Marginal symmetry and quasi symmetry of general order. (English) Zbl 0735.62057

Bei \(s\) Variablen \(R_ k\), die \(r\) Werte annehmen, sei \(\pi({\mathbf i})=P({\mathbf R}={\mathbf i})\), wobei \({\mathbf R}=(R_ 1,\dots,R_ s)\) und \(i=(i_ 1,\dots,i_ s)\) ist. In der \(r^ s\) Kontingenztafel \(\pi=[\pi({\mathbf i}), i_ \sigma=i,\dots,r; \sigma=1,\dots,s]\) bedeutet totale Symmetrie, daß \(\pi\) unverändert ist, wenn die Komponenten permutiert werden, marginale Symmetrie der Ordnung k bedeutet totale Symmetrie aller Untervektoren der Ordnung \(k\). Quasisymmetrie ist definiert auf log-linearen Wechselwirkungen von \(\pi\).
Zusätzlich zum Hauptresultat, daß marginale und Quasisymmetrie zusammen gleichwertig mit totaler Symmetrie sind, wird bewiesen, daß sie parametrisch komplementär sind.
Reviewer: P.Nüsch


62H17 Contingency tables
Full Text: DOI


[1] Bhapkar, V. P., On Hypotheses and Test of Marginal Symmetry and Quasi-Symmetry in Multidimensional Contingency Tables (1978), University of Kentucky, Department of Statistics Technical Report No. 131
[2] Bhapkar, V. P., On tests of marginal symmetry and quasi-symmetry in two and three-dimensional contingency tables, Biometrics, 35, 417-426 (1979) · Zbl 0419.62045
[3] Bhapkar, V. P., On tests of symmetry when higher order interactions are absent, J. Indian Statist. Assoc., 17, 17-26 (1979)
[4] Bishop, Y. P.; Fienberg, S. E.; Holland, P. W., (Discrete Multivariate Analysis (1975), The M.I.T. Press: The M.I.T. Press Cambridge, Massachusetts)
[5] Darroch, J. N., The Mantel-Haenszel test and tests of marginal symmetry; Fixed effects and mixed models for a categorical response, Internat. Statist. Rev., 49, 285-307 (1981) · Zbl 0484.62067
[6] Darroch, J. N.; McCloud, P. I., Category distinguishability and observer agreement, Austral. J. Statist., 28, 371-388 (1986) · Zbl 0609.62140
[7] Darroch, J. N.; Speed, T. P., Additive and multiplicative models and interactions, Ann. Statist., 11, 724-738 (1983) · Zbl 0556.62032
[8] McCloud, P. I., Unpublished Ph.D. thesis (1987)
[9] McCullagh, P., Some applications of quasisymmetry, Biometrika, 69, 303-308 (1982) · Zbl 0497.62051
[10] Barndorff-Nielsen, (Information and Exponential Families in Statistical Theory (1978), Wiley: Wiley New York) · Zbl 0387.62011
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