Hostname: page-component-cd9895bd7-jkksz Total loading time: 0 Render date: 2025-01-06T02:07:58.889Z Has data issue: false hasContentIssue false
  • English
  • Français

Allowing for Infeasible Pairings in the Matching Paradigm

Published online by Cambridge University Press:  01 January 2025

Raphael Gillett
Raphael Gillett*
Affiliation:
University of Leicester
*
Requests for reprints should be sent to Raphael Gillett, Department of Psychology, University of Leicester, Leicester LE1 7RH, GREAT BRITAIN.
Get access Rights & Permissions [Opens in a new window]

Abstract

The objective of research in the matching paradigm is to determine whether a one-to-one pairing configuration between objects in two arrays contains more pairings of a particular kind than expected under the null hypothesis. The presence of infeasible pairings, that is, of particular pairings which can not possibly take place, has the effect of altering the null distribution that would otherwise obtain. To enable researchers to determine the appropriate null distribution, a generalization of classical rook methodology is developed which can accommodate infeasible pairings in the matching paradigm.

Keywords

matching distributioninfeasible pairingsrook polynomialrestricted permutations
Type
Original Paper
Information
Psychometrika , Volume 50 , Issue 3 , September 1985 , pp. 265 - 274
Copyright
Copyright © 1985 The Psychometric Society

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

Barton, D. E. (1958). The matching distributions: Poisson limiting forms and derived methods of approximation. Journal of the Royal Statistical Society, 20, 73–92.CrossRefGoogle Scholar
Cohen, J. (1960). A coefficient of agreement for nominal scales. Educational and Psychological Measurement, 20, 37–46.CrossRefGoogle Scholar
David, F. N., Barton, D. E. (1962). Combinatorial chance, London: Griffin.CrossRefGoogle Scholar
Edgington, E. S. (1969). Statistical inference: The distribution-free approach, New York: McGraw-Hill.Google Scholar
Feller, W. (1968). An introduction to probability theory and its applications, Vol. 1 3rd ed.,, New York: Wiley.Google Scholar
Gillett, R. (1985). The matching paradigm: An exact test procedure. Psychological Bulletin, 97, 106–118.CrossRefGoogle ScholarPubMed
Harter, H. L. (1969). A new table of the percentage points of the Pearson Type III distribution. Technometrics, 11, 177–187.CrossRefGoogle Scholar
Hubert, L. (1977). Kappa revisited. Psychological Bulletin, 84, 289–297.CrossRefGoogle Scholar
Hubert, L. (1979). Matching models in the analysis of cross-classifications. Psychometrika, 44, 21–41.CrossRefGoogle Scholar
Hubert, L., Golledge, R. (1983). Rater agreement for complex assessments. British Journal of Mathematical and Statistical Psychology, 36, 207–216.CrossRefGoogle Scholar
Kaplansky, I., Riordan, J. (1946). The problem of the rooks and its applications. Duke Mathematical Journal, 13, 259–268.CrossRefGoogle Scholar
Riordan, J. (1958). An introduction to combinatorial analysis, New York: Wiley.Google Scholar
Vernon, P. E. (1936). The matching method applied to investigations of personality. Psychological Bulletin, 33, 149–177.CrossRefGoogle Scholar
Wackerly, D. D., McClave, J. T., Rao, P. V. (1978). Measuring nominal scale agreement between a judge and a known standard. Psychometrika, 43, 213–223.CrossRefGoogle Scholar