New Nonparametric Tests for Comparing Multivariate Scales Using Data Depth

In this paper, we introduce several nonparametric tests for testing scale differences in the two-and multiple-sample cases based on the concept of data depth. The tests are motivated by the so-called DD-plot (depth versus depth plot) and are implemented through a permutation test. Our proposed tests are completely nonparametric. An extensive power comparison study indicates that our tests are as powerful as the parametric test in the normal setting but significantly outperform the parametric one in the non-normal settings. As an illustration, the proposed tests are applied to analyze an airline performance dataset collected by the FAA in the context of comparing the performance stability of airlines.