Abstract
This article provides an improvement of the network algorithm for calculating the exact p value of the generalized Fisher's exact test in two-way contingency tables. We give a new exact upper bound and an approximate upper bound for the maximization problems encountered in the network algorithm. The approximate bound has some very desirable computational properties and the meaning is elucidated from a viewpoint of differential geometry. Our proposed procedure performs well regardless of the pattern of marginal totals of data.
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