## 33rd Annual Convention; San Diego, CA; 2007

### Event Details

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Symposium #144 |

Equivalence Analyses of Complex Processes |

Sunday, May 27, 2007 |

9:00 AM–10:20 AM |

Del Mar AB |

Area: EAB; Domain: Basic Research |

Chair: Lanny Fields (Queens College, City University of New York) |

Abstract: The present symposium will consider consider how an equivalence class analysis can be used to address two complex processes: 1) teaching college students about the interactive effects of independent variables, and 2) identifying the conditions that enable an individual to assign sets of symbols or words to different equivalence classes based on sorting instructions (contextual cues) and the features that had been acquired by the symbols prior to class assignemnt. For each topic, one presentation will be a theoretical analysis of the phenomenon, and the second will provide an experimental analysis of the conditions that led to the establishment of each of these complex repertoires. |

Establishing Equivalence Classes of Representations of Interaction: A Conceptual Analysis. |

EYTAN DAVID YADLOVKER (Queens College and The Graduate Center, City University of New York), Robert Travis (Queens College and The Graduate Center, City University of New York), Jason S. Rockwell (Queens College and The Graduate Center, City University of New York), Deborah Roy (Queens College, City University of New York), Peter Sturmey (Queens College, City University of New York), Lanny Fields (Queens College, City University of New York) |

Abstract: Some college students have difficulties in describing how behavior is influenced by the joint effects of two concurrently manipulated independent variables. In some cases, the effect of one independent variable is shifted by a constant factor with changes in the value of a second independent variable. That combination of effects shows an additive rather than an interactive effect of the independent variables. In other cases, variations in the value of a second independent variable modulates the effect of the first independent variable. When that occurs, the two variables are said to interact. There are three major patterns of interaction, each of which is described by a different name. They are cross over interactions, divergent interactions, and synergistic interactions. The present paper will illustrate how an equivalence class approach can be used to induce relations among different representations of different sorts of interaction.
Four types of interaction based classes will be considered: no interaction (1), cross over interaction (2), divergent interaction (3), and synergistic interaction (4). Each type of interaction can be represented in by name (A), by line graphs (B), by a description of the data in a graph (C), and by generic description (D), as bar graphs (E), as a table of data (F), and as a summary table of a statistical analysis (G). We will use only the first four in this analysis. A student can demonstrate an understanding of each type of interaction by identifying the substitutability of each representation in a set for the other representations. Thus, each type of interaction could be viewed as a potential equivalence class. Once established, then, a student would be able to identify the substitutability of four representations of four different sorts of interaction, after the establishment of only a few of the relations. Gaining an understanding of interaction, then, could be engendered by the establishment of equivalence classes corresponding to each type of interaction. |

Establishing Equivalence Classes of Representations of Interaction: An Empirical Analysis. |

ROBERT TRAVIS (Queens College, City University of New York), Deborah Roy (Queens College, City University of New York), Eytan David Yadlovker (Queens College and The Graduate Center, City University of New York), Jason S. Rockwell (Queens College and The Graduate Center, City University of New York), Peter Sturmey (Queens College, City University of New York), Lanny Fields (Queens College, City University of New York) |

Abstract: As noted in the previous paper, four classes of interaction will be considered: no interactions (class 1), cross over interaction (class 2), divergent interaction (class 3), and synergistic interaction (class 4). Each type of interaction can be represented in at least four ways: by name (A), graphically (B), by a description of the data in a graph (C), and by generic description (D). Thus, 4-member equivalence classes were established for each of the four types of interaction. To begin, subjects were given a paper and pencil test with new interaction questions. Most subjects responded with low accuracy on this test which demonstrated the absence of the classesa of interaction. Then, subjects were given a test that contained all pair-wise representations in each set in the absence of reinforcement on a computer using trials presented in a MTS format. Once again, performances were inaccurate. Thereafter, the simple to complex protocol will be used to establish the four 4-member classes of statistical interaction. Training involved AB training, BA symmetry testing, BC training, CB symmetry testing, AC testing, and CA testing, in that order. Passage of all tests demonstrated the emergence of four 3-member classes of interaction. Then, subjects were presented with a mixed test that contained all relations to confirm the maintenance of four 3-member classes. Thereafter, CD was trained and followed with a test that included the all emergent relations probes needed to document the expansion of the 3-member classes to 4-member classes. All training and testing was conducted using a 2-choice MTS trial format along with the use of multiple negative comparisons across trials. After class formation, subjects were given a paper and pencil test with new interaction questions. Most subjects responded with high accuracy on this test which demonstrated the generalization of the relations established during MTS training and testing to questions presented in a paper and pencil format. These results show that an equivalence class formation can be used to induce recognition of different representations of the interactive effects of the combined effects of two independent variables. Further, the relations among stimuli established during training generalize to new examples presented in a format traditionally used in typical classroom evaluations. |

