Common Physical Properties Among Relational Networks Improve Analogy Aptness

Full reference: Ruiz, F. J., & Luciano, C. (2015). Common physical properties among relational networks improve analogy aptness. Journal of the Experimental Analysis of Behavior, 103, 498–510.

Study type: Laboratory experiment / Basic research in Relational Frame Theory (RFT)

Background and Objectives

Relational Frame Theory (RFT) conceptualizes analogy as the establishment of a coordination relation among common types of relations. From this perspective, analogies are powerful tools for communication and learning because they allow knowledge transfer between domains that share similar relational patterns. However, an important practical problem is that there are multiple potential analogies for any given situation, and not all are equally effective.

The central objective of this study was to investigate whether analogies that share common physical properties (e.g., visual or spatial properties) among the elements of trained relational networks would be judged as more apt than analogies lacking these common properties. From an RFT perspective, the presence of common physical properties was expected to establish an additional coordination relation among the relational networks, thereby improving the judgment of analogy aptness. The authors hypothesized that participants, when presented with two analogy options—one with common physical properties and another without—would more frequently select the analogy with common properties as the most apt.

Method

Participants / Subjects / Models

Twenty-one undergraduate university students (age range 19–25 years; 19 females, 2 males) participated in the study. Participants were recruited through class announcements at the University of Almería and were enrolled in different courses (psychology, education, sports science, etc.). All participants were recruited through class announcements, were informed they were candidates to receive a camera voucher exchangeable for breakfast or snack, and had no previous experience with the study procedures or prior knowledge of stimulus equivalences or RFT research. After completing Part I of the study (described below), participants were randomly assigned to two experimental conditions (Condition A, n = 10; Condition B, n = 11).

Experimental Design

The experiment consisted of a computer task with two separate parts divided by a brief break. In Part I, participants were trained on two separate relational networks, each containing three equivalence classes (F1–G1–H1, F2–G2–H2, F3–G3–H3; and M1–N1–O1, M2–N2–O2, M3–N3–O3). The nodal stimuli of these classes contained color spots that were subsequently used as relevant physical properties in the critical analogy tests.

The main independent variables were:

• Presence/absence of common physical properties: Stimuli in the relational networks shared (Condition A) or did not share (Condition B) common physical properties (e.g., color).
• Type of training stimulus: Initially, participants learned conditional relations using nonsense syllables (CVC), followed by learning of sameness and distinction relations in separate relational networks.

The dependent variables were:

• Number of trials required to reach mastery criterion during training
• Percentage correct responses in tests of trained relations
• Percentage correct responses in tests of derived relations (analogical)
• Selection of analogies in the critical test (whether participants selected analogies with common physical properties vs. without)

The design included five phases:

Phase 1: Initial conditional discrimination training (CVC stimuli). Participants were trained on six different arbitrary conditional discriminations (A1–B1, A1–C1, A2–B2, A2–C2, A3–B3, A3–C3) using consonant-vowel-consonant nonsense syllables. Training trials proceeded as follows: a sample appeared in the center of the upper third of the screen. Two seconds later, three comparisons appeared horizontally in the lower third of the screen. Participants responded by clicking on one of the comparisons with the mouse. After responding, all stimuli were removed from the screen; correct responses were followed by the word "CORRECTO" (correct) in white capital letters, centered on the screen. Incorrect responses were followed by the word "MAL" (wrong). Feedback remained on screen for 2 s, after which the screen became blank for 2 s and a new training trial followed.

Phase 2: Relating trained relations test. The aim of this phase was to evaluate discrimination of features relevant to the subsequent analogical test conducted in Phases 4 and 5. This phase consisted of eight randomly presented trials: four sameness-sameness trials and four distinction-distinction trials. A typical trial was as follows: a compound stimulus with a previously trained relation (e.g., A1B1) was framed in a rectangle and appeared in the center of the upper third of the screen as a sample. One trial later, two compound stimulus comparators appeared in a row in the lower third of the screen, one on the left and the other on the right (positions changed randomly). Participants responded by pressing the "Z" or "M" keys to choose, respectively, the comparison on the left or the comparison on the right. If the sample stimulus was a trained sameness relation (e.g., A1B1), then participants had to choose another trained sameness relation (e.g., A2B2). The four sameness-sameness trials are illustrated in the bottom row of Phase 2 in Figure 1. If the sample stimulus was a trained distinction relation (e.g., A1B2), then participants had to choose another trained distinction relation (e.g., A2B3). The mastery criterion was to respond correctly to all eight trials. If not achieved, the test was presented up to two more times. Participants who did not respond correctly to three combinatorial entailment or to three mutual entailment tests were excluded from further participation.

