The marginal totals of a 2×2 table

Abstract

Inferences about the odds ratio of a 2×2 contingency table are usually based on the distribution of any one frequency conditional on the observed values of the marginal totals. The reason is given that the marginal totals are ancillary statistics which contain no information about the odds ratio. We consider inferences about the odds ratio when the likelihood function is derived from the marginal totals. Standard procedures for making statements about an unknown parameter are found to be inconclusive.