Normal Approximation of a Discrete Distribution on Exact Test of Uniform Association in a 2 × 3 Table

For the analysis of 2 × 3 tables, TOMIZAWA (1993) considered an exact test of uniform association, which is an extension of independence, and then derived a discrete distribution. This paper gives a normal approximation of the discrete distribution and describes that the normalized statistic can test a one-sided hypothesis on the uniform association. Also it points out that the square of the normalized test statistic is equal to the Pearson's chi-squared statistic for testing the uniform association.     

Unbiased Confidence Intervals for the Odds Ratio of Two Independent Binomial Samples with Application to Case–Control Data

The problem of confidence interval construction for the odds ratio of two independent binomial samples is considered. Two methods of eliminating the nuisance parameter from the exact likelihood, conditioning and maximization, are described. A conditionally exact tail method exists by putting together upper and lower bounds. A shorter interval can be obtained by simultaneous consideration of both tails. We present here new methods that extend the tail and simultaneous approaches to the maximized likelihood. The methods are unbiased and applicable to case-control data, for which the odds ratio is important. The confidence interval procedures are compared unconditionally for small sample sizes in terms of their expected length and coverage probability. A Bayesian confidence interval method and a large-sample chi2 procedure are included in the comparisons.