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A Theory of Consistency of Ordering Generalizable to Tailored Testing

Published online by Cambridge University Press:  01 January 2025

Norman Cliff
Norman Cliff*
Affiliation:
University of Southern California
*
Requests for reprints should be sent to Norman Cliff, Department of Psychology, University of Southern California, University Park, Los Angeles, California 90007.
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Abstract

Measures of consistency and completeness of order relations derived from test-type data are proposed. The measures are generalized to apply to incomplete data such as from tailored testing. The measures are based on consideration of the items-plus-persons by items-plus-persons matrix as an adjacency matrix in which a 1 means that the row element, whether item or person, dominated the column element. From this the number of item-item and person-person dominance relations can be derived. Indices of consistency are developed which compare the number of dominance relations in a matrix to the number that would occur if it were perfectly consistent and to the number in a random matrix; relations to other indices are noted.

Keywords

computerinteractiveGuttman
Type
Original Paper
Information
Psychometrika , Volume 42 , Issue 3 , September 1977 , pp. 375 - 399
Copyright
Copyright © 1977 The Psychometric Society

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Footnotes

The research reported here was supported by the Office of Naval Research, Contract N00014-75-C-0684, NR150-373. The author wishes to thank Dr. Thomas J. Reynolds for a number of helpful discussions of this material.

References

Reference Note

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