Updating exact P- values for the conditional likelihood ratio test of independence

Abstract

We consider the exact likelihood ratio test of independence conditioned on row and column margins in an r × c contingency table with multinomial sampling. We develop an update algorithm to compute the exact Pvalue of the test and show it is better than the network algorithm in terms of computing speed. In the algorithm the P-value is reduced to a sum of probabilities for 2 × 2 contingency tables, which we compute using the hyper-geometric distribution. The same algorithm can also be used for testing homogeneity of independent multinomial populations.