depth-based nonparametric multivariate analysis and its application in review of new treatment methodology on osteoarthrotic

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.