This article explores a reparameterization of a 2 × 2 table. This reparameterization turns out to be useful in considering the consequences of amalgamating several 2 × 2 tables. A formal theorem is derived that permits characterization of Yule's association paradox. The same theorem also permits discussion of the likely direction of error incurred when using capture–recapture methods to estimate the size of a population. This has implications for the “wily trout” argument in the census correction controversy.