A Nonparametric version of the bartlett-nanda-pillai multivariate test. asymptotics, approximations, and applications

We consider a nonparametric version of the Bartlett-Nanda-Pillai multivariate test that has been introduced in Bathke and Harrar (2008) in the asymptotic context of a large number of treatments and small sample sizes per treatment (large a, small n). The test is based on separate rankings for the different variables. Here, we derive its asymptotic distribution for large n_i and small a. Also, two small sample approximations are presented, and their performance is investigated in a simulation study. In the presence of outliers, the proposed nonparametric version shows far superior power than the parametric Bartlett-Nanda-Pillai test. Similar to the parametric case, there is no clear ordering when comparing the nonparametric versions of Bartlett-Nanda-Pillai, Lawley-Hotelling, and ANOVA type test. We show how to apply the test in practice, using SAS. The application is demonstrated with two different data sets conforming to the two different asymptotic frameworks, large a and large n_i respectively.