C1, A2B2C2, A1B3C2, A3B1C2, A3B3C3, A1B2C3, A2B1C3). But did the subjects learn all these compounds? Because in both these studies, each C stimulus was conditionally related to multiple AB stimuli with no element in common, the subjects could have reduced the "memory load" by remembering only one AB combination for each C stimulus, and linking any other compound with no element in common to the same C stimulus. In the present study, the subjects could have learned to relate only A1B1 to C1, and from that point on to (a) relate any other compound with no element in common to C1, and (b) relate all other compounds to C2. Thus, when given A2B2 (no element in common with A1B1), the subjects selected C1, and when given A1B2 (one element in common with A1B1) they selected C2. Likewise, in the study by Markham and Dougher (1993), the subjects could have learned to relate A1B1 to C1, A2B2 to C2, and A3B3 to C3; and to relate any AB compound that had no element in common with any of these three reference compounds to the same C stimulus. Thus when given A2B3, the subjects selected C1 because A2B3 had no element in common with A1B1.
Third, the separable compound account does not explain how the compounds come to be separable. Interchangeability of compound elements surely is not a given. Consider a recent study by Cullinan, Barnes, and Smeets (1998) in which adults were exposed to eight pairs of sequentially presented stimuli: an A stimulus followed by a B stimulus, or a B stimulus followed by a C stimulus (A1[right arrow]B1, A2[right arrow]B2, A1[right arrow]B2, A2[right arrow]B1, B1 [right arrow]C1, B2[right arrow]C2, B1[right arrow]C2, B2[right arrow]C1). The subjects were trained to make a bar pressing response after presentation of two same-class stimuli (e.g., A2[right arrow]B2) and not to make that response after presentation of two stimuli from different classes (e.g., A1[right arrow]B2). Subsequent same-format probes showed that most subjects responded class consistently when the sequential order of the stimuli was reversed (e.g., B2[right arrow]A2, C1[right arrow]B1; symmetry test) but not when the C stimuli preceded the A sti muli (C[right arrow]A; equivalence test). Although alternative accounts can be and have been put forward, these findings suggest that the sequentially presented A and B, or B and C stimuli, produced inseparable AB and BC compounds. If correct, the accurate performances on the symmetry tests (e.g., B1[right arrow]A1[right arrow]PRESS, B1[right arrow]A2[right arrow]NO PRESS) could be accounted for by primary stimulus generalization, should be seen as false positives for symmetry, and formed no basis for symmetric transitivity (Smeets, Barnes-Holmes, & Cullinan, 2000). The discrepancies between symmetry and equivalence measures were less pronounced when match-to-sample tasks were used for training (A-B, B-C) or testing (B-A, C-B, C-A), and least pronounced when match-to-sample tasks were used for training (A-B, B-C) and testing (B-A, C-B, C-A). Thus, separability of compounds may, to an important degree, be the product of the match-to-sample task itself. Future studies might, therefore, assess whether the presen t findings could be replicated with conditional discrimination tasks other than standard match-to-sample tasks.
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|Author:||CARPENTIER, FRANCK; SMEETS, PAUL M.; BARNES-HOLMES, DERMOT|
|Publication:||The Psychological Record|
|Date:||Sep 22, 2000|
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