Nonparametric hypothesis testing for equality of means on the simplex
  In the context of data that lie on the simplex, we investigate use of empirical and exponential empirical likelihood, and Hotelling and James statistics, to test the null hypothesis of equal population means based on two independent samples. We perform an extensive numerical study using data simulated from various distributions on the simplex. The results, taken together with practical considerations regarding implementation, support the use of bootstrap-calibrated James statistic. 
Michail Tsagris, Simon Preston and Andrew T.A. Wood
stat.ME