A comparison of algorithms for exact analysis of unordered 2 × K contingency tables

Abstract

We present a comparison of two efficient algorithms for exact analysis of an unordered 2 × K table. First, by considering conditional generating functions, we show that both the network algorithm of Mehta and Patel ( J. Amer. Statist. Assoc. 78 (1983)) and the fast Fourier transform (FFT) algorithm of Baglivo et al. ( J. Amer. Statist. Assoc. 82 (1992)) rest on the same foundation. This foundation is a recursive polynomial relation. We further show that the network algorithm is equivalent to a stage-wise implementation of this recursion while the FFT algorithm is based on performing the same recursion at complex roots of unity. Our empirical results for the Pearson X 2, likelihood ratio, and Freeman-Halton statistics show that the network algorithm, or equivalently, the recursive polynomial multiplication algorithm is superior to the FFT algorithm with respect to computing speed and accuracy.