A New Non-parametric Test Procedure for the Median of an Asymmetrical Population

摘要

This paper proposes and investigates the performance of a new non-parametric test procedure for the median of a non-normal population when the symmetry assumption is suspected. The new test procedure uses the Yeo-Johnson family of power transformations and the Shapiro-Wilk test of normality to modify the classical normal scores test. Under skewed models, simulation results show that the proposed test procedure is superior to all competitor tests under consideration in terms of preserving the empirical size of the test at its nominal level and also having higher empirical powers.