Algorithms for the Analysis of Several $2 \times 2$ Contingency Tables
Marcello Pagano, David Tritchler · SIAM Journal on Scientific and Statistical Computing · 1983
This paper presents algorithms for calculating the exact permutation distributions of several $2 \times 2$ contingency tables. They address both the hypothesis of constant relative odds across the tables and inference about this common value. The efficiency of the algorithms is due to their not requiring the enumeration of all the tables consistent with the given marginals.