Extremely efficient permutation and bootstrap hypothesis tests using R

TL;DR

This paper introduces a highly efficient computational method for permutation and bootstrap hypothesis tests, specifically for Pearson correlation and two-sample t-tests, reducing the computational burden of resampling methods.

Contribution

The paper presents a novel, general approach to efficiently compute permutation-based p-values for correlation and t-tests, applicable to similar statistical tests.

Findings

Significantly reduces computation time for permutation tests

Applicable to Pearson correlation and two-sample t-tests

Potentially adaptable to other resampling-based tests

Abstract

Re-sampling based statistical tests are known to be computationally heavy, but reliable when small sample sizes are available. Despite their nice theoretical properties not much effort has been put to make them efficient. In this paper we treat the case of Pearson correlation coefficient and two independent samples t-test. We propose a highly computationally efficient method for calculating permutation based p-values in these two cases. The method is general and can be applied or be adopted to other similar two sample mean or two mean vectors cases.