Contextually Controlled Symbol Categorization through Features Acquired by the Symbols: A Conceptual Analysis. |

LANNY FIELDS (Queens College, City University of New York), Pamela DeRosse (The Graduate Center, City University of New York) |

Abstract: The contextually determined categorization of symbols into different equivalence classes based on the acquired properties of the symbols characterizes many of our every day performances. This phenomenon was first mentioned by Bush, Sidman, & DeRose (1988), and is illustrated in the following example. Each of nine individuals has a name, one of three nationalities, and one of three vocations. Thus, each names has a unique nationality and vocation, i.e. acquired features. When asked to sort the names by nationality, the names will be categorized into three sets where membership in a set is based on the commonality of a particular nationality. In this case, however, the names in a set will differ in terms of vocation. Conversely, when asked to sort the names by vocation, the names will be categorized into three different sets where membership in a set is based on the commonality of a particular vocation. In this case, the names in a set will differ in terms of nationality. The names of the individuals then function as members of different equivalence classes based on the joint control of class assignment by the contextual cue (sort by nationaliity or vocation) and the particular nationality or vocation previously acquired by each name. In addition, the assignment to class occurs in the absence of the nationality of vocation labels and without direct training. Although it was first mentioned by Bush, Sidman, & DeRose (1988), the conditions needed to establish such a complex emergent repertoire have not been studied. This presentation by will involve a logical analysis of the stimulus control repertories that would have to be established as the prerequisites fo the emergence of such a complex repertoire. It will also consider the test trials that would be needed to document the emergence of the contextually controlled categorization of symbols into different equivalence classes based on acquired properties of the symbols. |

Contextually Controlled Symbol Categorization through Features Acquired by the Symbols: An Empirical Analysis. |

PAMELA DEROSSE (Center For Autism and Related Disorders, Graduate ), Lanny Fields (Queens College, City University of New York) |

Abstract: College students were used to study the conditions needed to induce the contextually determined categorization of symbols based on the acquired properties of the symbols, as characterized in the prior presentation. The analogs of the nationality and vocation category labels were represented by !!!!! and %%%, respectively. !!!!! and %%% are represented by N and V, respectively. Nonsense syllables were used as the analogs of the names of individuals mentioned in the prior presentation and were represented by the numerals 1-9. Nonsense syllables were also used as the analogs of three nationalities and three vocations. The three nationalities will be represented by the letters A, F, and G which stand for American, French, and German. The three vocations will be represented by the letters P, C, and W which stand for Painter, Composer, and Writer. First, a set of conditional discriminations were established between the nonsense syllables that stand for different nationalities and the Nationality label, (N-A/F/G) along with the nonsense syllables that stand for the different vocations and the vocation label (V-P/C/W). Second, nationality based equivalence classes were established in which each class contained three of the numbers that refer to peoples names and a given nationality (123-A, 456-F, and 789-G). Third, three other vocation based equivalence classes were formed with the nine numerals, where each class contained three numbers that represented names and one vocation (147-P, 258-C and 369-W). At this point, each “name” had acquired a particular nationality and vocation label. The fourth stage evaluated the emergence of a relation between each name and both acquired features, e.g., 1-AP or 5-FC. Thereafter, subjects were presented with contextual control trials that included N or V as the contextual cue, with three numerals as sample and comparisons. One comparison shared the nationality feature with the sample but not the vocation feature. The other comparison shared the vocation feature with the sample but not the nationality feature.
The subjects learned the category name/label conditional discriminations, formed the nationality and vocation based equivalence classes, and demonstrated the emergence of a relation between each numeral and the joint presence of a nationality and vocation feature. In the final contextual control test, two of the four subjects selected the comparison numeral that shared the nationality based feature wth the sample numeral.. |