A major improvement to the Network Algorithm for Fisher's Exact Test in 2×c2×c contingency tables

Based on the Network Algorithm proposed by Mehta and Patel for Fisher's Exact Test on 2×c2×c contingency tables, the relations between maximum subpath lengths are studied. A recurrence relation between maximum subpath lengths is obtained and an ordering of the maximum path lengths is established. Based on these results, some modifications in the Network Algorithm for 2×c2×c tables are proposed. These modifications produce a drastic reduction in computation time which in some cases is higher than 99.5% compared to StatXact-5. Moreover, and with purely practical objectives, a grouping in intervals of subpath lengths of the Network Algorithm is proposed which enable us to obtain the pp-value with a limited number of exact figures which is more than sufficient in practice, while with a drastic reduction in the amount of memory required and additional reductions in computational time. The proposed modifications are valid for any 2×c2×c contingency table, and are compatible with other improvements already proposed for the Network Algorithm, and especially with the Hybrid Algorithm of Mehta and Patel.