Statistical analysis procedure in two-sample treatment difference, as well as alternative hypothesis, may play a central role in statistical inference, especially in small sample size case. In this paper, simple non-parametric two-sample permutation tests for scale difference based on the Hodges–Lehmann estimator are reformulated, and are applied to a study examining whether previous styrene exposure increases (thus a one-sided alternative hypothesis rather than a two-sided one) the human liver's metabolic ability to convert styrene into styrene oxide, in which a three-compartment physiologically based pharmacokinetic (PBPK) model was used to compare the estimated metabolic constant κamong the previously exposed and unexposed groups. Contrary to the previous conclusion, the proposed tests for scale difference identified from a mixed-effects model showed a significant result.