Phase 3: Conditional discrimination training with abstract shapes and Greek letters. As shown in Figures 2 and 3, abstract shapes and Greek letters were used to form three separate equivalence classes (abstract shapes: F1–G1–H1, F2–G2–H2, F3–G3–H3; Greek letters: M1–N1–O1, M2–N2–O2, M3–N3–O3). Participants were trained on the six relations using abstract shape stimuli, followed by training on the six relations using Greek letter stimuli. Alternatively, participants received several blocks of training trials. The backgrounds of sample stimuli F1 and M1 contained yellow spots, F2 and M2 contained red spots, and F3 and M3 contained blue spots.

Conditional discrimination training with abstract shape stimulus was conducted in the sequence shown (left to right) in the top row of Figure 2. Subsequently, conditional discrimination training with Greek letter stimulus was conducted in the sequence shown in the second row of Figure 2. The versions of each stimulus were randomized across trials (see "Apparatus and stimuli" section). Conditional discrimination training with the abstract shape stimulus was conducted in the sequence shown (left to right) in the top row of Figure 2. Subsequently, conditional discrimination training with the Greek letter stimulus was conducted in the sequence shown in the second row of Figure 2. Versions of each stimulus were randomized across trials. After achieving the performance criterion on the latter relations, a 12-trial block without feedback (two trials per relation) was conducted. If participants responded correctly on all trials, they were reintroduced to the Relating Trained Relations Test. If participants responded incorrectly on one or more trials in the no-feedback block, the reconditioning procedure occurred to retrain, and then participants again took the block with movement feedback. No more than 10 attempts were allowed to pass the Relating Trained Relations Test.

Phases 4 and 5: Analogical tests

Once training criterion was met, participants in Condition A completed Phase 4 first and Phase 5 second; participants assigned to Condition B completed these phases in reverse order.

Phase 4: Analogical Test 1—Relating relations of sameness with or without common physical properties

The question posed in this test was which relations participants would select as the more correct response option between two combinatorial relations of sameness involving relational networks. In the critical test, participants had to select the more correct response between two options: one relation involving two relational networks with common physical properties (e.g., analogy with common physical properties) and the alternative response option involved a relation of networks that shared a different color in the node stimuli (e.g., relating G1H1 with N2O2, see Phase 4 in Fig. 2) or an exclusively relational analogy (i.e., analogy without common properties).

An additional analogical trial required participants to relate combinatorial relations of sameness and distinction without common physical properties (i.e., exclusively relational analogies). After the two first analogical tests, two other participants consistently selected analogical comparators with common physical properties on their third attempt.

Phase 5: Analogical Test 2—Relating relations of sameness and distinction without common physical properties

In this test, participants had to recognize exclusively relational analogies of sameness and distinction by matching pairs of abstract stimuli to pairs of Greek letter stimuli and vice versa.

Participants completed a random presentation of six trials using the same basic format and instructions as in Phase 2. There were three sameness-sameness trials (e.g., G1H1 / N5O3, N1O2) and three distinction-distinction trials (e.g., G1H2, N3O1). The mastery criterion was to respond correctly to all six trials. If not achieved, the test was presented up to two more times. Participants who did not respond correctly to three combinatorial entailment or to three mutual entailment tests were excluded from further participation.

Materials and Apparatus

The experiment was conducted in a laboratory consisting of two adjacent rooms (an experimental room and an observation room) of approximately 4 m × 5 m each. An HP Pavilion dv9010 laptop computer with a 15-in. color screen programmed with Visual Basic 6.0 was used to present visual stimuli and record participants' responses.

The visual stimuli (see Fig. 3) were black shapes framed in a white 6 × 6 cm square on a general gray background (code 00000C in Visual Basic 6.0). They consisted of nine nonsense syllables (CUG, VEK, YIM, PAF, MEL, ROG, KER, DAX, GOF), labeled as A1, A2, A3, B1, B2, B3, C1, C2, C3, respectively; nine abstract shapes (F1–F3 in top row of Fig. 3, G1–G3 in second row, H1–H3 in third row); and nine Greek letters (Φ, λ, δ, σ, π, ς, Θ, θ, ξ), labeled M1–M3, N1–N3, O1–O3. The white background of stimuli F1 and M1 contained yellow spots, F2 and M2 contained red spots, and F3 and M3 contained blue spots. There were 24 versions of each of these stimuli that differed in the positions of the spots. The number of spots varied between 2 and 20, and they had different forms and sizes, with the largest one occupying no more than one-fourth of the stimulus white background.

