Open Access
April, 1971 Marginal Homogeneity of Multidimensional Contingency Tables
S. Kullback
Ann. Math. Statist. 42(2): 594-606 (April, 1971). DOI: 10.1214/aoms/1177693409


Tests of marginal homogeneity in a two-way contingency table given by [1], [3], and [13] do not seem to lend themselves easily to extension to the problem of $m$-way marginal homogeneity in an $N$-way $r \times r \times \cdots \times r$ contingency table, $m < N$. The principle of minimum discrimination information estimation and the associated minimum discrimination information statistic applied in [5] to the problem of marginal homogeneity in an $r \times r$ contingency table can be easily extended to the case of a multidimensional contingency table. Estimates of the cell entries under the hypotheses of $m$-way marginal homogeneity are given. Relationships among the tests of homogeneity for $m$-way, $m = 1, 2, \cdots, N - 1$, marginals are given by an analysis of information. Numerical results are given for two sample $3 \times 3 \times 3$ tables, and two $5 \times 5$ tables.


Download Citation

S. Kullback. "Marginal Homogeneity of Multidimensional Contingency Tables." Ann. Math. Statist. 42 (2) 594 - 606, April, 1971.


Published: April, 1971
First available in Project Euclid: 27 April 2007

zbMATH: 0215.54305
MathSciNet: MR297084
Digital Object Identifier: 10.1214/aoms/1177693409

Rights: Copyright © 1971 Institute of Mathematical Statistics

Vol.42 • No. 2 • April, 1971
Back to Top