IMPROVED EXACT INFERENCE ABOUT CONDITIONAL ASSOCIATION IN 3-WAY CONTINGENCY-TABLES

We propose modified exact inferential methods for contingency tables. Ordinary ''exact'' inference is conservative, because of the discreten ess. For estimating a common odds ratio in several 2 X 2 tables, two m odifications of the ordinary ''exact'' confidence interval maintain at least a fixed confidence level but tend to be much narrower. One appr oach inverts results of a test with a modified P value utilizing the t est statistic and table probabilities. The second approach inverts one two-sided test rather than two one-sided tests. This approach is much less conservative when the true odds ratio is relatively small or lar ge. We also generalize results of Cohen and Sackrowitz and relate modi fied P values to construction of exact, unbiased, and admissible tests for an ordinal alternative to conditional independence.