Abstract
Pearson's Chi-square statistic for frequency tables depends on what is hypothesized as the expected frequencies. Its partitions also depend on the hypothesis. Lancaster (J R Stat Soc B 13:242---249, 1951) proposed ANOVA-like partitions of Pearson's statistic under several representative hypotheses about the expected frequencies. His expositions were, however, not entirely clear. In this paper, we clarify his method of derivations, and extend it to more general situations. A comparison is made with analogous decompositions of the log likelihood ratio statistic associated with log-linear analysis of contingency tables.
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