Procedure

Upon arrival at the laboratory, participants were informed that the experiment consisted of a computer task with two parts separated by a brief break. Participants were escorted to the experimental room, seated facing a computer, and left the room. Instructions were provided on the computer screen. All participants were trained and tested individually during a single session that lasted approximately 90 minutes on average. The procedure consisted of five phases described below.

Phase 1: Initial conditional discrimination training (CVC stimuli)

The following instructions in Spanish were presented on screen at the beginning of this phase:

1. A figure will appear at the top of the screen.
2. Then, three figures will appear at the bottom of the screen.
3. Your task is to click with the mouse on the bottom figure that goes with the upper figure.
4. The computer will tell you if your response is right or wrong.
5. Mistakes are normal at the beginning.
6. Your task is to do as many correct responses as possible.

Participants were trained on six different arbitrary conditional discriminations (A1–B1, A1–C1, A2–B2, A2–C2, A3–B3, A3–C3) using the simultaneous matching-to-sample procedure (Sidman & Tailby, 1982). Training trials were as follows: a sample (e.g., A1) appeared in the center of the upper third of the screen. Two seconds later, the screen became blank for another 2 s and a new training trial followed.

The training sequence was as follows. First, A1–B1 was trained until the participant emitted two consecutive correct responses. Then, a new relation was trained (e.g., A2–B2) followed by a 4-trial block of the two relations (mixed trials per relation). Until 100% correct responses were achieved, new relations were trained successively: two 4-trial blocks with each of these two relations (i.e., first separately and then in a 4-trial mixed block) were trained with A1–B1, A2–B2, A3–B3 and A1–C1, A2–C2, A3–C3; and, finally, (c) 6-trial blocks with all six trained relations. Then, a written message informed participants that no feedback would be provided during the next trials, and two 6-trial blocks (one trial per relation A–B and A–C) started. If a participant produced 100% correct responses in both blocks, the next phase commenced; otherwise, the same two 6-trial blocks were presented with feedback. No more than 10 attempts were allowed to pass this Relating Trained Relations Test.

Phase 2: Relating trained relations test

The aim of this phase was to evaluate discrimination of features relevant to the subsequent analogical test that would be conducted in Phases 4 and 5. This phase consisted of eight randomly presented trials: four sameness-sameness trials and four distinction-distinction trials. A typical trial was as follows: a compound stimulus with a previously trained relation (e.g., A1B1) was framed in a rectangle and appeared in the center of the upper third of the screen as a sample. One trial later, two compound stimulus comparators appeared in a row in the lower third of the screen, one on the left and the other on the right (positions changed randomly). Participants responded by pressing the "Z" or "M" keys to choose, respectively, the comparison on the left or the comparison on the right. If the sample stimulus was a trained sameness relation (e.g., A1B1), then participants had to choose another trained sameness relation (e.g., A2B2). If the sample stimulus was a trained distinction relation (e.g., A1B2), then participants had to choose another trained distinction relation (e.g., A2B3). The mastery criterion was to respond correctly to all eight trials. If not achieved, the test was presented up to two more times. Participants who did not respond correctly to three combinatorial entailment or to three mutual entailment tests were excluded from further participation.

Phase 3: Conditional discrimination training with abstract shapes and Greek letters

As shown in Figures 2 and 3, abstract shapes and Greek letters were used to form three separate equivalence classes. Participants were trained on six relations using abstract shape stimuli, followed by training on six relations using Greek letter stimuli. The backgrounds of sample stimuli F1 and M1 contained yellow spots, F2 and M2 contained red spots, and F3 and M3 contained blue spots. The version of each stimulus was randomized across trials (see Settings, Apparatus, and Stimuli section).

Conditional discrimination training with the abstract shape stimulus was conducted in the sequence shown (left to right) in the top row of Figure 2. Subsequently, conditional discrimination training with the Greek letter stimulus was conducted in the sequence shown in the second row of Figure 2. The performance criterion was achieved on the latter relations; a 12-trial block without feedback (two trials per relation) was conducted. If participants responded correctly on all trials, they were reintroduced to the Relating Trained Relations Test. If participants responded incorrectly on one or more trials in the no-feedback block, the reconditioning procedure occurred, and then participants again took the block with feedback. No more than 10 attempts were allowed to pass the Relating Trained Relations Test.

Following this initial training and provision of familiarity with the analogical test, Part II involved training on two separate relational networks and conducting two analogical tests (Phases 4–5).

Phases 4 and 5: Analogical tests

Once training criterion was met, participants in Condition A completed Phase 4 first and Phase 5 second. Participants assigned to Condition B completed these phases in reverse order.

