The Combination of Tests Based on Discrete Distributions

Abstract A method of drawing a single conclusion from the results of a number of independent tests of a statistical hypothesis was pointed out some years ago by Fisher. Modifications of Fisher's method to better adapt it to the case where the underlying probability distributions are discrete have been proposed by Wallis, Lancaster, and Pearson. The relationship between these can be clarified by comparing each of them with a modified form of Pearson's method. The computations needed to apply Lancaster's method can be simplified with the aid of a table appended to the present paper.