Efficiently establishing concepts of inferential statistics and hypothesis decision making through contextually controlled equivalence classes

Computerized lessons that reflect stimulus equivalence principles were used to teach college students concepts related to inferential statistics and hypothesis decision making. Lesson 1 taught participants concepts related to inferential statistics, and Lesson 2 taught them to base hypothesis decisions on a scientific hypothesis and the direction of an effect. Lesson 3 taught the conditional influence of inferential statistics over decisions regarding the scientific and null hypotheses. Participants entered the study with low scores on the targeted skills and left the study demonstrating a high level of accuracy on these skills, which involved mastering more relations than were taught formally. This study illustrates the efficiency of equivalence-based instruction in establishing academic skills in sophisticated learners.     

The contextually controlled, feature-mediated classification of symbols

The classification of names of people or objects based on the features acquired by the names and the sorting instructions provided is a commonplace occurrence. For example, given the names Renoir, Pollock, James and Voltaire the average adult would be able to classify them differentially based on the instruction to classify them based on vocation or nationality. In general, such a repertoire reflects the reclassification of symbols (i.e, the names of individuals) in terms of contextual cues (instructions to sort by vocation or nationality) and the features acquired by the symbols (the specific nationalities and vocations). The present experiment studied this phenomenon with the use of arbitrary stimuli that did not have clear preexperimental associations. Two of 4 participants classified the symbols into different equivalence classes based on the prevailing contextual cues and the features that had been acquired by the symbols. Using an ABA reversal design we then demonstrated that 1 participant classified the symbols in accordance with the contextual cues and acquired features when present, but not in the absence of the contextual cues. A 3rd participant showed symbol classification that differed from that predicted by the procedures, and the 4th classified the symbols based on one set of features but not on context. These data describe one set of conditions that could account for the establishment of complex classification repertoires that occur in natural settings.     

Associative symmetry by pigeons after few-exemplar training

The present experiment investigated whether pigeons can show associative symmetry on a two-alternative matching-to-sample procedure. The procedure consisted of a within-subject sequence of training and testing with reinforcement, and it provided (a) exemplars of symmetrical responding, and (b) all prerequisite discriminations among test samples and comparisons. After pigeons had learned two arbitrary-matching tasks (A-B and C-D), they were given a reinforced symmetry test for half of the baseline relations (B1-A1 and D1-C1). To control for the effects of reinforcement during testing, two novel, nonsymmetrical responses were concurrently reinforced using the other baseline stimuli (D2-A2 and B2-C2). Pigeons matched at chance on both types of relations, thus indicating no evidence for symmetry. These symmetrical and nonsymmetrical relations were then directly trained in order to provide exemplars of symmetry and all prerequisite discriminations for a second test. The symmetrical test relations were now B2-A2 and D2-C2 and the nonsymmetrical relations were D1-A1 and B1-C1. On this test, 1 pigeon showed clear evidence of symmetry, 2 pigeons showed weak evidence, and 1 pigeon showed no evidence. The previous training of all prerequisite discriminations among stimuli, and the within-subject control for testing with reinforcement seem to have set favorable conditions for the emergence of symmetry in nonhumans. However, the variability across subjects shows that methodological variables still remain to be controlled.     

Stimulus equivalence instruction of fraction-decimal relations

Stimulus control technology was applied to the instruction of fraction ratio (e.g., (1/5)) and decimal (e.g., 0.20) relations, with 7 students who demonstrated difficulty in fraction and decimal tasks. The students were trained to match pictorial representations of fractions (B comparison stimuli) to printed counterpart fraction ratios (A sample stimuli), and to match printed decimals (C comparison stimuli) to pictorial representations of counterpart quantities (B sample stimuli). Posttest performance by all participants indicated the emergence of equivalence relations between fractions represented as ratios, decimals, and pictures. Limited generalization of fraction-decimal relations was observed.     

Reversal of baseline relations and stimulus equivalence: I. Adults

Following the emergence of two four-member equivalence classes (A1B1C1D1 and A2B2C2D2), 5 students were exposed to a series of phases including a baseline conditional discrimination reversal (i.e., choosing D2 was reinforced and D1 punished given Sample A1; choosing D1 was reinforced and D2 punished given Sample A2), the delayed introduction of CD/DC transitivity/equivalence probes, DE conditional discrimination training, a second baseline conditional discrimination reversal (i.e., choosing C2 was reinforced given B1, etc.), and a return to original baseline reinforcement contingencies. Results showed that baseline and symmetry probe performances were extremely sensitive to baseline modifications. In contrast, patterns on transitivity/equivalence probes remained predominantly consistent with the originally established equivalence classes, although there were exceptions on some E probe relations for 2 subjects. The dissociation between baseline and symmetry versus transitivity/equivalence patterns may have important implications because it is not easily accounted for by current models of equivalence phenomena.     

