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ERIC Number: ED344933
Record Type: RIE
Publication Date: 1992-Apr
Pages: 26
Abstractor: N/A
Reference Count: N/A
Tree Representation of Similarity and Dominance Relations between Tests and Items.
Beller, Michal
It has previously been shown by M. Beller (1990) that an additive tree (Addtree, a hierarchical tree representation of similarity data developed by S. Sattath and A. Tversky in 1977), may be useful for representing the structure between tests and items through the similarity among them as measured by their intercorrelations. In this study, the preference tree (Pretree, a hierarchical tree representation of preferences among alternatives developed by A. Tversky and S. Sattath in 1979) is proposed as suitable for representing dominance relations among test items, as measured by their relative difficulties. The key assumption underneath the Pretree model tested by the trinary condition will serve as a means for testing hypotheses about the similarity structure among the items. The dominance relation is examined under the scalogram model, the local independence assumption, and item response theory models. Data from the Psychometric Entrance Test administered to applicants to the Hebrew University in Jerusalem (Israel) provide an illustration. Pretree suggests a parsimonious way of representing sets of items with different degrees of dependencies among them. The tree structure will represent the dissimilarity among items. The length of branches will reflect the difficulty level of each item and the ratio of these branches will reflect the degree of dominance between the items. One table, multiple figures, and 19 references are included. (SLD)
Publication Type: Reports - Evaluative; Speeches/Meeting Papers
Education Level: N/A
Audience: N/A
Language: English
Sponsor: N/A
Authoring Institution: N/A
Identifiers: Additive Trees; Dominance Hierarchies; Hierarchical Decision Models; Israel; Local Independence (Tests); Preference Trees; Similarity (Concept)
Note: Paper presented at the Annual Meeting of the American Educational Research Association (San Francisco, CA, April 20-24, 1992).