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A t-test is considered a standard procedure for inference on population meansand is widely used in scientific discovery. However, as a special case of alikelihood-ratio test, t-test often shows drastic performance degradation dueto the deviations from its hard-to-verify distributional assumptions.Alternatively, in this article, we propose a new two-sampleLq-likelihood-ratio-type test (LqRT) along with an easy-to-use Python packagefor implementation. LqRT preserves high power when the distributionalassumption is violated, and maintains the satisfactory performance when theassumption is valid. As numerical studies suggest, LqRT dominates many otherrobust tests in power, such as Wilcoxon test and sign test, while maintaining avalid size. To the extent that the robustness of the Wilcoxon test (minimumasymptotic relative efficiency (ARE) of the Wilcoxon test vs the t-test is0.864) suggests that the Wilcoxon test should be the default test of choice(rather than "use Wilcoxon if there is evidence of non-normality", the defaultposition should be "use Wilcoxon unless there is good reason to believe thenormality assumption"), the results in this article suggest that the LqRT ispotentially the new default go-to test for practitioners.

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