Exponential increase of the power of the independence and homogeneity chi-square tests with auxiliary information

TL;DR

This paper demonstrates that incorporating auxiliary information can exponentially enhance the power of chi-square tests of independence and homogeneity, reducing sample size needs and increasing test sensitivity across various data types.

Contribution

It introduces a computational method to exponentially improve chi-square tests' power using auxiliary information, applicable across diverse non-parametric data analyses.

Findings

Power of tests increases exponentially with auxiliary info

Sample size can be reduced for desired power

Method is applicable to any non-parametric data

Abstract

This paper is an extension of the work about the exponential increase of the power of two non-parametric tests: the $ Z $-test and the chi-square goodness-of-fit test. Subject to having auxiliary information, it is possible to improve exponentially relative to the size of the sample the power of the famous chi-square tests of independence and homogeneity. Improving the power of these statistical tests by using auxiliary information makes it possible either to reduce the probability of accepting the null hypothesis under the alternative hypothesis, or to reduce the size of the sample necessary to reach a predefined power. The suggested method is computational and some simple statistical applications are presented to illustrate these results. The framework of this work is non-parametric, so it can be applied to any kind of data and any area using statistics.