This paper explores a reparameterization of a 2x2 table. This reparameterization turns out to be useful in considering the consequences of amalgamating several 2x2 tables. A formal theorem is derived permitting a characterization of Yule's Association Paradox. The same theorem also permits discussion of the likely direction of error in using tag-retag methods to estimate the size of a population. This has implications for the "wily trout" argument in the census correction controversy.