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Accuracy of Kendall's Chi-Square Approximation to Circular Triad Distributions

Published online by Cambridge University Press:  01 January 2025

Gerald Knezek ,
Susan Wallace  and
Peter Dunn-Rankin
Gerald Knezek*
Affiliation:
Department of Technology and Cognition, University of North Texas
Susan Wallace
Affiliation:
Department of Computer and Information Sciences, University of North Florida
Peter Dunn-Rankin
Affiliation:
Department of Educational Psychology, University of Hawaii
*
Requests for reprints should be sent to Gerald Knezek, Department of Technology and Cognition, P. O. Box 311337, University of North Texas, Denton, TX 76203. E-mail: [email protected]
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Abstract

This paper contains an assessment of the accuracy of Kendall's chi-square approximation to circular triad distributions. Estimated indices are compared to enumerated values across the upper and lower tails of cumulative proportions of circular triad distributions for 5–15 objects. In general, the approximation is found to be quite good. The median difference between the exact distribution and Kendall's approximation is .000692. Critical value approximations are never in error by more than one circular triad and are almost always in the conservative direction. A researcher can be confident that little meaningful error will be present when using Kendall's approximation for experiments outside the range of tabled values. It appears that the chi-square approximation will be accurate to at least two decimal places for distributions beyond 15 objects.

Keywords

circular triad distributionschi-square approximationcomputational psychometrics
Type
Original Paper
Information
Psychometrika , Volume 63 , Issue 1 , March 1998 , pp. 23 - 34
Copyright
Copyright © 1998 The Psychometric Society

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Footnotes

The authors wish to acknowledge the helpful suggestions for manuscript modifications provided by Previous Editor Lawrence J. Hubert, USA, and by Akira Sakamoto of Ochanomizu University, Japan. We also wish to thank the Mathematics and Computer Science Division, Argonne National Laboratory, USA, for the use of ACRF computers.

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