In this article, first, we introduce depth function as a function for center-outward ranking. Then we present and
use half space or Tukey depth function as one of the most popular depth functions. In the following, multivariate
nonparametric tests for location and scale difference between two population are expressed by ranking and statistics
based on depth versus depth plot. Finally, according to these tests, performance of the suggested non-invasive
distraction method for pain intensity, life quality, operative ability and inflation rate is evaluated for osteoarthritic
and is compared with usual invasive distraction method.