Abstract
When samples are taken independently from I populations and the subjects classified into J categories, can the Pearson's chisquare statistic X2 testing the homogeneity model on the resulting I×J two-way table be decomposed into components familiar in the analysis of variance? Will the X2 testing the homogeneity model on tables derived by collapsing columns in the spirit of orthogonal comparisons in factorial experiments be asymptotically independent? The answers to both questions are generally negative. This paper gives a theoretical justification.
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