Yule's association paradox and ignored stratum heterogeneity in capture-recapture studies

This article explores a reparameterization of a 2 x 2 table. This reparamet erization turns out to be useful in considering the consequences of amalgam ating several 2 x 2 tables. A formal theorem is derived that permits charac terization of Yule's association paradox. The same theorem also permits dis cussion of the likely direction of error incurred when using capture-recapt ure methods to estimate the size of a population. This has implications for the "wily trout" argument in the census correction controversy.