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• W2074393200 abstract "We discuss a variety of test statistics for the hypothesis of conditional independence in three-way contingency tables. Statistics that are designed to detect association between nominal variables, between ordinal variables, and between nominal and ordinal variables are presented. Tests previously presented by Birch (1965) and Landis et al. (1978) are efficient score statistics for alternative hypotheses corresponding to loglinear models that assume homogeneous associations across levels of the control variable. Additional score statistics are presented for loglinear model alternatives that permit interaction, in the form of heterogeneous associations. Ordinary asymptotic chi-squared inference is well established for both types of alternatives. For small samples or sparse data, however, software for exact conditional inference is currently unavailable for most cases having multiple levels of response variables. Monte-Carlo simulation of exact distributions is computationally simple and quick, even for large sparse tables. It results in precise estimates of P-values for exact conditional tests, and hence ‘nearly exact’ tests, for cases lacking software or cases that are likely to be computationally infeasible in the indefinite future. The tests with homogeneous association alternatives also can be applied to nearly exact testing of marginal homogeneity for multivariate responses having the same categorical scale for each component." @default.
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• W2074393200 date "1997-03-01" @default.
• W2074393200 modified "2023-10-14" @default.
• W2074393200 title "Nearly exact tests of conditional independence and marginal homogeneity for sparse contingency tables" @default.
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• W2074393200 doi "https://doi.org/10.1016/s0167-9473(96)00038-2" @default.
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