Nodal structure and stimulus relatedness in equivalence classes: post-class formation preference tests

Three experiments used postclass formation within-class preference test performances to evaluate the effects of nodal distance on the relatedness of stimuli in equivalence classes. In Experiment 1, two 2-node four-member equivalence classes were established using the simultaneous protocol in which all of the baseline relations were trained together, after which all emergent relations probes were presented together. All training and testing was done using match-to-sample trials that contained two comparisons. After class formation, the effects of nodal distance were evaluated using within-class preference tests that contained samples and both comparisons from the same class. These tests yielded inconsistent performances for most participants. Experiment 2 replicated Experiment 1, but a third null comparison was used on all trials during class formation. Thereafter, virtually all of the within-class probes, for all participants, evoked performances that were consistent with the predicted effects of nodal distance, that is, the selection of comparisons that were nodally closer to the samples. It appears, then, that the establishment of the equivalence classes with a third null comparison induced control by nodal structure of the classes. Experiment 3 demonstrated the generality of these findings with larger classes that contained more nodal separations, that is, three-node five-member classes. Emergent-relations tests conducted immediately after the within-class tests showed the classes to be intact. Thus, the differential relatedness of stimuli in a class or their interchangeability depended on the content of a test trial: within-class probes occasioned responding indicative of differential strength among the stimuli in the class, while cross-class tests occasioned responding indicative of interchangeability of stimuli in the same class.     

EQUIVALENCE CLASS FORMATION: A METHOD FOR TEACHING STATISTICAL INTERACTIONS

Many students struggle with statistical concepts such as interaction. In an experimental group, participants took a paper‐and‐pencil test and then were given training to establish equivalent classes containing four different statistical interactions. All participants formed the equivalence classes and showed maintenance when probes contained novel negative exemplars. Thereafter, participants took a second paper‐and‐pencil test. Participants in the control group received two versions of the paper‐and‐pencil test without equivalence‐based instruction. All participants in the experimental group showed increased paper‐and‐pencil test scores after forming the interaction‐indicative equivalence classes. Class‐indicative responding also generalized to novel exemplars and the novel question format used in the paper‐and‐pencil test. Test scores did not change with repetition for control group participants. Implications for behavioral diagnostics and teaching technology are discussed.     

EQUIVALENCE CLASS FORMATION IN A TRACE STIMULUS PAIRING TWO‐RESPONSE FORMAT: EFFECTS OF RESPONSE LABELS AND PRIOR PROGRAMMED TRANSITIVITY INDUCTION

Three experiments identified factors that did and did not enhance the formation of two‐node four‐member equivalence classes when training and testing were conducted with trials presented in a trace stimulus pairing two‐response (SP2R) format. All trials contained two separately presented stimuli. Half of the trials, called within‐class trials, contained stimuli from the same class while the other half, called cross class trials, contained stimuli from different classes. On within class trials, making a YES response was correct and making a NO response was wrong. On cross class trials, making a NO response was correct and making a YES response was wrong. In Experiment 1, similar intermediate percentages of participants (about 50%) formed classes, regardless of whether the responses were labeled YES and NO or SAME and DIFF. Response labeling thus did not influence class formation. Regardless of response labels, failures of class formation were primarily due to failure of class‐indicative responding produced by within‐class transitivity probes. In Experiment 2, only 50% of participants formed classes without prior training, as in Experiment 1, but 100% of participants formed equivalence classes after the establishment of a generalized transitivity repertoire by use of a programmed transitivity induction protocol. Experiment 3 examined two components of the programmed transitivity induction protocol and found that the exclusion of AC trials had no effect on the percentage of participants who formed equivalence classes, while presenting the stimulus sets in randomized order interfered with equivalence class formation. A further analysis found that a number of stimulus control topographies differentiated between individuals who did and did not form equivalence classes. In general, then, these experiments demonstrate that equivalence classes can be formed reliably when training and testing are conducted in an SP2R format, supporting the view that equivalence class formation can account for the development of conceptual categories in natural settings.     

The formation of a generalized categorization repertoire: effect of training with multiple domains,samples, and comparisons

The present experiment explored the effects of three variables on the spontaneous categorization of stimuli in perceptually distinct and novel domains. Each of six stimulus domains was created by morphing two images that were the domain endpoints. The endpoints of the domains were male and female faces, two abstract drawings, a car and a truck, two banded-elevation satellite land images, a tree and a cat, and two false-color satellite images. The stimulus variants at each end of a domain defined two potential perceptual classes. Training was conducted in a matching-to-sample format and used stimuli from one or two domains, one or three variants per class as samples, and one or three variants per class as comparisons. The spontaneous categorization of stimuli in the untrained stimulus domains showed the emergence of a generalized categorization repertoire. The proportion of spontaneously categorized stimuli in the new domains was positively related to the number of domains and samples used in training, and was inversely related to the number of comparisons used in training. Differential reaction times demonstrated the discriminability of the stimuli in the emergent classes. This study is among the first to provide an empirical basis for a behavior-analytic model of the development of generalized categorization repertoires in natural settings.     

Effects of a meaningful, a discriminative, and a meaningless stimulus on equivalence class formation

Thirty college students attempted to form three 3-node 5-member equivalence classes under the simultaneous protocol. After concurrent training of AB, BC, CD, and DE relations, all probes used to assess the emergence of symmetrical, transitive, and equivalence relations were presented for two test blocks. When the A-E stimuli were all abstract shapes, none of 10 participants formed classes. When the A, B, D, and E stimuli were abstract shapes and the C stimuli were meaningful pictures, 8 of 10 participants formed classes. This high yield may reflect the expansion of existing classes that consist of the associates of the meaningful stimuli, rather than the formation of the ABCDE classes, per se. When the A-E stimuli were abstract shapes and the C stimuli became S(D)s prior to class formation, 5 out of 10 participants formed classes. Thus, the discriminative functions served by the meaningful stimuli can account for some of the enhancement of class formation produced by the inclusion of a meaningful stimulus as a class member. A sorting task, which provided a secondary measure of class formation, indicated the formation of all three classes when the emergent relations probes indicated the same outcome. In contrast, the sorting test indicated "partial" class formation when the emergent relations test indicated no class formation. Finally, the effects of nodal distance on the relatedness of stimuli in the equivalence classes were not influenced by the functions served by the C stimuli in the equivalence classes.