Exact methods for the partitioning of Pearson's chi-square are criticized on the grounds that they lead to tests of a set of hypotheses in which, in general, each test is appropriate only on the assumption that other hypotheses in the set are true. The specific case of a 4 × 2 contingency table is examined in detail, and an alternative partitioning of the likelihood ratio chi-square is shown to lead to a more appropriate set of tests. Additive partitions in general lead to a set of tests in which some tests are valid only on the condition that hypotheses other than the one being tested are true. Alternative ways of obtaining unconditional tests of hypotheses are described.
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