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 K among 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.
