LqRT: Robust Hypothesis Testing of Location Parameters using Lq-Likelihood-Ratio-Type Test in Python

TL;DR

This paper introduces LqRT, a robust hypothesis test for comparing population means that outperforms traditional t-tests and other non-parametric tests in power and robustness, with an easy Python implementation.

Contribution

The paper proposes a novel Lq-likelihood-ratio-type test (LqRT) that is more robust and powerful than existing tests, along with a user-friendly Python package.

Findings

LqRT outperforms Wilcoxon and sign tests in power while maintaining size.

LqRT remains effective under distributional assumption violations.

Numerical studies demonstrate LqRT's superiority in various scenarios.

Abstract

A t-test is considered a standard procedure for inference on population means and is widely used in scientific discovery. However, as a special case of a likelihood-ratio test, t-test often shows drastic performance degradation due to the deviations from its hard-to-verify distributional assumptions. Alternatively, in this article, we propose a new two-sample Lq-likelihood-ratio-type test (LqRT) along with an easy-to-use Python package for implementation. LqRT preserves high power when the distributional assumption is violated, and maintains the satisfactory performance when the assumption is valid. As numerical studies suggest, LqRT dominates many other robust tests in power, such as Wilcoxon test and sign test, while maintaining a valid size. To the extent that the robustness of the Wilcoxon test (minimum asymptotic relative efficiency (ARE) of the Wilcoxon test vs the t-test is 0.864) suggests that the Wilcoxon test should be the default test of choice (rather than "use Wilcoxon if there is evidence of non-normality", the default position should be "use Wilcoxon unless there is good reason to believe the normality assumption"), the results in this article suggest that the LqRT is potentially the new default go-to test for practitioners.