A significant minimization of Pearson’s X2 statistics in 2x2 contingency tables: preliminary results for small samples

Abstract

The Pearson’s chi-square test or X² test represents a nonparametric test more used in Medicine, Biology and Social Sciences, but it introduces some error for 2x2 contingency tables, therefore Yates introduces a continuity correction. This correction produces a very conservative result of X² statistics with overestimation of p-value and consequently a type II error is very likely. The goal of this paper is to define, with a statistical approach, a significant minimization of Pearson’s X² statistics for small data sample, based on concept of arithmetic mean, that could be a possible efficient statistic for reducing the type II error in the calculation of p-value.