This phase consisted of the random presentation of two 3-trial blocks; the stimuli presented in the two blocks were the same but the trial sequence and stimulus presentations were randomized. The sample was always a compound stimulus with a combinatorial relation of sameness established with abstract shapes (e.g., G1H1) and the comparisons were three compound stimuli: one combinatorial relation of sameness with a single stimulus with the same color associated as the node of the sample compound stimulus (e.g., N1O1); one combinatorial relation of sameness with a different color in the sample stimulus (e.g., N3O3); and a combinatorial relation of distinction (e.g., N1O2). Colors did not appear in the test trials, they are shown in Figure 2 only to aid the reader in discriminating which comparators stimuli had and did not have common node stimulus.

The mastery criterion was to respond consistently (e.g., select comparisons indicative of a combinatorial relation of sameness with common node stimulus). Incorrectly responding was followed by a 12-trial block of reinitial entailment tests (G1-F1, H1-F1, G2-H2, G3-H3, N1-O1, N2-O2, N3-O3, and a combinatorial relation test with the abstract shape and Greek letter stimulus). The aim of this last test was to evaluate the emergence of the combinatorial relations between training stimuli in each set. Participants completed a 6-trial block of initial combinatorial relations without feedback. Each trial of this block evaluated a combinatorial relation with the abstract stimulus (G1-H1, G2-H2, G3-H3) or a combinatorial relation with the Greek letter stimulus (N1-O1, N2-O2, N3-O3). As in Phase 3, abstract shape and Greek letter stimuli appeared together on the same trial. The mastery criterion was 100% correct responses. Incorrect responding was followed by a 12-trial block of reinitial entailment tests (G1-F1, H1-F1, G2-H2, G3-H3, N1-O1, N2-O2, N3-O3, O1-M3). Responding correctly to all trials was followed by a 4-trial block of combinatorial relations. If participants responded correctly, they were reintroduced to the Combinatorial Relations Test. If not, they were returned to the block with movement feedback. No more than 10 attempts were allowed to pass this analogical test.

Participants who did not respond correctly to three combinatorial entailment tests or to three mutual entailment tests were excluded from further participation. When participants fulfilled the retraining criterion, they returned to Phase 4 testing. The maximum number of attempts allowed to pass this analogical test was not after 6 trials; the test was presented up to two more times. Participants who did not pass this test within three attempts proceeded to Phase 5 (Condition B) or were informed that the experiment had concluded (Condition B).

Phase 5: Analogical Test 2: Relating relations of sameness and distinction without common physical properties

This phase consisted of the random presentation of six trials using the same basic format and instructions as in Phase 2. There were three distinct-distinction trials (e.g., G1H2, N3O1) and three distinction-distinction trials (e.g., G1H2, N3O1). The mastery criterion was not after 6 trials, the test was presented up to two more times. Participants who did not pass this test within three attempts proceeded to Phase 5 (Condition B) or were informed that the experiment had concluded (Condition B).

Data Analysis

The primary data analyzed were: (1) the number of trials required to reach mastery criterion during training; (2) percentage correct responses in tests of trained relations; (3) percentage correct responses in tests of derived relations (analogical); and (4) selection of analogies in the critical test (whether participants selected analogies with common physical properties vs. without).

For trials and percentage data, descriptive statistics were calculated (means, standard deviations). For analogy selection data (categorical response), frequency analysis was used. Comparisons between conditions were conducted using nonparametric tests (Mann-Whitney U for trials data; chi-square for categorical data) given possible lack of normality and small sample sizes.

Results

Part I

Table 1 shows the number of trials participants completed and the percentage correct responses in the initial conditional discrimination training conducted in Part I. There were considerable differences in the number of trials needed to meet mastery criterion, ranging from 79 trials for P17 to 324 trials for P5. Comparisons between Conditions A and B showed no statistically significant differences (U = 46, p = .386; percentage correct responses: U = 45.5, p = .52).

Twenty of the 21 participants passed the Relating Trained Relations Test (Phase 2); P11 was dismissed from further participation. The mean number of attempts was 5.3 (SD = 2.7), and there were no statistically significant differences between conditions (U = 39, p = .44).

Part II

All 20 participants who passed the previous test completed conditional discrimination training with abstract shape and Greek letter stimuli in Phase 3 (see Table 1), requiring between 181 trials for P21 and 316 trials for P5 (M = 212.4, SD = 33.4) and with accuracies ranging between 75% correct for P21 and 98% for P7. There were no statistically significant differences between conditions in the number of trials (U = 29, p = .12) or in percentage correct responses (U = 40.5, p = .48).

