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Exact tests for two-way symmetric contingency tables

Exact tests for two-way symmetric contingency tables
Exact tests for two-way symmetric contingency tables
A two-way contingency table in which both variables have the same categories is termed a symmetric table. In many applications, because of the social processes involved, most of the observations lie on the main diagonal and the off-diagonal counts are small. For these tables, the model of independence is implausible and interest is then focussed on the off-diagonal cells and the models of quasi-independence and quasi-symmetry. For ordinal variables, a linear-by-linear association model can be used to model the interaction structure. For sparse tables, large-sample goodness-of-fit tests are often unreliable and one should use an exact test. In this paper, we review exact tests and the computing problems involved. We propose new recursive algorithms for exact goodness-of-fit tests of quasi-independence, quasi-symmetry, linear-by-linear a ssociation and some related models. We propose that all computations be carried out using symbolic computation and rational arithmetic in order to calculate the exact p-values accurately and describe how we implemented our proposals. Two examples are presented.
0960-3174
391-399
McDonald, J.
dcfb784a-6724-4dda-adc8-bf4edb34f480
DeRoure, David C.
02879140-3508-4db9-a7f4-d114421375da
Michaelides, Danius T.
a6df5175-d71a-4cd4-befc-26c48235fb92
McDonald, J.
dcfb784a-6724-4dda-adc8-bf4edb34f480
DeRoure, David C.
02879140-3508-4db9-a7f4-d114421375da
Michaelides, Danius T.
a6df5175-d71a-4cd4-befc-26c48235fb92

McDonald, J., DeRoure, David C. and Michaelides, Danius T. (1998) Exact tests for two-way symmetric contingency tables Statistics and Computing, 8, (4), pp. 391-399.

Record type: Article

Abstract

A two-way contingency table in which both variables have the same categories is termed a symmetric table. In many applications, because of the social processes involved, most of the observations lie on the main diagonal and the off-diagonal counts are small. For these tables, the model of independence is implausible and interest is then focussed on the off-diagonal cells and the models of quasi-independence and quasi-symmetry. For ordinal variables, a linear-by-linear association model can be used to model the interaction structure. For sparse tables, large-sample goodness-of-fit tests are often unreliable and one should use an exact test. In this paper, we review exact tests and the computing problems involved. We propose new recursive algorithms for exact goodness-of-fit tests of quasi-independence, quasi-symmetry, linear-by-linear a ssociation and some related models. We propose that all computations be carried out using symbolic computation and rational arithmetic in order to calculate the exact p-values accurately and describe how we implemented our proposals. Two examples are presented.

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Published date: 1998
Organisations: Web & Internet Science

Identifiers

Local EPrints ID: 250799
URI: http://eprints.soton.ac.uk/id/eprint/250799
ISSN: 0960-3174
PURE UUID: c0eb1f50-8d67-4a87-9546-4189c8b8dd64
ORCID for David C. DeRoure: ORCID iD orcid.org/0000-0001-9074-3016

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Date deposited: 15 May 2001
Last modified: 18 Jul 2017 10:33

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Contributors

Author: J. McDonald
Author: David C. DeRoure ORCID iD
Author: Danius T. Michaelides

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