The structure of equivalence classes

THE STRUCTURE OF EQUIVALENCE CLASSES CAN BE COMPLETELY DESCRIBED BY FOUR PARAMETERS: class size, number of nodes, the distribution of "singles" among nodes, and directionality of training. Class size refers to the number of stimuli in a class. Nodes are stimuli linked by training to at least two other stimuli. Singles are stimuli linked by training to only one other stimulus. The distribution of singles refers to the number of singles linked by training to each node. Directionality of training refers to the use of stimuli as samples and as comparison stimuli in training. These four parameters define the different ways in which the stimuli in a class can be organized, and thus provide a basis for systematically characterizing the properties of stimuli in a given equivalence class. The four parameters can also be used to account for the development of individual differences that are commonly characterized in terms of "understanding" and connotative meaning.Methods are described for generating all possible combinations of parameter values, and a formula is introduced which specifies all of the parameter values for an equivalence class. Its utility for interrelating experimental procedures is demonstrated by analyzing a number of representative experiments that have addressed equivalence-class formation.     

The psychometric properties of several measures of body image

Despite the recent upsurge of interest in the construct of body image, there is relatively little information on the psychometric properties of the instruments used to measure it. This study investigated the reliability and validity of several measures of body image and compared bulimics and normals on these measures. One hundred ten normal weight females, half of whom were diagnosed as bulimic, were administered two measures of affect toward one's body, two measures of perceptions of one's entire body, and three measures of perceptions of the size of specific body sites (face, shoulders, waist, and hips). In themain, the measures provided reliable indices of body image. Examination of the correlation matrix for the measures disclosed convergence for the affective measures of body image and for all but one of the perceptual measures of body image. There was also significant covariation between the affective and the perceptual measures. The multitrait-multimethod technique was used to investigate the construct validity of the measures concerned with perceptions of the size of body sites. The multitrait-multimethod matrices disclosed substantial convergence between perceptions of face, shoulder, waist, and hip size across the three measures. However, the measure which used kinesthetic estimates of body-site size produced low reliabilities and all three of the measures showed substantial method variance. Bulimics and normals differed significantly on both the affective and the perceptual components of body image.This study is based on the first author's masters thesis. Portions of this study were represented at the 1986 meeting of the Southeastern Psychological Association. A grant to the third author from the Anclote Psychiatric Center provided support for this research project.     

AN EVALUATION OF THE RELATIONSHIP BETWEEN RECEPTIVE SPEECH SKILLS AND EXPRESSIVE SIGNING

We examined the effects of receptive speech on the acquisition of manual signing among three mentally retarded children. In an alternating treatments design, we compared the acquisition of expressive signs that were, versus were not, in a child's receptive vocabulary. The children were trained via total communication in which pictorial referents were named during sign training. Signs corresponding to known words were generally acquired faster and retained better than signs corresponding to unknown words. We conducted posttests to assess the stimulus control of signing and any changes in expressive and receptive signing and speech. Observed changes in performance could be accounted for by attention to aspects of the stimulus complex during training and functional equivalence of stimuli established by training.     

Equivalence class formation in language-able and language-disabled children

Stimulus equivalence seems to have relevance to the study of semantics and of language more generally. If so, there may be a relation between language use and the demonstration of stimulus equivalence. This was examined in three groups of children ranging in chronological age and matched on a conventional measure of mental age: normally developing preschoolers, retarded children who used speech or signs spontaneously and appropriately, and retarded children who did not. All children were taught a series of four related discriminations and were then tested to determine if classes of equivalent stimuli had formed. All of the language-able children (retarded and normal) formed equivalence classes, whereas none of the language-disabled children did so. Although the exact nature of the relation between stimulus equivalence and language remains to be clarified, these results support the view that stimulus equivalence is a phenomenon with relevance to language.     

Stimulus equivalence and transitive associations: A methodological analysis

When a number of two-stimulus relations are established through training within a set of stimuli, other two-stimulus relations often emerge in the same set without direct training. These, termed "transitive stimulus relations," have been demonstrated with a variety of visual and auditory stimuli. The phenomenon has served as a behavioral model for explaining the emergence of rudimentary comprehension and reading skills, and the development of generative syntactic repertoires. This article considers the range of relations that can arise between a given number of stimuli in a class, the number of directly established two-stimulus relations necessary for the emergence of transitive relations, the forms that training sets of stimuli can take, and the number of transitive two-stimulus relations that can be induced without direct training. The procedures needed to establish and assess transitive stimulus control, the possible interactions between the training and testing procedures, and the constrainst these interactions place upon the analysis of transitive stimulus control are also examined. The present analysis indicates that in a transitivity test, choice among such stimuli may be controlled by (1) the relation between the sample and the positive comparison stimulus (transitive stimulus control), (2) the relation between the sample and the negative comparison stimulus (S- rule control), and (3) possible discriminative properties that may inadvertently be established in the positive and negative comparison stimuli (valence control). Methods are described for distinguishing these three forms of stimulus control.     

Transfer of contextual stimulus function via equivalence class development

In a conditional discrimination, 6 college students arranged six Cyrillic letters into groups of three based upon which of two additional Cyrillic letters (contextual stimuli) was present. All subjects demonstrated symmetry and transitivity within each class of equivalent stimuli. In a second conditional discrimination, two more Cyrillic letters were related to each contextual stimulus. Testing of symmetrical and transitive relations between the original contextual stimulus and the two new ones confirmed the development of two three-member classes of contextual stimuli. Subsequent tests demonstrated that the new contextual stimuli controlled the previously trained sample-comparison relations for all subjects.     

Conditional discrimination and equivalence relations: A theoretical analysis of control by negative stimuli

A detailed analysis is presented of the ways in which control by the negative stimulus in two-comparison conditional discriminations may be expected to affect the outcome of tests for the properties of equivalence relations. Control by the negative stimulus should produce the following results: (a) no observable effect on symmetry tests; (b) reflexivity test results should look like “oddity” rather than “identity”; and (c) transitivity tests that involve an odd number of nodes should yield results that are 100% opposite to tests that involve an even number of nodes. The analysis also considers the effects of variation in the type of comparison-stimulus control between and within baseline conditional discriminations. Methods are suggested for experimentally regulating the type of control, and for verifying the predictions that the analysis generates. If suggested experiments continue to support the analysis, investigators who use two-comparison conditional discriminations to study equivalence relations will either have to control explicitly whether the positive or the negative comparison governs their subjects' choices, or they will have to abandon two comparisons and use three or more comparisons instead.     

Classroom applications of stimulus equivalence technology

We review basic concepts and methods of stimulus equivalence research and suggest applications in teaching rudimentary language arts skills in the classroom. We describe methods of establishing equivalence-based networks of matching-to-sample, writing, and naming performances. The methods may be used as a supplement to classroom instruction to assess whether standard curriculum-based approaches establish such integrated networks. Methods derived from equivalence research may be useful for remediation when traditional teaching approaches fail. Recent research suggests that direct focus on spelling performances may be required if entire networks of language arts skills are to be acquired. In addition, the equivalence relations themselves may require concentrated teaching in some children.