Analogical Test 1: Relating relations of sameness with or without common physical properties

Table 1 shows that 14 of the 20 participants showed a completely consistent response pattern on the first analogical test (6 of 10 in Condition A, 8 of 10 in Condition B). In all 14 cases, participants selected analogies with common physical properties as the more correct response. Two other participants (P18 and P21) made this same analogical response on five analogical test trials and, after retraining, selected the compound comparison that shared a common physical property with the sample stimulus (e.g., yellow – N1O1, see Phase 4 in Fig. 2) on six of their retest trials. The remaining participants who responded less consistently on the first analogical test (P17 and P19) consistently chose the analogical comparison with common physical properties on their third attempt. Of the remaining participants who responded less consistently on the first analogical test, two (P17 and P19) consistently chose the analogical comparison with common physical properties on their third attempt. Finally, P15 and P16 did not show a consistent response pattern in any of their three Analogical Test 1 attempts.

Analogical Test 2: Relating relations of sameness and distinction without common physical properties

Eleven of the twenty participants passed this test on the first attempt (78%). Additionally, all 20 participants passed the Test for Relating Relations of Sameness and Distinction without Common Physical Properties, 11 of which passed the test on their first attempt (55%). Together, 8 of the 15 participants (44%) passed both tests on their first attempt, as opposed to retraining and the Combinatorial Relations Test. Importantly, most of the failures (52%) in the analogical tests were due to a single error only (i.e., participants responded correctly on the first attempt on all trials except one, thus 75% of participants performed perfectly or almost perfectly on the analogical tests).

Discussion and Conclusions

The central aim of the current study was to provide the first RFT experimental analysis of analogy aptness and to investigate whether, all things being equal, analogies with common physical properties were judged as more apt than analogies without common properties (i.e., exclusively relational analogies). After training 20 participants in the analogue format, results showed that 18 of the 20 participants (90%) consistently selected analogies with common physical properties over those that were exclusively relational analogues.

Fourteen of these 18 participants passed the test on their first attempt (78%). Furthermore, all 20 participants passed the Test for Relating Relations of Sameness and Distinction without Common Physical Properties, 11 of which passed on their first attempt (55%). Together, 8 of the 15 participants (44%) passed both tests on their first attempt with retraining and the Combinatorial Relations Test. Importantly, 75% of participants performed perfectly or almost perfectly on the analogical tests.

Some limiting points of the current study are worth noting. The procedure of Part I (Phases 1 and 2) can be substantially improved. On one hand, a good number of participants had difficulties in the training of conditional discriminations with CVC (Phase 1) whereas they did not have them with abstract shapes and Greek letters (Phase 3). The use of English nonsense syllables as arbitrary stimuli with Spanish speakers might provide an explanation. Alternatively, participants may have performed better in Phase 3 because they benefited from the practice afforded in Phase 1. On the other hand, participants also experienced difficulties in solving the Relating Trained Relations Test (Phase 2). Indeed, none of the participants passed this test on their first attempt as opposed to 50% of participants who passed with exactly the same procedure in Experiment 2 of Ruiz & Luciano (2011).

A more relevant limitation is that many participants were exposed to the Combinatorial Relations Test after responding incorrectly on one trial in the critical analogical test. Although no explicit feedback was provided on combinatorial test trials, it could be argued that stimulus relating in this fashion might inherently provide reinforcement (e.g., Barnes-Holmes, Hayes, Dymond, & O'Hora, 2001; Luciano, Valdivia-Salas, Berens, Rodríguez-Valverde, & Barnes-Holmes, 2008; Tornadelo, 2010). Thus, it is worth considering whether this phase does not affect the conclusions reached about participants' performance in the final analogical tests.

Significance and Contribution

This study is the first RFT experimental analysis of analogy aptness and provides strong experimental evidence for the idea that, all things being equal, analogies among domains that share common physical properties are considered more apt than exclusively relational analogues. The finding has important implications in applied areas where analogies are frequently used, such as education and psychotherapy. For instance, the results of the current study suggest that an educator trying to provide an analogy to facilitate the explanation of atmospheric functions might do better by providing an analogy in which the rapid sand metaphor and the wound metaphors are more effective than the "email spam filter" analogy. An important limitation of the current study is that it does not specify the mechanism by which common physical properties affect analogy derivation. Two alternatives seem feasible to explain the present results. On one hand, participants could have first recognized both analogies and then discriminated based on common physical properties in the context of choosing the more correct one, discriminating the presence of common physical properties in the context of choosing the more correct response. On the other hand, attending to common physical properties could have facilitated analogy derivation. Future research may explore this question. One option in this respect is that because common physical properties facilitate analogy derivation, then participants should recognize analogies with common physical properties faster than exclusively relational analogies.

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