Synergies and Motor Equivalence in Voluntary Sway Tasks: The Effects of Visual and Mechanical Constraints

The authors used two analyses developed within the framework of the uncontrolled manifold hypothesis to quantify multimuscle synergies during voluntary body sway: analysis of intertrial variance and analysis of motor equivalence with respect to the center of pressure (COP) trajectory. Participants performed voluntary sway tasks in the anteroposterior direction at 0.33 and 0.66 Hz. Muscle groups were identified in the space of muscle activations and used as elemental variables in the synergy analyses. Changing mechanical and vision feedback–based constraints led to significant changes in indices of sway performance such as COP deviations in the uninstructed, mediolateral direction and indices of spontaneous postural sway. In contrast, there were no significant effects on synergy indices. These findings show that the neural control of performance and of its stability may involve different control variables and neurophysiological structures. There were strong correlations between the indices of motor equivalence and those computed using the intercycle variance analysis. This result is potentially important for studies of patients with movement disorders who may be unable to perform multiple trials (cycles) at any given task, making analysis of motor equivalence of single trials a viable alternative to explore changes in stability of actions.     

Equivalence‐based instruction of academic skills: Application to adolescents with autism

This study evaluated the efficacy of three equivalence‐based instruction procedures on the acquisition of novel academic skills by 3 adolescents diagnosed with autism in a school setting. The skills targeted for instruction were related to topics in history, science, and mathematics, and were taught using different training structures from the PEAK‐E curriculum. All participants demonstrated mastery of the trained relations and the tested derived relations following all variants of equivalence‐based instruction.     

Formation of new stimulus equivalence classes by exclusion

This study presents three experiments that aimed to show the formation of stimulus equivalence relations among stimuli that had been previously related only by exclusion. In Experiment 1, participants were trained on baseline conditional discriminations to establish two 3‐member equivalence classes. Then, they were exposed to exclusion trials, without feedback, in which undefined stimuli had to be matched by rejecting the defined baseline stimuli. Finally, participants responded to test trials evaluating the emergence of symmetry and transitivity among the undefined stimuli from the exclusion trials. For half of the participants, the stimuli related by exclusion were introduced as S‐ stimuli in the baseline trials, whereas for the other half they were not. Further, half of the participants were assessed for emergent relations with stimuli from all the classes, whereas the other half was assessed for emergent relations with only the stimuli related by exclusion. In Experiment 2, the S‐ comparisons in the emergent relations test trials with stimuli only related by exclusion were stimuli from a null class. In Experiment 3, the number of exclusion trials was doubled. Across experiments, most participants showed emergence of equivalence relations among the stimuli related by exclusion. Some conditions of stimulus control associated with exclusion learning and the emergence of equivalence relations are discussed.     

Equivalence‐based instruction to establish a textual activity schedule in an adult with Down syndrome

Transfer of control from picture to text‐based activity schedules has been shown to occur following conditional discrimination training in children with autism. This study extended this research by evaluating if conditional discrimination training could promote transfer of control in an adult with Down syndrome. The participant was taught to select photographs and pictures of kitchen tools when provided with dictated names. Then, he completed a text‐based activity schedule, matched printed words to photographs, and orally named printed words without direct training.     

Equivalence relations and the contextual control of multiple derived stimulus functions

Contextual control is a key aspect in equivalence research to support the claim that stimuli may have multiple functions or symbols may have multiple meanings. The present study investigated the contextual control of multiple derived stimulus functions in two experiments. In Experiment 1, equivalence classes were formed and one stimulus set from each class was used to establish two different functions: one via positive reinforcement (key-pressing) and another via negative reinforcement (button clicking), both under contextual control of two different background colors. Later, other stimuli from the equivalence class were presented on those background colors and contextual control of multiple derived stimulus functions was assessed. Experiment 2 added a third background in which no programmed response was reinforced, that is, responses were extinguished. Transfer-of-function tests revealed contextual control of three different functions, including derived extinction. Implications for equivalence relations as a behavior-analytical model of symbolic functioning are discussed.