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

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.