Exact Inference for Contingency Tables with Ordered Categories

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Abstract
This article proposes an efficient numerical algorithm for small-sample exact inferences in contingency tables having ordinal classifications. The inferences, which apply conditional on the observed marginal totals, also provide an exact analysis for the log-linear model of linear-by-linear association for cell probabilities. An exact test of independence has a one-sided P value equal to the null probability that model-based maximum likelihood estimates of odds ratios are at least as large as the observed estimates. The conditional nonnull distribution yields confidence intervals for odds ratios having a linear-by-linear structure. The computations utilize an extension of the network algorithm proposed by Mehta and Patel (1983).

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