A new method for calculating p-value under unconditional exact test

Abstract

An unconditional exact test is a classic method to test the significant difference between two independent binomial proportions or multinomial distributions. The p-value based on the unconditional exact test is computed by maximizing the probability of the tail region. The grid search method and polynomial method are able to find the maximum with sophisticated enough partition of the parameter space, while they require a rather long time to compute and those methods are computationally intensive for a study beyond two groups. In this paper, we pro-pose a new method to obtain the solution of the global maximum which can diminish the computing time based on the fixed-point iterative algorithm. Addition-ally, both simulation and experiment indicate that this method is more competitive compared with the grid search and the polynomial method on the basis of guaranteed accuracy.